34, Volume 2018 (2019)

Advances in Operations Research

Decision-Making for Urban Planning and Regional Development

Lead Guest Editor: Marta Bottero Guest Editors: Alessandra Oppio and Chiara D’Alpaos Decision-Making for Urban Planning and Regional Development Advances in Operations Research

Decision-Making for Urban Planning and Regional Development

This is a special issue published in “Advances in Operations Research.” All articles are open access articles distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Editorial Board

Juan Aparicio, Spain Imed Kacem, France Khosrow Moshirvaziri, USA Igor L. Averbakh, Canada Ioannis Konstantaras, Greece Panagiotis P. Repoussis, Greece Eduardo Fernandez, Mexico Demetrio Laganà, Italy Shey-Huei Sheu, Taiwan Kevin Furman, USA Ching-Jong Liao, Taiwan Konstantina Skouri, Greece Ahmed Ghoniem, USA Yi-Kuei Lin, Taiwan Wolfgang Stadje, Germany Mhand Hifi, France Viliam Makis, Canada Hsien-Chung Wu, Taiwan Dylan F. Jones, UK Lars Mönch, Germany Contents

Decision-Making for Urban Planning and Regional Development Marta Bottero , Chiara D’Alpaos, and Alessandra Oppio Editorial (2 pages), Article ID 5178051, Volume 2019 (2019)

A New Robust Dynamic Data Envlopment Analysis Approach for Sustainable Supplier Evaluation Hava Nikfarjam , Mohsen Rostamy-Malkhalifeh , and Abbasali Noura Research Article (20 pages), Article ID 7625025, Volume 2018 (2019)

Multicriteria Evaluation of Urban Regeneration Processes: An Application of PROMETHEE Method in Northern Italy Marta Bottero , Chiara D’Alpaos, and Alessandra Oppio Research Article (12 pages), Article ID 9276075, Volume 2018 (2019)

Measuring Conflicts Using Cardinal Ranking: An Application to Decision Analytic Conflict Evaluations Tobias Fasth ,AronLarsson , Love Ekenberg, and Mats Danielson Research Article (14 pages), Article ID 8290434, Volume 2018 (2019)

Minimizing Cost Travel in Multimodal Transport Using Advanced Relation Transitive Closure Rachid Oucheikh , Ismail Berrada, and Lahcen Omari Research Article (7 pages), Article ID 9579343, Volume 2018 (2019)

Multiobjective Optimization for Multimode Transportation Problems Laurent Lemarchand ,DamienMassé ,PascalRebreyend ,andJohanHåkansson Research Article (13 pages), Article ID 8720643, Volume 2018 (2019)

Integration between Transport Models and Cost-Benefit Analysis to Support Decision-Making Practices: Two Applications in Northern Italy Paolo Beria ,AlbertoBertolin ,andRaffaeleGrimaldi Research Article (16 pages), Article ID 2806062, Volume 2018 (2019) Hindawi Advances in Operations Research Volume 2019, Article ID 5178051, 2 pages https://doi.org/10.1155/2019/5178051

Editorial Decision-Making for Urban Planning and Regional Development

Marta Bottero ,1 Chiara D’Alpaos,2 and Alessandra Oppio3

1 Department of Regional and Urban Studies and Planning, Politecnico di Torino, Italy 2Department of Civil, Environmental and Architectural Engineering, University of Padua, Italy 3Department of Architecture and Urban Studies, Politecnico di Milano, Italy

Correspondence should be addressed to Marta Bottero; [email protected]

Received 26 November 2018; Accepted 26 November 2018; Published 10 January 2019

Copyright © Marta Bottero et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Urban and regional development can be considered as mul- e paper “A New Robust Dynamic Data Envelopment tidimensional concepts which involve socioeconomic, eco- Analysis Approach for Sustainable Supplier Evaluation” by logical, cultural, technical, and ethical perspectives. Decision Nikfarjam et al. presents a new dynamic Data Envelopment problems in the domain of urban and regional development Analysis (DEA) approach for suppliers selection which takes processes represent “weak” or unstructured problems as into account social, environmental and economic criteria they are characterized by multiple actors, many and o en and considers differently from previous literature, contiguous conflicting values and views, a wealth of possible outcomes, time periods. In detail efficient Decision Making Units and high uncertainty. (DMUs) are identified in each time period and as well as Under these circumstances, evaluation of alternative an ideal DMU by implementing a robust scenario-based projects is therefore a complex decision problem, where dif- optimization approach. ferent aspects need to be considered simultaneously, and both e paper “Multicriteria Evaluation of Urban Regener- technical elements, based on empirical observations, and ation Processes: An Application of PROMETHEE Method non-technical elements, based on social visions, preferences, in Northern Italy” by M. Bottero et al. proposes an original and feelings, need to be taken into account. is complexity multimethodological evaluation procedure, which combines requires multidimensional approaches and specific qualita- SWOT Analysis, Stakeholders Analysis, and PROMETHEE tive/quantitative methods to analyse and synthesize the full method, to evaluate alternative renewal strategies in an urban variety of aspects involved in transformation processes, that area in Northern Italy and provide decision-makers with range from the environmental impacts of urban renewal to useful tools in making welfare-maximizing urban planning its impacts on energy consumption/production patterns and decisions. mobility; from the social and economic impacts of a specific e paper “Measuring Conflicts Using Cardinal Ranking: urban transformation strategy to its effects on landscape and An Application to Decision Analytic Conflict Evaluations” cultural heritage. by T. Fasth et al. provides: (a) an application of the cardinal is special issue addresses recent advances on the role of ranking method for preference elicitation to inform decision- evaluation in supporting decision-makers in urban planning makers with respect to controversies; (b) and two indexes to and regional development. papers are published in this measure potential conflicts within a group of stakeholders or special issue; each paper was reviewed by at least two between two groups of stakeholders. reviewers and revised according to review comments. e e paper “Minimizing Cost Travel in Multimodal Trans- accepted papers show the role of evaluation procedures to port Using Advanced Relation Transitive Closure” by R. support decisions in the context of urban management and Oucheikh et al. proposes a new method for travel cost opti- territorial transformations. mization, which can be applied either on path optimization Advances in Operations Research for graphs or on binary constraint reduction in Constraint Satisfaction Problem (CSP). In addition, it introduces the mathematical background for the transitive closure of binary relations. e paper “Multiobjective Optimization for Multimode Transportation Problems” by L. Lemarchand et al. presents a model to solve service facilities localization problems in a multimode transportation context, by implementing an adapted �-constraint multiobjective method and exploring the implementation of heuristic methods based on evolutionary multiobjective frameworks. e paper “Integration between Transport Models and Cost-Benefit Analysis to Support Decision-Making Practices: Two Applications in Northern Italy” by P. Beria et al. con- tributes to the assessment of sustainable mobility transport plans and infrastructure projects, and presents an operative application of Cost Benefit Analysis to the evaluation of alternative scenarios, complemented by the implementation of transportation models and GIS. e papers in this special issue represent a scientifically based support to address the complexity of decisions making in urban planning and regional development, improve the effectiveness and soundness of choices, and increase transparency in collective decision-making, by enhancing shared learning processes. We hope that this special issue will attract attention for further research into complex urban/territorial transformation processes, and will prove to be a valuable resource in the improvement of knowledge that the development of future cities and society requires.

Conflicts of Interest is is to conﬁrm that as guest editors of the special issue titled “Decision-Making for Urban Planning and Regional Development” we have not any possible conﬂicts of interest or private agreements with companies. Marta Bottero Chiara D’Alpaos Alessandra Oppio Hindawi Advances in Operations Research Volume 2018, Article ID 7625025, 20 pages https://doi.org/10.1155/2018/7625025

Research Article A New Robust Dynamic Data Envlopment Analysis Approach for Sustainable Supplier Evaluation

Hava Nikfarjam ,1 Mohsen Rostamy-Malkhalifeh ,2 and Abbasali Noura2

Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

Correspondence should be addressed to Mohsen Rostamy-Malkhalifeh; mohsen [email protected]

Received 8 November 2017; Accepted 14 November 2018; Published 9 December 2018

Academic Editor: Yi-Kuei Lin

Copyright © 2018 Hava Nikfarjam et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Supplier selection is one of the intricate decisions of managers in modern business era. Tere are diferent methods and techniques for supplier selection. Data envelopment analysis (DEA) is a popular decision-making method that can be used for this purpose. In this paper, a new dynamic DEA approach is proposed which is capable of evaluating the suppliers in consecutive periods based on their inputs, outputs, and the relationships between the periods classifed as desirable relationships, undesirable relationships, and free relationships with positive and negative natures. To this aim various social, economic, and environmental criteria are taken into account. A new method for constructing an ideal decision-making unit (DMU) is proposed in this paper which difers from the existing ones in the literature according to its capability of considering periods with unit efciencies which do not necessarily belong to a unique DMU. Furthermore, the new ideal DMU has the required ability to rank the suppliers with the same efciency ratio. In the concerned problem, the supplier that has unit efciency in each period is selected to construct an ideal supplier. Since it is possible to have more than one supplier with unit efciency in each period, the ideal supplier can be made with diferent scenarios with a given probability. To deal with such uncertain condition, a new robust dynamic DEA model is elaborated based on a scenario-based robust optimization approach. Computational results indicate that the proposed robust optimization approach can evaluate and rank the suppliers with unit efciencies which could not be ranked previously. Furthermore, the proposed ideal DMU can be appropriately used as a benchmark for other DMUs to adjust the probable improvement plans.

1. Introduction (SCM) [2]. In recent years, sustainability factors have played pivotal role in supplier evaluation and selection process [3]. Supplier selection is an important strategic decision of Ratan et al. [4] discussed that sustainability principles force managers for the economic and industry. In recent decades companies to select the suppliers which develop products scholars and practitioners have paid special attention to and services, preserve environmental resources and look this issue. To name a few relevant samples we can refer to afer manpower and communities. Beamon [5] introduced Khan et al. [1] who analyzed the suppliers regarding their ethical and social responsibilities criteria as fundamental ability in transferring the technology. However, they merely requirements of sustainable SCM for future decades. considered economic criteria in evaluation of four levels of A wide range of multiple criteria models and approaches technology transfer among suppliers of auto industries in suchasfuzzy,AHP,ANP,TOPSISandDEAhavebeen Pakistan. Nowadays, the decision-maker duty (in supplier proposed to deal with supplier selection issue over the last selection) has become more and more intricate. Tis means two decades. Some of the following researchers applied fuzzy, that they must care specifcally about sustainability criteria AHP/ANP-based methods to deal with multi-criteria sup- while supplier selection. Sustainable supplier evaluation and plier selection problems (e.g. [6–12]). Some other researchers selection concept is resulted from incorporating environ- used TOPSIS based methods to evaluate the suppliers (e.g. mental and social responsibility factors into economic factors [9, 13, 14]). For instance, using fuzzy inference system, when making decisions regarding supply chain management Amindoust et al. [15] proposed a ranking model based on 2 Advances in Operations Research fuzzy inference system for sustainable supplier selection. other words, in this paper, we extend the dynamic DEA Wen et al. [3] introduced a model for sustainable supplier model to evaluate suppliers in diferent periods based on their evaluation using intuitionistic fuzzy sets’ group decision- inputs, outputs and the relationships between the periods making models. classifed as desirable relationships, undesirable relationships Another applied method is DEA which is capable to and free relationships with positive and negative natures. evaluate the suppliers based on weighted ratio of outputs to Te proposed model is used to evaluate suppliers based on input. According to Kumar et al. [16], DEA is an applicable sustainable supplier criteria such as social, economic and and efective tool for supplier selection problem. In the DEA environmental criteria. approach, the importance or weights of inputs and outputs In a methodological point of view, the recent hybrid- are determined through model itself in a pairwise compari- approach studies by Tavana et al., 2017; Shabanpour et al., son manner without any human’s interference [17]. Diferent 2017a; Shabanpour et al., 2017b; Yousef et al., 2016 and Yousef models of DEA have been developed in the literature to et al., 2015 have played fundamental roles in creating the evaluate the potential suppliers. For this purpose, Weber et main idea and the contributions of this study. Tavana et al. (2000) proposed a hybrid multi-objective programming al., [29] developed a hybrid DEA framework for Sustainable (MOP)-DEA model. Farzipoor Saen [18] proposed a DEA Supplier Evaluation. Tey combined the goal programming model for ranking suppliers in the presence of imprecise and dynamic DEA model to assess efciency of suppliers data, weight restriction, and nondiscretionary factors. Also, over several periods. Teir approach enables the decision- Farzipoor Saen [19] suggested a DEA model for supplier maker to provide improved solutions for inefcient suppliers selection in the presence of undesirable outputs and impre- based on the extent to which the suppliers achieve future cise data. Noorizadeh et al. [20] introduced a model for goals (benchmarks). Merging dynamic DEA with ANN supplier selection in the presence of dual-role factors, nondis- models, Shabanpour et al., [30] created a novel framework cretionary inputs, and weight restrictions. To help managers for assessing and forecasting prospective efciency of green for ranking and selecting the best suppliers in the presence of suppliers. Likewise, another relevant survey was conducted undesirable outputs and stochastic data, Azadi and Farzipoor by Shabanpour et al., [31]. Tey applied robust values to defne Saen [21] developed a new slack- based measure model. Azadi managerial goals (improvement solutions) for evaluating et al. [22] developed a chance-constrained DEA (CCDEA) suppliers. Given the fact that the management goals are model for supplier selection in the presence of stochastic data inherently uncertain as well as based on human interference, and nondiscretionary factors. Kumar et al. [16] proposed a they created a new robust double-frontier DEA model to unifed green DEA (GDEA) model for selecting the best sup- assess and rank sustainable suppliers. Yousef et al., [32] pliers using a comprehensive environment friendly approach. developed a scenario-based robust DEA technique to deal with sustainable suppliers’ evaluation. Yousef et al., [33], fur- 2. Literature Review thermore, combined goal programming and network DEA andproposedanovelDEAframeworktoevaluatesupply Reviewing the relevant literature reveals that traditional chains. Teir approach has the potential of predicting the models of DEA evaluate efciency of DMUs merely in DMUs’ efciencies in prospective periods. Accordingly, the one specifc past period. Hence, Dynamic DEA (D-DEA) decision-maker can not only evaluate suppliers/supply chains was an appropriate approach which was initially developed but also rank them based on their efciency trend in several by Sengupta [23] and, nowadays, it is used for evaluating time periods. Tanskanen et al. [34] consider relationship DMUs in diferent periods [24]. In the literature related to strategies for levels of suppliers with respect to sustainable dynamic DEA, Fare¨ and Grosspkof [25] proposed a dynamic criteria. Varoutsa and Scapens [35] evaluate the supply chain’s production frontier using an intermediate output which agents inside the organization. Patala et al. [36] consider relates annual production processes. Tone and Tsutsui [26] sustainable criteria such as economic, environmental and introduced a new dynamic slack-based measure (DSBM) social criteria in supplier evaluation. model to assess DMUs in diferent periods, using carry- Te ideal DMU, as another assessment method, has over variables (links). Tey introduced four types of carry- been used in diferent performance evaluation problems over overs (links) as desirable, undesirable, discretionary, and the past decade. Wang et al. [37] created an interval DEA non-discretionary (fxed) links. Nevertheless, one of the def- model in which efciency was calculated within the range ciencies of the existing dynamic DEA models is their inability of an interval. Te upper bound of the interval was set to in introducing a strictly efcient DMU with efciency score one and the lower bound was established by introducing a of unity in all periods. In fact, strictly efcient DMUs are virtual IDMU, whose performance was superior to any DMU. defned as those that have unit efciency in all periods. If Jahanshahloo et al. [38] developed two ranking methods efciency score of a DMU in one of the periods has less using positive IDMU. Tey ranked 20 Iranian bank branches than unity, it won’t be considered as a strictly efcient unit. by two ranking methods. Hatami-Marbini et al. [39] provided Tis defciency can be seen in the works by Yousef et al. a four-phase fuzzy DEA framework based upon the theory of [27] and Cook et al. [28]. To overcome this problem, we displaced ideal. Tey made two hypothetical DMUs namely propose a new method for constructing the ideal DMU the ideal and nadir DMUs as reference points to rank the (IDMU) where in each period a diferent DMU with unit DMUs. Jahanshahloo et al. [40] proposed an interval DEA efciency is selected. In fact, the ideal DMU is constructed model to attain an efciency interval, including evaluations by a combination of diferent strictly efcient DMUs. In from both the optimistic and the pessimistic perspectives. In Advances in Operations Research 3

their method, the lower bounds of the DMUs are increased is defned (Model RIa/ROa) along with the corresponding to obtain the maximum value. Te derived points from this linear form (Model LRIa/LROa). Aferwards for step “b,” the method were called ideal points. Ten, the ideal points are proposed robust input/output-oriented dynamic DEA model employed to rank DMUs. Wang et al. [41] developed new is defned (Model RIb/ROb) along with the corresponding DEA models for cross-efciency evaluation by introducing a linear form (Model LRIb/LROb). In Section 4 the proposed virtual IDMU and a virtual anti-ideal DMU (ADMU). Te robust dynamic DEA models are investigated on a case study purpose of their study was to measure the cross-efciencies for supplier selection. Finally, in Section 5 conclusions are in a neutral and more logical way. brought along with future research directions. Tis paper aims to evaluate the suppliers of a home appliance company based on sustainable suppliers’ criteria 3. Problem Statement and Formulation using a new robust dynamic DEA model which is capable to evaluate and rank the suppliers with unit efciencies Te purpose of this paper is to evaluate suppliers of a which could not be ranked in the previously developed company in consecutive periods based on sustainable criteria approaches. Furthermore, a new method is developed to within three categories: (1) social, (2) economic, and (3) construct an ideal DMU. Te proposed ideal DMU is made environmental. In each period, there are a number of inputs up of a combination of DMUs with unit efciency in each and outputs for each supplier. Also some materials may be period.ItispossibletohavemorethanoneDMUwithunit transferred from one period to the next period(s) such as efciency in each period thus resulting in diferent combi- backorders and uncashed checks. Tese make relationships nations or scenarios. Terefore, a two-step scenario-based between periods which some of them are desirable and some robust approach is employed to deal with these scenarios are undesirable. In the context of DEA, each supplier is all with unit efciencies. Te proposed ideal DMU can be considered as a DMU. Since the suppliers are evaluated in appropriately used as a benchmark for other DMUs to adjust multiple periods, dynamic version of DEA is appropriate. the probable improvement plans. Dynamic DEA aims at evaluating � DMUs during � periods Te main contributions of this paper are summarized as with respect to relationships between periods. For every follows: DMU, in each period, n inputs and � outputs are considered. Also, three types of relationships such as desirable, undesir- (i) Presenting a new method for constructing an ideal able and free are considered which ensure the link between DMU in the dynamic DEA model (since it is unlikely periods. Relationships with desirable and undesirable nature to fnd a DMU with unit efciency in all periods, in need to be maximized and minimized, respectively. Free each period a diferent DMU with unit efciency can relationships are those that lack any essence and their nature be considered) cannot be recognized some of them have positive nature and (ii) Presenting a two-step robust method to deal with some have negative nature. Figure 1 graphically illustrates the diferent scenarios for ideal DMU (it is possible to proposed dynamic DEA. have more than one DMU with unit efciency in each In the dynamic DEA, usually a strictly efcient unit called period and therefore diferent combinations of DMUs ideal DMU is specifed to be considered as a benchmark so result in diferent scenarios) that inefcient DMUs try to reach it. In fact, the ideal DMU is (iii) Presenting robust ranks and improvement plans for the one that in all periods has unit efciency and it is a strictly all efcient and inefcient units efcient unit. In most cases such a DMU which is efcient in all periods does not exist and according to the existing Correspondingly, the following research questions are defnition no ideal DMU can be recognized. To overcome this expected to be addressed in this paper: problem, we introduce a new method for constructing the (i) What is the efciency of suppliers in diferent periods ideal DMU where in each period a diferent DMU with unit with respect to sustainable criteria? efciency in that period is selected. Obviously, the proposed ideal DMU is virtual and does not exist in reality. To clarify, (ii) What is the rank of suppliers when more than one consider 3 DMUs in 5 periods (Figure 2). According to the supplier with unit efciency exists? existing method for constructing the ideal DMU, no DMU is (iii) How can an ideal DMU be constructed to present selected as an ideal DMU whereas according to the proposed better improvement methods when no DMU exist method in this paper, the ideal DMU is composed of DMU 1, with unit efciency in all periods? DMU 2, DMU 3, DMU 2, and DMU 1, respectively. (iv) What if when multiple DMUs have unit efciency in In the dynamic DEA, the efcient frontier is constructed aperiod? in a pairwise comparison between units where units with maximum ratio of outputs to inputs are selected to construct Te rest of the paper is organized as follows. In Sec- the efcient frontier as presented by dotted line in Figure 3. tion 2 the proposed dynamic DEA model is presented; Te improvement method is presented for inefcient units to frst the deterministic model (Model D) is introduced and push them towards this efcient frontier. Tis issue can be then the standard form of the model is written (Model S). mentioned as another shortcoming of the existing dynamic Section 3 introduces the proposed two-step robust method DEA models where the benchmark(s) as well as improvement which are proposed for the dynamic DEA; For step “a,” the plans are merely introduced for inefcient units. Actually, proposed robust input/output-oriented dynamic DEA model those models do not present improvement methods for 4 Advances in Operations Research

Xijp xijp+1

z d,z u ,z f Period p ijp ijp ijp Period p+1 Y Y ijp+1 ijp

Figure 1: Representation of the proposed dynamic DEA.

for all DMUs. Even when all DMUs obtain similar efciency, DMU1 1 0.91 0.79 0.55 1 the proposed model can rank those units by considering an Period1 Period2 Period3 Period4 Period5 absolutely efcient unit called ideal DMU. Actually, the ideal DMU can be used as a unique benchmark based on which DMU2 0.87 1 0.81 1 0.75 improvement methods can be presented for other DMUs. As a matter of fact, initially DMUs are evaluated based on Period1 Period2 Period3 Period4 Period5 a dynamic DEA approach and then diferent scenarios are constructed for the ideal DMU (ideal supplier) through a DMU3 0.67 0.78 1 0.85 0.94 combination of efcient DMUs in each period. Altogether, the proposed ideal DMU addresses the fol- Period1 Period2 Period3 Period4 Period5 lowing concerns about the existing DEA models:

ideal DMU4 DMU1 DMU2 DMU3 DMU4 DMU5 (i) Presenting the improvement methods for efcient Period1 Period2 Period3 Period4 Period5 units (in existing models the improvement methods can only be presented for inefcient units) Figure 2: Demonstrating the proposed ideal DMU. (ii) Considering requirements and opinions of experts in presenting the improvement methods (these opinions 14 are considered in inputs and outputs values of the 12 ideal DMU). 10 8 (iii) Modifying the benchmarks in case these units are not 6 acceptable from DM’s perspective.

OUT PUT 4 2 Since in this paper diferent models are presented, to prevent 0 misunderstanding, we number the models using the follow- 0 2 468 10 12 14 ing acronyms. IN PUT Acronyms for Models I DUM D: Deterministic model DUM S: Standard model Figure 3: Efcient frontiers by the ideal DMU and efcient units. RIa: Robust Input-oriented model step a RIb: Robust Input-oriented model step b ROa: Robust Output-oriented model step a ROb: Robust Output-oriented model step b benchmarks themselves. Te proposed ideal DMU, shown by LRIa: Linear Robust Input-oriented model step a an asterisk in Figure 3, can be introduced as a benchmark LRIb: Linear Robust Input-oriented model step b for both inefcient units and efcient units. Te boundary LROa: Linear Robust Output-oriented model step a which is presented by the solid line in Figure 3 is the frontier LROb: Linear Robust Output-oriented model step b which has been constructed by the ideal DMU. As mentioned Before describing the models, the used notations can be earlier, the proposed ideal DMU consists of periods with unit described as follows. efciencies which do not necessarily belong to a DMU. It is possibletohavemorethanoneDMUwithunitefciency Notations in a specifc period. Terefore, diferent scenarios may exist m:IndexofDMUs for the ideal DMU. To deal with these scenarios, we employ n:Indexofinputs a scenario-based robust optimization approach and propose s: Index of outputs a robust dynamic DEA model to present improvement plans p:Indexoftimeperiods Advances in Operations Research 5

m ��, ��,��: Total number of desirable, undesirable, and free u u p ziop ≥ ∑zijp�j relationships, respectively. j=1 (D-5) �� : �th input of the jth DMU in period p (i=1,2,3,...... , (�=1,...,� ; �=1,...,�) n) � �� : �th output of the jth DMU in period p (i=1,2,3,...... , f s) ziop:freeofsign � (D-6) �� : Desired relationship for the jth DMU in period p, (�=1,...,��; �=1,...,�) (i=1,..,��), (j=1,..., m), (p=1,..., P). � �� : Undesirable relationship for the jth DMU in period p �j ≥0 (j =1,...,m : p =1,...,P) (D-7) p.(i=1,..,��), (j=1,..., m), (p=1,..., P). � �� :Freerelationshipforthejth DMU in period p. Objective function (D-1-IN) and (D-1-OUT) maximizes (i=1,..,��), (j=1,..., m), (p=1,..., P). the efciency of the under investigation DMU. (D-1-IN) �� :Benchmarkforthejth inefcient DMU in period p. is the objective function of the input-oriented model and o: Index for the under investigation DUM ( 1 ) − D- -OUT is the objective function of the output-oriented �� :Weightofthe�th input ( 1 ) + model. At each time either objective function D- -IN or �� :Weightofthe�th output ( 1 ) ( 2) � D- -OUT is considered. Constraint set D- ensures that � :Weightofthepth period the �th input of the under investigation DMU in period � be �∗ ��: Efciency of the under investigated DMU in period greater than or equal to weighted sum of input � in period p (input-oriented model) � for all DMUs. Constraint set (D-3) ensures that the �th ∗ Φ0 : Total efciency of the under investigated DMU output of the under investigation DMU in period � be less (input-oriented model) than or equal to weighted sum of output � in period � for ∗ ��: Efciency of the under investigated DMU in period all DMUs. Constraint set (D-4) indicates that the value of p (output-oriented model) the �th desirable relationship of the under investigation DMU ∗ � Ψ� : Total efciency of the under investigated DMU in period be less than or equal to weighted sum of the (output-oriented model) desirable relationship � in period � for all DMUs. Constraint set (D-5) indicates that the value of the �th undesirable relationship of the under investigation DMU in period � be .. e Proposed Mathematical Model for the Deterministic greater than or equal to weighted sum of the undesirable Dynamic DEA (Model D) relationship � in period � for all DMUs. Constraint set (D-6) defnes the free relationship variables which are free of sign. Constraint set (D-7) defnes the weight variables of � �∗ ∗ �� improvement plans. max Φ0 = ∑ (D-1-IN) Note that the right hand sides of the above constraints, �=1 � � u i.e., �� , �� , and �� , are positive values. Te lef hand � ∗ � � �� side of the mentioned constraints, i.e., ��, ��, ��, ��,and Ψ∗ = ∑ ( 1 ) max � D- -OUT �� p �=1 � ��, is connected together through j . Te continuity of the fow representing the relationship between pth and (p+)th � ∝ � ≥ ∑� �� periods is ensured through (1), where is a general index �� which can be d, u, or � representing desirable, undesirable, �=1 ( 2) D- andfreerelationships.Teseconstraintsareimportantinthe (�=1,...,�; �=1,...,�) proposed dynamic DEA model, since they connect period � to period p+ and ensure having a series of time periods. � � ≤ ∑� �� m m �=1 (D-3) ∝ p ∝ p+1 ∑xijp�j = ∑zijp�j (�=1,...,�∝; �=1,...,�) (1) (�=1,...,�; �=1,...,�) j=1 j=1

� � � � �� ≤ ∑�� .. e Standard Mathematical Model for the Deterministic �=1 (D-4) Dynamic DEA (Model S). Afer writing the standard form for the constraints of model (D), the fnal standard model (S) (�=1,...,��; �=1,...,�) whose constraints have equal sign is obtained as follows:

− − n u n �− 1 P 1 n w s � s � s Φ∗ = ∑ � [1− (∑ i ip + ∑ ip + ∑ ip )] ( 1 ) min 0 � w � + � + � u f S- -IN p=1 [ � � i=1 xiop i=1 ziop i=1 ziop ] 6 Advances in Operations Research

+ + � n �+ � � � � �� 1 1 � 1 � �� sip max = ∑� [1− (∑ + ∑ + ∑ )] (S-1-OUT) Ψ∗ � � + � + � � �� f � �=1 [ � � �=1 �� =1 �� i=1 ziop ]

m ∑ p − ( ) xiop = xijp�j + sip �=1,...,�; �=1,...,� (S-2) j=1

� = ∑� �� −�+ (�=1,...,�; �=1,...,�) �� (S-3) �=1

� �� = ∑�� −�� (�=1,...,� ; �=1,...,�) �� (S-4) �=1

m u u p u ziop = ∑zijp�j + sip (�=1,...,��; �=1,...,�) (S-5) j=1

m f f p f ziop = ∑zijp�j + sip (�=1,...,��; �=1,...,�) (S-6) j=1

f sip : free of sign (∀i, p), u sip ≥0, p sip ≥0, ( 7) + S- sip ≥0,

− sip ≥0, p �j ≥0

In model (S) like model (D), two alternative cases are con- weighted mean of the efciencies in all periods whose value ∗ ∗ sidered to calculate the efciency of the under investigated is between 0 and 1, i.e., (0≤Φ� ≤1), (0≤�� ≤1). Te DMU. One is input-oriented (S-1-IN) and the other is output- optimal value for the efciency of period p in input-oriented oriented (S-1-OUT) which are described in the followings. model is according to As a matter of fact, the choice of these objective functions ∗ depends on the DEA approach, i.e., whether it is input- �� oriented or output-oriented, which is used for presenting improvement plans. =1 ( 1 ) Objective function S- -IN represents the total efciency − − n u n �− 1 n w s � s � s (2) of the input-oriented model. Tis objective function is based − (∑ i ip + ∑ ip + ∑ ip ), u f on the nonredial input-oriented model which considers � + �� + �� i=1 xiop i=1 ziop i=1 ziop � �− undesirable relationships, i.e., �� and sip ,alongwithsurplus − (�=1,...,�) of inputs, i.e., �� , which should be simultaneously minimized. If all these variables become zero, the efciency of the Objective function (S-1-OUT) represents the total efciency considered DMU in period p is one. Obviously, a DMU with of the output-oriented model. Te optimal value for the overall efciency equal to one is the one which has unit efciency of period � in output-oriented model is according efciency in all periods. Tis objective function calculates the to

∗ 1 �� = n , (�=1,...,�) � + + �� + f (3) 1−(1/(� + �� + ��)) (∑�=1 (�� /��)+∑�=1 (�� /��)+∑i=1 (sip /ziop)) Advances in Operations Research 7

Te denominator of the objective function deals with the results obtained from the dynamic DEA. Te proposed ideal + slack of outputs, �� , free relationships with positive nature, DMU is made up of diferent periods each of which contains �+ � DMUs with unit efciency. As a matter of fact, in each sip ,anddesirablerelationships,�� .Ifthesevaluesbecome period, DMUs are evaluated and DMU(s) with unit efciency zero, the denominator becomes one and therefore the ef- areselectedtoconstructtheidealDMU.Sincemorethan ciency of the considered DMU in period � is one. If these one DMU with unit efciency may exist in each period, slacks get values more than one, the denominator becomes diferent combinations of DMUs may be generated for the more than one. Terefore, the efciency of the considered ideal DMU. Each of these combinations is called a “scenario”. DMU in period � is less than one. Consequently, the total More than one DMU with unit efciency in each period leads efciency in the objective function gets a value between zero ∗ ∗ to diferent combinations or scenarios for the ideal DMU and one, i.e., (0≤Ψ ≤1), (0≤� ≤1). � �� whose probabilities of occurrence are considered the same ( 2) − � In Constraint S- ,sip represents the slack for the th in this paper. Diferent scenarios for the ideal DMU result input in period �. Te lef hand side of this constraint is in diferent improvement plans. By taking the advantages of the inputs of the underinvestigated DMU in period �.If − the scenario-based robust optimization method and applying the value of sip be zero, it means that the supplier does it for the studying dynamic DEA, we evaluate and rank the not have excess consumption for that input in period �. suppliers with respect to these scenarios for the ideal DMU. + In constraint (S-3),sip represents the surplus for the �th Tis process is done in two steps. Te frst step (step a) � � � formulates the robust optimization model where one of the output in period �. In the rest of the constraints, �� ,�� ,��, scenarios is under investigation. Te second step (step b) respectively, represent the slack of the desirable relationship, formulates the robust optimization model where other DMUs surplus of the undesirable relationship, and the deviation of along with the selected scenario unit are under investigation. the free relationship. Note that the auxiliary variables used Te procedure for the proposed supplier evaluation and to standardize constraints have negative natures. For inputs rank model is summarized in the following procedure. it means excess consumption, for outputs it means shortage in production, for desirable relationships it means shortage Procedure: Supplier Evaluation and Rank through the Proposed in this relationship, for undesirable relationships it means Robust Dynamic DEA excess in this relationship, and for free relationships it means Begin deviation in this relationship. Constraint (S-6) contains a free of sign variable. Te deviation of the free relationship can (1) Determine inputs, outputs, desirable, and undesirable either be stated as slack or surplus. Terefore, to deal with the relationships for suppliers in each period. f f− f+ free of sign variable sip, two positive variables, sip and sip , (2) Consider each supplier as a DMU and employ are defned and the following constraints are considered: the dynamic (input/ouput-oriented) DEA model to f = f− − f+ determine the efciency values of each supplier in sip sip sip each period. f+ f− sip ∗ sip =0, (4) (3) If there is a DMU with unit efciency values in all periods consider it as a strictly efcient unit. f− f+ sip ≥0, sip ≥0 (4) Otherwise, build a virtual ideal DMU whose periods belong to DMUs with unit efciency thus leading to Consequently, the following constraints are substituted for diferent scenarios for the ideal DMU. Constraint (S-6): (5) In step “a,” evaluate and rank scenarios (with equal m �− probability and based on the punishment and encour- f = ∑ f �p + ziop zijp j sip agement values considered for each scenario) using j=1 (S-6-1) the proposed linear (input/output-oriented) robust / (�=1,...,� ; �=1,...,�) dynamic DEA model (LRIa LROa). Te best scenario � is considered as a unique benchmark for presenting m improvement plans. f = ∑ f �p − �+ ziop zijp j sip (6) In step “b,” consider the selected scenario from step j=1 ( 6 2) S- - “a” along with other suppliers (resulting in m+ number of DMUs) and evaluate the suppliers through (�=1,...,��; �=1,...,�) models (LRIb/LROb). 4. Robust Dynamic DEA Model End. As mentioned previously, one of the defciencies of the Notations Used in the Proposed Robust Method existing dynamic DEA is the lack of a strictly efcient unit as ^�: Te probability of occurrence for scenario s � a unit that can be introduced as a benchmark. To overcome �� :Teunitcostfor�th input of sth scenario in period p. � this defciency, we introduce a new method for constructing �� :Teunitcostfor�th undesirable relationship of sth the ideal DMU which is constructed by making use of the scenario in period p. 8 Advances in Operations Research

� �� :Teunitcostfor�th free relationship of sth scenario in At each time one of the scenarios is under investigation and period p. the efciencies of scenarios for the ideal DMU are calculated � ℎ� : Te unit revenue for �th output of sth scenario in and they are ranked. Te high ranked scenario is selected period p. based on which the improvement plan is presented. As a � �� : Te unit revenue for �th desirable relationship of sth matter of fact, the best scenario has more distance from other scenario in period p. DMUs (see Figure 3) and the improvement plan for other � �� : Te unit revenue for ith free relationship with positive DMUs is presented in the worst case. Terefore, the proposed nature of sth scenario in period p. improvement plan is robust against diferent scenarios which couldbeconsideredfortheidealDMU. .. Step a: A Scenario Unit Is under Investigation. In this section the efciency of scenarios are investigated through ... Robust Optimization for Input Oriented DEA Model models RIa or ROa, depending on the decision-maker’s Step a (RIa) approach which could be input-oriented or output-oriented.

� min �×Average +(1−�)×∑^� �=1 � � � P � � 1 1 � × � ∑ � [ ] − � � w n n �− Average� (RIa-1) �� 1−(1/(� + � + � )) (∑n ( − − / )+∑ � ( u / u )+∑ � ( / f )) � � p=1 [ � � i=1 wi sip xiop i=1 sip ziop i=1 sip ziop ] �

� � � � �� p � u p � �− � � � � d p � �+ � + ∑^� (∑�� xsisp�Ss + ∑�� zsisp�ss + ∑V� �� − ∑ℎ� �� − ∑�� zsisp�ss − ∑�� ) �=1 �=1 �=1 �=1 �=1 �=1 �=1

− − n u n �− � 1 P 1 n w s � s � s k = ∑^ × ∑ � [ − (∑ i isp + ∑ i�p + ∑ isp )] ( 2) A erage � w 1 u f RIa- � � + �� + �� xiop z �=1 p=1 [ i=1 i=1 iop i=1 ziop ] m = ∑ �p + � p + − (� = 1,...,�; � = 1,...,�; � = 1,...,�) xisp xijp j xsisp Ss sisp (RIa-3) j=1

� �� = ∑� �� + �� − �+ (� = ,...,�; � = ,...,�; � = ,...,�) �� 1 1 1 (RIa-4) �=1

m �f = ∑ f �p + f � p + �− (� = 1,...,� ; � = 1,...,�) z iop zijp j zsisp ss sisp � (RIa-5) j=1

m f = ∑ f �p + f � p − �+ (� = 1,...,� ; � = 1,...,�) zsiop zijp j zsisp ss sisp � (RIa-6) j=1

� �� = ∑�� + d � p − �� (� = ,...,� ; � = ,...,�) �� zsisp ss �� 1 � 1 (RIa-7) �=1

m u = ∑ u �p + u � p + u (� = 1,...,� ; � = 1,...,�; � = 1,...,�) zsisp zijp j zsisp ss sisp � (RIa-8) j=1

u sisp ≥ 0,

+ sips ≥ 0,

− sisp ≥ 0, p �j ≥ 0, p ss ≥ 0, Advances in Operations Research 9

�+ sisp ≥ 0,

�− sisp ≥ 0,

� �� ≥ 0

(RIa-9)

Te objective function (RIa-1) consists of three terms. Te It is worth noting that since each scenario is a combi- frst term calculates the average efciency of scenarios. Te nation of DMUs with unit efciency selected from diferent second term calculates the deviation of efciency of scenarios periods, the efciency of each scenario is one. Terefore, the from the average value. Te third term calculates the total average efciency of all scenarios is one and consequently the proft or loss resulted from scenarios. In fact, in each scenario, standard deviation is zero. outputs, desirable relationships and free relationships with positive natures, yield return. Whilst inputs, undesirable () Linear Robust Input-Oriented Model Step a (LRIa). To deal with the absolute function and make the model linear, two relationships, and free relationships with negative natures + − result in cost. Note that in this term, the values of returns are positive variables �� and �� are defned. subtracted from the values of costs. Terefore, if this term is negative it means that the considering scenario is proftable; otherwise it makes losses.

∗ min Φ0

� + − = � × Akerage +(1 − �)×∑^� ×(�� + �� ) �=1 (LRIa-1) � � � � �� p � u p � �− � � � � d p � �+ � + ∑^� (∑�� xsisp�Ss + ∑�� zsisp�ss + ∑V� �� − ∑ℎ� �� − ∑�� zsisp�ss − ∑�� ) �=1 �=1 �=1 �=1 �=1 �=1 �=1

− − n u n �− 1 P 1 n w s � s � s ∑ � [ − (∑ i isp + ∑ isp + ∑ isp )] − k = �+ �− ( 2) w 1 u f A erage � - � LRIa- � � + �� + �� xiop z p=1 [ i=1 i=1 iop i=1 ziop ]

Other constraints of model (RIa)hold. objective function and also in the average and the linearized constraints. Other constraints are the same for both. ... Robust Optimization for Output-Oriented DEA Model Step a (ROa). Te robust optimization for the output- oriented model difers with the input oriented model in the

� min � × Akerage +(1 − �)×∑^� �=1 � � � + + � � n �+ � � � � � � � � � � � 1 � [ 1 � �� sip ] � × � ∑� 1 − (∑ + ∑ + ∑ ) − Akerage� (ROa-1) �� + � + � � �� f � � �=1 [ � � �=1 �� =1 �� i=1 ziop ] � � � � � �� p � u p � �− � � � � d p � �+ � + ∑^� (∑�� xsisp�Ss + ∑�� zsisp�ss + ∑�� − ∑ℎ� �� − ∑�� zsisp�ss − ∑�� ) �=1 �=1 �=1 �=1 �=1 �=1 �=1

+ + � n �+ � � � � � �� 1 � [ 1 � �� sip ] Akerage = ∑^� × ∑� 1 − (∑ + ∑ + ∑ ) (ROa-2) � � + � + � � �� f �=1 �=1 [ � � �=1 �� =1 �� i=1 ziop ]

Other constraints of model (RIa)hold. 10 Advances in Operations Research

Like the input-oriented model, the objective function efciencies with weight importance of 1- �. Finally, the third (ROa-1) consists of three terms. Te frst term minimizes term calculates the total proft or loss resulted from scenarios. the average efciency of scenarios with weight importance � () Linear Robust Output-Oriented Model Step a (LROa). By of . Te second term minimizes the standard deviation of + − considering two positive variables �� and �� and substituting it with the absolute function, the model is linearized.

� + − min � × Akerage +(1 − �)×∑^� ×(�� + �� ) �=1 ( 1) � � LROa- � � �� p � u p � �− � � � � d p � �+ � + ∑^� (∑�� xsisp�Ss + ∑�� zsisp�ss + ∑�� − ∑ℎ� �� − ∑�� zsisp�ss − ∑�� ) �=1 �=1 �=1 �=1 �=1 �=1 �=1

+ + � n �+ � � � � �� [ 1 � [ 1 � �� sip ] ] + − ∑� 1 − (∑ + ∑ + ∑ ) − Akerage = � − � (LROa-2) � � + � + � � �� f � � [ �=1 [ � � �=1 �� =1 �� i=1 ziop ] ]

Other constraints of model (RIa)hold. along with the strictly efcient DMU (i.e., the selected scenario as an ideal DMU) as a benchmark. Ten the improve- .. Step b: A DMU from Other DMUs Is under Investigation. ment methods can be presented for other DMUs based on In the previous section the under investigation DMU was one their distance from the efcient frontier and image inefcient of the scenarios and we evaluated scenarios and selected the DMUs to the efcient frontier. Te main diference of model suitable one. In fact, model (RIa/ROa) calculates beneft or (RIb)withmodel(RIa)isthatinmodel(RIb)thenumber loss resulted from each scenario and we can select the best of DMUs is m+1. Another diference is that the objective one accordingly. In this section, other DMUs are evaluated function consists of two terms, i.e., the average efciency and along with the selected scenario and therefore the number of the standard deviation of efciencies of the considered DMU � DMUs increases by one (i.e., m+1). Actually the best scenario in diferent periods respectively with importance weights 1−� is considered in model (RIb/ROb). and . Note that the objective function of model (RIb) does not consider the cost since by taking the ideal DMU into consideration; we can rank DMUs and present improvement ... Robust Optimization for Input-Oriented DEA Model Step methods. b(RIb). Te following model (RIb)evaluatesotherDMUs

∗ min Φ0

− − n u n �− � 1 P 1 n w s � s � s (RIb-1) =�× +(1−�)×∑^ ×( ∑ � [1− (∑ i ip + ∑ ip + ∑ ip )] − ) Average � w u f Average � � + �� + �� xiop z �=1 p=1 [ i=1 i=1 iop i=1 ziop ]

− − n u n �− � 1 P 1 n w s � s � s . . = ∑^ × ∑ � [1− (∑ i ip + ∑ ip + ∑ ip )] ( 2) s t Average � w u f RIb- � � + �� + �� xiop z �=1 p=1 [ i=1 i=1 iop i=1 ziop ]

m+1 p − xiop = ∑ xijp�j + sip (�=1,...,�; �=1,...,�; �=1,...,�+1) (RIb-3) j=1

�+1 � + �� = ∑ �� −�� (�=1,...,�; �=1,...,�; �=1,...,�+1) (RIb-4) �=1

m+1 u u p u ziop = ∑ zijp�j + sip (�=1,...,��; �=1,...,�; �=1,...,�+1) (RIb-5) j=1

m+1 f f p �− z�iop = ∑ zijp�j + sip (�=1,...,��; �=1,...,�; �=1,...,�+1) (RIb-6) j=1 Advances in Operations Research 11

m f = ∑ f �p − �+ (�=1,...,� ; �=1,...,�; �=1,...,�+1) zsiop zijp j sip f (RIb-7) j=1

� �� = ∑�� −�� (�=1,...,� ; �=1,...,�; �=1,...,�+1) �� (RIb-8) �=1

u sip ≥0,

+ sip ≥0,

− sip ≥0, �p ≥0, j (RIb-9) �+ sip ≥0,

�− sip ≥0,

� �� ≥0

() Linear Robust Input-Oriented Model Step b (LRIb). By + − considering two positive variables �� and �� and substituting it with the absolute function, the model is linearized.

� ∗ + − min Φ0 =�×Average +(1−�)×∑^� ×(�� +�� ) (LRIb-1) �=1

− − n u n �− � 1 P 1 n w s � s � s . . = ∑^ × ∑ � [1− (∑ i ip + ∑ ip + ∑ ip )] ( 2) s t Average � � w � + � + � u f LRIb- �=1 p=1 [ � � i=1 xiop i=1 ziop i=1 ziop ]

− − n u n �− 1 P 1 n w s � s � s ∑ � [1− (∑ i ip + ∑ ip + ∑ ip )] − =�+ −�− ( 3) w u f Average � � LRIb- � � + �� + �� xiop z p=1 [ i=1 i=1 iop i=1 ziop ]

Other constraints of model (RIb)hold.

... Robust Optimization for Output-Oriented DEA Model Step b (ROb)

∗ min Φ0 =�×Average +(1−�)

+ + � � n �+ � � � � � � � � (ROb-1) 1 � [ 1 � �� sip ] × ∑^� ×( ∑� 1 − (∑ + ∑ + ∑ ) − Average) � � + � + � � �� f �=1 �=1 [ � � �=1 �� =1 �� i=1 ziop ]

+ + � n �+ � � � � � �� 1 � [ 1 � �� sip ] s.t. Akerage = ∑^� × ∑� 1 − (∑ + ∑ + ∑ ) (ROb-2) � � + � + � � �� f �=1 �=1 [ � � �=1 �� =1 �� i=1 ziop ]

Other constraints of model (RIb)hold. () Linear Robust Output-Oriented Model Step b (LROb). By + − considering two positive variables �� and �� and substitut- 12 Advances in Operations Research

ing them with the absolute function, the model is linearized.

� ∗ + − min Φ0 =�×Average +(1−�)×∑^� ×(�� +�� ) (LROb-1) �=1

+ + � n �+ � � � � � �� 1 � [ 1 � �� sip ] s.t. Akerage = ∑^� × ∑� 1 − (∑ + ∑ + ∑ ) (LROb-2) � � + � + � � �� f �=1 �=1 [ � � �=1 �� =1 �� i=1 ziop ]

+ + � n �+ � � � � �� 1 � [ 1 � �� sip ] + − ∑� 1 − (∑ + ∑ + ∑ ) − Average =� - � (LROb-3) � � + � + � � �� f � � �=1 [ � � �=1 �� =1 �� i=1 ziop ]

Other constraints of model (RIb)hold. opinion using 9-point Likert spectrum according to Table 1. Likert scale is used to convert qualitative 5. Case Study Implementation and factors into quantitative values [42]. Tere are variety of scales which can be rated as 1 to 5, 1 to 7, and 1 Performance Evaluation to 9. Valuation of factors in this scale is performed In this section, the performance of the proposed robust according to concept of each factor [43]. dynamic DEA approach is investigated via a case study taken (2) Green research and development (as a free relation- from NANIWA (http://www.naniwa.ir) appliances produc- ship and an environmental criterion): Te corre- tion plant. Te mentioned frm aims at evaluating its 35 sponding budget per year (in $100). Green research suppliers in 4 time periods based on environmental, social, and development is a dual-role factor which plays the and economic criteria. For the purpose of evaluation, for each role of both undesirable and desirable factors. Green supplier as a DMU, 4 inputs, 3 desirable and undesirable research and development can be considered as an relationships, and 4 outputs are considered. undesirable criterion since it is cost of performing green researches. On the other hand, green research Inputs and development is a desirable criterion, because it (1) Price ofered by suppliers (as an economic criterion): implies innovations in manufacturing green products It is the money (in $1000) that is paid to suppliers for and services and environmental efciency enhance- each unit of products. ment. (2) Cost of recoverable packages (as an environmental (3) Shortages (as an undesirable relationship and an criterion): Tis input is the cost (in $100) that is economic criterion): Te amount of shipments (in imposed to the company by the supplier for using terms of pallets) that have not delivered in the past recoverable packages. It is worth noting that it is period and should be met in the next period by the mandatory for Naniwa Company to ship their prod- supplier. ucts in suitable pallets with recoverable packages to prevent damaging the environment. Outputs (3) Final transportation cost (as an economic criterion): (1) Obtaining ISO certifcates and observance of stan- Tis is the fnal cost (in $100) which is imposed dards: this kind of output is scored by expert’s opinion by the supplier to the frm for transportation of using 9-point spectrum with respect to qualitative shipped pallets. Te farthest the supplier is and the and environmental criteria and standards and also less accessible the paths are, the more cost imposed. workplace standards. Table 2 shows the 9-point spec- Tis cost is the main concern of the decision-makers trum. in the company. (2) Quality (as an economic criterion): Quality of prod- (4) Work safety and labor health (as a social criterion): ucts is evaluated by Likert scale. In Table 3, using Tisisthecostthateachsupplierpaysfordangersthat a 9-point Likert scale, valuation of quality of parts exist and accidents which happen in the workplace. supplied by suppliers is presented. Te less damage and casualties are, the less cost is paid (3) Supply capacity (g 2): maximum amount of materials by each supplier. that supplier can send to Naniwa Co. Relationships (4) Efciency of energy consumption (as an environmen- (1) Used technology in the production line of suppliers tal criterion): Efciency of the energy consumption is (as a desirable relationship and an economic cri- the third output which is an environmental criterion. terion): Te used technology is scored by expert’s To determine an appropriate scale for evaluating Advances in Operations Research 13

Table 1: 9-point Likert spectrum for Technologic power.

Value 9 7 5 3 1 2-4-6-8 Intermediate High Medium Very weak Technology Good Technology Weak Technology values for Technology Technology Technology Technology

Table 2: 9-point Likert spectrum for Standards.

Value 9 7 5 3 1 2-4-6-8 High Very Weak Intermediate values ISO standards Good Standards Medium Standards Weak Standards Standards Standards for Standards

�� efciency of energy consumption we apply a scoring �� : Unit cost for input j for all scenarios (j: price, method which is shown by A+++ to G scale. Te letter packaging, transportation cost, and workforce health cost): A+++ shows the lowest energy consumption. Te this is a penalty that is imposed to a scenario by the decision- letter G indicates the highest energy consumption. maker for each unit of inputs. �� Using 100-point scale. Table 4 shows the energy ℎ� : Unit income for output j for all scenarios (j: consumption of the suppliers. quality, production capacity, the number of acquired ISO and standards, and efciency of the energy consumption): this is Figure 4 illustrates the proposed dynamic DEA approach on the encouragement that is considered for a scenario for each the case study to evaluate suppliers in periods 2011 to 2014. unit of outputs. Te inputs, outputs, and relationships between periods is �� illustrated in this fgure. 1 :Unitcostofshortagesinshippedpalletsforall Te inputs, relationships, and outputs data for scenarios (undesired relationships): this is the penalty that is 35 suppliers in 4 time periods are presented in decided by the decision-maker for each unit of this undesired Table 5 in the Appendix. relationship.Inthispaperforbacklogsorgoodsshippedwith In Table 6, the DMUs (i.e., 35 suppliers) are evaluated a delay a penalty is considered for the supplier in that period. �� by making use of the existing input-oriented dynamic DEA 1 : Unit cost of green research and development for all model on data shown in the Table 5 presented in the scenarios (free relationships): if the free relationship be an Appendix. Te DEA model is selected according to the DM’s undesired relationship a penalty value will be assigned for approach for which he/she want to present their proposed each unit of this relationship. In our case study, if the green improvement plans. Table 6 shows the efciency values for R&Disconsideredasanundesiredrelationshipfortheunder 35 suppliers in 4 periods from 2011 to 2014. investigation DMU, a penalty is considered for that supplier Te results of Table 6 show that none of the suppliers for each unit of this relationship. �� have unit efciency values in all 4 periods. Terefore, none 1 : Unit income of green research and development for of them are strictly efcient. To construct a strictly efcient all scenarios (free relationships): if the free relationship is a unit as a benchmark for other units, in each period the DMU desired relationship an encouragement value will be assigned with unit efciency is selected as a candidate. As a result, 8 for each unit of this relationship. In our case study, if the green scenarios are generated for ideal DMU which are diferent R&Disconsideredasadesiredrelationshipfortheunder combinations of DMUs (suppliers) with unit efciency in investigation DMU, an encouragement value is considered for each period. Tese resulting scenarios are presented in Table7 that supplier for each unit of this relationship. �� with probability of 0.125 for each one. If these scenarios are �1 : Unit income of technological power for all scenarios taken into consideration and evaluated along with other 35 (desirable relationships). suppliers, the efciency of scenarios becomes one because As mentioned earlier, the existing dynamic DEA model they consist of DMUs with unit efciencies in all periods. cannot rank diferent scenarios for the ideal supplier. In this Terefore, we can claim that the existing dynamic DEA model paper, frst we evaluate and rank these scenarios through cannot evaluate and rank the scenarios. In the proposed the proposed input-oriented robust dynamic DEA model model (RIa), since all scenarios have unit efciency, the (RIa). In Table 9, the punishment and encouragement for average efciency is also one and the deviation of efciencies each scenario resulting from model (RIa) is presented. As is zero. Terefore, we set �=1,1−�=0.Todealwiththis presented in Table 9, the second scenario is the best scenario difculty, a punishment (Cost) and encouragement (Income) since it has the maximum value of beneft. Generally, if the value is considered for the inputs, outputs, and relationships objective function of model (RIa) is positive, the scenario of each scenario. will generate loss while it is negative the scenario will make Te costs and incomes associated with inputs, outputs, benefts. If all scenarios generate loss, the scenario with and relationships are presented in Table 8 with the following minimum loss will be selected. Te values of landa obtained notations: from model (RIa) admit that the scenarios can be considered 14 Advances in Operations Research

Table 3: 9-point Likert spectrum for Quality.

Value 9 7 5 3 1 2-4-6-8 Intermediate values Quality High Quality Good Quality Medium Quality Weak Quality Very Weak Quality for Quality

Table 4: Spectrum for efciency of the energy consumption.

Score 100 90 80 70 60 50 40 30 20 10 Efciency of the energy consumption A+++ A++ A+ A B C D E F G as a benchmark. In the next step, the second scenario which as a strictly efcient unit which is efcient in all periods. Our is the best scenario is considered as the ideal DMU and it is contribution is introducing a new method for constructing evaluated along with other DMUs (suppliers) through model the ideal DMU such that apart from the previous defnition (RIb). Te ideal DMU which is actually the ideal scenario for ideal DMU which considers one of the DMUs which has is considered as a unique benchmark which owns both the unit efciency in all periods as an ideal DMU, a virtual DMU property of a real supplier in that it consists of some periods is considered as an ideal DMU. Te new proposed ideal DMU and the property of a virtual supplier in that it is strictly has the ability of presenting an improvement method for all efcient and consists of periods with unit efciency. Tere- suppliers and also ranking the suppliers with the same ef- fore, the proposed ideal DMU can present improvement ciency. Te proposed ideal DMU introduces a strictly efcient plans for all suppliers and can rank the suppliers with same ( ) unit by building a combination of DMUs with unit efciency efciency. Te results obtained from model RIb are reported in each period. It is possible that multiple DMUs have unit in Table 10. As presented in Table 10, the ideal DMU gives efciency in a period. Terefore, diferent combinations of the ability of ranking the suppliers that had the same rank these units lead to diferent scenarios for the ideal DMU each in Table 6. From Table 6 we can see that suppliers 2 and 13, of which can happen with a specifc probability. Te existing 19 and 3, 8 and 31, 6 and 4, two by two have the same rank dynamic DEA model cannot evaluate and rank the scenarios because the total efciency of these DMUs are equal. Using which all have unit efciency. To deal with these scenarios, the proposed model (RIb) for evaluating the suppliers and a scenario-based robust optimization model for the dynamic constructing an ideal DMU help us to rank the suppliers. DEA is developed which is capable of ranking the scenarios Tis ranking considers the standard deviation of efciencies based on a punishment and encouragement value assigned to in calculating the efciency of each supplier. Furthermore, the each scenario. proposed ideal DMU gives us the opportunity of presenting Te proposed robust method is implemented in two improvement methods for all DMUs. As a matter of fact, the steps and it is is able to obtain a solution which is immu- improvement methods are presented based on their distance nized against diferent scenarios exist in constructing the from the ideal DMU (supplier). Te high ranked scenario ideal DMU. In the frst step, at each time one of the resulting from model (RIa), which is the second scenario, has scenarios is under investigation. Te high ranked scenario maximum distance from other suppliers and it is the worst case that can be happen for an ideal scenario based on which which has more distance from other DMUs is selected as a unique benchmark based on which the improvement plan improvement plans can be presented. Trough model (RIb) other suppliers can be ranked based on their distance from is presented in the worst case. In fact, in the second step this worst case ideal scenario. Terefore, we could claim that other DMUs along with the worst case scenario are under the resulting ranks and improvement plans cannot get worse investigation and improvement plans are proposed based on when each of the other scenarios, which could be happen with their distance from the ideal DMU. Terefore, the proposed a given probability, is considered thus resulting in a robust method can rank the suppliers with the same efciency solution. and propose an improvement plan which is robust against diferent scenarios which could be considered for the ideal 6. Conclusions and Future Research Directions DMU. For future study on this work, apart from the uncertainty Tis paper proposed a new DEA approach for evaluating in diferent scenarios for ideal DMU, one can consider the suppliers based on sustainable supplier criteria such as social, input, output, and relationship values as uncertain param- economic, and environmental criteria. Te proposed model eters which can vary in a convex uncertainty set. Ten a considers suppliers in diferent periods thus leading to a hybrid robust optimization approach, i.e., a hybridization of dynamic DEA model. Existing dynamic DEA models just the scenario-based and robust counterpart methods, can be present improvement plans and do not have the ability of developed to deal with these uncertainties. ranking DMUs. Te proposed model apart from having the ability of ranking DMUs can present improvement plans. Appendix In most DEA models, when diferent time periods are considered in evaluating DMUs, no DMUs can be introduced See Table 5. Advances in Operations Research 15 Table 5: Te inputs, relationships and outputs data for 35 suppliers in 4 time periods. IN12631293026343216293033282431292625292831351533212624282330272631252933 IN11933322729292830323336292832312928323328301529332830292927323033292538 IN2 5 7 9 7 9 710910 IN3 7 9149 15 9 5 7 9105 13 18 12 23 7 7 9 5 7 814197 11 22 10 20 19 9 913121056 14 6IN21216252422201618161720261923221918201618201016211914201615201620181618 IN33 9 7 17 2 18 8 19 10 25 6 22 9 20 18 9 17 11 16 14 23 5 19 8 22 6 19 9 10 5 19 13 7 15 3 16 9 17 8 19 12 20 5 18 12 6 16 7 16 8 18 9 21 10 5 8 12 9 N1986 191890980 99866789106889 8109811899106978102 IN410978964 IN4 4 11 8 9 8 9 10 6 9 7 9 10 9 13 12 9 8 10 8 6 9 5 11 10 9 8 7 5 6 7 9 8 6 7 10 DMU U1 4658496 9 5765445678634 5874576546598 OUT14 678665 7 6867865867586 9 7856687765867 OUT19 U2 659569 7 9 8757867968779 7768787997687 OUT28 OUT3 78 53 59 678655 8 9 9969877686987 6678586789788 64 69 71 88OUT29 OUT3 68 95 63 59 59 60 55 70 49 77 69 66 72 68 66 67 52 81 70 71 59 63 63 65 52 73 73 78 95 72 62 69 56 73 84 69 79 74 83 72 78 69 66 89 69 73 59 66 74 95 78 66 76 85 91 65 73 72 60 85 80 66 80 OUT4609080809090601008090607090808060705060504010070708060605070604070605080 OUT4100808080908050608070507070808070705060604010070707060606080605070705080 IK8786796 9 5579786895567 9 9865886786678 LINK18 9 7 8777777687787 6678677786678 LINK19678887 LINK22831303229283518262627293033272529302729271525263732342629292826333425 LINK3 20 16 17 18 13 15LINK21230283133292925192834363328342925323330262030312826293032252729322628 15LINK3 2 5 15 12 18 10 16 11 18 17 15 16 13 15 6 13 8 17 9 16 7 14 6 11 10 8 11 11 15 3 12 12 12 19 17 15 14 13 12 14 16 6 5 16 10 9 10 11 17 12 10 14 12 15 11 10 18 14 13 15 18 12 10 2011 16 Advances in Operations Research Table 5: Continued. IN13132342630262932353230263030292229313025322628322931302826332830262415 IN12034372934333236373434353432332832343331303032343033323030353332282815 IN3 14 10 14 13 11 8 9IN3 8 4 8 14 10 15 8 15 13 9 12 9 12 11 10 15 10 8 12 10 10 7 10 8 11 8 14 12 17 10 16 12 8 18 10 10 12 11 8 15 8 12 9 9 10 14 6 15 7 9 8 7 8 10 4 12 2 14 10 16 9 10 5 IN2181827252422191919182228172525171924191922191823171821171722182119159 IN4 15 14 12 11 10IN21422302827262520232420262027292022262021252119261921232120242122201712 10 12IN4 8 8 7 15 9 14 10 13 12 12 10 12 15 9 14 10 11 12 10 10 14 10 9 11 9 10 10 18 10 13 15 12 14 11 10 13 11 10 12 10 10 13 5 12 14 8 11 8 12 11 11 9 14 10 12 4 9 11 10 14 11 9 7 DMU U1 979899877989697889988698769 9 78867 9 OUT17 779988897789978697988987789 9 88798 9 OUT19 OUT3 63 70 72 64 86 70 64 65OUT3 65 89 60 59 70 63 60 72 65 73 85 72 80 68 75 68 80 60 70 68 65 67 83 73 82 72 70 66 65 64 80 69 81 65 75 43 76 70 55 72 65 71 80 74 50 73 80 70 77 72 65 66 67 95 59 68 75 63 78 69 59 95 U2 898697868799867998798678998 8 98798 9 OUT26 OUT4 70 70 999797979899887998898889999 9 80 98998 9 60 90 70OUT29 50 60OUT41009080809070606090705060609070807080706050506080708060701006060807070100 70 50 40 70 60 80 70 70 70 70 60 60 50 60 70 70 70 80 60 50 80 60 60 70 70 60 100 IK8788959755767678 778987965796785858786878687 68878 9 LINK18 8 88898 778998977897886869797869788 9 LINK19 LINK3151921201918171614151918161715121817131516141012141113151614121516122 LINK3 5 9 11 10 14 16 13 11 12 10 14 16 16 18 5 17 16 18 15 10 10 13 12 14 16 7 10 21 18 14 11 13 15 10 3 LINK23332272930343139283030363329313026272930313634332930322937293433262810 LINK22030293032323335293232353430333228293029303536343132343230323630253122 Advances in Operations Research 17

Table 6: Efciency values for 35 suppliers in 4 periods (Input-oriented dynamic DEA model).

DMU �2011 �2012 �2013 �2014 Φ� RANK 1 0.856 1 0.986 1 0.9605 1 2 0.763 0.943 0.915 0.966 0.8967 4 3 0.88 0.849 0.965 0.824 0.8795 11 4 0.867 0.825 0.814 0.894 0.85 26 5 0.728 0.831 0.824 0.872 0.8137 33 6 0.809 0.941 0.769 0.881 0.85 26 7 0.911 0.817 0.964 0.764 0.864 19 8 1 0.866 0.813 0.821 0.875 13 9 0.766 0.835 0.849 0.938 0.847 29 10 0.849 0.961 0.827 0.933 0.846 31 11 0.867 0.985 0.863 0.74 0.8637 20 12 0.857 0.938 0.917 0.768 0.87 16 13 0.892 0.846 0.965 0.884 0.8967 4 14 0.893 0.851 0.824 0.825 0.8482 28 15 0.846 0.837 0.764 0.864 0.8277 32 16 0.937 0.84 0.819 0.897 0.8732 15 17 0.967 0.869 0.893 0.831 0.89 7 18 0.955 0.815 0.84 0.843 0.8632 21 19 0.934 0.834 0.933 0.817 0.8795 11 20 0.871 0.769 0.968 0.934 0.8855 9 21 0.768 0.941 0.824 0.92 0.8632 22 22 1 1 0.866 0.819 0.9212 3 23 0.869 0.911 0.814 0.8349 0.8572 24 24 0.942 0.771 0.867 0.822 0.8505 25 25 0.852 0.764 0.789 0.796 0.8002 34 26 0.789 0.859 0.984 0.753 0.8462 30 27 0.844 0.915 0.943 0.749 0.8627 23 28 0.809 0.864 0.972 0.921 0.8915 6 29 0.78 0.91 0.928 0.966 0.8842 10 30 0.922 0.752 0.846 0.946 0.8665 18 31 0.818 0.92 0.837 0.925 0.875 13 32 0.846 0.881 0.819 0.933 0.8697 17 33 0.856 0.825 0.935 0.928 0.886 8 34 0.736 0.714 0.966 0.784 0.8 35 35 0.855 0.891 1 1 0.9365 2

Table 7: Diferent scenarios for Ideal DMU. Ideal DMU Period 2011 Period 2012 Period 2013 Period 2014 Scenario 1 Supplier 22 Supplier 22 Supplier 35 Supplier 1 Scenario 2 Supplier 22 Supplier 22 Supplier 35 Supplier 35 Scenario 3 Supplier 22 Supplier 1 Supplier 35 Supplier 1 Scenario 4 Supplier 22 Supplier 1 Supplier 35 Supplier 8 Scenario 5 Supplier 8 Supplier 22 Supplier 35 Supplier 1 Scenario 6 Supplier 8 Supplier 22 Supplier 35 Supplier 35 Scenario 7 Supplier 8 Supplier 1 Supplier 35 Supplier 1 Scenario 8 Supplier 8 Supplier 1 Supplier 35 Supplier 35 18 Advances in Operations Research

Production capacity Technological power Workforce health Cost of recoverable packages Workforce health

ISO standards

Green research and development Cost of recoverable packages

Deduction or shortages

Final transportation Efciency of cost energy consumption

price

Quality Final transportation price cost

Figure 4: Demonstration of the proposed dynamic DEA on the considered case study.

Table 8: Costs and incomes associated with inputs, outputs and relationships.

�� Parameters �1 �2 �3 �4 �1 V1 Costs �� Parameters ℎ1 ℎ2 ℎ3 ℎ4 �1 �1 Incomes

Table 9: Evaluating diferent scenarios for the Ideal DMU (Model RIa).

Scenario 1 2 3 4 5 6 7 8 Worst case Efciency 1 1 1 1 1 1 1 1 1 Beneft/loss 10027 10988 10103 9655 10320 10768 9435 9883 10147.375

Table 10: Evaluating suppliers along with the ideal supplier (Model RIb).

DMU 1 2 3 4 5 6 7 8 9 Efciency 0.489 0.478 0.445 0.354 0.317 0.359 0.412 0.437 0.341 RANK 2 5 13 28 34 27 20 15 30 DMU 10 11 12 13 14 15 16 17 18 Efciency 0.325 0.406 0.428 0.475 0.348 0.321 0.432 0.469 0.401 RANK 32 21 17 6 29 33 16 8 22 DMU 19 20 21 22 23 24 25 26 27 Efciency 0.449 0.462 0.392 0.481 0.377 0.362 0.309 0.332 0.384 RANK 12 10 23 4 25 26 35 31 24 DMU 28 29 30 31 32 33 34 35 IdealDMU Efciency 0.472 0.458 0.416 0.439 0.422 0.466 0.305 0.484 0.5 RANK 7 11 19 14 18 9 36 3 1 Advances in Operations Research 19

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Research Article Multicriteria Evaluation of Urban Regeneration Processes: An Application of PROMETHEE Method in Northern Italy

Marta Bottero ,1 Chiara D’Alpaos,2 and Alessandra Oppio3

1 Department of Regional and Urban Studies and Planning, Politecnico di Torino, Italy 2Department of Civil, Environmental and Architectural Engineering, University of Padova, Italy 3Department of Architecture and Urban Studies, Politecnico di Milano, Italy

Correspondence should be addressed to Marta Bottero; [email protected]

Received 23 April 2018; Revised 7 September 2018; Accepted 11 October 2018; Published 14 November 2018

Academic Editor: Mhand Hif

Copyright © 2018 Marta Bottero et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Te paper illustrates the development of an evaluation model for supporting the decision-making process related to an urban regeneration intervention. In particular, the study proposes an original multi-methodological approach, which combines SWOT Analysis, Stakeholders Analysis and PROMETHEE method for the evaluation of alternative renewal strategies of an urban area in Northern Italy. Te article also describes the work carried out within an experts’ panel that has been organized for validating the structuring of the decision problem and for evaluating the criteria of the model.

1. Introduction governance perspective. A critical review of the notion of reuse over time has revealed an emerging attention to the In recent years many European cities have implemented quality issue that does not only depend on development and relevant renewal programmes for enhancing physical, envi- design tools focused on environmental targets, but also on ronmental, social, and economic long-term development the managerial approach of local authorities in structuring of old industrial sites or areas under decline. Integrated multiform partnerships [6]. regeneration processes represent the main concern in many Under these circumstances, evaluation plays a crucial experiences. Physical transformations are embedded within role since it allows to codefne and rank alternative projects social, environmental, and economic as well as institutional with respect to both technical elements, which are based on aspects [1]. How to achieve a balance among interrelated and empirical observations, and non-technical elements, which ofen confictual goals in order to improve the quality of are based on social visions, preferences, and feelings [7]. urban systems is still an open challenge. On one side the need In this context, a very useful support is provided by Mul- of replacing top-down strategies with collaborative models, tiple Criteria Decision Analysis (MCDA) techniques, which based on needs, expectations, and values shared by all the are used to make a comparative assessment of alternative parties involved, is widely acknowledged as one of the driver projects or heterogeneous measures [8, 9]. Tese methods of success [2–4]. On the other one, local oppositions ofen allow several criteria to be taken into account simultaneously arise against both public and private works, thus causing in a complex situation and they are designed to help decision- interruptions and delays to development processes [5]. makers (DMs) to integrate the diferent options, which refect Territorial and urban regeneration programmes specif- the opinions of the involved actors, in a prospective or ically point out the need of developing new combinations retrospective framework. Participation of decision-makers in between analytical tools and participatory approaches, in the process is a central part of the approach. order to strengthen the choices’ legitimacy and to address Aware of the advantages and disadvantages of the many the wealth of contradictory visions, and preferences of the available MCDA techniques, this paper aims at testing the diferent actors to a shared vision according to a multilevel PROMETHEE (Preference Ranking Organisation Method 2 Advances in Operations Research for Enrichment Evaluations), as an outranking method [10] of the PROMETHEE, namely PROMETHEE TRI to solve to support decisions in urban planning and regeneration sorting problems, and PROMETHEE CLUSTER for nominal processes. Given the lack of robust assumptions on the deci- classifcation. sion maker preferences, the PROMETHEE can be efectively In this paper we implement PROMETHEE II in order to integrated with participatory methods in order to get enough rank alternatives according to diferent criteria which have information to understand whether one alternative is at least to be maximized or minimized. Once the decision group as good as another. was constituted, we proceeded according to the following In particular, the paper refers to the assessment of subsequent steps. diferent urban regeneration scenarios for the city of Collegno (Italy). Diferently from Bottero et al. [11], who modeled Step 1 (construction of an evaluation matrix). A double urban resilience dynamics in Collegno by using Fuzzy entry table for the selected criteria and alternatives has Cognitive Maps, and complementing Bottero et al. [12] been compiled by using cardinal (quantitative) and ordinal who combined Stakeholder Analysis and Stated Preference (qualitative) data. Tis matrix accounts for deviations of Methods to assess the social value of urban regeneration evaluations on pairwise comparisons of two alternatives, a scenarios in Collegno and their related willingness to pay, we and b, on each criterion. combine the PROMETHEE approach with SWOT Analysis ( , ) and Stakeholder Analysis, to rank six urban regeneration Step 2 (identifcation of the preference function Pj a b alternatives and identify the solution that outranks the others, for each criterion j). Te preference function is used to determine how much alternative � is preferred to alternative thus providing decision-makers with useful tools in mak- � ing welfare-maximizing urban planning decisions. We thus and it translates the diference in evaluations of the two aim to contribute framing a multimethodological evaluation alternatives into a preference degree. Tese preferences are process which can be transferred, once validated, in other represented in a numerical scale ranging between 0 and 1. decision contexts [13]. Te value “1” represents a strong preference of alternative a over b, whereas “0” represents the indiferent preference Te remainder of the paper is organized as follows. value between the two alternatives. Six types of preference Section 2 provides a methodological background and a brief functions have been proposed by the developers of the literature review; Section 3 illustrates the application of PROMETHEE methodology: Usual criterion, Quasi criterion PROMETHEE in the evaluation of urban renewal projects in (U-shape), Criterion with linear preference (V-shape), Level the city of Collegno (Italy); in Section 4 results are discussed criterion, Linear criterion, and Gaussian criterion [15, 21]. and conclusions are drawn. Step 3 (calculation of the overall preference index Π(�, �)). 2. Methodological Background Te overall preference index Π(�, �) represents the intensity of preference of � over � and it is calculated as follows (1): Te PROMETHEE method is one of the most recent Mul- k ticriteria Decision Analysis (MCDA) methods which was Π (a, b) = ∑wjPj (a, b) (1) frstly proposed by Brans in the early Eighties [10] and j=1 subsequently extended by Brans and Vincke [14], Brans et al. [15], Brans and Mareschal [16], and Brans and Mareschal [17]. where Π(�, �) is the overall preference intensity of � over b � Usually a multicriteria problem is an ill-posed mathematical with respect to all of the K criteria, j is the weight of criterion � (�, �) � � problem as it does not fnd a solution which optimizes all ,andPj is the preference function of over with � Π ∼ of the criteria simultaneously. As other multicriteria meth- respect to criterion .Clearly (a,b) 0 implies a weak global Π ∼ ods, the PROMETHEE requires additional information to preference of a over b, whereas (a,b) 1impliesastrong overcome the poorness of dominance relation on Preference global preference of a over b. (P) and Indiference (I), thus enriching the dominance graph Step 4 (calculation of the outranking fows, i.e., positive fow [18]. Te PROMETHEE is an outranking method for ranking + − Φ (�) and negative fow Φ (�)). In PROMETHEE method a fnite set of alternative actions when multiple criteria, two fow measures can be determined for each alternative. which are ofen conficting, and multiple decision-makers Tere are a positive fow (it expresses how alternative a is are involved [8]. PROMETHEE uses partial aggregation and outranking all the others) by a pairwise comparison of alternative actions, it allows to 1 verify whether under specifc conditions one action outranks Φ+ ( ) = ∑Π ( , ) a −1 a b (2) or not the others. Te PROMETHEE methods are a family n b∈A of outranking methods [19]: PROMETHEE I (partial ranking); PROMETHEE II (complete ranking); PROMETHEE III and negative fow (it expresses how alternative a is outranked (ranking based on intervals); PROMETHEE IV (continuous by all the others) case); PROMETHEE V (including segmentation constraints); 1 Φ− ( ) = ∑Π ( , ) and PROMETHEE VI (evaluating the degree of hardness of a −1 b a (3) n b∈A a multicriteria decision problem with respect to the weights given to the criteria, i.e., for human brain representation). In Step 5 (comparison of the outranking fows to defne the alter- addition, in 2004 Figueira et al. [20] proposed two extensions natives complete ranking). In detail, PROMETHEE II, here Advances in Operations Research 3 implemented, provides a complete ranking of the alternatives to other four multicriteria decision aiding/making methods by calculating the net fow (4): (i.e., ELECTRE, AHP, WSM, and TOPSIS) in rehabilitation + − planning of urban water networks. Φ (�) =Φ (�) −Φ (�) . (4) Te higher the net fow, the better the alternative. When 3. Application PROMETHEE II is considered, no incomparability remains, as all the alternatives are comparable on all the criteria. It is Te case study considered in the present paper is related worth noting that the net fow provides a complete ranking to the urban regeneration program of the city of Collegno, and thus can be compared with a utility function. located in the metropolitan area of Torino (Northern Italy). Te program, promoted by the Municipal Administration, In the past decade, a growing interest arose in identifying aims at fnding answers to the economic and social needs of solutions which refect reality as much as possible by mod- the city and to provide a coherent development strategy to a eling it in a clear and understandable way by both analysts territory aficted by an unregulated development and by the and decision-makers. Conceptually, PROMETHEE is a rather presence of many abandoned areas. simple ranking method compared with other methods for Te objectives of the program are mainly related to the multicriteria analysis [15] and the number of its applications regeneration of the city as “Collegno Social Town”. Te to real world decision problems increased signifcantly [22]. creation of a nice and livable place and the elimination of Te applications of PROMETHEE methods are varied and physical and environmental limits are the key elements of the cover as major felds environmental management, water development strategy. Te area of the Fermi metro station, management, business and fnancial management, logistics including the site of Campo Volo, represents a crucial portion and transportation, and energy management [22]. Tere are of the territory under investigation. several applications as well in social sciences starting from seminal works by D’Avignon and Mareschal [23] and Urli 3.1. Structuring of the Decision Problem. Te frst step for the and Beaudry [24] on hospital services and allocation of evaluation refers to the structuring of the decision problem, funds to development programs, respectively. Nonetheless, i.e. identifying the possible alternative strategies for the urban PROMETHEE applications in urban and territorial planning regeneration program and defning the criteria to be included are quite recent. Mavrotas et al. [25] adopted PROMETHEE in the model. For this purpose, an integrated framework for comparatively evaluating control strategies to reduce air has been proposed in the present application that aims pollution in Tessaloniki and base their procedure on active at setting the problem and highlighting its key elements. involvement of local and central authorities; Anton et al. [26] More precisely, two diferent analyses have been performed, applied PROMETHEE for the management and disposal of namely, the SWOT Analysis and the Stakeholders Analysis. solid wastes in an Andine area; Juan et al. [27] used the In detail, PROMETHEE method combined with fuzzy set theory to determine the priority of 13 urban renewal projects in Taipei (i) the SWOT (Strengths, Weaknesses, Opportunities, City, whereas Roozbahani et al. [28] combined PROMETHEE and Treats) Analysis is a technique used to defne with Precedence Order in the Criteria (POC) to urban water strategies, in those context which are characterized by supply management in Melbourne to assess operation rules complexity and uncertainty, such as urban regenera- in single or group decision-making contexts. More recently tion. Te analysis was used for a critical interpretation Cilona and Granata [29] implemented the PROMETHEE of the case under investigation and for supporting the approach to support prioritization of subprojects in complex defnition of the goal of the transformation and the renewal projects at neighborhood scale; Esmaelian et al. [30] construction of the alternative projects; implemented PROMETHEE IV and GIS to identify most (ii) the Stakeholders Analysis allows to defne who are the vulnerable urban areas to earthquakes and they prove its actors of the process under investigation. As stated by efcacy in electing the most suitable locations for the con- Yang (2013), in the context of urban transformation struction of emergency service stations; Polat et al. [31] pro- real-world problems, only if stakeholders’ interests posed an integrated approach which combines the Analytic are identifed, it is possible to sufciently empower Hierarchy Process (AHP) and the PROMETHEE method them in the decision-making process. Moreover, the to support construction companies to select urban renewal analysis permits to defne which resources and objec- projects to invest in; Bottero et al. [32] used PROMETHEE tives the actors are able to bring into play, showing methods to analyze diferent urban regeneration scenarios possible conficts. Finally, by means of Stakeholders in Gran Canaria island; Cerreta and Daldanise [33] pro- Analysis the complexity of the decisional process can posed PROMETHEE to support urban regeneration by a be represented, suggesting the evaluation criteria to learning and negotiation process; Dirutigliano et al. [34] be considered for the comparison of the alternative applied PROMETHEE as a support tool for promoting energy strategies (Figure 1). retroftting of urban districts in Torino; Mendonc¸a Silva et al. [35] used PROMETHEE method to solve an urban planning 3.2. Alternative Transformation Projects. In this experimen- confict in Recife; Wagner [36] adopted PROMETHEE to tation, we have implemented an integrated approach to assist the decision-making process in spatial urban planning, evaluate six diferent alternatives related to the development whereas Tscheikner-Gratl et al. [37] compared PROMETHEE of the urban regeneration program of the city of Collegno. 4 Advances in Operations Research

3.3. Defnition and Evaluation of the Criteria. In accordance POWER/INTEREST MATRIX with the results of the two aforementioned analyses, we identifed the most important drivers of the transformation high 5 that can be summarized in Table 1. In particular, SWOT and Stakeholders Analysis allowed breaking down the complexity 7 of the problem and identifying general aspects that character- 2 4 ize the transformation to be defned, namely, environmental, 3 1 economic, social, regeneration, mobility, and services factors. 6 Tese aspects have been then further investigated in order to obtain a set of measurable attributes for the evaluation of the alternatives.

Power Te subsequent step consists in assessing the performance 9 of the alternatives from the point of view of the evaluation

19 criteria and in assigning a preference function with related 11 thresholds of the criteria (q, p) (Table 2). 8 10 14 12 17 13 3.4. Weights Determination. For the development of the 16 18 15 20 PROMETHEE II method, diferent decision scenarios have low Interest high been taken into account. Te diferent scenarios refect the point of view of diferent actors who can face the problem LIST OF STAKEHOLDER under investigation. For this purpose, in the application 1. Italian Government 13. Campovolo 2.Regione Piemonte 14. Neighbourhood committees of the methodology personal interviews with experts in 3. Torino Metropolitan Area 15. Residents 4. City of Collegno 16. Commuters diferent felds and local decision-makers were developed. In 5. Private investigators 17 Associations (environmental, historical, cultural 6. Local Transport Authority (GTT) 18. Social groups particular, 5 experts have been considered for the evaluation, 7. Developers 19. Università degli studi di Torino (Department of whose expertise was in urban design, economic evaluation, 8. Sponsors Agricultural, Forestry and Food Sciences) 20. Tourists 9. Trade unions 21. Designers (architects, planners, landscapers) history of architecture, landscape architecture, and sociology. 10. Mass media 11. Firms According to the revised Simos procedure [38], the interviews 12. Traders were carried out through the set of cards methodology that Figure 1: Stakeholders mapping for the case under investigation. allows for setting the criteria weights and determining their priority, according to actors’ preferences. Te weight values obtained by diferent experts are shown on the axes of radar charts displayed in Figure 3. As it is possible to see, all the In detail, starting from the alternatives analyzed by Bottero actors agreed in considering the regeneration aspects as the et al. [11, 12], we have selected six alternative projects, which most important ones. On the contrary, the criteria related we consider the most relevant according to the SWOT and to parking spaces and new commercial developments are Stakeholders Analyses. Tese alternatives can be described as not important according to all the actors involved in the follows (Figure 2): evaluation. (1) Cultural district: this strategy is based on the creation 3.5. Results. Te ranking of alternative options was derived of new cultural services for the area, including a new by implementing the decision support sofware Visual public library and residences for university students. PROMETHEE 1.4 [39]. (2) Smart City: the goal of this strategy consists in Figure 4 shows the fnal ranking of the alternative strate- providing a new identity to the area based on the gies with reference to the sets of weights resulting from the concept of smart city. interviews to diferent actors involved. By direct inspection (3) Start up: this project focuses on the creation of of Figure 4, it emerges that the ranking is preserved in all the innovative business activities in the area. cases and for all the strategies. Te “Sharing city” alternative (4) City and craf: this strategy is based on the valoriza- is confrmed as the best performing strategy for the successful tion of the small economic activities in the area and implementation of the urban transformation/regeneration on the creation of a new urban park in the Northern process. According to our results, the “Green infrastructures” part of the area. alternative is worth of consideration too, as it is placed as second in the actors’ ranking. (5) Sharing city: the objective of this project is mainly To complement the discussion of our results, we consider related to the valorization of the public spaces in worth of mentioning the novelty of our approach to the the area, with special attention to innovative shared evaluation of complex urban transformation processes and solution for living and working. their long-term efects. (6) Green infrastructure: the main intent of this strategy Decision problems in urban planning, and specifcally is to improve the livability of the territory, with those which are concerned with the design and imple- particular attention to the creation of new green mentation of urban transformation/regeneration process, are infrastructures, such as pedestrian and bicycle paths. ofen ill-structured problems, as they involve multiple actors Advances in Operations Research 5

Table 1: Evaluation criteria for the PROMETHEE model [Table 1 is reproduced from Bottero et al. [11]].

Criteria Description

C1 Public/private spaces Ratio between public and private surfaces Surface of the structures for workshop, C2 Co-working spaces meeting, training courses Number of residents in new co-housing C3 Co-housing inhabitants buildings

C4 Permeable surface/territorial Ratio between permeable areas and overall surface territorial surface of the program Total area used for community and private C5 Urban gardens urban gardens Amount of waste produced in a year by the C6 Waste production activities of the program

C7 Residential areas Surface for residential functions

C8 Retail areas Surfaces for commercial functions

C9 Sport and leisure areas Surfaces for sport and cultural activities Index that describes the functional mix of the C10 Mixit´eindex area Surface of the pedestrian tracks and bicycle C11 Slow mobility lanes

C12 New public parking Number of new public parking lots

C13 Car sharing/bike sharing Number of car and bike sharing points Estimate of the social benefts delivered by the C14 Total Economic Value program

C15 Investment cost Total cost of the program

C16 New jobs Number of new jobs created

C17 Regeneration Regenerated surface Qualitative index showing the level of the C18 Via De Amicis regeneration regeneration of Via De Amicis Ratio between the maximum buildable volume C19 Territorial index and the territorial surface

SCENARIO 1: CULTURAL DISTRICT SCENARIO 2: SMART CITY SCENARIO 3: START UP

SCENARIO 4: CITY AND CRAFTS SCENARIO 5: SHARING CITY SCENARIO 6: GREEN INFRASTRUCTURES

Figure 2: Alternative strategies considered in the evaluation model [Figure 2 is reproduced from Bottero et al. [11]]. 6 Advances in Operations Research ) 2 ´ eindex 0,13 0,16 0,52 0,23 0,38 0,40 buildable volume and surface (m Mixit the territorial Ratio between the maximum ) 2 3 5 5 5 4 4 cultural activities sport and Amicis Surface for (SLP in m of Via De Qualitative regeneration Index for the ) 2 REGENERATION SERVICES functions 0,2 Surface for 0,51 0,12 0,20 0,36 commercial 0,06 (SLP in m SLP) surface SLP/Total Regenerated (Regenerated ) 2 in m residential Surface for function (SLP No. of new jobs created waste Amount of year by the activities of the program produced in a (€) Total cost of the program ECONOMICS urban gardens used for Total area community and private (a) (b) ENVIRONMENT 531.155 231.527.860 768 537.692 279.468.,021 1.545 7.471.328 183.948.594 736 (VET in €) delivered by the program Estimate the social benefts overall program areas and territorial permeable surface of the Ratio between 3 2 3.500.000 100.000.000 300 7 2.550.746 233.336.184 1.010 14 7.707.778 494.055.026 3.229 19 12 points bike sharing No. of car and new No. of Table 2: Input matrix for the PROMETHEE evaluation. buildings co-housing residents in No. of new parking lots training meeting, workshop, MOBILITY SOCIAL structures for Surface of the ) 2 (m 16.000 2.100 68.326 1.385 251.831 1.394 132.541 1.137 171.609 2.567 1,33 49880 255 0,58 25.569 2.692.663 82.330 95.000 26.960 1 4,31 20425 398 0,69 8.527 1.350.845 70.880 28.031 48.150 0,71 624.933 1.689 3,258,352,76 24260 11328 5108 150 421 2513 0,39 0,52 0,53 2.130 66.894 2.332.234 23.118 1.817.205 117.736 3.014.301 164.925 538.018 59.169 84.248 40.192 81.796 21.458 114.725 0,46 0,30 0,30 4,20 3300 1036 0,71 12.888 1.631.941 75.252 25.515 37.920 0,64 pedestrian tracks and private services bicycle lanes Surface of the public and Ratio between START UP CITY AND CRAFTS SHARING CITY GREEN INFRASTRUCTURE SMART CITY CULTURAL DISTRICT CULTURAL DISTRICT SMART CITY START UP SHARING CITY GREEN INFRASTRUCTURE CITY AND CRAFTS Advances in Operations Research 7

PUBLIC-PRIVATE SPACES TERRITORIAL INDEX CO-WORKING SPACES

VIA DE AMICIS REGENERATION CO-HOUSING INHABITANTS

REGENERATION RATIO PERMEABLE SURFACE/ TERRITORIAL SURFACE

NEW JOBS URBAN GARDENS

INVESTMENT COST WASTE PRODUCTION

TEV RESIDENTIAL AREAS

BIKE/CAR SHARING RETAIL AREAS

NEW PUBLIC PARKING SPORT AND LEISURE AREAS SLOW MOBILITY MIXITE’ INDEX

URBAN DESIGN HISTORY OF ARCHITECTURE LANDSCAPE ARCHITECTURE ECONOMIC EVALUATION URBAN SOCIOLOGY

Figure 3: Sets of weights resulting from the diferent actors.

Urban design History of Landscape Economic Urban architecture architecture evaluation sociology 1.0 1.0

-1.0 -1.0

SCENARIO 1 SCENARIO 2 SCENARIO 3 SCENARIO 4 SCENARIO 5 SCENARIO 6

Figure 4: Ranking comparison for the diferent actors. 8 Advances in Operations Research and stakeholders, ofen conficting objectives and views and strongly interconnected and cannot be addressed by referring are characterized by signifcant uncertainty over potential exclusively to economic issues: urban renewal projects are outcomes of alternative design options and planning actions. ofen faced by many challenges, such as destruction of In this context the valuation of alternative scenarios is a existing social networks, expulsion of vulnerable groups, and complex process, where various aspects need to be accounted adverse impacts on the living environment. for simultaneously. Tese aspects comprise both technical Terefore, in urban planning, due to intrinsic complex- and non-technical issues and characteristics. Te formers ities and to the high number of stakeholders and actors build on empirical observations, whereas the latters are involved in the decision process, multicriteria techniques usually based on social visions, preferences and feelings [13]. and methodologies can be efciently implemented to iden- In this paper we adopted a mixed-method research tify efcient solutions, which accounts for decision-makers approach to address the issue of urban planning and projects and actors preferences, as well as for public choice policy evaluation. In detail, in accordance with Creswell et al. [40], objectives [46]. To some extent, urban planning is meant we developed a multiphase mixed-method that allows for to respond to challenges, improve communication between considering the subsequent phases of projects formulation government or public administrations and stakeholders, and implementation, and thus considering as inputs for the allocate budgets according to a list of priorities, and favor next analysis the results/outputs of the previous one. We long and mid-term investments. In addition, to be efective combined diferent methods for the design and selection of and successful, urban planning requires a commitment by alternative urban regeneration projects and strategies, and the government to achieve strategic goals, a common under- structured a multiphase decision aiding process meant to standing on prioritization of actions, and the involvement of support strategic planning. To structure the decision prob- the society and the private sector that collaborate to develop lem we implemented a SWOT Analysis and a Stakeholder and implement strategic plans. Analysis. Problem structuring is in fact a fundamental phase Tis paper shows how the PROMETHEE II method can in any decision problem, which involves multiple actors be usefully implemented in decision problems related to and perspectives, and conficting stakes to be conciliated, urban planning and development projects; namely, in this but it becomes of greater importance when alternatives paper the PROMETHEE method is used to determine the are not a priori designed in detail as in this case [41–45]. projects’ priority. In detail, we evaluated diferent regenera- We frstly carried out a SWOT Analysis, which provided tion scenarios for the city of Collegno according to a set of an in-depth knowledge of the problem and context under qualitative and quantitative criteria, which account for social, investigation, and of the correlation between endogenous and environmental, mobility and economic key factors. As the exogenous factors. In this phase, data and information were dominance relation is poor on preference and indiference, collected, the objectives were identifed and potential alter- incomparability holds for most of pairwise comparisons and native scenarios were defned at a preliminary stage. We then additional information is needed to make a decision. By performed a Stakeholder Analysis, informed by the SWOT outranking relations, the PROMETHEE method provides Analysis, through which we identifed the actors involved realistic enrichments of the dominance relation despite in the problem, and their values and objectives. Stakeholder incomparability relations are not completely eliminated. In Analysis allowed to identify conficting interests at an early this respect, the integration of SWOT Analysis and Stake- stage of the process and develop a strategic view of the holder Analysis increased the information useful for ranking human and institutional framework, the relationships among the scenarios, thus confrming the importance of supporting diferent actors and their concerns. In fact it plays a key cross-sector approaches in sustainable regeneration projects. role in strategic planning and urban regeneration processes. Te scenarios under investigation were evaluated accord- Te above-mentioned analyses informed the last phase of ing to experts judgments, local stakeholders and decision- the mixedmethod approach (e.g., criteria express actors’ makers’ preferences, values and objectives. objectives and needs), in which PROMETHEE method According to the results of PROMETHEE II, scenario was implemented to assess the alternative scenarios under 5 the “Sharing city project” is the most desirable and com- investigation, obtain a list of priorities, and identify the best prising alternative to implement, whereas scenario 6 the performing urban regeneration strategy. Table 3 provides an “Green Infrastructure” is ranked as second, except for the insight in our multiphase decision aiding process, synthetizes judgments expressed by the expert in landscape architecture. strengths and limitations of SWOT Analysis, Stakeholder Our results show that the other alternatives cannot be listed Analysis and PROMETHEE method respectively, and illus- in the same descending order of their net fows for each trates main results obtained from their implementation in the expert. As multiactor analysis shows, the “Sharing City” city of Collegno case study. alternative encompasses the preferences of the entire group of fve experts involved in the decision process. Te results 4. Discussion and Conclusions obtained from the Visual PROMETHEE sofware highlight the usefulness of multicriteria outranking methods in spatial Multicriteria Analysis is nowadays widely implemented in decision-making problems. Multiactors analysis was indeed decision and valuation processes, and specifcally in urban useful in clarifying the most appropriate project, by taking planning. Urban planning and urban regeneration processes into account the point of views of diferent actors. are multidimensional concepts and involve socioeconomic, Te comprehensive and integrated approach proposed in environmental, technical, and ethical perspectives, which are this paper accounts for key factors in urban renewal, provides Advances in Operations Research 9 transformation/regeneration. alternative scenarios for urban proved to be relevant actors as well. Results from the city of Collegno case study urban regeneration process. Te Municipality of Te SWOT Analysis allowed the defnition of the of relevant actors in the transformation and relative guidelines for the design and implementation of the transformation process layout. It played a key role in general masterplan as well as the identifcation of the Te Stakeholders Analysis provided the identifcation investors and developers, who have fnancial resources Collegno and the social groups involved in the process supporting experts and planners in the identifcation of values and perspectives. Tese actors are mostly private available for undertaking investments and carry out the Open nature and unstructured methodPreliminary level of analysis Tendency to overemphasize opportunities Lack of prioritisation of factors (no requirement for Risk of oversimplifcation Risk of over-subjectivity in the generation of factors Need for great reliance on quantitative approaches to Need for iterative processes in data collection and Inappropriateness of feedback of results when Uncertainty over validity and reliabilityPotential biases of generated results by analysts who become Strengths and Limitations + Improvement of overall understandingdecision problem of general the framework + Provision of a systematic approach todecompose analyse complex and problems + Identifcation of correlation between internal factors, strengths and weaknesses and external factors, opportunities and threats + Ease of use and− understanding of results − − − their classifcation and evaluation) − − + Improvement in stakeholders management and mobilization of their support+ in Identifcation achieving of a purpose goal interest and time-dimension of + Identifcation of time-frame+ and Provision resource of availability comprehensive analysisproduce new meant knowledge to about policy-making processes + Prediction or encouragement− of stakeholder alliances data collection − analysis − stakeholders may infuence or− control analysis results − implicitly stakeholders who bring to theown analysis values, their perspectives and problem understanding Table 3: Strengths and limitations of the proposed evaluation methods and relative results from the city of Collegno case study. Evaluation method SWOT Analysis Stakeholders Analysis 10 Advances in Operations Research best option. Te analysis performed by implementing the Results from the city of Collegno case study regeneration process. Te results show that the urban transformation alternative options and the considered sets of weights converge in ranking the PROMETHEE method allowed the comparisons of identifcation of the best performing solution for the “Sharing city” alternative as the most preferred option, and the “Green infrastructure” alternative as the second Table 3: Continued. Non triviality in preference structuringAssignment in of detail weights that does not build on aNo clear information on the cost-efectiveness or Assignment of values that does not build on a clear Difculties in selecting the generalized criterion Computational limitations with respect to the Strengths and Limitations +Easeofuse + Provision of a complete+ ranking Accuracy of results + Adoption of the concordance non-discordance principle in the defnitionindex of the overall preference + Limited total compensation between pros+ and No cons assumption on theproportionate requirement of criteria to+Avoidance be of the commensurability problem − − method − proftability of alternatives (are they welfare-maximizing?) − method − functions and the associated thresholds forcriterion each − number of decision alternatives Evaluation method PROMETHEE Approach Advances in Operations Research 11

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[27] Y.-K. Juan, K. O. Roper, D. Castro-Lacouture, and J. H. Kim, [41] C. D’Alpaos and P. Bragolusi, “Multicriteria Prioritization of “Optimal decision making on urban renewal projects,” Manage- Policy Instruments in Buildings Energy Retroft,” Valori e ment Decision, vol. 48, no. 2, pp. 207–224, 2010. Valutazioni,vol.21,pp.15–26,2018. [28]A.Roozbahani,B.Zahraie,andM.Tabesh,“PROMETHEE [42] M. Bertolini, C. D’Alpaos, and M. Moretto, “Do Smart Grids with Precedence Order in the Criteria (PPOC) as a New Group boost investments in domestic PV plants? Evidence from the Decision Making Aid: An Application in Urban Water Supply Italian electricity market,” Energy,vol.149,pp.890–902,2018. Management,” Water Resources Management,vol.26,no.12,pp. [43] C. D’Alpaos and P. Bragolusi, “Prioritization of Energy Retroft 3581–3599, 2012. Strategies in Public Housing: An AHP Model,” in New [29] T. Cilona and M. F. Granata, “Multicriteria prioritization for Metropolitan Perspectives,F.Calabr`o, L. Della Spina, and C. multistage implementation of complex urban renewal projects,” Bevilacqua, Eds., vol. 101 of Smart Innovation, Systems and Lecture Notes in Computer Science (including subseries Lecture Technologies, pp. 534–541, Springer International Publishing, Notes in Artifcial Intelligence and Lecture Notes in Bioinformat- Cham, 2019. ics): Preface,vol.9157,pp.3–19,2015. [44] M. Bottero, M. Bravi, F. Dell’Anna, and G. Mondini, “Valuing [30] M. Esmaelian, M. Tavana, F. J. Santos Arteaga, and S. Moham- buildings energy efciency through Hedonic Prices Method: are madi, “A multicriteria spatial decision support system for solv- spatial efects relevant?” Valori e Valutazioni,vol.21,pp.27–40, ing emergency service station location problems,” International 2018. Journal of Geographical Information Science,vol.29,no.7,pp. [45] M. Bottero, C. D’Alpaos, and F. Dell’Anna, “Boosting invest- 1187–1213, 2015. ments in buildings energy retroft: Te role of incentives,” in [31] G. Polat, A. Damci, A. P. Gurgun, and I. Demirli, “Urban New Metropolitan Perspectives,F.Calabr`o, L. Della Spina, and Renewal Project Selection Using the Integration of AHP and C. Bevilacqua, Eds., vol. 101 of Smart Innovation, Systems and PROMETHEE Approaches,” in Proceedings of the 5th Creative Technologies, pp. 593–600, Springer International Publishing, Construction Conference, CCC ’16,pp.339–346,Hungary,June Cham, 2018. 2016. [46] M. Bottero, F. Dell’Anna, and M. Nappo, “Evaluating tangible [32] M. Bottero, I. Baudino, and P. Antonelli, “Strategic assessment and intangible aspects of cultural heritage: An application of and multicriteria analysis: An application of the PROMETHEE the promethee method for the reuse project of the Ceva–Ormea method for the analysis of urban regeneration scenarios,” railway,” Green Energy and Technology Part F8, pp. 285–295, Geoingegneria Ambientale e Mineraria,vol.148,no.2,pp.5–16, 2018. 2016. [33] M. Cerreta and G. Daldanise, “Community branding (Co-bra): A collaborative decision making process for urban regeneration,” Lecture Notes in Computer Science (including subseries Lecture Notes in Artifcial Intelligence and Lecture Notes in Bioinformatics): Preface, vol. 10406, pp. 730–746, 2017. [34] D. Dirutigliano, C. Delmastro, and S. Torabi Moghadam, “Energy efcient urban districts: A multi-criteria application for selecting retroft actions,” International Journal of Heat and Technology,vol.35,no.1,pp.S49–S57,2017. [35]M.M.Silva,K.W.Hipel,D.M.Kilgour,andA.P.C.S.Costa, “Urban planning in Recife, Brazil: Evidence from a confict analysis on the New Recife Project,” Journal of Urban Planning and Development,vol.143,no.3,2017. [36] M. Wagner, “A Research Proposal on the Parametric City Governance,” in Smart and Sustainable Planning for Cities and Regions-Results of SSPCR, 2015, Green and Energy Technology, A.Bisello,D.Vettorato,R.Stephens,andP.Elisei,Eds.,pp.205– 219, Springer, Green and Energy Technology, 2017. [37] F. Tscheikner-Gratl, P. Egger, W. Rauch, and M. Kleidorfer, “Comparison of multi-criteria decision support methods for integrated rehabilitation prioritization,” Water (Switzerland), vol. 9, no. 2, 2017. [38] J. Figueira and B. Roy, “Determining the weights of criteria in the ELECTRE type methods with a revised Simos’ procedure,” European Journal of Operational Research,vol.139,no.2,pp.317– 326, 2002. [39] B. Mareschal and Y. De Smet, “Visual PROMETHEE: Develop- ments of the PROMETHEE & GAIA multicriteria decision aid methods,” in Proceedings of the IEEE International Conference on Industrial Engineering and Engineering Management, IEEM 2009, pp. 1646–1649, Hong Kong, December 2009. [40] J. W. Creswell, A. C. Klassen, V. L. Plano Clark, and K. Clegg Smith, Best Practices for Mixed Methods Research in the Health Sciences, National Institutes of Health, Bethesda, 2011. Hindawi Advances in Operations Research Volume 2018, Article ID 8290434, 14 pages https://doi.org/10.1155/2018/8290434

Research Article Measuring Conflicts Using Cardinal Ranking: An Application to Decision Analytic Conflict Evaluations

Tobias Fasth ,1 Aron Larsson ,1,2 Love Ekenberg,1,3 and Mats Danielson1,3

1 Dept. of Computer and Systems Sciences, Stockholm University, Box 7003, SE-164 07 Kista, Sweden 2Dept. of Information Systems and Technology, Mid Sweden University, SE-851 70 Sundsvall, Sweden 3International Institute of Applied Systems Analysis, IIASA, Schlossplatz 1, A-2361 Laxenburg, Austria

Correspondence should be addressed to Tobias Fasth; [email protected]

Received 23 February 2018; Revised 28 May 2018; Accepted 11 July 2018; Published 27 September 2018

Academic Editor: Alessandra Oppio

Copyright © 2018 Tobias Fasth et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

One of the core complexities involved in evaluating decision alternatives in the area of public decision-making is to deal with conficts. Te stakeholders afected by and involved in the decision ofen have conficting preferences regarding the actions under consideration. For an executive authority, these diferences of opinion can be problematic, during both implementation and communication, even though the decision is rational with respect to an attribute set perceived to represent social welfare. It is therefore important to involve the stakeholders in the process and to get an understanding of their preferences. Otherwise, the stakeholder disagreement can lead to costly conficts. One way of approaching this problem is to provide means for comprehensive, yet efective stakeholder preference elicitation methods, where the stakeholders can state their preferences with respect to actions part of the current agenda of a government. In this paper we contribute two supporting methods: (i) an application of the cardinal ranking (CAR) method for preference elicitation for confict evaluations and (ii) two confict indices for measuring stakeholder conficts. Te application of the CAR method utilizes a do nothing alternative to diferentiate between positive and negative actions. Te elicited preferences can then be used as input to the two confict indices indicating the level of confict within a stakeholder group or between two stakeholder groups. Te contributed methods are demonstrated in a real-life example carried out in the municipality of Upplands V¨asby, Sweden. We show how a questionnaire can be used to elicit preferences with CAR and how the indices can be used to semantically describe the level of consensus and confict regarding a certain attribute. As such, we show how the methods can provide decision aid in the clarifcation of controversies.

1. Introduction instance, Hansson et al. [6] describe that the development plans of Husby, a suburb to Stockholm, had been on hold for One of the core complexities involved in evaluating decision several years due to conficts. Another example is given in alternatives in the area of public decision-making is to deal Danielson et al. [5], where three infrastructure decisions in with conficts. Te stakeholders afected by and involved Nacka, a municipality in the Stockholm region, were delayed in the decision ofen have conficting preferences regarding for several years due to conficts between stakeholders. the actions under consideration. For an executive authority, Terefore, to avoid stakeholder conficts it is important for these diferences of opinion can be problematic during the executive authority to involve the stakeholders in the both implementation and communication, even though the process and to get an understanding of their preferences decision is rational with respect to an attribute set perceived [7, 8]. to represent social welfare; see, e.g., [1–3]. Tis calls for a desire to become better informed with Of particular interest for the decision-making forum regard to potential controversies, and it has been discussed are preferential conficts between stakeholders, since such in contemporary decision analysis literature that interac- conficts may cause delays in the decision process due to tion with stakeholders using web-based techniques is one obstructions, hassles, and/or locked negotiations [4–6]. For feasible approach to obtain stakeholder preferences and 2 Advances in Operations Research then inform decision-makers by utilizing decision analysis stakeholder group or between two stakeholder groups. An techniques. For instance, French et al. [1] suggest that web- action is a nonconficting action when the stakeholders have basedapproachescanbeusedtosupportandstructurethe similar preferences. democratic process. Hansson et al. [6] suggest that a solution to the above-mentioned problem of conficts could be to 1.1. Case Setting. In this paper, we describe a case conducted actively interact with stakeholders early in the process by the in Upplands Vasby¨ municipality slightly north of Stockholm use of social media. City. In this case, we analyzed the citizens preferences regard- In this approach, an important frst step is to elicit ing a set of actions that could be implemented in the future. the opinions or attitudes of the citizens regarding a set A previous reporting of the case can be found in Chapter 7 of “actions”. Tese are potential actions that in the future of Ekenberg et al. [13], in which a simplifed confict measure may be redefned into more well-defned projects. It has was utilized. In the reported method, the stakeholders were been recognized that the selected methods must be easy divided into two groups, the con- and the pro-group. Te to use for less experienced stakeholders and at the same confict index was then measured as the diference between time be sufciently powerful to enable them to provide the arithmetic means of the groups part-worth values. Te meaningful feedback [9]. To facilitate scalable elicitation, methods presented in this paper are rather based on Ward’s many approaches (including ours) promote the use of web- method [11]. based surveys or questionnaires distributed to stakeholders Typically, the actions are described quite briefy, for early in the planning phase [3]. example, in short sentences such as “Build residential area In this paper we contribute with an application of the near the lake” or “Build apartments in the town centre”. cardinal ranking (CAR) method [10], extended with a feature In the paper, we use the term “action” to distinguish from for confict evaluations, and a method for measuring confict the more traditional term “alternatives” employed within within a stakeholder group and between two stakeholder the feld of decision analysis. In our setting, an action is groups. Te contributions support the decision process in a a tentative project proposal without an associated cost but public decision-making setting. rather a line of direction for a future project. Tis is somewhat Cardinal Ranking for Confict Evaluations. To the best similar to the tentative proposals defned as “topics” by of our knowledge, no method exists that utilizes preferences [14]. elicited by a cardinal ranking approach in confict evalua- In order to understand attitudes, the questionnaire must tions. In this application of CAR [10], the respondents, in allow for the participating stakeholders to state positive addition to cardinally ranking the elements, state the perfor- or negative preferences regarding an action’s performance mance of the elements relative to a do nothing alternative. For relative to a do nothing action. In order to measure con- example, supporting statements are like “action 1 is better than fict, the statements need to be represented in a manner action 2, and both actions are negative relative the do nothing allowing for such a measure to be meaningful. Tus, the alternative and “action 2 is much better than action 3, action 2 attitudes must be represented using a measurable value is positive whereas Action 3 is negative relative the do nothing function where the questionnaire is used as a tool for elic- alternative”. iting preferences. Conventional preference elicitation meth- Confict Indices. In a group decision analysis setting, it ods for approximating such value functions are typically is of interest to investigate whether a certain alternative is considered to be cognitively demanding [15]. Te nature confict-prone with respect to one or more attributes. Te of the actions being so loosely defned renders the use of preferences elicited by the application of CAR can be used for more elaborate preference elicitation techniques, since they assessing the level of confict within or between stakeholder rely on well-defned alternatives. To resolve this situation, groups. We describe two such indices, the Within-Group the questionnaire we propose is inspired by the attitude Confict Index and the Between-Group Confict Index, both surveys ofen employing diferent versions of the Likert utilizing a sum of squares, used in Ward’s clustering method scale. [11, p. 466] and extended with a positive stakeholder scal- An alternative approach to reducing the cognitive burden ing constant. Te underlying group formation is similar of the decision-maker is to use preference disaggregation to the collective attractiveness and unattractiveness indices techniques. Te techniques do this by utilizing global pref- presented by [12]. Te approaches difer in how the value erences, e.g., a ranking of a subset of alternatives, or by a functions are created and utilized. Bana e Costa [12] creates pairwise comparison of alternatives, to infer value functions; one value function per criterion by applying MACBETH and see, e.g., [16–19] for details. its semantic categories. In our approach the respondents use Te questionnaire, which was previously reported in CAR to create their individual value functions per criterion. [13, Ch. 7], enables the capturing of negative and positive In turn, this enables individual value estimates of the do attitudes of the actions relative to a do nothing action. nothing alternative which is not necessarily viewed as a Ten, methods for cardinal ranking are used to interpret “neutral” alternative. the responses in terms of surrogate values and attribute With this we contribute to the frst important step in weights. Lastly, the questionnaire contains a section where a participatory group decision process by elucidating both the respondent enters demographic information. Tis infor- confict-prone actions and nonconficting actions. An action mation can then be used to analyze the preferences of the is confict-prone when there are strong opposing preferences citizens, e.g., to fnd stakeholder groups with conficting regarding the performance of the action, either within a interests. Advances in Operations Research 3

� 2. Modeling of Preferences where �� is the part-worth value of attribute �� to � � � alternative �� for stakeholder ��; i.e., �� =�� ⋅V�� .Henceforth In the decision analysis feld, we distinguish between two � types of preference representation functions, the value in this paper, �� notation for a stakeholders part-worth value function and the utility function. A value function represents will be used, and we will denote the stakeholder ��’s value � preferences over certain outcomes, as opposed to the utility of alternative �� under attribute �� with V�� .Inorderto function which represents preferences over lotteries with obtain these values, diferent approaches have been suggested uncertain outcomes, and the two representations are based to elicit them from decision-makers. For an overview of upon diferent axiom systems. Te focus in this paper is elicitation methods, see, e.g., [22, 23]. on preference representations under certainty, and in the absence of uncertain consequences (or risk), preferences over objects � are typically represented by means of a value 3. Rank-Based Elicitation function V(�) ��→ [ 0 , 1 ] , such that the object � is preferred Te procedure in rank-ordering methods is to elicit the to object � (commonly denoted by �≻�)bythedecision- preferences as ranks, which are then converted into cardinal maker if and only if V(�) > V(�).IfV(�) = V(�) then the surrogate weights. Two such methods, rank-sum (RS) and decision-maker is indiferent between the two objects. Te rank-reciprocal (RR), are described in [24], and a third value function is measurable and is defned over an interval method the Rank Order Centroid (ROC) is described in scale if V(�) − V(�) > V(�) − V(�) and V(�) > V(�), V(�) > [25, 26]. V(�) entails that exchanging � for � is preferred compared to Rank-ordering methods have desirable advantages over exchanging � for �; see [20] for a comprehensive treatment. more precise elicitation techniques, such as (i) being easier Inthecaseofmultipledecision-makersorstakeholders to elicit the vague preferences (less cognitively demanding) �1,�2,...,�� having diferent individual measurable value 1 2 � and (ii) having increased likelihood for a group to come to functions V (), V (),...,V (),ingroupdecisionanalysis,itis agreement [27, 28]. But rank ordered weight elicitation may of concern to aggregate the set of individual value functions be problematic. For example, Jia et al. [29] point out that, using some proper preference aggregation rule providing a in a real-life setting, uncertainty may exist regarding both group value function sharing the properties of the individual the magnitudes and ordering of weights, and even though value functions. For this purpose, given that all individual information regarding the diference in importance may � V� value functions of stakeholder are of the form and that exist, the information is not considered in the transformation domain and range are shared among the stakeholders, it has from rank orders into weights. been shown that an additive aggregation of individual mea- A method taking the diference in importance into con- surable value functions provides a measurable group value sideration is the cardinal ranking (CAR) method [10, 30]. In �(� ) � �(� )= function � for an alternative �,suchthat � CAR, a prerequisite is an ordinal ranking, to which cardinal � � ∑��V (��),whereV (��) is the value of alternative �� for information is added; see Figure 1 for a visualization of the stakeholder ��,and�� are stakeholder scaling constants diference between ordinal and cardinal ranking. Te cardinal subject to �� ≥0and ∑�� =1whenever exchange information is used to denote the strength of preference independence is satisfed (if all stakeholders are indiferent between pairs of elements in the ranking. Tis strength of between two exchanges then the whole group must also be preference is interpreted as the number of steps between indiferent) [21]. each pair of elements on an underlying importance scale. In the multiattribute setting, considering a set of eval- Te notation ≻� is used for describing this, where � is the uation attributes � ={�1,�2,...,��},thevalueofan number of steps. Te cardinality can be described by semantic alternative �� is obtained by aggregating the corresponding expressions, e.g., obtained from a linguistic analysis, set of value functions V1(�1), V2(�2),...,V�(��).Temost common way of aggregation is the additive approach such ∼0 equally important, 0 steps that the value �(��) of �� is given by �(��)=∑� ��V�� , ≻1 slightly more important, 1 step where V�� is the value of alternative �� under attribute ��, and �� is the weight of attribute �� under the condition that ≻2 more important, 2 steps 0≤�� ≤1and ∑� �� =1. Tis additive aggregation ≻3 much more important, 3 steps provides a measurable multiattribute value function given that the conditions of mutually preferential independence Tis enables the decision-maker to make statements such as and diference independence hold; see, e.g., [22]. Te weights the following: �� then act as attribute scaling constants, scaling the value contribution to an alternative from an attribute. Te scaled (i) Attribute A is equally important (∼0)asattributeB value �� =�� ⋅ V�� is called the “part-worth” value of attribute ≻ �� to alternative ��. In a group setting, the group’s value of (ii) Attribute B is slightly more important ( 1)than alternative �� is then given by attribute C

(iii) Attribute C is more important (≻2)thanattributeD � �(� )=∑� ∑� (iv) Attribute D is much more important (≻3)than � � �� (1) � � attribute E 4 Advances in Operations Research

18765432

A1 A2 A3 A4 A5 A6 A1 A2 A3, A4 A5 A6

Figure 1: Te lef picture visualizes an ordinal ranking of six elements, while the right picture visualizes a cardinal ranking of the elements.

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A1 A2 A3 A4 A1 A2 A A3 A4

Figure 2: Te lef picture visualizes a cardinal ranking of the four alternatives. Te right picture visualizes a cardinal ranking of the alternatives, with the do nothing alternative inserted between alternatives � 2 and � 3.

Note that similar linguistic translations are commonly (3) A do nothing alternative �� is inserted into the used in other MCDA methods such as AHP [31] and MAC- ranking by providing it with a position �. BETH [32, 33]. (4) Te cardinal ranking is normalized to a proportional Te CAR method has been demonstrated using both [0, 1]-value scale according to the following equation: linear inequalities to represent cardinal ranking statements [34] and closed formulas for obtaining surrogate weights [10, �−�(�) VCAR = 30]. More recently, rank-based methods have been suggested � �−1 (2) for probability elicitation as well, with a particular aim for use in time scarce environments [35]. 4.1. Example of CAR for Confict Evaluations. Assume that a decision-maker evaluates the performance of four alterna- 4. Cardinal Ranking for Conflict Evaluations tives, {�1,...,�4},withregardtoattribute�1.

In this section we introduce an application of CAR which (1) Te decision-maker orders the alternatives as �1 ≻ captures negative or positive preferences with regard to an �2 ≻�3 ≻�4. alternative’s performance relative to a do nothing alternative (2) He/she adds cardinal information to the ordinal over a set of attributes. Te method enables respondents to ranking by introducing cardinality (strength of pref- express the strength of preference between ordered pairs of erence) steps between pairs of alternatives: alternatives using steps of preference intensities and at the same time express whether the alternatives are negative or (i) �1 is much better (≻3)than�2, positive relative to a do nothing alternative. (ii) �2 is better (≻2)than�3 Assume that we have a set of alternatives � ={�1,�2,..., (iii) �3 is much better (≻3)than�4, ��} which are evaluated against a set of attributes � = {� ,� ,...,� } 1 2 � . To capture the negative or positive prefer- which gives the following cardinal rank �1≻3�2≻2 � ences we need to introduce a do nothing alternative � to the �3≻3�4;seeFigure2. set of alternatives. Te do nothing alternative represents the (3) He/she states that alternatives �1 and �2 are consid- current state; i.e., it should be considered whether the actions � � under consideration are better/worse than this alternative. ered to be positive and 3 and 4 negative relative to the do nothing alternative. Te do nothing alter- See, e.g., Lahdelma et al. [36] for arguments supporting this � 0 technique. native � is therefore inserted at position , between �2 and �3, giving the following cardinal ranking, We conform to the CAR method’s procedure for eliciting � ≻ � ≻ � ≻ � ≻ � the alternatives’ values [10, 30] but extend it with a third step, 1 3 2 1 � 1 3 3 4;seeFigure2. the step where the do nothing alternative is inserted in the (4) Te cardinal ranking results in the following positions ranking: on the underlying scale:

(1) An ordinal number is assigned to each position on the (i) �1 at position �(4), underlying measurement scale. (ii) �2 at position �(1), � �(0) (2) Te underlying scale consists of � positions in (iii) � at position , decreasing order of importance. Alternative �� has (iv) �3 at position �(−1), �(�) 1≤�(�)≤ aposition on the scale, such that (v) �4 at position �(−4). �,where�≥�.Testrength,orcardinality, of preference �� between two adjacent alternatives Tese positions are then mapped onto a proportional � ≻ � � = |�(�) − �(�)| [0, 1] � �� ,isthen � . -value scale, giving the alternatives the following Advances in Operations Research 5

values, where V�� denotes alternative ��:s value under In a two-stakeholder setting, given that attribute confict � � � � � attribute �. As [37] points out, the do nothing exists for attribute �� such that �� <�� and �� ≥��,wewill alternative is not always assigned a score of 0. Note arguethatitisreasonabletobaseameasureofconfictupon that in our approach the do nothing alternative can the value diferences: be assigned a value between 0 and 1 depending on its � � �=9 �� = �� −�� position in the ordinal ranking. In this example, �� (3) and �(4) = 1, �(1) = 4, �(0) = 5, �(−1) = 6 and �(−4) = 9 . Te intuition behind (3) is that stakeholder �� considers � |�� −�� | (i) V4 = 1.000, � to be �� worse than the do nothing alternative while � � (ii) V3 = 0.625, another stakeholder �� considers �� to be |��−��| better than (iii) V� = 0.500, the do nothing alternative. Given two stakeholders ��,�� and (iv) V2 = 0.375, two alternatives �1,�2 such that V = 0.000 (v) 1 . � � � ��1 ≤��2 ≤�� (4) 4.2. Conficts. In a group decision analysis setting, it may �� ≥�� ≥�� , be of interest to investigate whether a certain alternative is �1 �2 �� (5) confict-prone with respect to one or more attributes. Te then confict cannot be smaller for �2 compared to �1. preferences elicited in the application of CAR for confict � � � evaluations can be used for assessing the level of confict Further, confict is larger for 1 compared to 2 if � would rather exchange �1 for �� than exchange �2 for ��,orif�� within or between stakeholder groups. In the following � � � � section, we will propose two such indices, the within-group would rather exchange � for 1 than exchange � for 2. confict index and the between-group confict index. Based However, a generalized measure of confict should con- upon these indices we can defne consensus properties that sider more than two stakeholders. In addition to measuring textually describe the level of confict associated with an how far from the do nothing alternative two stakeholders attribute with respect to a specifc alternative. A similar in confict are, we need to consider disparities between approach was presented by Bana e Costa [12]. sets of stakeholders. For this reason we adopt a cluster Before presenting the indices, we stipulate the following distance approach to confict measurement by partitioning conditions for the concept of confict. the stakeholders into two sets based upon their preferences towards the alternative. � ={�,� ,...,� } Defnition 1 (confict). Given a set of stakeholders � and a set Let 1 2 � be a set of stakeholders. For each � � attribute �� and alternative ��, we partition the stakeholder of alternatives , confict exists in if there are two or more − stakeholders in � with positive scaling constants and these set � into two partitions, the con-group �� and the pro-group + − � have difering preferences towards at least one alternative �� .Temembersofthe�� evaluated V�� to be less than the �� ∈ �.Formally,theremustexist��,�� ∈ � with ��,�� >0 � � � � � value of the do nothing alternative V��, and the stakeholders such that V� < V� and V� ≥ V�. + � � in �� evaluated V�� to be greater than or equal to V��;seethe Defnition 1 explicitly says that if all stakeholders share following equations: preferences towards an alternative, there is no confict. In � �− = {� ∈ � : V� < V� } this sense it can be argued that this defnition is a very �� =1 (6) strong defnition of confict. In the case of multiple attributes, � �+ ={� ∈ � : V� ≥ V� } Defnition 1 can be extended to attribute confict. Needless to �� =1 (7) say, given an attribute �� with a positive weight �� >0we � � � � � � have that V�� < V�� implies �� <�� and V�� ≥ V�� implies Hence, the do nothing alternative �� is used to separate − + � � � � the stakeholders into either �� or �� .Teintuitionbehind �� ≥�� since �� =��V�� . We can now defne the meaning the confict index is to measure the distance between these behind attribute confict and measurable confict. − + two groups such that if two stakeholders �� ∈ �� ,�� ∈ �� in Defnition 2 (attribute confict). Given a set of stakeholders generaldisagreetoalargeextent,i.e.,theybothhavealarge � � � � � � � ,asetofalternatives , and a set of evaluation attributes , diferences |�� −��| and |�� −��|, then the confict is greater � ∈ � � ,� ∈ � � ,� >0 confict exists for � if there exist � � with � � than if they have smaller diferences. Further, it can be argued � � � � − + such that �� <�� and �� ≥��. that if the power balance between �� and �� is more equal, then the confict is stronger since it has been demonstrated 4.2.1. Measurable Confict. Te defnitions above do not that less powerful stakeholders are more willing to accept an consider diferent opinions on how “good” (or “bad”) two alternative even though they deem it counterproductive [38]. alternatives are given that they are both considered as pro- In our case, this is represented as follows: if the diference ductive (or counter-productive) to count for confict. In other words, the defnitions do not account for value diferences, ∑ �� −∑�� − + (8) which lead us to measurable confict. ��∈�� ∈�� 6 Advances in Operations Research

Table 1: Te positions on the underlying measurement scale produced by the cardinal rankings.

Stakeholder Position

�� (� 1)�(�2)�(�3)�(�4)�(�5)�(��)

�1 8681 18

�2 8681 18

�3 878218

�4 878318

�5 878318

�6 121581

�7 121581

�8 121681

�9 131781

�10 132781

is small, then the power balance is more equal entailing larger 0, and all stakeholders in the pro-group rank such that �� =0 � confict. and �� =1and the power balance is equal. Further, �� =0 To measure these properties refecting the distance occurs if either the con-group or the pro-group is empty. between the groups, we utilize three sums of squares similarly to how Ward’s clustering method measures distances between clusters [11, p. 466]. We obtain the sum of squared diferences 4.3. Consensus Properties. Te semantic meaning of the � confict indices can then be explained by dividing the confict between each � and the group’s mean distance, i.e., the �� range [0, 1] into a number of subintervals each describing a diferences certain level of consensus. We defne the points � and � as ∑ �� the interval’s lower and upper bound and stipulate � interval � ��∈�� − � � (9) points {�1,�2,...,��−1,��}. Tese points are to divide the �� scale into the � intervals such as [�, �1], [�1,�2],...,[��−1,�]. Each interval is then associated with a consensus property for the con-group (12), the pro-group (13), and the combined label describing the level of consensus, e.g., consensus aligned group (14), respectively. attribute, potentially controversial attribute, and controversial attribute, with regard to a specifc action. Defnition 3 (within-group confict index). A within-group � confict index �� for stakeholder set � with two or more 4.4. Example. Assume that ten stakeholders � ={�1,...,�10} stakeholders, under attribute �� and alternative ��,isgiven evaluate the performance of fve actions {�1,...,�5},with by regard to attribute �1 using CAR for confict evaluations. Te actions’ positions on the underlying measurement are �� = √�(�� −(�� +��)) (10) �� presented in Table 1 and the normalized values in Table 2. Attribute �1 is for illustrative purposes given the weight of where 1. 1 � �= Properties of 1 for each action can now be defned. First, 2 (11) ∑� ∈� �� we stipulate classes of controversy based upon the magnitude � of confict. Assume four such classes which range from � 2 “consensus aligned”, i.e., low confict, to “very controversial” ∑� ∈�− �� =∑� 2 (�� − � �� ) where the confict is high; see Table 3. Note that the subranges �� −� (12) − �� and the semantical labels are defned by the authors for ��∈�� illustrative purposes. In a real setting the ranges and labels � 2 should be defned by the decision-maker. ∑� ∈�+ �� =∑� 2 (�� − � �� ) To analyze confict within the stakeholder group, for each �� +� (13) + �� action we form a con-group (6) and a pro-group (7) and ��∈� � �� subsequentially calculate the squared distance within the 2 ∑ �� con-group (12) and the pro-group (13), the squared distance � 2 � ��∈�� =∑� (� − � � ) (14) between the con- and pro-group (14), and the within-group �� ∈�� confict index �� (10). � Te results are shown in Table 4. Action �1 has � =0; � [0, 1] 1,1 In (10), is used to normalize the value onto .Itcan i.e., there exists no confict between the stakeholders since 0≤�� ≤1 �� =1 be noted that �� ,where �� occurs when all all stakeholders are members of the pro-group and no stake- stakeholders in the con-group rank such that �� =1and �� = holders are members of the con-group. As seen in Table 2, Advances in Operations Research 7

Table 2: Te stakeholders’ cardinal rankings normalized to a proportional [0, 1]-value scale.

Stakeholder Value Weight � � � � � � �� V1,1 V1,2 V1,3 V1,4 V1,5 V1,� �1

�1 0.00 0.29 0.00 1.00 1.00 0.00 1.00

�2 0.00 0.29 0.00 1.00 1.00 0.00 1.00

�3 0.00 0.14 0.00 0.86 1.00 0.00 1.00

�4 0.00 0.14 0.00 0.71 1.00 0.00 1.00

�5 0.00 0.14 0.00 0.71 1.00 0.00 1.00

�6 1.00 0.86 1.00 0.43 0.00 1.00 1.00

�7 1.00 0.86 1.00 0.43 0.00 1.00 1.00

�8 1.00 0.86 1.00 0.29 0.00 1.00 1.00

�9 1.00 0.71 1.00 0.14 0.00 1.00 1.00

�10 1.00 0.71 0.86 0.14 0.00 1.00 1.00

Table 3: Te table shows four confict index intervals, each associ- stakeholder groups, e.g., people living in diferent parts of the ated with a consensus property label which semantically describes town or belonging to diferent generations. the level of consensus. Te between-group confict index measures the confict Confict index interval Consensus property label between two stakeholder groups. Te intuition behind the [0.00, 0.10) Consensus aligned between-group confict index is that if the two groups disagree to the same extent on the same matters, there is [0.10, 0.20) Potentially controversial [0.20, 0.50) low confict between the groups. Te between-group confict Controversial should thus reveal to what extent two groups disagree [0.50, 1.00] Very controversial diferently from each other. Let � and � be two subsets of �.Foreachalternative�� and attribute ��, we partition � �− and � into two partitions: the con-group �� and the pro- all stakeholders placed �1 on the same position as �� in �+ �− group �� for �,andthecon-group�� and the pro-group the cardinal ranking. However, stakeholders �1,...,�5 stated ��+ � ��− ��− that all other actions were better than �1,andstakeholders �� for .Temembersof �� and �� estimated the part- � ,...,� � 6 10 stated that all other actions were worse than action worth value �� to be less than the part-worth value of the � 1. Tus, when the ranking was normalized to proportional �� + ��+ [0, 1] � do nothing alternative ��,andthemembersof �� and �� -value scale, the value of action 1 for stakeholders � � � �1,...,�5 was V1,1=0, and for stakeholders �6,...,�10 the value estimated it to be greater than or equal to �� ;seethefollowing � � equation: was V1,1=1. Action �2 has d1,2 =0.2, since both the con-group and the pro-group estimated the value of action to lie close to �− � � � � �� ={�� ∈�:�� <��} ��.Action�3 hasanevenlowerconfictindex,�1,3 = 0.0429, �=1 since all stakeholders except one are members of the pro- � ��+ ={� ∈�:�� ≥�� } group. Te pro-group members estimated the value of �3 to �� =1 be equal to the value of ��, and the member of the con-group (15) � �− � � � estimated the value of 3 to be slightly less than the value of �� ={�� ∈�:�� <��} � �=1 ��.Action�4 has �1,4 = 0.7857 since, as seen in Table 2, the stakeholders of both groups estimated it to lie closer �+ � � � �� ={�� ∈�:�� ≥��} towards the most preferred or least preferred alternative for �=1 � both groups, action �5. Lastly, action �5 has �1,5 =1,since � � �,� Te squared distances within the con-group �� ,�� ,�� all members of the con- and pro-group estimate it to be the � � �,� worst and, respectively, best action. See the classifcation of (12), and the pro-group �� ,�� ,�� (13), and the squared � � �,� the actions in Table 5. distance between the con- and pro-group �� ,�� ,�� (14) Note that the confict index measures the disagreement for groups � and � are then obtained according to the given between the con-group and the pro-group. If either the con- equations. Te confict with respect to alternative �� under � � � group or the pro-group is empty, �� (or �� )cancels�� out. attribute �� between the two groups � and � can now be �,� represented by the between-group confict index �� . 4.5. Between-Group Confict Index. Of interest for the application case was frst to measure the confict within one Defnition 4 (between-group confict index).

� � 1 group of stakeholders, i.e., the within-group confict index. ��,� = √� �(��,� −(�� +��)) − (��,� −(�� +��)) + (��,� −(�� +��))� �= �� ( �� where 2 ∑ �� (16) Second, it was of interest to measure the confict between two � ∈� � 8 Advances in Operations Research

Table 4: Te distance within the con- and pro-group, the distance between the con- and pro-group, and the confict index.

�1 �2 �3 �4 �5 � �1� 0.0000 0.0002 0.0000 0.0008 0.0000 � �1� 0.0000 0.0002 0.0000 0.0008 0.0000 � �1� 0.0000 0.0045 0.0002 0.0634 0.1000 � �1� 0.0000 0.2000 0.0429 0.7857 1.0000

Table 5: Te classifcation of the actions consensus properties.

Consensus Property � 1 �2 �3 �4 �5 Consensus aligned ×× Potentially controversial × Controversial Very controversial ××

Table 6: Te con- and pro-indices for both groups and the confict between the groups.

�1 �2 �3 �4 �5 � ��1 0.0000 0.0000 0.0000 0.0000 0.0000 � ��1 0.0000 0.0002 0.0000 0.0008 0.0000 � ��1 0.0000 0.0002 0.0000 0.0008 0.0000 � ��1 0.0000 0.0002 0.0000 0.0008 0.0000 � ��1 0.0000 0.0000 0.0000 0.0000 0.0000 � ��1 0.0000 0.0002 0.0002 0.0008 0.0000 �,� ��1 0.0000 0.0002 0.0000 0.0008 0.0000 �,� ��1 0.0000 0.0002 0.0000 0.0008 0.0000 �,� ��1 0.0000 0.0045 0.0002 0.0634 0.1000 �,� ��1 0.0000 0.2000 0.0143 0.7857 1.0000

Te intuition behind the between-group confict index is (�6,...,�10) are members of the pro-group and that they all that confict increases when two stakeholder groups’ con- and placed �1 onthesamepositionas�� in the cardinal ranking; pro-groups have greater value diferences between them. Tis i.e., no con-groups exist. Te stakeholders in � expressed �,� �,� � can be noted by observing that 0≤�� ≤1,where�� =1 that all other actions were better than 1,andstakeholders � when the two stakeholders groups have opposing preferences; in expressed that all other actions were worse than action �� =0�� =0��,� =0�� =0�� =0 �1. Tus, when the ranking was normalized to proportional for example, �� , �� , �� , �� , �� , � �,� � � �,� [0, 1]-value scale, the value for �1 was V =0 for �1,...,�5, � =0, � =0, � =0, � =1; i.e., (1 − (0 + 0)) − ((0 − 1,1 �� V� � ,...,� � ��,� =0.2 (0 + 0)) + (0 − (0 + 0))) = 1. and 1,1=1 for 6 10.Action 2 has 1,2 ,since the two stakeholder groups have similar preferences. Both groups estimated the value of the action to lie close to ��. 4.6. Example. Using the preference data in Table 2, we divide �,� Action �3 has �1,3 = 0.0143, note that this is because only the group of stakeholders into two sets, �={�1,�2,�3,�4,�5} stakeholder �10 estimates that the action is negative, and all and �={�6,�7,�8,�9,�10}, based on some demographic other stakeholders estimate it to be equal to ��.Action�4 variable, e.g., age or sex. Tese sets are further divided into ��,� = 0.7857 ��− ��− ��+ has 1,4 ,sincethetwostakeholdergroupshave the con-group sets �� and �� and the pro-group sets �� ,� = ��+ opposing preferences, as seen in Table 2. Action 5 has 1,5 and �� . Te confict between the stakeholder groups is then 1,sinceallmembersof� estimate that the action is the best ��,� given by the confict index �� . Te results of the calculations of all actions, and all members of � estimate that the action is are presented in Table 6. the worst of all actions. Te results of the classifcation of the As in the within-group confict index, the between-group actions are presented in Table 7. confict index range is [0, 1]. In this example we use the consensus properties defned in the within-group example in Section 4.4; see the confict index intervals and the associated 5. Application of CAR for Conflict Evaluations consensus properties in Table 3. �,� at Upplands Väsby Municipality As seen in Table 6, the result for action �1 is �1,1 =0, since there is no confict between the groups. Table 2 shows In a current research project, researchers from Stockholm that all stakeholders of both subsets � (�1,...,�5)and� University cooperate with the Royal Institute of Technology Advances in Operations Research 9

Table 7: Te classifcation of the actions consensus properties.

Consensus Property � 1 �2 �3 �4 �5 Consensus aligned ×× Potentially controversial × Controversial Very Controversial ××

Table 8: Analysis I: the number of members of the con- and pro-groups, the con- and pro-indices, and the confict in the total population.

�1 �2 �3 �4 �5 − |�8�| 88 11 24 133 120 + |�8�| 851 928 915 806 819 � −7 −8 −8 −7 −7 �8� 1.04 ⋅ 10 2.74 ⋅ 10 7.32 ⋅ 10 1.64 ⋅ 10 1.52 ⋅ 10 � −6 −6 −6 −6 −6 �8� 4.91 ⋅ 10 5.57 ⋅ 10 5.54 ⋅ 10 4.87 ⋅ 10 4.68 ⋅ 10 � −6 −6 −6 −6 −6 �8� 7.12 ⋅ 10 6.01 ⋅ 10 6.25 ⋅ 10 7.09 ⋅ 10 6.64 ⋅ 10 � �8� 0.0444 0.0197 0.0244 0.0440 0.0412 in developing models for public planning and decision In total we received 939 answers; of these 465 were male, 456 processes in Swedish municipalities. We investigate how to female, 15 did not want to disclose their gender, and 3 selected increase expressiveness of the media used for communication other/agender. Te analysis consists of two parts, the analysis between the parties in these processes. Te focus here lies of (i) the diference in preferences in the total population and on developing tools that enrich this kind of communication. (ii) the diference in preference between females and males. As a part of the project we conduct three case studies, of which one is in cooperation with civil servants and politicians 5.1.1. Results. Five actions �1,...,�5 are evaluated under the at Upplands Vasby¨ (UV), a municipality in the Stockholm focus area/attribute �8 School: region. (i) �1 reduces preschool child groups.

5.1. A Case Study. As reported in [13, Ch. 7], the politi- (ii) �2 raises the quality of teaching. cians and civil servants wanted to get in-depth information (iii) �3 increases professional development for schools regarding the citizens preferences regarding actions, which and teachers. possibly could be implemented in the future. It was espe- � cially of interest to investigate if there were any actions (iv) 4 increases modern information technology (IT) in that potentially could lead to citizen conficts. To facilitate education. this, it was decided to use a web-based questionnaire (the (v) �5 involves caretakers more in school. Appendix) as a front-end for preference elicitation. Te Te respondents assess the afect associated with each content of the questionnaire was developed together with action with regard to a do nothing alternative (current state). civil servants at UV. Te questionnaire consisted of four Note that this assessment may not be related to the cost of parts: implementing the action, rather the feeling/afect related to Part I consisted of ten questions regarding diferent the implementation. In the questionnaire implementation of “focus areas” (or criteria in an MCDA setting). Under each the CAR for confict evaluations (Figure 3) the do nothing focus area, the respondents used an implementation of CAR alternative is represented by the tick mark located in the for confict evaluations to rank fve actions; see Figure 3. middle of the scale. Part II consisted of one question where the ten focus Analysis I: Confict in the Population. In the frst areas are given weights using an implementation of CAR; see analysis we investigate the diference in preference in the Figure 4. total population. We used four consensus property labels to Part III consisted of three questions where the respon- semantically describe the level of confict. Te within-group dents stated their preferences regarding two contradicting confict index range [0, 1] was divided into four subranges actions. each representing one level of consensus; see Table 3. Note Part IV consisted of questions regarding demographic that the subranges and the consensus properties are defned information. by the authors for illustrative purposes. An invitation letter containing a URL to the questionnaire Te results of this analysis are presented in Table 8. Te was sent by mail to 10,000 citizens. Te sample was chosen results show that all actions have a very low confict index, by conducting simple random sampling on a sampling frame indicating that the respondents have similar preferences. �8,1 �8,1 consisting of 31,408 citizens. In the section below we present Actions �1 (� = 0.0444), �4 (� = 0.0440), and �5 �8,5 an analysis of the results from the eighth focus area, School. (� = 0.0412) have the largest confict indices. Actions �3 10 Advances in Operations Research

Figure 3: Question 1 from Part 1 of the questionnaire translated to English. A handle on the slider represents one action. Actions to the lef of “Neither good nor bad” are regarded to be worse, and actions to the right are considered to be better than the do nothing action. Te preference intensity is represented by a colored gradient on the slider (red to the lef of Neither good nor bad, and green to the right). A textual description of the strength of preference between pairs of actions is found underneath the slider. Te questionnaire text was originally in Swedish.

Figure 4: Te weighting of the focus areas translated to English. A handle on the slider represents one focus area. Te importance of a focus area is represented by the blue colored gradient on the slider, and the rightmost focus area is the most important one. A textual description of the strength of preference between pairs of actions is found underneath the slider. Te questionnaire text was originally in Swedish.

�8,3 and �2 have the lowest confict indices of � = 0.0244 that the consensus properties are defned by the authors for � and � 8,2 = 0.0197, respectively. Te attribute properties are illustrative purposes. presented in Table 9, showing that all actions are consensus Te results of the calculations are presented in Table 10. aligned. All actions have very low confict indices, which also is Analysis II: Te Diference in Preference between refected in the attribute properties (Table 11), where all actions are consensus aligned. Te action with the highest Females and Males. In the second analysis we investigate the � � � � 8,1 = 0.0107 � � 8,4 = diference in preference between females and males. We use confict index is 1 ( ), followed by 4 ( �8,3 �8,5 the same consensus property labels as in the frst analysis to 0.0052), �3 (� = 0.0027), �5 (� = 0.0019), and �2 � semantically describe the level of confict. Te between-group (� 8,2 = 0.0005). Te diference in value between the actions’ confict index range [0, 1] was divided into four subranges confict indices is small since both groups have very similar each representing one level of consensus; see Table 3. Note preferences. Advances in Operations Research 11

Table 9: Analysis I: the classifcation of the actions consensus properties.

Consensus Property � 1 �2 �3 �4 �5 Consensus aligned ××××× Potentially controversial Controversial Very Controversial

Table 10: Analysis II: the number of members of the con- and pro-groups, the con- and pro-indices, and the confict between females and males.

�1 �2 �3 �4 �5 �− |�8� | 25 6 10 60 57 �+ |�8� | 431 450 446 396 399 �− |�8� | 60 5 13 69 61 �+ |�8� | 405 460 452 396 404 � −8 −8 −8 −8 −8 �8� 3.60 ⋅ 10 1.29 ⋅ 10 6.00 ⋅ 10 6.45 ⋅ 10 6.87 ⋅ 10 � −6 −6 −6 −6 −6 �8� 2.39 ⋅ 10 2.70 ⋅ 10 2.68 ⋅ 10 2.07 ⋅ 10 2.31 ⋅ 10 � −6 −6 −6 −6 −6 �8� 3.20 ⋅ 10 2.94 ⋅ 10 3.07 ⋅ 10 2.95 ⋅ 10 3.20 ⋅ 10 � −8 −8 −9 −8 −8 �8� 6.82 ⋅ 10 1.56 ⋅ 10 6.20 ⋅ 10 9.61 ⋅ 10 8.70 ⋅ 10 � −6 −6 −6 −6 −6 �8� 2.57 ⋅ 10 3.02 ⋅ 10 3.03 ⋅ 10 2.85 ⋅ 10 2.52 ⋅ 10 � −6 −6 −6 −6 −6 �8� 3.86 ⋅ 10 3.24 ⋅ 10 3.33 ⋅ 10 4.23 ⋅ 10 3.62 ⋅ 10 �,� −7 −8 −8 −7 −7 �8� 1.05 ⋅ 10 2.85 ⋅ 10 7.39 ⋅ 10 1.61 ⋅ 10 1.57 ⋅ 10 �,� −6 −6 −6 −6 −6 �8� 5.05 ⋅ 10 5.72 ⋅ 10 5.71 ⋅ 10 4.99 ⋅ 10 4.83 ⋅ 10 �,� −6 −6 −6 −6 −6 �8� 7.27 ⋅ 10 6.18 ⋅ 10 6.41 ⋅ 10 7.22 ⋅ 10 6.82 ⋅ 10 �,� �8� 0.0107 0.0005 0.0027 0.0052 0.0019

Table 11: Analysis II: the classifcation of the actions consensus properties.

Consensus Property � 1 �2 �3 �4 �5 Consensus aligned ××××× Potentially controversial Controversial Very Controversial

6. Concluding Remarks stakeholders groups and how the confict can be conceptu- alized into semantic attribute properties. Te results of such Public decision problems can be complex. Tey involve an analysis can aid decision-makers in the process of making multiple actions and multiple stakeholders which may have well-informed decisions by clarifying the actions that can be conficting preferences with regard to the actions. A problem confict-prone. in such situations is that these opposing preferences might lead to conficts between stakeholders, which may lead to delays in the decision process. An approach that can be used Appendix to increase the understanding of the stakeholders’ opinions is to allow them to state their opinions, e.g., by using a web- The Questionnaire based questionnaire. In this paper, we showed how the CAR method can Part I. What Should Upplands Vasby¨ Focus on in the Future? be applied, enabling respondents to state negative or positive preferences with regard to an alternative’s performance (1) Parks and greenbelts relative to a do nothing alternative. We applied CAR for (1a) Preserve existing larger greenbelts confict evaluations in a case study conducted in cooperation with Upplands Vasby¨ municipality. Te citizens’ preferences (1b) Build parks in existing urban districts were elicited by a web-based questionnaire that used an (1c) Build homes near greenbelts implementation of the method. We showed how the method (1d) Renovate existing parks can be used to highlight confict between and within diferent (1e) Improve accessibility to major greenbelts 12 Advances in Operations Research

(2) Diversity in housing supply (7b) Increase cultural and recreational activities for children and young people (2a) Ofer more housing types (7c)Improvecarefortheelderlyinthemunicipality (2b) Ofer more apartment sizes (7d) Increase youth centres and feld assistants (2c) Ofer small-scale land ownership (7e) Reduce preschool child groups (2d) Preserve the conceptual foundations of the buildings from the 1970s (8) School (2e) Ofer more housing near the water (8a) Reduce preschool child groups (3) Vitalize common places (8b) Raise the quality of teaching (8c) Increase professional development for schools (3a) Mix diferent types of trafc and teachers (3b) Place parking along the streets (8d) Increase modern information technology (IT) (3c) Turn entrances to streets in education (3d) Place public locales in transparent ground foors (8e) Involve caretakers more in school (3e) Secure parking solutions under houses (9) Safety

(4) Communications (9a) Increase safety around the station area (4a) Pair the new streets with existing ones to (9b) Increase police presence in central Vasby¨ strengthen the connection to the adjacent (9c) Improve the lighting in the centre of Vasby¨ neighborhoods and reduce the barriers that the (9d) Narrow opening hours for alcohol outlets in main roads pose. central Vasby¨ (4b) Improve communications at night between var- (9e) Extend the opening hours of shops in the city ious parts of the municipality center (4c) Improve communications to and from Uppsala (10) Sustainable development (4d) Improve the north-south and east-west routes through a fne-mesh and well-integrated (10a) Reduce energy consumption metropolitan area networks. (10b) Reduce transport and sound pollution (4e) Improve communications to and from down- (10c) Increase climate change adaptation and recy- town Stockholm cling (5) Culture and recreation (10d) Prioritize environmentally friendly transport modes (walking, cycling, public transport) (5a) Expand the range of cultural sports and recre- (10e) Reducing environmental toxins and hazardous ational activities chemicals in nature (5b) Create better opportunities for festivals and concerts Part II. How Important Is Each Focus Area? (5c) Create more opportunities for outdoor sports (5d) Create outdoors marketplaces (11) Weighting (5e) Provide municipal grants for cultural and recre- (1) Parks and greenbelts ational projects (2) Diversity in housing supply (6) Education (3) Vitalize common places (4) Communication (6a) Renovate older schools (5) Culture and recreation (6b) Build new schools (6) Education (6c) Improve the physical environment of school- (7) Care yards (8) School (6d) Improve the quality of primary education (9) Safety (6e) Improve the quality of secondary education (10) Sustainable development (7) Care Part III. Contradictions (7a) Increase cultural and recreational activities for the elderly (12)Waterorhousing Advances in Operations Research 13

(12a) Build homes near water (vi) What is your gender? (12b) Preserving nature and shorelines intact (a) Female (13) Services or green areas (b) Male (c) Other/agender (13a) Densify the city centre and increase the range of services (d) Do not want to disclose (13b) Preserve green areas Data Availability (14) Regional centre or smaller urban areas Te dataset is available on data.world, https://data.world/ (14a) Develop central Upplands Vasby¨ samuel-bohman/2015-upplands-vasby-municipality. (14b) Develop smaller urban areas Conflicts of Interest Part IV. Your Background Te authors declare that they have no conficts of interest. (i) Where do you live? (Tis question consisted of 41 residential areas to choose among) Acknowledgments (ii) What is your highest level of education? Tis research is partly funded by Te Swedish Research (a) Not fnished elementary school or equivalent Council Formas, grant 2011-3313-20412-31. compulsory school (b) High school or equivalent compulsory school References (c) High school, folk high-school or equivalent [1] S. French, D. Rios Insua, and F. Ruggeri, Decision Analysis,vol. (d) College/university 4, no. 4, pp. 211–226, 2007. (e) Other post-secondary education [2] C. Bayley and S. French, “Designing a participatory process for (f) Postgraduate stakeholder involvement in a societal decision,” Group Decision and Negotiation,vol.17,no.3,pp.195–210,2007. (iii) What is your main occupation? [3] M. Riabacke, J. Astr¨˚ om, and A.˚ Grönlund, “eParticipation galore? extending multi-criteria decision analysis to the public,” (a) Employed International Journal of Public Information Systems,vol.70,no. (b) Self-employed 2, 2011. (c) Student [4] M. Danielson, L. Ekenberg, J. Idefeldt, and A. Larsson, “Using a sofware tool for public decision analysis: the case of nacka (d) Pensioner/retired municipality,” Decision Analysis,vol.4,no.2,pp.76–90,2007. (e) Sickness or activity compensation [5]M.Danielson,L.Ekenberg,A.Ekengren,T.Hökby, and J. (f) Long term sick leave (more than 3 months) Lidén, “Decision process support for participatory democracy,” (g) Leave of absence or parental leave Journal of Multi-Criteria Decision Analysis,vol.15,no.1-2,pp. (h) Job seeker or in labour market activity 15–30, 2008. (i) Homemaker [6]K.Hansson,G.Cars,M.Danielson,L.Ekenberg,andA.Lars- son, “Diversity and public decision making. in world academy (j) Other of science, engineering and Technology 71,” in Proceedings of the 2012 International Conference on e-Democracy and Open (iv) How long have you lived in Upplands Vasby?¨ Government, pp. 1678–1683, 2012. [7] B. Enserink, “A quick scan for infrastructure planning: Screen- (a) 0-4 years ing alternatives through interactive stakeholder analysis,” (b) 5-9 years Impact Assessment and Project Appraisal,vol.18,no.1,pp.15– (c) 10 years or more 22, 2000. [8]M.S.Reed,A.Graves,N.Dandyetal.,“Who’sinandwhy?A (v) How old are you? typology of stakeholder analysis methods for natural resource management,” Journal of Environmental Management,vol.90, (a) 0-14 no. 5, pp. 1933–1949, 2009. (b) 15-24 [9] R.Efremov,D.R.Insua,andA.Lotov,“Aframeworkforpartici- (c) 25-34 patory decision support using Pareto frontier visualization, goal (d) 35-44 identifcation and arbitration,” European Journal of Operational Research,vol.199,no.2,pp.459–467,2009. (e) 45-54 [10] M. Danielson and L. Ekenberg, “Te CAR Method for Using (f) 55-64 Preference Strength in Multi-criteria Decision Making,” Group (g) 65+ Decision and Negotiation,vol.25,no.4,pp.775–797,2016. 14 Advances in Operations Research

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Research Article Minimizing Cost Travel in Multimodal Transport Using Advanced Relation Transitive Closure

Rachid Oucheikh ,IsmailBerrada,andLahcenOmari

Faculte´ des Sciences Dhar El Mahraz, Universite´ Sidi Mohamed Ben Abdellah, Fez, Morocco

Correspondence should be addressed to Rachid Oucheikh; [email protected]

Received 21 February 2018; Revised 8 June 2018; Accepted 19 June 2018; Published 23 August 2018

Academic Editor: Marta Bottero

Copyright © 2018 Rachid Oucheikh et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Te optimization computation is an essential transversal branch of operations research which is primordial in many technical felds: transport, fnance, networks, energy, learning, etc. In fact, it aims to minimize the resource consumption and maximize the generated profts. Tis work provides a new method for cost optimization which can be applied either on path optimization for graphs or on binary constraint reduction for Constraint Satisfaction Problem (CSP). It is about the computing of the “transitive closure of a given binary relation with respect to a property.” Tus, this paper introduces the mathematical background for the transitive closure of binary relations. Ten, it gives the algorithms for computing the closure of a binary relation according to another one. Te elaborated algorithms are shown to be polynomial. Since this technique is of great interest, we show its applications in some important industrial felds.

1. Introduction describing the problem. First, we begin by defning the binary constraints on which the elaborated method is based. Te optimization computation is an essential branch of A binary constraint is a relation between two variables. operations research which aims to minimize the resource Concretely, a relation can be, for example, an association of consumption and maximize the generated profts. It is employees’ names and their salaries, or a pairing of calendar primordial in many technical and industrial felds: system years with automobile production fgures. In the case when design, supply chain management, transport, energy, fnance, we have relationships between just two elements, the relation networks, etc. Tis type of computation has enjoyed a great is called a binary relation and it is represented by set of growth in the last century, and it presents the goal of many ordered pairs (x, y) where x and y are objects of sets A and works in operations research and graph theory. B, respectively, and x bears a relation to y. Tis paper introduces a new method for cost optimiza- Many binary relations display identifable properties. For tion, applied either on path optimization for graphs or on example, the relation “less than or equal to” has the property binary constraint reduction for Constraint Satisfaction Prob- that if an object bears a relation to a second which further lem (CSP). It is a problem-solving technique that is applied to bears the same relation to a third then the frst bears this improve decision-making and efciency. Tis method aims relation to the third ( x < yandy< zandthenx< z). Such to fll the gap in the binary constraints optimization, in relations are said to be transitive. particular where these constraints are of diferent structures. Transitivity is an important property used in several In addition, it has a low algorithmic complexity that is shown domains. However, it is not satisfed by many relations. In to be polynomial. Moreover, it can be widely used in many fact, the transitive closure computation has been identifed as operations research application felds, namely, management, an important and frequent problem in many computer sci- decision-making, network optimization, scheduling, etc. ence applications, we mention among others path optimiza- Before citing the related works and making the com- tion, redundant synchronization removal [1], reachability parison with what is done in the literature, we start by analysis of transition graphs in communication networks [2], 2 Advances in Operations Research

construction of parsing automata in compilers [3], evaluation Let X =(x1,...,xk) be a vector of distinct variables and of recursive database queries, and iteration space slicing and V(X)=(v(x1),...,v(xk)) be the vector which associates with code generation [4, 5]. each variable in the vector X its valuation. � In this paper, we investigate a new extension of the Defnition 2. Aset�⊆N is said to be denoted by Φ(X) where transitive closure concept: “the transitive closure according to Φ is Presburger formula with variables in x1,...,xk} if S = a given property.” Tat is, for a given property P,and a relation {V(X)|V ⊨Φ}. S is called a Presburger set. R, we are interested in computing the smallest transitive relation containing R such that the property P holds. To Teorem 3. Guinsburg and Spanier proved in [12] that the � begin, we enumerate the main contributions of this paper: family of Presbureger sets of N is identical with the family of N� (i)Teintroductionoftheconceptoftransitiveclosure semilinear sets of . according to a given property. From this theorem, we can deduce that the works above (ii) Te proposition of a new algorithm to compute this are insufcient since the nonsemilinear sets are not studied. To explain this, we give a concrete example where a set B is transitive closure. i defned as B ={i | i ∈ N}. Tis latter is not a Presburger set (iii) Te proft of our new concept in many research since it is not semilinear. operations applications, especially those requiring the Within Presburger logic, we consider a relation R over N constraints reduction or path optimization. defned as {[�] �→[�] | � = �+3 ∨ � = �+4}where (�, �) ∈ ∗ ∗ N. Let A be the partition of singletons on R (R designate the Related Works. Many efcient algorithms of transitive clo- transitive closure of R). We defne the following mapping: for sure have been developed in the feld of algorithmic graph 1/� 1/� 2 2 each x in B we associate (� ,� +1)in N ∩� .Takethe theory: we mention Roy Warshal algorithm [6] and Warren �(�) = ∃�, � = 2�. algorithms [7] based on a matrix representation of the graph. following property on elements of B: Assuming this data, up to now, there is no elaborated We cite also the Schmitz algorithm [8] which takes beneft of method which computes the transitive closure of R according Tarjan’s algorithm. Other interesting works in the same line to a property P in this case. are those of Ioannadis [9]. However, all these previous works Other close techniques are hypergraph theory and linear consider only the computation of the transitive closure. To programming. Te hypergraphs do not express more than the best of our knowledge, the concept of transitive closure one relation. In fact, they present a simple generalization of according to a given property has not been introduced before the graphs in which an edge can join any number of vertices. and there is no elaborated technique to solve this problem. Tis means that each hypergraph includes just one relation In the case of many relations, Wlodzimierz, Verdoolaege, even if it is not binary. Cohen, and Beletska [10, 11] worked on transitive closure of Moreover, linear programming (LP) aims to optimize a the union of afne relations on integer tuples. Te general linear objective function subject to linear inequality conform of a parameterized afne integer tuple relation is � straints. In our case there is no objective function to optimize. {[�] �→ [�] | ⋁�=1(∃�i, Ai(x, y,�i)≥bi)} wherex,y,and In addition, computation complexity using LP is higher than �i are integer tuples, Ai is an integer matrix, and b� is a tuple the complexity of our method. of integers and symbolic value. Tey presented iterative algo- Te rest of this paper is organized as follows: In Section 2, rithms to calculate the exact, the underapproximation, and we present the basic defnitions, concepts, and notations the overapproximation transitive closure of such relations, used in this paper. In Section 3, we show the properties of within Presburger arithmetics. However, they consider only our closure and we elaborate the computation algorithm. In the union of integer tuple relations that are commutative and Section 4, we apply our method in multimodal transport by have the same dimensions. adapting the algorithm to minimize the cost travel. Finally, To show the insufciency of their study, let us discuss an we conclude and draw perspectives in Section 5. example of a closure case that is not included in their work. 2. Background and Basic Definitions For this purpose, we begin by giving some defnitions. In the following, R denotes the set of real numbers and ∧ Defnition 1. Let N be the set of nonnegative integers and k (reps. ∨ ) logical conjunction (resp. disjunction). �⊆N� be a positive integer. A set is a linear set if there Defnition 4. Let A and B be two sets. A binary relation R , ,..., N� ={ | = exist vectors v0 v1 vt in such that S v v fromA(calleddomainofR)toB(calledcodomainofR)is + +⋅⋅⋅+ , , ,..., N} v0 a1v1 atvt for a1 a2 at in .V0 is constant defned by a subset G of A ∗ B. If (x, y)∈G, we say that x is , ,..., vector and v0 v1 vt are called generators of the linear set related to y and we write x R y. S (called also periods). When A = B, we say that R is a binary relation over A or � AsubsetofN for �∈N is semilinear if it is a fnite union defned on A. Some important properties of a binary relation of linear sets. RoverAareasfollows: (i) Refexivity: ∀� ∈ �, ��. N2 ={(, )| ≥4} Example.In the set A x y x is a linear set, ∀ , ∈ 2,( )�⇒( ) namely, the constant vector is (4, 0), and the generators are (ii) Symmetry: x y A xRy yRx . 3 (1, 0) and (0, 1). (iii) Transitivity: ∀�, �, � ∈ � , (��) ∧ (��) �⇒ (��). Advances in Operations Research 3

A relation that is refexive, symmetric, and transitive is Te system has two types of inequalities: called an equivalence relation. When R is an equivalence �∈� (i) Variable inequalities of the form �� − �� ≤ �� with relation over A, the equivalence class of an element 3 is the subset of all elements in A that bear this relation to x. (��, ��, ��)∈R . Note that the equivalence classes are disjoint. Te quotient set (ii) Inequalities of maximal bound diference of the form 4 of A by R is the set of the equivalence classes. Cr will denote max(��−��) ≤ max(��−�� with (��, ��, ��, ��)∈R . the cardinal of this quotient set. Te set of solutions of this system, when it is not empty, Defnition 5. Te transitive closure of a relation R on a set A is included in the intersection of the half-planes defned by is the smallest transitive relation R* over A containing R. individual inequalities of type 1. It is therefore a convex set. Directly from this defnition, we can deduce the following Now, we have to check if this convex set is not empty and in properties: this case compute its canonical form (the representation in ∗ which all inequalities are maximally tight). Tis problem may (i) If R is transitive, then R = R � be expressed as transitive closure of a relation R according to (ii) Any transitive relation R defned on A, containing R, ∗ arelationSasfollows: contains also R (i) R ={(��, ��)|�� − �� ≤ ��} In this paper, we will investigate the problem of comput- ={(� , � ), (� , � )| (� −� )≤ (� −� )} ing the smallest transitive relation containing R such that a (ii) S � � � � max � � max � � . given property P holds. Tis problem may be viewed as an Firstly, we close transitively R. Tis gives us �3 − �4 ≤ 6 extension of the usual transitive closure problem: we are not instead of 8. As we have this implication (�3, �4)�(�1, �2)∧ looking only for the smallest transitive relation but a relation �3��4 �⇒ �1��2 then �1 − �2 ≤ 6. Terefore, computing R� which satisfes also a given property. Formally, one has the will give us the canonical form of the previous system. following. Sincetheclosureisdoneinaniterativeway,wewill introduce the following additional notations: for a relation R Defnition 6. Let A and B be two sets, R be a relation over 2 2 (reps. S) over A (resp. A ). A, � be a mapping from B to � , and P be a logical formula on elements of B. Te transitive closure of R with respect to (i) Completeness: (R)s = R ∪{(z, w)| P is the smallest transitive relation defned on A, noted R�, ∃(x, y), (x, y)S(z, w)∧xRy} ∀� ∈ �, �(�) �⇒ �(�) ∈ � containing R, such that, �. (ii) Iteration: for �∈N, P expresses desired properties using a given logic. � maps 2 0 each element of B to an element of A .Inthiscase,Rp is �� =� ��=0 the smallest transitive relation containing R such that if an � �−1 ∗ (2) element of B satisfes the property P then its image must be in � =((� ) ) ��ℎ�� Rp. Computing ��in general case can be hard and depends ∗ Since �⊂�, it is easy to show that for all �∈N we have on the decidability of the used logic. So, in this paper we will �� ⊂��+1 � =⋃∞ �� consider only the following case: � � and � �=0 �. 2 (i) �=� and �(�) = � ∀� ∈ �. Example 9. Tisexampleshowstheutilityofthisclosureina � � state machine with variables. (ii) �(�) = ∃� ∈�� ∧��,whereSisagivenrelation Let G be a graph and A =(v1,...,vn) be the set of its over B. 2 edges. We assume that B = N , the property on elements of B In this case, Defnition 6 becomes as follows. is �(�, �) : �+� = 0 �� 3, and we suppose that the mapping �(�, �) associates for each (x, y) in B an element (vx, vy).We Defnition 7. Let R (resp. S) be a relation over a set A (resp. 2 afrm that for each two elements in B that satisfy property P, A ). Te transitive closure of R according to S is the smallest their images by the mapping � are linked by the relation R. transitive relation over A, noted Rs, and containing R such 4 that, ∀(�, �, �, �) ∈ � ,(�,�)�(�,�)∧��⇒��. Figure 1 shows the closure steps, in the frst stage we have the graph presenting the relation R, and then, in the second Example 8. To illustrate this concept, let us consider the step, we close transitively this graph. In the third step, we following system of inequalities: close the obtained graph according to the desired property.

�1 −�2 ≤12 Tese last two steps are repeated iteratively until the graph is stationary. �3 −�4 ≤8

�3 −�5 ≤4 (1) 3. Properties of the Transitive Closure of a Relation according to Another One �5 −�4 ≤2 2 Let R (resp. S) be a relation over A (resp. A ). In this section, (� −� )≤ (� −� ) max 1 2 max 3 4 we will dress the fundamental properties of Rs. 4 Advances in Operations Research

4 4 4 3 3 3

2 2 2 3 3 3 8 8 8 6 1 1 6 6 1

0 0 0 3 3 3

1 1 1 (a) Graph with just the relation R (b) Te transitive closure of R (c) Te transitive closure of R according to a property

Figure 1: Illustration of the closure steps.

3.1. Case of Equivalence Relation. Te following theorem Based on all the above, the following results are deducted: states the maximal number of iterations to achieve the tran- When S is an equivalent relation, we have the maximal sitive closure of a relation according to another equivalence number of iterations as follows: relation. �2 −� �2 −� �� = min (��, )�� ≤[ ] Teorem 10. If S is an equivalence relation, then the transitive 2 2 (4) closure of R according to S is 2 2 � −� � �� = min (� −��, )��ℎ�� 2 � �� = ⋃ �� =�� (3) �=0 Hence one has the desired result. 2 2 with �� = min(��,� −��,(� −�)/2). Recall that �� is the cardinal of the quotient set of S. 3.2. General Case of the Relation S. Te following theorem Intuitively, when S is an equivalence relation, this funda- determines the maximal number of iterations to achieve �� the transitive closure of a relation according to any other mental theorem gives a way to compute �� ,bycomputing�� . relation.

Proof. In each step of the closure, we have at least a couple ∗ Teorem 11. Let C be the cardinal of � . Te transitive closure that has just been connected by S and which will connect all � � � � =⋃ �� =� �� the pairs that belong to its class. of R according to S is � �=0 � � with � ≤� ∀� > � To prove that �� it sufces to show that � �2 −� � �� we have �� =�� . �� =[ ]��<� � �� 2 First, we have �� =(⋃�=1 ��)∪(⋃�=� +1 ��). � (5) �� 2 Since ⋃�=1 �� =�,thenwewillhave�� =�∪ � −� � � � �� =[ ]��ℎ�� (⋃ � )=�=� � 2 �=��+1 � � . However, when each class contains two couples, the � [�2/2] Proof. In each iteration ,weshouldhaveatleastonecouple maximal bound is a bit diferent; it is (we denote by ( , ) 2 ��−1� [x] the entire part of x). x y in A such that � (the transitive closure should at In addition, the relations of type (z, t) S (x, x),for least bring this relation in the previous iteration) and which 3 is in relation S with at least another couple (z, t): (x, y) S (z, t). (�, �, �) ∈ � (resp. (x, x) S (z, t)), are not useful since they no Te relations of type (z, t) S (x, x) (resp. (x, x) S (z, t))do longer advance the process of the closure (i.e., they do not link not advance the process of closure. Ten, the couples of type any two elements by R). Tus, the classes of type [(x, x), (z, t)] (x,x) should be deleted, and their minimum number that we should be eliminated; their minimum number that one can can have is n. Hence the result is have is equal to n/2. Terefore, to have the fnal closure we 2 can never exceed (� −�)/2iterations. �2 −� 2 �� =[ ] (6) If �� >[(� +1)/2]then there are classes that contain only 2 one pair. Each class of them reduces the number of iterations If we take into consideration the links closed in the frst by one, since if the couple is linked in a step we will have no ∗ infuence in the next steps. Hence, we deduce that if �� > step (by R ),notedC,wewillensurethatifC > n, then 2 2 2 [(� +1)/2]then �� =� −��. �� =[(� −�)/2]. Advances in Operations Research 5

Input: R, S: Two binary relations, i: integer Output:RS: Transitive closure of the relation R according to S 0 �� ←� � i i−1 ∗ Do { Rs ←� ( Rs ) // Use of any algorithm which computes the simple i transitive closure of Rs (i.e. Floyd-Warshall algorithm) i ←� ( i ) i Rs Rs s // update Rs using the relation S i ←� i +1 } While (i ≤ Nmax)

Algorithm 1: Algorithm skeleton of transitive closure computation (RS).

ＲＲ 16 ＲＲ11 12 17

ＲＲ10 15 Ｒ13 x9 Ｒ14

x3 x6 x8

x1 x2 x7 Railway

Road x4 x5 Transfer edges

Figure 2: Multimodal transport graph.

� (�,�) 3.3. Algorithm Skeleton of Transitive Closure (Rs)Computa- graph � constituted by two modes. Te frst mode is tion. We have shown the maximal number of iterations we the roads (m1) and the second one presents the railways (m2). need to have the closure of a relation according to another Each mode has its set of nodes �� ⊂�(its cardinal noted ni) � ⊂� � one. We can give the closure computation algorithm as shown and its edges �� . Te graph contains also a set of transfer in Algorithm 1. edges Et that allows the mode change. Tese edges are mostly directed; therefore we note the set of their heads H and the 4. Application on Minimizing Cost Travel in set of their tails T. During the transportation, we are facing constraints on Multimodal Transport mode changing, such as minimizing the number of transfers, Multimodal transport is a logistic problem in which a set viability, time of conveyance waiting, etc. of goods have to be transported to diferent places with the For some reasons such as congestion, we can change the combination of at least two modes of transport, without mode only if we will reduce the transport cost. For example, � � � � a change of container for the goods. Tus, it consists of we can choose the path 1 4 instead of 2 6 path only if the ��(� � )≤��(�� ) using in the same path or trip several modes of transport following condition is fulflled: 1 4 2 6 .In ��(� � )≤��(�� ) (� ,�)∈�2 (truck, car, train, plane ...). Tis technique has emerged to general, we have � � � � ,for � � 2 deal with problems such as pollution and energy consump- and (��,��)∈� . tion and especially for reason to reduce congestion. Given these data and fowing in both modes, the problem Several issues arise from this idea; we can cite planning is to fnd the lowest cost between any two points of the graph. of multimodal transportation tasks [13, 14] and modeling the multimodal transportation networks. A lot of algorithms 4.1.2. Lowest Cost in Multimodal Transport. We present the have been elaborated to fnd the viable shortest path under transport network by a binary relation noted R. Based on matrix representation, this relation will be represented by a objectives such as travel time and number of modal transfers � matrix of dimension n (n is the number of nodes): � = [15, 16]. Te most important among them remains the � calculation of multimodal shortest path. {(�� )0≤�,�≤�}={(��)0≤�,�≤�},with�� being the cost needed to achieve the node j from i. Te transfer edges are not presented 4.1. Case of Two Modes here. Te constraints on mode changes are expressed by another binary relation, noted S, represented by a matrix of 2 � � � 4.1.1. Formulation of the Problematic. Assume that we have a dimension � .� ={(��)0≤�,�≤�2 |�� =1��(��)≤ transport network as shown in Figure 2. It is presented by a ��(��) with �=�(�−1)+�and �=�(�−1)+�,0��}. 6 Advances in Operations Research

Input: Two matrices representing the two transport mode graphs Output: Canonical form of the matrix that represents the merge multimodal graph Do { // Step 1: Use any algorithm which computes the simple R transitive closure of M . Next, we use Floyd-Warshall. For i: 1�→n { For j: 1�→n � � � � { For k: 1�→n �� = min(�� ,�� +�� )}} // Step 2:UpdateMRusingMS For i: 1 �→ n { For j: 1�→n � If �� =∞̸ then 2 { for k: 1�→n � If �(�−1)�+�,� == 1 then � � � �[�/�]+1,�−[�/�]∗� = min(�� ,�[�/�]+1,�−[�/�]∗�) // [�/�]:entirepartof�/� End if } End if }} a ←� a +1}While (�≤��)

Algorithm 2: Lowest cost in multimodal transport graph.

Te constraints on mode changes are expressed by allows us to value the correspondent couples, (��,��) with another binary relation, noted S. min(��(��,��), ��(��,��) + ��((��,��), (��,��))). Tis operation will be repeated until the matrix is stationary. Te algorithm is then like Algorithm 2. 4.1.3. Te Applied Algorithm. Firstly, we accomplish the transitive closure of R. Aferwards, we scan the matrix ∗ updated of R looking for the coordinates which has non- 4.2. Case of More Tan Two Modes. Te previous algorithm � provides the shortest path only if the following proposition infnite cost. Ten, for every coordinate �� =∞̸ we (� ,� ) � is considered: between two crossings of the same mode we point out to the line corresponding to � � in M in pass through an odd number of modes. Tis implies that order to select the coordinates having the cost equal to 1. the start point and the arrival point belong to the same Assume, for instance, that ��((��,��), (��,��)) = 1;this (� ,� ) mode. Consequently, to hold the same computation, the use allows us to value the correspondent couples, � � with order of modes in the general case should be as follows: min(��(��,��), ��(��,��)). ��,��,��,��,��,��,��,��,��,��,��,...,��. Tis operation will be repeated until the matrix is sta- In this way, we will have the lowest cost between each two tionary, which corresponds to �� iterations as showed in 3 points using the previous algorithm. Teorem 10. Ten, the algorithm complexity is Θ(� ��) where n is the number of system variables. 5. Conclusion 4.1.4. General Case. Sometimes, for reason of loading/ Tis paper fts in the frame of the application of operations unloading cost, we can change the mode only if we will earn research in urban planning and transportation. It brought at least a defnite supplementary cost. Tis can be expressed a new optimization method that consists in the concept of 2 as ��(��)−��(��)≤�for (��,��)∈�and the “transitive closure of a given relation with respect to a 2 property.” In the literature there is no work that addresses (��,��)∈�. Tis time, the binary relation S is represented � � � this issue; therefore we have cited the close works done on � ={(�) 2 |� = by the following matrix: �� 0≤�,�≤� �� the transitive closure with many relations. Aferwards, we �� (��)−��(��)≤�� with �=�(�−1)+ � �=�(�−1)+�,0��} � situated our technique vis-a-vis` hypergraph theory and linear and ,where �� presents the cost programming. that should be earned in order to change the mode. Te contributions of this paper are both theoretical and It is the same as the previous example with some practical. We elaborated methods to compute the transitive modifcations. Afer fnishing the transitive closure of R, we ∗ closure of a relation according to a property and in particular scan the matrix updated of R looking for the coordinates the case where the property is another relation. Afer proving which have noninfnite cost. Ten, for every coordinate the completeness of the closure and the number of necessary �� =∞̸ �� , we change the coordinates having the non- iterations to achieve the solution, we design the applied S infnite costs in the line corresponding to (��,��) in M . algorithms. What is more interesting is the low algorithmic Take as an example ��((��,��), (��,��)) =∞̸ ;this complexity that is shown to be polynomial. It is in the order Advances in Operations Research 7

3 of Θ(� ) where � is the number of the constraint system Proceedings of the 18th International Static Analysis Symposium, variables, which presents also the number of nodes in the Lecture Notes in Computer Science, vol. 6887, pp. 216–232, 2011. multimodal graph. Tese algorithms are also useful in many [12]S.GinsburgandE.H.Spanier,“Semigroups,presburgerformu- real world problems such as optimal solutions, Constraint las, and languages,” Pacifc Journal of Mathematics,vol.16,no.2, Satisfaction Problem, graph optimization, search engines, pp. 285–296, 1966. and system verifcation. [13] J. E. Fl´orez,A.T.Arias,G.Javieretal.,“PlanningMulti-Modal Transportation Problems,” in Proceedings of the International Conference on Automated Planning and Scheduling, AAAI Press, Data Availability 2011. Te data used to support the fndings of this study are [14]J.Zhang,F.Liao,T.Arentze,andH.Timmermans,“Amulti- modal transport network model for advanced traveler informa- included within the article. tion systems,” Procedia Computer Sciences, vol. 5, pp. 912–919, 2011. Conflicts of Interest [15] T. Grabener, A. Berro, and Y. Duthen, “Time dependent multiobjective best path for multimodal urban routing,” Electronic Te authors hereby declare that there are no conficts of Notes in Discrete Mathematics,vol.36,pp.487–494,2010. interest regarding the publication of this paper. Being the [16] F. Gueye, Algorithmes de recherche d’itinΘraires en transport authors of the paper, they certify on their honour the accuracy multimodal [Ph.D. thesis], Laboratory for Analysis and Archi- of this information. tecture of Systems - CNRS, France, 2010.

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Research Article Multiobjective Optimization for Multimode Transportation Problems

Laurent Lemarchand ,1 Damien Massé ,1 Pascal Rebreyend ,2 and Johan Håkansson 2

1 Lab-STICC UMR CNRS 6285, University of Brest, Brest, France 2DalarnaUniversity,Falun,Sweden

Correspondence should be addressed to Pascal Rebreyend; [email protected]

Received 5 December 2017; Accepted 15 April 2018; Published 7 June 2018

Academic Editor: Alessandra Oppio

Copyright © 2018 Laurent Lemarchand et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

We propose modelling for a facilities localization problem in the context of multimode transportation. Te applicative goal is to locate service facilities such as schools or hospitals while optimizing the diferent transportation modes to these facilities. We formalize the School Problem and solve it frst exactly using an adapted �-constraint multiobjective method. Because of the size of the instances considered, we have also explored the use of heuristic methods based on evolutionary multiobjective frameworks, namely, NSGA2 and a modifed version of PAES. Tose methods are mixed with an original local search technique to provide better results. Numerical comparisons of solutions sets quality are made using the hypervolume metric. Based on the results for test-cases that can be solved exactly, efcient implementation for PAES and NSGA2 allows execution times comparison for large instances. Results show good performances for the heuristic approaches as compared to the exact algorithm for small test-cases. Approximate methods present a scalable behavior on largest problem instances. A master/slave parallelization scheme also helps to reduce execution times signifcantly for the modifed PAES approach.

1. Introduction (i) dispersion problem:the�-dispersion problem consists of spanning the � facilities by maximizing the min- Localization of facilities such as public services (schools, hos- imal distance between two of them. Tis objective pitals, etc.) is an important problem for social planners and function is suitable to locate business franchises and policymakers. Most of the time, this problem is formulated also when locating obnoxious facilities [5]. as the (single objective) �-median problem which is a central � � problem in Operations Research (see, for example, [1, 2] for (ii) -center problem:the -center problem [6] aims at surveys). Te �-median was introduced by Hakimi [3] who minimizing the maximal distance of demand nodes describes its basic properties. Its basic variant can be defned from their facility, or the average distance of a fraction as follows: given a set of � demand nodes, distance values for of those that are the farthest from their closest facility, each pair of nodes, and a fxed number � of facilities, locating e.g., 5% farthest of them. Tis problem formulation each facility at one of the nodes, while minimizing the sum of can be applied to locate emergency services such as distances from each node to its closest facility. fre stations. Recent developed algorithms solve the single objective (iii) multimode transportation location (MTL) problem:in version exactly for instances of thousands of nodes (e.g., many real cases, transportation can be done by difer- 25.000 nodes in [4]). However, for a policymaker, considering ent means (by foot, bike, car, buses, etc.) depending on additional objectives would be useful when solving �-median criteria like a threshold on the distance to the nearest problems on real cases, leading to diferent variants; e.g., facility. As an example, pupils are going to school by 2 Advances in Operations Research

foot (category A) or by public transportation (cate- well-known population-based approach such as NSGA2 is gory B), with a threshold on the distance defning the outperformedbythesingleindividualmethod,PAES[7], 2 categories, e.g., 2 km. Te objective is then to mini- thanks to our hybrid approach. Efcient parallelization helps mize both the mean distance for those of category A for handling large test-cases. As shown in Section 2, similar and the number of people in category B. approaches exist for MOO �-median, but with diferent multiple objectives and local search algorithms. Furthermore, In the following we will focus on the MTL problem with to our knowledge, no results have been presented for the multiple objectives. Te practical context is to optimize loca- parallelization of these approaches. tion of schools. Tis School Problem is a typical multimode Section 2 introduces related work for multiple objective transportation problem since, depending the distance, pupils optimization problems embedding �-median like formula- cangotoschoolbyfootorbybus.MTLproblemscanbe tion. Next, in Section 3, we formalize our bicriteria mul- seen as multiobjective optimization problems if means of timode transportation problem, with its specifc objective transportation have impact on each other. Optimizing the functions. In Section 4, we present an exact approach for cost for one of them can degrade the other objective value. solving the problem, with an �-constraint like technique. Te When considering a multiple objective optimization problem problem can also be solved using popular MOO heuristic (MOO), a single solution optimizing all of the objectives approaches like NSGA2 and PAES. We show how to adapt simultaneously rarely exists. Let �:�→�be an objective thoseframeworkstoourproblemsolving,couplingthem function mapping solutions �∈�, the search space, to the with an aggregation technique for performing local search. � objective space �,with�=R . MOO algorithms look for Te MOO frameworks are presented in Section 5, and solutions �∈�such that �=�(�)is optimized (in the the local search, using limited neighborhood, is detailed in � sequel, we consider minimization). �∈R is a point of the Section 5.2, along with its exploitation by the MOO methods. objective space �, with each of �� =��(�), � ∈ [1..�] being Evaluation and comparison of the proposed algorithms are one of the objective function values to be minimized. Many realized with the hypervolume standard metric [10], over approaches rely on the dominance concept to choose, among a Beasley’s benchmark [11] in Section 6. Last, conclusion and set of solutions �, those ones that represent the best trade-ofs perspectives are detailed in Section 7. of objectives within the search space. We say that a solution � � �∈�dominates another one � ∈�if ∀� ∈ [1..�], ��(�) ≤ ��(� ) � � 2. Related Work and ∃� ∈ [1..�], ��(�) < ��(� ). It is denoted as �≻�.Namely, � � � is as good as � on all objectives and better than � for at A few works extend the �-median problem with multiple least one of them. Solutions that are not dominated by any objectives. Te �-median problem is ��-hard [12], and member of � are efcient solutions and constitute the Pareto MOO versions are also ��-hard since they embed the set PS. Te set of points �∈�corresponding to the efcient single objective version. Tus, if some exact algorithms exist, � solutions is the Pareto front PF ={�∈R |∃� ∈ �, �(�) = heuristic approaches are preferred for large test-cases. � � � and ∄� ∈�,� ≻�}.Inthesequel,wesayforshortthata Te MOO �-median problem with an additional facility � � � � point �∈�dominates � ∈�if �=�(�),� =�(�), � ≻ � . cost objective is dealt with in [13]. Each facility is weighted Te goal of MOO algorithms is generally to determine or by a building cost, and the goal is to minimize the sum of approximate points of PF and associated solutions. distances to locations (�-median objective) and the sum of Solving multiobjective �-median instances is of course costs of the opened locations. Te authors in [13] used two related to �-median problem exact and heuristic resolution approaches.Tefrstisan �-constraint like formulation that is approaches but also to general approaches used for solv- a mix of two-phases algorithms [14] and classical �-constraint ing MOO problems, either exactly or approximately. Te approach [15]. According to the authors, it leads to a close former are ofen based on Integer or Binary Programming approximation of the full Pareto front. Even if its second (Multiobjective Integer Programming, MOIP), the latter on objective is diferent (facility cost instead of number of pupils Evolutionary Multiobjective Algorithms (EMOA). Our main by public transportation), the technique used is similar to our contribution is to develop and evaluate the two kinds of approach concerning the �-constraint problem formulation. approaches, in order to be able to solve exactly medium size However, since the number of nodes varies in our case for the cases of the School Problem and approximately very large distance count (for instance, pupils going to school by public scale cases. We exploit some mathematical properties of our transportation are not taken into account for the distance of targeted problem in order to model it with MOIP and solve demands from facilities), the method must be adapted, as it exactly with an �-constraint algorithm. Large test-cases it will be shown in Section 4. Te second approach used in are handled with 2 diferent general EMOA frameworks, [13] helps to handle large test-cases and is based on MOGA namely, the Pareto Archived Evolution Strategy (PAES, [7]) framework, with a path relinking local search procedure for and Nondominated Sorting Genetic Algorithm 2 (NSGA2, [8]). mixing solutions. Problems with uniform demand at each We have modifed the former and mixed it with a local search location (unitary problems) and with up to 400 demands and technique: we have adapted to the multiple objective case an 20 facilities are processed. As MOGA, NSGA2, which we are efcient neighborhood evaluation procedure [9] developed testing, also uses a population-based approach. for the �-median problem. NSGA2 can also use our local In [16], the authors formulate a biobjective �-median search technique, as a postprocessing step. We show that, problem with the following objectives : (1) minimal distance in many cases, for an equivalent computational efort, a to the closest facility (�-median traditional objective) and Advances in Operations Research 3

(2) maximization of the minimal distance between facilities Te modelling of the School Problem can be stated as (�-dispersion problem objective). Tey formulate and solve follows: it as a MOIP, with an �-constraint algorithm and also with ∑� (ℎ .� . ∑� � .� ) a customized approach, based on threshold fxing for the �=1 � � �=1 �� minimal distance between facilities. Taking into account the minimize � (1) ∑ ℎ�.�� threshold leads to additional constraints in a single objective �=1 subproblem. Te algorithm iterates on subproblems, in order � to provide the exact Pareto front of the biobjective initial minimize ∑ℎ�.(1−��) (2) problem. Once again, our second objective is diferent and �=1 implies an adaptation of the �-constraint algorithm. Further- � more, the modifed MOIP developed in [16] is specifc to the subject to ∑�� =� (3) dispersion problem, since it iterates on a threshold value of �=1 dispersion (minimal closeness of selected locations). Problems similar to multiobjective �-median have to also ∀�, 1 ≤ � ≤ �, be examined in the context of disasters management [17], or ∀�,1≤�≤�, tsunami exposure. In [18], the authors solve approximatively (4) a 3-objective optimization problem for school localization. �� =1�⇒ Similarly to our heuristic method, it uses the NSGA2 framework mixed with a local search procedure, but the objective �� =1 is not exactly the same as with �-median problems, since thenumberoffacilitiesisnotfxedbutdrivenbyacost ∀�, 1 ≤ � ≤ �, minimization objective. Te second objective is related to � tsunami risk exposure, and the third one takes into account (5) ∑�� =1 both the distance to school and the number of pupils not able �=1 to go to school, as it is considered too far away (meaning, to go by foot). As we will see in the next section, this objective ∀�, 1 ≤ � ≤ � is in fact a mix of ours. Te �-median problem and its multiobjectives variants have also some military applications. Localization of repairs, ( ∑ ��)=0⇐⇒ (6) {�|1≤�≤�∧� ≤�} supply, or security facilities can be modelized and addressed �� as �-median problems (see [19] for a survey). Common objec- � =0 tives are cost of localization, coverage of areas, and rapidity � of deployment and also security of the localization that must ∀�, 1 ≤ � ≤ �, be resilient. As an example, in [20], a multiobjective model, solved using a genetic annealing heuristic, takes into account ∀�,1≤�≤�, cost and response time for Canadian forces prepositioning. �� ∈ {0, 1} , (7) 3. The Multimode Transportation � ∈ {0, 1} , Problem Modelling � � ∈ {0, 1} We want to optimize the location of services, such as schools, �� in such a way that users go by foot to the closest service if it is where possible (according to a threshold � on the distance they can walk) and others take public transports. In the following, we (i) � is the number of demand nodes; will focus on a particular case of multimode transportation � problem,theSchoolProblem.TeSchoolProblemisstatedas (ii) isthenumberofcandidatenodes(numberof follows: given a set of � demand nodes holding pupils and a possible locations for a school); set of � candidate nodes for locating schools, a value of �,and (iii) � is the number of candidate nodes to be selected as distances �� between each couple (demand node, candidate school nodes; 1≤�≤�1≤�≤� � node) ( , ), defne a set of locations (iv) � is the threshold on walking distance; for setting up schools (school nodes) among the � candidate ℎ � nodes with the following objectives: (v) � is the number of pupils located at demand node ; (vi) �� is the distance between demand node � and (i) Te mean distance of demand nodes to the closest candidate node �; school node is minimized for those demand nodes that have a distance to closest school node less than (vii) �� is a decision variable, indicating if the pupils at node the threshold �. � go to school by walk or not (category A nodes).;

(ii) Te total number of demand nodes with a distance to (viii) �� is a decision variable, indicating if the candidate the closest school greater than � is minimized. node � is selected or not as a school node; 4 Advances in Operations Research

(ix) �� is a decision variable, indicating if the demand �� , which replaces the set of (Boolean) variables �� .Te node � closest school node is � or not. If �� =1,we semantics of � variablesisthefollowing:�� =0̸ if demand say that (demand node) � is covered by (school node) node � is covered by school node � and � is in category � (i.e., � � . �� =1)and,inthiscase,�� =1/∑�=1 ℎ��. Equations (1) and (2) refect the objectives stated above, Using this semantics, objective (1) becomes linear, as (1 ) � taking into account the number of pupils located at each shown in a . Notice that, by removing the variables �� , � � demand node. Equation (3) fxes the number of selected we “forget”, for each demand node in category (i.e., with � =0 school nodes. Equations (4) and (5) ensure that the single � ), which school node covers it. It is possible to keep this selectedcandidatenodeforpupilsatademandnodeis information, but it is useless for the resolution of the problem efectively a school node. Equation (6) ensures that pupils (as long as there is at least one school). � atademandnodeareaccountedtogowalkingifandonly To satisfy the semantics of the variables �� and specif- � if a candidate node is selected for school location in the cally specify 1/ ∑�=1 ℎ��,wealsoaddacontinuousvariable neighborhood of the node. �� for each demand node � and a continuous variable �.Te Tis formulation induces that candidate nodes are resulting model is as follows: restricted to demand nodes, but it could be extended to an � � arbitrary set of candidate nodes. Also notice that distance minimize ∑ (ℎ�.∑�� .�� ) (1a) data can correspond to Euclidean distances, with known �=1 �=1 geographical locations for the diferent nodes, or to shortest path values, computed with an algorithm as Floyd-Warshall if � the nodes are embedded within a routing graph, with moving minimize ∑ℎ�.(1−��) (2) cost values on the edges (e.g., time by walking, distance, and �=1 transportation cost). In the latter case, the value and meaning � ofthethresholdaretobeadapted.Teuseofthethreshold subject to ∑�� =� (3) refects the public Swedish policy where authorities ofer free �=1 transportation to some pupils based on the walking distance � ≤� ∀�,1≤�≤�,∀�,1≤�≤� to school. If ∀1≤�≤�,ℎ� =1,wespeakabouttheunitary �� (4a) version of the School Problem. � We show in the next section how to model this problem ∑�� +(1−��)≥� ∀�,1≤�≤� (5a) as a MOIP and how to solve it with an ad-hoc technique. �=1

4. Exact Problem Formulation and Solving �� ≥�� (6a) It is possible to solve exactly multiple objective problems ∀�,1≤�≤�,∀�,1≤�≤�,�� ≤� using �-constraint approaches. Tese techniques require a linear formulation of the aimed problem. Since the frst objective function of our model is nonlinear (1) and nonconvex, �� ≤ (∑��) ∀�,1≤�≤� (6b) those techniques are not directly applicable. In Section 4.1, {�|1≤�≤�∧�� ≤�} we present the problem as a multiobjective mixed integer � ≤� ∀�,1≤�≤� linear program (MOMILP). Its resolution would allow for � (R1) computing the optimal value of each objective (by removing � ≤� ∀�,1≤�≤� ( 2) other objectives from the formulation and using a MILP � � R solver as CPLEX, [21]). However, even computing only the � mean distance (our frst objective) with this model required ∑ℎ�� ≥1 (R3) high execution times, as detailed in Section 4.1. �=1 Terefore, we consider a simplifed MOIP in Section 4.2 � ∈ {0, 1} ∀�, 1 ≤ � ≤ � where the computation of the mean distance is replaced by a � computation of the cumulative distance. Using this model, we � ∈ {0, 1} , cancomputetheParetofrontPF andassociatedsolutionset � � using an adapted -constraint [22]-like approach presented �� ∈ [0, 1] in Section 4.3. We show that this method provides the exact Pareto set for the problem stated in Section 3. ∀�, 1 ≤ � ≤ � (8)

4.1. MOMILP Modelling. We studied the translation of the �� ∈ [0, 1] School Problem to a MOMILP problem mainly to compute ∀�,1≤�≤�,∀�,1≤�≤� directly the minimum mean distance (1) using a MILP solver. Since this objective function is continuous, its linearization �∈[0, 1] requires using continuous variables. Indeed, starting from the modelling of the School Problem presented in Section 3, we In this model, (R1), (R2) and (R3),ensurethat�≥ � can linearize (1) using a new set of (continuous) variables 1/ ∑�=1 ℎ��:from(R2) and (R3) (and since �� are binaries), we Advances in Operations Research 5

� � � ∈ 0, 1 ∀�,1≤�≤� have ∑�=1 ℎ�� ≥1.By(R1),weget∑�=1 ℎ��≥1,which � { } (16) gives the lower bound of �. � ∈ {0, 1} ∀�, 1 ≤ � ≤ � From this result, (5a) states that when demand node � is � (17) � in category � (i.e., �� =1), ∑�=1 �� ≥�(the minimization of �� ∈ {0, 1} ∀�,�,1≤�≤�,1≤�≤� (18) (1a) ensures that only one �� is equal to � and the other �� are zero). Equation (4a) implements Constraint (4), whereas Compared with the previous model, we replace (6b) by the implementation of Constraint (6) is done by (6a) and (6b) (12), (13), and (14), which ensure that demand node � cannot (note that the former is needed for the frst objective while the be in � if there is no school node at distance �. latter is needed for the second one). Notice that (13) and (15) both use �,butwithdiferent We have tried to exploit this formulation for computing meanings: the former ensures that a pupil cannot walk to a the minimal mean distance, with the CPLEX MILP solver distant node (to minimize the second objective), while the [21], using the single objective function (1a). In practice latter prevents an artifcial minimization of the cumulative this approach did not work, except on our smallest example distance by covering a demand by a distant node where a (100 nodes and 5 schools). On the other test-cases, CPLEX closer one is available. returned possibly nonoptimal solutions afer reaching its As we have seen before, our School Problem is formalized memory limit. We think that this failure stems from two only approximately by SP,since(9)usesthecumulative issues. Te frst issue is the variability of � (and, as a result, distance instead of the mean distance for pupils in category the values of all nonzero �� )whichmakesnodeselectiona A.Whiletheminimizationofthecumulativedistancecanbe hard problem. Te second issue is that when solving relaxed compared to the �-median problem (indeed, we can get the problems, with �� and �� partly continuous, (5a) enables �-median problem by adding �� =1for all � and removing putting ∑ �� =0even when �� is close to 1, since � � (13)), its exact resolution using MOIP solvers can be more is very small. As a result, the algorithm needs to force � � difcult, as the relaxed problem (with continuous variables) almost all � (and �) to integral values before getting a has more solutions. To explain this issue, let us consider only meaningful minimal bound. Since both issues are related to two demand nodes (which are also candidate nodes) 1 and 2 the computation of a mean distance, we considered a MOIP such that �12 ≤�and one location (�=1). With the relaxed using the cumulative distance instead. �-median problem (�1 =�2 =1), the solver gives directly the optimal cumulative distance �12,whateverthevaluesof 4.2. MOIP Modelling. Te MOIP formulation of the School �1 and �2.UsingtherelaxationofSP,theoptimalsolution Problemwiththecumulativedistancecanbeseenasa sets all variable to 1/2 except �12 and �21 which are set to 0 simplifcation of the MOMILP formulation of the previous �=1 and the cumulative distance is 0. section. In fact, we just need to state that .Asaresult, Using this observation and the fact that the cumulative the �� variables are useless ((R1), (R2),and(R3) disappear). SP distance is still not the mean distance lead us to consider an From this result, we propose the MOIP formulation for adapted �-constraint method where the frst objective is (10). the School Problem, as follows:

� � 4.3. Exact Algorithm. �-constraint [22] methods proceed as minimize �1 = ∑ ∑ℎ�� (9) follows: a series of single objective (i.e., Integer Program, IP) �=1 �=1 problems are solved, transforming all but one of the objectives

� of the MOIP considered into IP constraints. Te constraint set is updated at each iteration to enforce the exploration minimize �2 = ∑ℎ� (1 − ��) (10) �=1 ofthewholeobjectivespace.Intheirpaper[23],Ozlenand Azizoglu˘ introduce a recursive algorithm to generate a Pareto � set for a MOIP problem. Tey use the set of already solved ∑� =� subject to � (11) subproblems and their solutions to avoid solving a large �=1 number of IPs. In [14], a two phases algorithm is applied for the biobjective assignment problem. In the 2 objectives �� −�� ≤0 (12) case, it frst determines the extreme points in the objective ∀�,�,1≤�≤�,1≤�≤� spacebydiscardingoneobjectiveatatimeandsolvingthe resulting single objective problem. Ten, in a second phase, �� =0 it partitions the objective space according to the range of (13) values found at the frst step and explores it by slices. It ∀�,�,1≤�≤�,1≤�≤�,�� >� also combines the approach with heuristics specifc to the assignment problem for enhancing the execution times. � � ∑� =� ∀�,1≤�≤� An adapted -constraint algorithm which computes all �� (14) � �=1 nondominated points sorted by 2 values (i.e., second objective) is presented in Algorithm 1 for solving SP.Tis � ≥� approach uses the fact that given a nondominated point �= � � � � � (�1,�2), other nondominated point � =(�1,�2) such that (15) � � � ∀�,�,1≤�≤�,1≤�≤�, �� ≤� �2 ≥�2 must satisfy both �1 <�1 and �2 >�2.Sincethe 6 Advances in Operations Research

Data: SP problem with objectives �1 =�1 (Eq. (9)) and �2 =�2 (Eq. (10)) and constraints set � = {Eq. (11)-(18)} Result: the Pareto front PF,storedin�� begin ��1:= +∞ ��2:= −∞ �� := 0 while true do add constraint {�1 ≤ ��1} to � add constraint {�2 ≥ ��2} to � solve problem P: min �2 =�2 subject to � if Pnotfeasiblethen End solve problem P: min �1 =�1 subject to �∪{�2 =�2} if Pnotfeasiblethen End add point (�1,�2) to �� :=�∪{�q.(21) } ��1:= �1-1 ��2:= �2+1 end end

Algorithm 1: An �-constraint based method for solving SP (with cumulative distance). minimal cumulative distance is hard to compute (and not Tus all efcient solutions for the School Problem are really useful as it may not be the minimal mean distance), we found by solving SP.Buttheconverseisnottrue,and do not compute the extreme point associated with it. nondominated points can also appear in the Pareto front for In SP, we consider the minimization of the cumulative SP that do not belong to the Pareto front for the School distance instead of the mean distance. Hence both objective Problem. However, since the solutions generated are sorted function parameters are of integer values (once all distances by the value of �2, it is easy to make the algorithm generate are converted into integers), which ensures that our �- only nondominated points for the School Problem: for each constraint method cannot miss any efcient solution for the generated nondominated point �,weaddthefollowing cumulative distance problem. Furthermore, one can check constraint to the problem: � �=(�,� ) that, for any feasible solution of value 1 2 ,themean � � distance for people in category � is ∑∑ ((� − �2).� �� −�1)ℎ�.�� ≤−1 (21) � � �=1�=1 1 = 1 ∑� ℎ .� �−� (19) �=1 � �� 2 Constraint (21) (which has only integer coefcients) �=∑� ℎ �=� ℎ =1 � ensures that any subsequent solution has a mean distance where �=1 �.Especially if � for all strictly less than the previous one. Including this constraint, (Unitary Problem). Hence, any efcient solution for the mean Algorithm 1 computes the Pareto front for the School Prob- distance problem is also an efcient solution of the cumula- lem. tive distance problem.

Teorem 1. Let � be a feasible solution for SP(associated with 5. Heuristic Problem Solving point �=(�1,�2) in objective space), such that it is efcient for � mean distance optimization, i.e., for each feasible solution � MOO problems search spaces are ofen intractably large � (point � ): [15].Manyheuristicshavebeendevelopedforsearchingover huge spaces, particularly using Evolutionary Multiobjective � �� Algorithms (EMOA). Genetic algorithms have been shown to 1 ≤ 1 � be interesting for solving very large instances of the �-median �−�2 �−�2 (20) problem in [24]. We investigate the extension of this work to � or �2 ≤�2 the MOO case, focusing on chromosome-based EMOA. We investigate the use of two algorithms, NSGA2 and PAES. Ten � is efcient for cumulative distance optimization. NSGA2 is a reference algorithm in the EMOA feld, � and it compares positively to PAES for standard benchmark Proof. If �2 ≤�2, the result is straightforward. Otherwise, � � � problems [8]. But as stated below, NSGA2 (and many other �1/(� − �2)≤�1/(� − �2) and �−�2 <�−�2,which EMOAs) iterates onto a population of individuals (each of � implies �1 <�1. them represents a solution), producing eventually a large Advances in Operations Research 7 ofspring at each generation. Even if this is an advantage and crossover onto a binary representation of chromosomes when exploring the search space for building an interesting it generates internally. We also provide a penalty metric front,itcanbeverycostlywhenemployingsuchanalgorithm that helps NSGA2 discarding unfeasible solutions (penalizing for solving a problem with a costly evaluation function. duplicated schools). Te evaluation function can be intrinsically complicated We will see in the two next sections how to adapt those (e.g., physics simulation) or time costly because it runs a strategies for mixing the various approaches with a fast local local search within the neighborhood of the solution to be search technique inspired from �-mediansingleobjective evaluated. We have already applied PAES successfully for the literature. former reason in the feld of Real-Time Scheduling [25]. We have also used a local search technique for the single objective 5.2. Local Search Technique for MOO. Many heuristic meth- �-median problem in [24]. Tus our goal is to compare ods have been developed for the (single objective) �-median PAES coupled with a local search technique to the reference problem (see surveys [1, 2]). Variable neighborhood search algorithm NSGA2 for the MOO School Problem. [9] is very popular, coupled with fast evaluation techniques We frst present and compare shortly NSGA2 and PAES [1]. Tose techniques, based on precomputing of the 2 closest and then we detail our declination of both frameworks with schools for each demand node, allow updating the solution a local search technique for solving the School Problem. cost faster when modifying only partially the solution itself during the local search process: for each demand node, for a 5.1. PAES and NSGA2. In many evolutionary algorithms, given set of schools (solution), the distance to closest school a solution is represented by a set of parameters called (�1, the one that covers the demand node) and the second chromosome (or genotype). Te encoding of solutions (i.e., the closest school (�2) and its distance to the node are stored. We data structure of a chromosome) is specifc for each problem. use a neighborhood operator called hypermutation,inspired Several researchers have proposed genetic algorithms (GA) from [24]. Te neighborhood size is controlled by the number for solving the �-median problem [26, 27]. Most of them of modifed school nodes (seeds): the neighborhood of a use a classical string representation; i.e., each chromosome is solution, for a fxed number of seeds �, is defned by replacing represented by a single array of integers of length � embed- one by one each seed node by all of the possible other ding the index of the selected candidate nodes. As stated in candidate nodes; i.e., those that are not yet selected as school [24], we will use the same encoding, i.e., the chromosome nodes within the solution. Te solution cost can be updated represents the list of school nodes in our case. We add the faster, using the precomputed tables mentioned above: when � constraint that in all chromosomes no school is duplicated. aschool� is replaced by � , demand nodes covered by it Te initial population (or frst solution) of our algorithms is (�=�1) are now covered by their second closest school (�2), � generated by picking up distinct random candidate nodes, except if � is closer to them than �2. Objective functions are leading to feasible solutions. All the candidate nodes have the updatedaccordingtothecase.Wefxthenumberofseedsto sameprobabilitytobechosen. �=��(�,5)for a School Problem, to obtain a reasonable Both EMOA’s goals are to produce a front that preserves neighborhood size. Tis size is �.(� − �),with� the number diversity of solution objective values, with points that are of seeds, � the number of candidate nodes, and � the number numerous and spread well along PF and the accuracy of this of schools. front, with points that are close to PF.Withinapopulation Te neighborhood and associated evaluation techniques setofsolutions,bothPAESandNSGA2useacrowdingmetric aredevotedtothesingleobjective�-median problem. Tey for handling diversity: PAES by defning an adaptive grid over canbekeptwhenrunningtheMOOcase.However,evaluat- the objective space and counting points within each portion ing and comparing to current front multiple neighbors result- of the grid and NSGA2 by measuring the distance between ing from multiple function evaluations could be very time points and their closest neighbor in each direction for each consuming: evaluation itself can be costly if applied to a large objective. To ensure accuracy, both algorithms embed an number of neighbors, and these numerous solutions must by elitism mechanism: the number of solutions that are kept compared against existing population or archive, with a dom- across generations (elitism) is given either by the population inance checking procedure. Tus, we propose an approach size (NSGA2) or by an external archive (PAES). Tis size also where the neighborhood exploration is run with a single controls the number aspect of diversity. In order to increase objective metric and only the most interesting solutions accuracy of solutions and convergence to PF,PAESuses found during the local search are compared to the current dominance locally, comparing current solution to a single of- solutions kept in population or archive. Tis algorithm is out- spring at each generation, while NSGA2 sorts its population lined in Algorithm 2. We transform, for the local exploration, into dominance classes. PAES eventually updates its archive the 2 objectives metric of the School Problem into a single with the ofspring, while NSGA2 renews its population by one by a classical aggregation technique: weights are given to generating a series of ofsprings at each generation, with a objectives and �� =�.�1 +(1−�).�2 is computed. �1 and dominanceclassbasedselection.Withbothalgorithms,when �2 are normalized values (according to the objective vector of comparing solutions, if they are nondominated against each the neighborhood search starting point). �� is evaluated other,thecrowdingmetricisusedtotiethem.Concerning for diferent values of � in order to explore the objective space the operators used for generating ofspring, we have imple- into diferent directions (e.g., {0.0, 0.25, 0.50, 0.75, 1.0}). Since mented a specifc mutation operator that preserves feasibility � is restricted to a few values, only a subset of the supported within PAES and NSGA2 applies standard binary mutation solutions can be found and of course unsupported ones 8 Advances in Operations Research

Data: a solution �� (set of � school nodes) to be evaluated, �, � (number of candidates nodes and schools), a set �� of � directions, a number of seeds � Result: aset�� of � solutions begin foreach �∈��do ��[�] := (−, ∞) { (��, V��) couples } end (�1,�2):=evaluate(��) choose randomly a subset �� ⊂ �� of size |��| = � foreach school � ∈ �� do � � foreach neighbor �� =��∪{� ∉��}\{�}do � � � (�1,�2):=fastEvaluate(�� ) {based on �� and (�1,�2)} foreach �∈��do � � V := �1.� + �2.(1 − �) if V < value(��[�]) then ��[�] := (��, V) end end end �� := 0 foreach �∈��do �� := �� ∪ {��(��[�])} end end

Algorithm 2: A local search method for supported solutions in � directions.

cannot be detected by the local search [28]. For each direction (i) Applying the local search for each individual: the searched, only the best solution (i.e., with the minimal �� ofspring of an individual is generated via the local value for the associated � weight) into the neighborhood is search procedure, with � directions of search. provided as a result at the end of the local exploration process. (ii) Using the local search as a refnement step: applying Tis approach can be related to the decomposition techniques local search to the members of the population or used in algorithms like MOEA/D [29]. archive obtained as a postprocessing step.

5.2.1. Cost of Evaluation. Te grain of the search is tuned by NSGA2 processes natively multiple ofsprings, but the � thenumberofseeds , leading to a neighborhood of size original PAES manipulates a single current solution and a �.(� − �) � ,andalsobythenumber of diferent values for single ofspring (it is a (1 + 1) procedure) that replaces (or � � .Let by the cost of a (standard) evaluation of a solution. It not) the current solution at next generation, depending on mainly consists of fnding the closest school for each children (1 + 1) 2 dominance checking. In the frst way of mixing, a and is in �(�.� .�). Evaluating a series of neighbors for a algorithm such as PAES must be adapted. Knowles proposes 2 neighborhood of (�.(�−�))costs�(�.(�−�).� .�),alsostated such a (1 + �) versionin[7].Weuseinsteadthesameselec- as �� = �(�.(� − �).�).Duringthe(fast)evaluationofa tion mechanism as in [30], developed for costly functions solution as a neighbor of another one, only a single school coupling with PAES and well adapted in the context of an is modifed and only the distances to school for its covered hybrid method combining EMOA with (time costly) local nodes are to be updated, in �(�/�) time. Tus evaluating a search. Te selection procedure is as follows: the � ofsprings � whole neighborhood takes �� = �(� + �.�.(� − �).�/�),with resulting from the local search are compared to the PAES 2 roughly, a �.� factor of gain as compared to ��. archive using PAES policy. Ten, the new current solution is chosen considering the whole archive as follows, based on 5.3. Mixing the Local Search Technique with EMOA Algo- a randomly selected optimization criteria: a random integer rithms. Tis local exploration procedure can be mixed with � in the interval [1..3] is generated. If it corresponds to an the diferent EMOAs into 2 diferent ways: objective function (i.e., � ∈ [1..2]), these criteria are chosen; Advances in Operations Research 9

Table 1: Number of candidate nodes � and school nodes � for the We compute the � threshold in such a way that 15% of the 40 test-cases of the Beasley benchmark. distances between nodes are lower than �. Te largest graph of this benchmark has 900 candidate #n p# n p # n p # n p nodes and is not particularly large according to the size 1 100 5 11 300 5 21 500 5 31 700 5 of problems current �-mediansolverscanmanage(e.g., 2 100 10 12 300 10 22 500 10 32 700 10 instances of up to 24,978 nodes solved exactly in [4]). 3 100 10 13 300 30 23 500 50 33 700 70 However, multiple objective optimization could lead to much 4 100 20 14 300 60 24 500 100 34 700 140 more costly evaluation of the solution space for the same 5 100 33 15 300 100 25 500 167 35 800 5 instances as compared to single-objective formulations, and 6 200 5 16 400 5 26 600 5 36 800 10 Beasley benchmark contains large enough instances for our 7 200 10 17 400 10 27 600 10 37 800 80 purpose, as execution times will show. It is also comparable � 8 200 20 18 400 40 28 600 60 38 900 5 to other biobjective -median problem instances used with others approaches (e.g., 402 nodes for the largest instance in 9 200 40 19 400 80 29 600 120 39 900 10 [13]). 10 200 67 20 400 133 30 600 200 40 900 90 (b) Algorithms Setup. Te exact method has been implemented in C. It is a modifed version of the AIRA sofware, �=3 otherwise ( ) the crowding criteria is selected. Te next a general purpose MOIP solver [33], and it uses CPLEX current individual is chosen randomly within the 10% best solver 12.3 as IP solver sofware [21]. As heuristic, we use the ones within the archive for the elected criteria. Concerning version of NSGA2 provided by Deb at [34], with the following crowding, the best individuals are those in the less crowded parameters: a population size of 100, and 500 generations. We areas of the grid. also use our own implementation of PAES, based on the C Tegoaloftheapproachistosolvelargesizeproblems version provided by J. Knowles at [35]. Te depth parameter with a high execution time cost induced by evaluation and of the algorithm is used to defne the grain of the grid used proportionally a small amount of time devoted to EMOA formeasuringthecrowdingoftheobjectivespacebythe internal computations. So we consider here that the cost of members of the PAES archive. It defnes the number of recur- choosing next current individual by processing the whole sive subdivisions of the range of values for each objective. archive is not a drawback for execution times according to Itissetto4,accordingtoPAESrecommendationsforsome the beneft in terms of quality of search that we expect. biobjective problems. Te archive size for PAES is of 100 and the number of generations of 1000. Te parameters for the 6. Algorithms Comparison localsearchare�=5(numberofdirectionsforsearch), corresponding to � ∈ {0.00, 0.25, 0.50, 0.75, 1.00} and �= Te multimode transportation problem or School Problem to ��(�, 5) = 5 for the number of seeds, since � is always be solved is specifc, and to our knowledge, no comparable greater than 5 for the Beasley benchmark test-cases (see algorithm exists for solving it (see Section 2). Tus, this Table 1). Tose parameters have been set in order to equi- evaluation section mainly compares the heuristic approaches � librate the computational efort of the diferent algorithms, that we have developed to our customized -constraint as execution times comparison will show. Tey lead to 1000 method. Te following algorithms are compared: (resp. 50.000) standard evaluations and 25.000×(� − �) (resp. 2.500×(�−�))fastevaluationsforhybridPAES(resp.hybrid (i) Exact: the �-constraint method presented in Sec- PF NSGA2) (see Section 5.2). All of the tests are performed onto tion 4, which provides the exact Pareto Front , a 48 processors (Xeon E5 at 2.2GHz) SMP machine, with (ii) EMOA approaches presented in Section 5, using 132GB of memory, and running Linux CentOS. NSGA2 and PAES algorithms. For both EMOAs, the standard and the hybrid versions tested: local (c) Quality Evaluation Procedure.Tesetsofsolutionspro- search realized at each generation with PAES and as videdbythealgorithmsaretobecomparedqualitatively. a postprocessing step for NSGA2. Many metrics exist [28] that must take into account both the quality of solutions obtained (accuracy) and their number We frst describe the benchmark set used for comparing andlocationalongtheParetofrontrange(diversity).Te algorithms results, detail algorithms setup, and then present hypervolume(HV)[10]isofenusedtocompare2setsof results for both quality and execution time aspects. solutions ��1 and ��2. It computes the area defned by each set; according to a reference point dominated by all (a) Data Set.TedatasetusedfortheevaluationistheBeasley of the points in the sets, the highest value is the best one. benchmark set, devoted to the �-median problem [11] and Figure 1 illustrates the comparison by HV for 2 fronts, with widely used for testing �-median solvers [26, 31, 32]. It is a set two objective functions �1 and �2 to be minimized. of 40 test-cases. Candidate and demand nodes are identical, For each test-case, we run each algorithm in competition with a unitary demand at each node. � (the number of nodes) 30 times. We collect all of the resulting individuals and com- varies from 100 to 900 and � value from 5 to 200. Test- pute the associated nondominated front. Tis front’s bounds cases are ordered by increasing � value and, for a given �,by on objectives are then computed and used for normalizing increasing � value as shown in Table 1. the objective vectors associated with the individuals into the 10 Advances in Operations Research

1.2 reference point (2.1, 2.1) Ｇ；Ｒ1 1 2.0 0.8

front1 0.6 1 f

hypervolume 0.4

values for front normalized 0.2 2 fronts ＧＣＨ1 1.0 0 ＧＣＨ2 Ｇ；Ｒ2 1 5 10 15 20 25 30 35 40 1.0 2.0 f2 Beasley test-cases

Hypervolume1 PAES NSGA2 Exact Hypervolume2 hybrid PAES hybrid NSGA2

Figure 1: Hypervolume (here an area, for 2 objective functions) for 2 Figure 2: Average compared quality of the solution obtained by the fronts (inspired from [36]). Objective functions are to be minimized. diferent algorithms for 30 runs on the 40 Beasley benchmark test- cases (10 frst ones for the Exact method). Quality of a solution is expressed as its hypervolume. range [1, 2].Tepoint(2.1, 2.1) is thus dominated by all of the vectors and can be used for computing hypervolumes (see values in Figure 1), leading to a maximal possible HV of from the resulting mean values 5 test-cases (#20, #24, #25, 2 (1.1) = 1.21,ifasingleobjectivevectordominatesallofthe #30, and #34): for those ones, NSGA2 (and thus also hybrid others. We provide results for each algorithm and also make NSGA2) does not provide any feasible solution for at least 5 a statistical analysis with the Kruskal-Wallis nonparametric runs (all runs for #30). Tis is due to the fact that unfeasibility test [37], for comparing the quality value series obtained by corresponds to duplicated schools in solutions, and this can running each algorithm 30 times for a given test-case: if and arise with a higher probability when � increases. For the only if a frst test for signifcance of any diferences between discarded test-cases, � is between 100 and 200 (see Table 1). the samples is passed (H0 hypothesis), at a given confdence Statistics are thus calculated over the 35 remaining test-cases. value (we use the standard 0.05 value), then the output will Figure 2 shows the average values of hypervolumes for be the one-tailored p values for rejecting a null hypothesis of the diferent algorithms in competition. On average over no signifcant diference between two samples, for each pair- the runs for the 40 test-cases, hybrid PAES provides the best wise combination. If the p value for a test-case is less than results for all test-cases, when considering only EMOAs. 0.05, we considerate that one algorithm beats the other for Itoutperforms,respectively,PAESof24.9%,NSGA2of this test-case with a sufcient confdence. On the contrary, if 58.7%,andhybridNSGA2of48.0%onaverage.Forthe10 series are not diferent enough, or the p value obtained for test-cases for which exact solution is known, it provides a characterizing the diferences is over 0.05, the test-case is not front with an HV that is, on average, at 7% of the optimal taken into account for comparing the couple of algorithms. one. Clearly, the generic NSGA2 framework do not allow to obtain good results, as compared to the specialization 6.1. Hypervolumes Comparison. We compare the hypervol- of PAES for the School Problem: within NSGA2 version, umes obtained for 5 algorithms: the only specifc component is the objective function, with (i) the Exact algorithm described in Section 4. Te 10 nonspecialized mutation and crossover operators that can frst test-cases of the Beasley benchmark can be solved lead to unfeasible solutions. Tis is managed with NSGA2 in less than 1 hour with this method, providing a by constraints penalties, but, unfortunately, this mechanism reference front for comparison with heuristics for this does not allow an efcient search of the feasible solution subset of the Beasley benchmark. space. As a symptom, the size of the fronts provided by the NSGA2 algorithm is on average 68% less that those found by (ii) the PAES algorithm, with our selection method, but hybrid PAES (63% less for hybrid NSGA2). It is 49% when without local search. comparing PAES and hybrid PAES, showing that local search (iii) the hybrid PAES algorithm, embedding local search at efectively helps in discovering nondominated solutions. Te each generation. result is that local search allows improving results: hybrid (iv) the NSGA2 algorithm, PAES outperforms PAES by 24.9% and the local search by hybrid NSGA2 allows improving NSGA2 results in terms of (v) and the hybrid NSGA2 algorithm, using the local HV by 32.7% on average. Te latter is very signifcant, for search as a postoptimization method a single local search phase, but the improvement is realized All the heuristics are applied onto the whole benchmark, on the (relatively to hybrid PAES) poor results obtained with with parameters as previously described. We have removed NSGA2, which leads room for optimization. Advances in Operations Research 11

Table 2: Number of test-cases, over the 40 test-cases of the Beasley NSGA2 versions, �� = 1000 for PAES and its hybrid benchmark, for which the Kruskal-Wallis nonparametric test vali- version). Tose parameters allow for exhibition experimen- dates the hypothesis that EMOAs beat each other for hypervolume. tally that execution times of tested algorithms depend on a combination of � and � (as shown in Section 5.2). Reminding beats ↱ PAES hybrid PAES NSGA2 hybrid NSGA2 the characteristics of the problems in Table 1, NSGA2 (and the PAES - 0 35 32 hybrid version) beats hybrid PAES for � values of 5 and 10 hybrid PAES 39 - 38 36 if the number of nodes � ≤ 200, and hybrid PAES is faster NSGA2 0 0 - 0 in the other cases. Furthermore, NSGA2 execution times hybrid NSGA2 7 1 39 - are positively correlated to the chromosome size for genetic operations, i.e., to the value of � (e.g., � = 100 for instances 60 1to5,with� from 5 to 33). Te decreasing steps in curve for the hybrid PAES correspond also to the increasing values of 50 �, for a fxed number of nodes (e.g., � = 600 for instances 26 to 30), but with the inverse efect as the one depicted for 40 NSGA2. Concerning hybrid PAES, for the local search, the number of seeds � is fxed (see Section 5.2), the number of �−� 30 alternatives for each seed is of ( ), leading to a size of �.(� − �) for the neighborhood. Tus, the more the � value, 20 the smaller the neighborhood. times in seconds (a) Parallelization. Hybrid PAES is promising in terms of 10 quality as compared to (hybrid) NSGA2 but time consuming as compared to PAES. We have implemented a master-slave 0 1 5 10 15 20 25 30 35 40 scheme for realizing the evaluation and local search in parallel Beasley test-cases for diferent individuals, inspired from [30]. Parallel hybrid PAES implementation (in C) uses multiple threads (one per PAES NSGA2 slave plus one for the master process). Te OS scheduler hybrid PAES hybrid NSGA2 allocateseachofthemtoacoreifthenumberofcoresis sufcient. Figure 4 shows the speedups Figure 3: Compared mean execution times (30 runs) for diferent algorithms on the Beasley benchmark. Exact algorithms execution exec. time parallel hybrid PAES with 1 slave (22) times, not presented, range from hours. exec. time parallel hybrid PAES with X slaves obtained when running the algorithm with more than one slave (and thus more than 2 cores) for the evaluation and Table 2 assesses the confdence that can be given when localsearchofindividuals.Teexecutiontimesareobtained comparing those mean results, by applying the Kruskal- using a 48 cores SMP system, ensuring that each slave (and Wallis nonparametric test to the hypervolume series. Even themaster)isrunonaseparatecore.Inordertoincreasethe if hybrid PAES always provides mean HV values better than computational efort, the number of generations is set to 5000 other EMOAs in competition, this is not completely assessed instead of 1000 in previous tests. by the statistical test for all of them; e.g., hybrid PAES beats Clearly, adding computing resources helps in speeding hybrid NSGA2 36 times only with the defned confdence of up the computations and especially when the computational 0.05. Tis can be explained by the closeness of the results efort is high (last test-cases). Te average speedup is 1.89 in some cases: for example, for test-case #6, mean HV is of (resp. 3.76, 7.48, 14.07, and 18.10) for 2 (resp. 4, 8, 16, and 32) 0.4061 for hybrid PAES and 0.3937 for hybrid NSGA2, with slaves. Speedups look linear according to the number of slaves respective standard deviation of 0.002 and 0.030, meaning forupto8slaves.Classically,thecostoftheparallelization that result values of the two algorithms overlap. is due to the bottleneck in communications induced by the master-slave scheme and also to parallelization itself: for 6.2. Execution Times. Average execution times of the difer- example, for test-case #35, the sequential version of hybrid ent heuristic approaches are depicted in Figure 3 for test-cases PAES runs in 29 seconds for 1000 runs (see Figure 3) and of Figure 2. theparallelversion,withasingleslave,runsin273seconds PAES algorithm runs in less than a second for all of the for 5000 generations (instead of expected 29 seconds × 5= test-cases, thanks to the single evaluation at each generation. 145 seconds). Te communication bottleneck degrades the Because of the local search executed only as a postprocessing speedupfor16slaves,butexecutiontimesarestillimproved step, hybrid NSGA2 execution time is very close to NSGA2’s in all cases as compared to 8 slaves version, except for test- one, with a local search realized, on average, in 1.62 seconds case #5 (average speedup of 14.07). But for 32 slaves, the for the 100 individuals of the population. One can see that improvement of speedup is very limited (18.10 on average). thesameorderofcomputationaleforthasbeenusedforthe Aswefndagainthesamestepsshapeoncurvesasthose diferent algorithms, by tuning population size and number observed in Figure 3 for sequential times, with roughly higher of generations (�� = 100 and �� = 500 for speedups for the most costly test-cases, it is possible that the 12 Advances in Operations Research

20 master-slave scheme. Te speedup of the algorithm is linear for up to 8 slaves, close to 14 for 16 slaves, but degrades with more slaves (speedup is only 18.2 for 32 slaves). We think 16 that this limitation on the parallelization degree is due to the grain of parallelism induced by the data and the algorithm’s setup for the experiments and that it will not hold for larger instances. We plan to apply it to real data, as realized in speedup 8 [24] for single objective �-median problems, dealing with country-scale instances, with nonuniform population distri- 4 bution. Tis is important because real problems may exhibit particularities in their data. Another direction of research is 2 to add a third objective function, related to facility implan- 1 5 10 15 20 25 30 35 40 tation costs, with a relaxation of the number of facilities (� Beasley test-cases becomesaboundinsteadofafxedvalue).Tiseconomiccost parallel hybrid PAES 1 slave 8 slaves is useful, for example, in disasters management. 2 slaves 16 slaves 4 slaves 32 slaves Conflicts of Interest Figure 4: Speedups obtained with up to 32 slaves for hybrid PAES Te authors declare that there is are conficts of interest on the Beasley benchmark. regarding the publication of this article.

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Research Article Integration between Transport Models and Cost-Benefit Analysis to Support Decision-Making Practices: Two Applications in Northern Italy

Paolo Beria ,1 Alberto Bertolin ,1 and Raffaele Grimaldi 2

1 DAStU, Politecnico di Milano, Via Bonardi 3, 20133 Milano, Italy 2Independent Researcher, Milano, Italy

Correspondence should be addressed to Alberto Bertolin; [email protected]

Received 22 December 2017; Accepted 18 March 2018; Published 23 May 2018

Academic Editor: Marta Bottero

Copyright © 2018 Paolo Beria et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Decisions on transport plans and projects involve relevant public investments and may also determine radical changes in users’ costs. Unfortunately, it is not rare that—especially at the strategic planning stage—decisions on alternative projects or scenarios are made on a qualitative basis or, at best, by setting some indicators and verifying how much they reach the politically decided targets (e.g., “increasing the use of bicycles by 10%”). In order to reduce subjectivity, a more quantitative and comprehensive approach to the evaluation is needed. A Cost-Beneft Analysis is a tool commonly used to assess public expenditure, but its application to mobility plans introduces further practical and theoretical complexities. In this paper, we will thus try to contribute to the topic of the assessment of both sustainable mobility transport plans and infrastructure projects by presenting the operative application of a CBA methodology that is, at the same time, theoretically coherent and rich in outputs to support the decision-maker. Moreover, we will discuss the possible use of GIS sofware in order to provide to the decision-makers a clear and immediate “picture” of the efects on the network linked to diferent scenarios. Te structure is as follows. Firstly, we discuss the complexities involved in the evaluation of plans with respect to a single infrastructure. Secondly, we introduce the available approaches for the assessment of consumer surplus, namely, the Rule of Half and the logsum function method, which allow the perfect integration between CBA and transport models. Tirdly, we present, through some operative case studies, the methodologies applied to the assessment and the network efects visualization of the urban mobility plan and new infrastructures. Finally, we underline how we can make the results more understandable to politicians, policy-makers, stakeholders, and citizens and in general improve the transparency and the awareness of the choices.

1. Introduction: Evaluating Transport Plans the promotion of city walkability, the development of bike and Infrastructural Projects transport, road pricing, park pricing, technological investments on networks, vehicles, and communications, smart Modern transport plans try to achieve diferent objectives mobility, vehicle sharing projects, incentives, redefnition of and, in general, try to obtain a more sustainable and inclusive fares structure, mobility credits, and so on. [1, 3, 4]. transport system, as suggested by the recent European Sus- When performing the evaluation of such complex plans, tainable Urban Mobility Plans (SUMPs) guidelines [1]. Tis is a mismatch occurs between the available assessment tech- usually done by foreseeing, simultaneously, the improvement niques and the contents and expectations of plans. In fact, of existing transport services and infrastructure, together the economic evaluation of transport investments is usually with the implementation of sustainable mobility policies. intended in terms of assessment of transport infrastruc- Tisalsoallowstakingadvantageofthebeneftsofpolicy ture, while plans include a broader range of actions, where packaging in terms of higher acceptability, efectiveness, and expected environmental and social impact can play a domi- efciency [2]. Among the available policies, we can recall nant role in policy evaluation [5]. 2 Advances in Operations Research

Table 1: Policy actions in a mobility plan and type of efect.

Investment costs are dominant versus Action/policy Costs Benefts other costs? New infrastructure (public transport, roads PU,T pr,C,t Yes capacity) New/modifed services on existing PU,t pr,d,t No infrastructure Innovative mobility (sharing, pooling, etc.) pr, d, t No Bicyclelanes,bikeparking,bikesharing PU,T pr,d,t Yes/No ITS, trafc management PU, t pr, d, t No Restrictive policies, car-free zones, trafc pr,d,t d,t No calming Parkandroadpricing pr,d,t PU,pr,d,t No Public transport fares PU/pr, d, t Pr/PU, d, t No PU: public bodies; pr: private users; C: concentrated in space or limited to groups; d: difused in space or spread among many users; T: punctual in time, lump sum; t: continuous in time.

Te mismatch lies also in the evaluation tools commonly which may be included and assessed in a complex urban used to support the design of mobility plans and the conse- mobility plan. quent public decisions, which are substantially referable to In plans, additive policies, such as new infrastructures whose costs are public and concentrated in time, coexist with (i) Traditional Cost-Beneft Analysis (CBA), required restrictive policies, such as trafc calming, pricing, and so on, practically everywhere to allocate public money for which changes mobility patterns through raising the private infrastructure investments, that is, in cases where costs. Tese two extremes must be assessed in a coherent way, thepublicdecisionisdominatedbythealternative but their efects and economic mechanisms are substantially allocation of lump sums [6–8]; diferent. (ii) Multicriteria analyses (MCA) and Indicators-based Moreover, the efects act synergistically, so that modal assessments, used to structure and clarify the goals shif is the efect of both the improvement of the destination and the (possibly positive) efects of the actions of a mode (e.g., public transport) and the worsening of the origin plan, such as the foreseen decrease in car ownership mode (e.g., private road transport). When the existence of or pollutants concentrations [9, 10]. such complex cost and beneft structures in the assessment In the assessment of a plan made of both “hard” (infras- of plans or projects is recognised, theoretical and practical tructural) investments and “sof” policies, both traditional problems may arise. As already mentioned, approaches using approaches may fail. In particular, a rigid CBA may not only indicators and MCA are not satisfactory for evaluating be able to catch all the efects of the plan [7, 8, 11, 12] the trade-ofs of public expenditure. At the same time, CBA in and, in addition, provides too concise outputs to support the “simple” form, as suggested by numerous guidelines (e.g., the dialogue with public opinion and stakeholders [13]. On [16, 17]), is not sufciently complex to handle the previously the other side, indicators and MCA are, by defnition, not mentioned problems and, in addition, fails in efectively able to measure the efciency of public expenditure, which representing the distribution of efects [18], especially for represents a key element of public decisions [7, 8]. Some non-win-win policies. EU members state that, in order to include nonmonetized Lastly, especially when CBAs are implemented to inves- impacts in infrastructure projects or policy evaluation, they tigate complex transport scenarios, problems can arise from optedforMCAinwhichaCBAiscontained[14,15]. the imbalance between expert knowledge and various stake- Moreover, one must consider that the “typical” scheme holders’ expectations on their “pet-projects” [13]. In order to of lump sum public costs versus distributed private benefts promote a constructive dialogue in the decision-making pro- is not always the case, especially with pricing or limitation cess, not only must CBAs be rigorous from a methodological policies. In these cases, the policy gives both advantages to point of view, but also their fnal and, possibly, intermediate some groups (e.g., public transport users) and disadvantages resultshavetobebothintuitiveandefectiveforageneral to others (e.g., car drivers), in some cases entailing no audience. signifcant public expenditure. A decision on this kind of For such reasons, in this paper, we will contribute to the policy, which is not simply “adding” new transport supply topic of decision-making for complex plans and projects in a for someone, should obviously take into account not only the threefold way: benefts, but also the public and the private costs necessary to (a)Howtomanagetheconsumersurplusfromatheoret- obtain them. ical viewpoint. While theoretical literature on meth- Table 1 provides an example of possible policy actions, ods is mature and clear, it does not appear helpful with diferent spatial and time boundaries of their efects, from the point of view of practical applications. On Advances in Operations Research 3

the other side, guidelines are ofen too simplistic to handle complex problems, or even misleading. (b) How to practically calculate the consumer surplus for both a mobility plan and an infrastructural project ＃＇1 basedontransportmodeloutputs. C (c) How to enrich the outputs of the evaluation in order to make the assessment useful to inform decision- makers’ choices. ＃＇2 Tepaperisstructuredasfollows.Section2discussesthe two correct ways to calculate consumer surplus, the Rule of Q Q Half and the logsum function method, underlining both their 1 2 Q pros and cons and in which situations they are recommended. Section 3 illustrates how these two methods can be calculated, Figure 1: Representation of the Rule of Half (our elaboration). in practice, by means of a transport simulation model, and how to modify the general formula when an active mode is included in simulations. Section 4 presents two evaluation cases: Milan’s Sustainable Urban Mobility Plan and the Milan Malpensa airport rail ring closure. Section 5 associates with his overall trip experience, including out-of- concludes. pocket expenses (tolls and fares), operating costs of vehicles (in private transport), and consumed time. Other factors like discomfort, crowding, landscape, and more personal atti- 2. Calculating the Consumer Surplus tudes can also reduce or increase the GC of the same trip for CBA is a widely used and codifed technique. Te transforma- diferent users (in the paper, we refer to the calculation of user tion into monetary values of the majority of variables taken surplus in terms of perceived (or private) costs, which—as intoaccountintheanalysiscanbedoneinanintuitiveway we discussed in a former working paper [20]—requires some (investment costs, running costs, environmental benefts, corrections to balance transfers (e.g., taxes and fares) among taxation, etc.; see, e.g., [16, 17]), but we cannot say the same diferent parts of society; another relatively widespread for the consumer surplus. Tis component, especially when approach, especially when the GC comparison is used, is to related to complex plans, may be misleading and concurring calculate the variation in user surplus directly in terms of in the introduction of double counts or internal incoherencies social costs; the considerations made in this paper remain [19, 20]. valid). Many guidelines indicate three possible approaches to Tus, intuitively, the variation between the GC before and estimate the consumer surplus. In practice, their application afer a project or policy implementation will return the gain is seldom discussed and the responsibility to choose among or loss in beneft (surplus) for a specifc user even when he them is lef to technicians. For example, in Italy the guideline shifs between diferent means of transport. provided by the Ministry of Transport [21] does not suggest Unfortunately, information on the single user trip expe- the application of a specifc method to calculate user surplus, rience is not always available. More realistically, when avail- while the Lombardy Region guidelines defne the Rule of Half able, we can use a transport model to obtain the average method as mandatory to evaluate infrastructural projects generalised costs of groups of users (see Section 3), also in [22]. Nevertheless, the three methods return results that are a very detailed way. Te problem that arises is how to treat not always comparable. In particular, the simplest approach, shifing users knowing only the GC average value and the the generalised costs comparison, has results that are ade- total quantity of users in each group. quate only under very specifc and seldom-present conditions Traditionally, the most robust and used method to calcu- [23]. Te other two methods ensure a diferent level of late the variations in user surplus when a transport model is robustness and precision and require diferent amounts of not available is to hypothesize the unknown demand curve as data but can both be suited to almost any application. In the a linear function between two points. Tese points, which are following, we will illustrate these two latter methods, and we always known, are codifed by the intersection between GCs will underline when they are almost perfectly substitutable and the total amount of users (�) before and afer the project and when; on the contrary, we can expect considerably implementation [16, 19, 20]. diferent outputs. Tis hypothesis allows the application of the so-called Rule of Half. Te area of the rectangle having base �1 2.1. Te Rule of Half (RoH) Method. Te consumer surplus (the number of existing users) and height GC1 − GC2 (the is defned as the diference between user willingness to pay reduction in generalised costs, that is, the unit beneft) to make a specifc trip and the “price payed” to make it represents the surplus variation of existing users. Similarly, [24]. In transport, the “payed price” by each user to make thesurplusofgeneratedorshifedusersisgivenbythearea a specifc trip is codifed in the so-called generalised cost of the triangle having base �2 −�1 (the number of new users) (GC). Te GC represents the monetary value that the user and the same height GC1 − GC2 (Figure 1). 4 Advances in Operations Research

Te variation in user surplus is thus given by the area of a used in calibration) for the users travelling for the purpose trapezius as in (1) (hence the name “of half”): group [�].

� ⋅ 1 � � GCod|�|� Δ� =(�)×( − )+ (� −� ) users 1 GC1 GC2 2 1 � |�|� = . (2) 2 od ��⋅GC |�|� ∑� � od ×( − ) GC1 GC2 (1) Tus, the unitary surplus variation is equal to the diference 1 in the composite utility (given by the logarithm of the denom- Δ� = (� +� )×( − ). users 2 1 2 GC1 GC2 inator of the logit formula (thus the name, “logsum”), divided by the calibration parameter), before and afer projects and/or Due to its simplicity and the relatively reduced amount of policies implementation. Once we multiply this unitary value data needed in the formula, this approach is very widespread. for the number of trips related to each single purpose, we Any other method requires both estimating the GCs’ absolute obtain the user surplus variation linked with that trip purpose values, a much more difcult task, and knowing the GC [Δ�] [25, 28–30] (Bates [31] states that “with a logit model, of “origin” modes (the estimation of the absolute value of there is a closed form solution for the integral under the demand generalised costs is not a simple exercise without a transport curve,” which is the surplus). model, especially in public transport and in active modes Δ� (walking and cycling); the related variation is instead usually od|� made only of easily measurable items, like time savings 1 and/or operating costs). = trips� ⋅ �� (3) Moreover, this method, by treating the whole of induced users (i.e., both generated and shifed from other modes, � ⋅ � ⋅ ⋅[(ln ∑ � � GC1,od|�|� )−(ln ∑ � � GC2,od|�|� )] . paths, time of the day, etc.) in the same way and not needing � � theabsolutevaluesoftheGCs,avoidsalltheproblems linked to the generalised costs comparison approach. Tese Tesumofthesevariationsforalltheusergroupsobviously problems are mainly determined by the impossibility of gives the total variation in consumer surplus associated with knowing the GC value for each single user [23]. the scheme or policy. If we expect generated demand to appear in the postpro- 2.2. Te Logsum Function Method. Te RoH assumes a ject scenario, and we want to keep using the logsum approach, certain distribution of users across average GCs. Depending Bates[31]suggestsapplyingtheRule of Half to the standard on the required level of detail (and, of course, on the available logsum formula (4): data), analysing, by disaggregating as much as possible users Δ� in homogenous groups (i.e., in terms of geography, trip od|� purpose, etc.) and applying the RoH to each group separately 1 1 = ⋅( + )⋅ can minimise the error equal to the distance between the trips1,� trips2,� 2 �� (4) single user GC and the average group value. Despite its methodology consistency, RoH returns an � ⋅ � ⋅ ⋅[(ln ∑ � � GC2,od|�|� )−(ln ∑ � � GC1,od|�|� )] . approximation of user surplus based on a “strong” prelimi- � � nary assumption: a linear distribution between demand and GCs. Despite being well-discussed in the literature quoted above, However, when a calibrated transport model is available, the logsum function method has been barely seen from an it is possible to use another method to assess the variation applicative point of view, when real projects and plans must in user surplus, which gives a much more detailed repre- be practically assessed. Te following part of this paper sentation of the benefts. By measuring, for all alternatives tries to go more deeply in this direction (a more detailed (modes), the variation in the composite utility (logsum) discussion on diferences between logsum and Rule of Half returned by the transport model, it is possible to calculate methods is presented in Mafi et al. [32], Cascetta [25], Geurs not only the average values of the GCs, but also their et al. [33], Grimaldi and Beria [20], and Bates [31]). implicit distribution among users, thus having a more precise variation in user surplus [25]. 3. Consistent Integration between Planning, Most transport models, in fact, estimate the share of users Modelling, and Assessment [�] that will choose a transport mode [�], on the origin- destination pair [od],forthetrippurpose[�],usingthe 3.1. Beneft from a Direct Integration of CBA and Transport multinomial logit formula described in (2) (if the model is Models. Te most complex aspect to model in a CBA is the based on a nested logit, this operation can be done on the demand curve and its relationship with the replaced assets frst (higher) level of the logit; the GC represents the disutility when generated demand is present. In the transport sector, of the trip) [26, 27]. Parameter [��] is a calibrated value the demand generated by a certain project is the sum of the that maximizes the probability that the expected (simulated) new demand induced by the lower transport cost (people who modal share is coherent with the observed value (real data now travel and who did not travel before, given their lower Advances in Operations Research 5 level of willingness to pay) and the demand attracted from is a way to overcome the issue, though with some loss of other means of transport. consistency (see, e.g., [34] or [29]). We divide the systematic Generally, transport problems are faced with four-stage utilitybythetimeparameter(whichisalwayspresent)instead multimodal models (guidelines from Lombardy Region [22, ofbythecostone,thusderivingageneralised time instead of p. 18] and the Italian Ministry of Transport [21, p. 30] defne the generalised cost. the use of multimodal transport models to evaluate infras- � od|�|� tructural projects as mandatory). Tese models allow both GT |�|� = . od �Time (7) the distribution of the existing and generated (induced and/or �|� attracted) demand between OD relations and, considering the relative generalised costs that determined the choices, the Ten we multiply this generalised time by an exogenous value calculation of users’ paths. of (in-vehicle) time (VoT), obtaining the generalised cost.

Within the four-stage models, the modal choice can GC |�|� = VoT ⋅ GT |�|�. (8) be assimilated to the application of a demand curve. A od od certain perceived cost (according to the CBA formulation) When the GCs are estimated, we can directly apply the or generalised cost (according to the modelling formulation), formulas of the surplus variation, discussed in Section 2. It corresponds to a certain quantity consumed. Terefore, the must be noticed that this passage is done at the highest level integration between models and CBAs allows greater preci- of disaggregation: per origin–destination pair (od),travel sion (ensured by the model) in determining the costs for all purpose (�), and mode (�). Tis is a computational burden, users on the entire network modelled (instead of considering involving even millions of operations if the study area is separately the users on specifc segments of the network) and divided into hundreds or thousands of zones, like in urban a perfect match between model and evaluation. or regional areas. However, this disaggregation allows for In conclusion, while without a model, the CBA must nec- enrichingthereadabilityandcompletenessofoutputs. essarily be based on rather strong assumptions (invariance of the demand or, in the case of demand generated or shifed, 3.3. Presenting the Results. In fact, a nonsecondary aspect assuming a linear trend for the demand curve); with a model, deals with the outputs of the analysis. Backing the surplus the descriptions of both demand and user surplus variation calculation methods with a calibrated model and working at will be much more detailed. Moreover, parameters such as the the origin–destination pair allows the representation of the value of time can be directly those of the calibrated model. benefts geographically, and not only in an aggregate way. Tis kind of representation may be a useful complement to the 3.2. Extracting Generalised Costs. When a transport model is aggregate CBA indicators (NPV, NBIR, B/C, IRR; [16]) both available, it is relatively easy to extract the GCs directly from in the consultation phase and, ultimately, in making better it, guaranteeing a complete consistency between the model decisions. and the following Cost-Beneft Analysis. Te GCs derived Indeed, the network efects visualization, thanks to a GIS this way can be used both with the Rule of Half and with the sofware, of a proposed project or policy allows for foreseeing logsum method. which parts of the territory (and, consequently, which citizen To obtain GCs, it is sufcient to extract the systematic groups)willgainorlosemoreifthatactiontakesplace. utilities used by the model, which is usually constructed like In the next section, we present the methodologies applied in (5)(with systematic utility � we mean, according to the for the assessment and network efects visualization of the defnition by Cascetta [25], “the mean or the expected value sustainable urban mobility plan of the Milan municipality of the utility perceived among all the users with the same (seeSection4.1)andtheproposedrailringoftheMalpensa choice context”; the perceived utility � is given by the sum airport (see Section 4.2). Due to their specifcities, for the of the systematic utility � and the random residual ¥ (which plan evaluation, we utilized the logsum method, which represents the deviation of the single user with respect to the assures that nonadditive policies do not bring the risk of average value): �=�+¥). double counts, and the RoH one for the rail project. � =�Time ⋅ +�Cost ⋅ od|�|� �|� Time �|� Cost (5) 4. Theory Application: Two Case Studies + . Other components 4.1. Milan’s Sustainable Urban Mobility Plan. For the assess- If we divide the systematic utility by the parameter related ment of the new Milan’s Sustainable Urban Mobility Plan to its monetary component, we express it in monetary terms [35] we interfaced the simulation model developed by the representing the monetary trade-of that users attribute to transport authority (AMAT), with the assessment procedure, their trips, which is the GC. based on the interaction between a database and spreadsheet sofware. Te transport model has been used extensively � = od|�|� . in the past years to plan all transport decisions in the city GCod|�|� Cost (6) ��|� and can rely on solid datasets of observations, used for the calibration. Not only CBA, but also Te Strategic Environ- Sometransportmodesmightnotbeassociatedwithany mental Assessment of Milan’s SUMP was based on the same direct monetary component (e.g., walking and cycling). Tere transport model outputs. However, these two evaluations 6 Advances in Operations Research

Tables of Attributes (generalised Multimodal transport Calculation of surplus time), of Quantities (users per model (AMAT) variations, total and mode) and of transfers (fares, etc.) per zone [SQL DB] estimated for each O/D couple

Map representation of surplus Tables of surplus variations, variations, of travel time and of time, and of quantities, per passengers [GIS] zone

＃＇1 C

＃＇2 Q Q Aggregated surplus variations 1 2 Tables of surplus variations, Q [Spreadsheet] of time, of quantities, total

Figure 2: Te assessment procedure implemented for the Milan’s Sustainable Urban Mobility Plan (SUMP).

difer for some assumptions on input data (e.g., CBA, in the parking tolls, the road pricing tolls, the driven km (useful the environmental efects calculation, considers, for the year to calculate the fuel duties paid). 2024, an equal distribution between the total number of Overall, the output consists of a database fle with Euro V and VI vehicles, while the latter defnes the vehicle’s tables of attributes (generalised time), quantities (amount feet starting from a regression model on gasoline sale of users), and transfers (fares, tolls, and taxes) per 390,452 trends). However, the overestimation “error” magnitude is origin–destination pairs and 24 (4 × 6) mode and travel contained and does not afect the overall CBA result [36, pag. purpose combinations. By means of SQL procedures, we 112]. estimated the surplus variation using the logsum method A schematic representation of the algorithm developed (as described in Section 2.2). It must be noticed that the for SUMP scenario’s assessment is depicted in Figure 2. corecalculationsaredoneatthehighestdisaggregationlevel, Te transport model provided the generalised cost com- that is, per OD pair, mode, and travel purpose. Later, we ponents of each origin–destination (OD) pair for fve difer- proceeded with the aggregation of the results in 829 origin ent travel purposes (plus the “back-to-home” purpose) and and destination zones, using the same zoning of the model. forfourmodes(car,motorbike,publictransport,andactive Te same thing has been done for all attributes, quantities, modes). Each segment of the simulated mobility is associated and transfers. with a set of calibrated � coefcients (5), including the values Once the aggregation is done, the datasets become more of time (per trip purpose and per mode). In addition, the manageable with other sofware programs. Te procedure is model provides the quantities, in terms of passengers/users then interfaced with a spreadsheet sofware for the CBA and during the peak hour, for every mode on each OD pair, with a GIS sofware to produce cartographical representa- allowing us to calculate the mode-shifing users. Finally, the tions of the main variables. model output also includes the data used to correct the Te entire process has been applied for 51 explorative sce- monetary transfers in the CBA, in particular the paid fares, narios. For this reason, we put particular care into automating Advances in Operations Research 7

COST BENEFIT ANALYSIS

ECONOMIC CBA FINANCIAL CBA

Investment and maintenance costs Investment and maintenance costs Running costs (& savings) Running costs (& savings) User benefts (cost & time savings, crowding Revenues from park and road pricing; fuel duties reduction, congestion reduction) Environmental benefts (local pollution, CO2, noise) Health benefts for active modes Safety benefts (& disbenefts) Revenues from park and road pricing; fuel duties Opportunity cost of public funds

+ DISTRIBUTIVE ANALYSIS + SENSITIVITY ANALYSIS

How C&B are distributed among users groups How CBA results change at the variation of some How C&B are distributed in space input parameters

Figure 3: Cost-Beneft Analysis components.

the procedure with scripts. At the same time, we track all the Table 2: SUMP explorative scenarios. intermediate results throughout every step to facilitate debug Number of subscenarios procedures. Some controls have been introduced intermedi- Explorative scenario (alternative options) ately to manually check the correctness of the results. Te Previous land use plan (PGT) processalsopointedoutsomelocalinconsistenciesofthe 3 transport model, which have been corrected. infrastructure Te CBA has been done within a spreadsheet sofware, in Metro line 1 extension 3 the two variants of Economic CBA and Financial CBA. Te Metro line 2 extension 5 elements included are listed in Figure 3, and the indicators Metro line 3 extension 3 calculated are the Net Present Value (NPV), the Net Beneft Metro line 4 extension 4 over Investment Ratio (NBIR), and the Beneft over Cost Metro line 5 extension 3 Ratio (B/C). In addition, we also developed in the same environment New Metro line 6 3 (explorative paths) the distributive analysis module (disaggregating the costs and Tram 7 extension 4 the benefts into six user categories, plus the nonusers, the Tram 24, 27, and 178 extensions 2 + 2 + 1 State, and the Local Administration) and a simple Sensitivity Reorganisation of tram lines in the city 1 Analysis, testing automatically the efects of user surplus centre estimation, investment cost, and running costs on results. New urban stations to support rail 7 Te CBA, shortly described here, was directly included in “circle line” services the planning process as suggested in European guidelines [1]. Change in a suburban rail line path 1 It is worth mentioning because this represents the frst case in Extensionofbikelanes 2 Italy. In fact, it was only in 2015 that the regional government, 30 km/h speed limit areas 1 within its guidelines, imposed the CBA as mandatory to assess transport projects [22] and, at the national level, this Road pricing (Area C) extension 4 Actions to increase commercial speed evaluation tool became compulsory one year later [21]. 2 of surface public transport 4.1.1. Scenarios. In a preliminary phase, planners, stakeholders, and politicians selected, among all the actions included in previous planning documents and/or indicated by citizens, 51 30 km/h speed limit areas). Table 2 provides an overview of explorative scenarios to be assessed via CBA. Tis preselec- all the scenarios considered in the analysis. tion was carried out by choosing, according to the political Te aim of this explorative evaluation was to identify goals,themostefectivealternativebetweencomparable those actions that returned positive CBA indicators or, in projects facing a single problem. case of negative performances, under which conditions it was Te selected policies and projects were heterogeneous possible to reduce their negative socioeconomic impact. For in nature, from heavy infrastructural investment (i.e., new example, in the case of the 30 km/h speed limit areas, negative metro lines) to punctual trafc calming solutions (i.e., indicators were returned when this action was assessed alone. 8 Advances in Operations Research

Figure 4: An example of Appraisal Summary Table organisation.

Tis intermediate result was a consequence of the reduction To do that, all the intermediate and fnal results of the in road capacity and, consequently, an increase in congestion scenarios were presented through the following outputs. and travel time for private vehicle users. However, the same (i) An Appraisal Summary Table,directlyinspiredbythe policy, evaluated in combination with other actions aimed at ones used in the UK [37] promoting a modal shif in favour of public transport, was associated with a positive impact in terms of user surplus. (ii) A Book of Maps, visualizing on a cartographic basis At the end of this explorative phase, all positively assessed the efects of the hypothesis on users’ behaviours and actionshavebeenincludedinthefnal Plan Scenarios and socioeconomic variables. evaluated together. Tis last scenario does not represent just a Te frst output included the socioeconomic assessment, the sum of all the positive/negative efects of the explorative ones, fnancial assessment, the distributive analysis, and a summary but takes into consideration the interdependency between the of the results complemented with some general comments diferent actions within them. (Figure 4). Duetothediferentnatureoftheactionstakeninto 4.1.2. Representing the Results. Tanks to the previously men- consideration, we provided a double version of the Net tioned procedure, we were able to draw semiautomatically Present Value (NPV), the Net Beneft over Investment Ratio the outputs for the numerous scenarios. Moreover, fnal (NBIR), and the Beneft Cost Ratio (B/C), calling them, documents and analyses clarify all the main aspects that respectively, “base” and “extended.” Te frst set is based should be considered for the decisions, not limited to the sole on a reliable quantifcation of all the monetized efects aggregate CBA indicators (NPV, NBIR, and B/C). Tis result related to the single scenario implementation (investment, is fundamental in order to simplify the decision process of user surplus, externalities, etc.). Te other set (extended), on City Council, allowing diferent stakeholders to potentially the contrary, was an attempt to quantify, from an economic revise their goals on the basis of a transparent and consistent viewpoint, efects related to “sof” mobility policies such as analytical process. health benefts for active modes, the opportunity cost of Advances in Operations Research 9 public funds, and an approximation of the possible wider Te main results of this new network were economic efects. In fact, in these cases, these aspects can be considered as the most relevant, and a CBA that does (1) an increase in user surplus of 209 M€/year; not include them is mainly incomplete. However, due to (2) a reduction in bus operating costs of 47.6M€/year; objective difculties in quantifying some of these efects, we (3) an increase in public transport revenues of introduce these indicators mainly to underline a possible 25.6 M€/year; positive or negative threshold in comparison with those of the frst set. For example, on health benefts related to bicycle (4) a reduction in negative externalities (accident, envi- users, diferent sources provide very variable values. From ronment, and climate change) of 12.1 M€/year. 0.03 €/km [38] up to 0.36 €/km [39] or 0.44 €/km [40]. For our analysis, we considered a weighted average value of 0.365 However, these apparently good outcomes are not capable €/km. Moreover, other nonmonetary elements were returned of counterbalancing the investment, operating, and main- only in a qualitative way (similar to what Sager [12] describes tenancecostsofthenewinfrastructureandservices.Te as a “narrow CBA”). Beneft/Cost ratio results are 0.80 for the conventional heavy metro version and 0.86 for the automatic light metro. Our aim, in fact, was to provide the decision-makers with Te fnancial impact for the public budget would exceed not only a synthetic “number” to quantify the goodness of an 330 M€/year. action, but also a set of tools, giving politicians a certain level of informed discretion on the fnal decision. In comparison, we tested a scenario based on a generalised speeding up of the entire overground (bus and tram) Te second output (Book of Maps) included, for each sce- public transport, mainly through trafc light coordination nario, 24 cartographies showing the variations, both in abso- and intersections redesign. Te interventions hypothesized in lute values and as a percentage, of user surplus, passengers the simulation consist of per means of transport, and travel times and distances. Data was aggregated once per zone of origins and subsequently on (1) an increase in the commercial speed of some tram line destinations, allowing a complete visualization of the network up to 18 km/h in the most congested part of the city; efects connected to single scenarios. (2) an increase of 10% in the commercial speed of all Tis detailed output allows us to depict, for example, that other bus and tram lines; users obtaining beneft from a metro or tram line extension are not only those citizens living or working next to it, (3) the reintroduction of 3 circular bus and tram lines butalsousersofotherzones,relatedtodiferentmeansof around the city centre; transport, benefting from road decongestion. Similarly, this (4) the implementation of the new peripheral tram line output is useful in directly visualizing the modal shif’s spatial in the northern part of the Milan municipality. extension. Tistoolisparticularlyefectiveinunderliningunbal- As for the PGT scenario, the result in terms of user beneft anced situations between diferent parts of the city (i.e., local was defnitely positive (221 M€/year), but the Beneft/Cost beneftor,onthecontrary,surpluslossduetopunctual ratio was outstandingly higher (above 15), considering an actions) and giving hints to policy-makers on how to address investment cost of 200 M€. specifc situations. From the distributive point of view, the traditional metro extension scenario (Figure 6) and the cheaper speed- 4.1.3. How Assessment Changed the Decisions. Tis approach up scenario (Figure 5) perform similarly. Te latter gives proved to be a fundamental support for the redefnition of homogeneous benefts to almost all zones of the city, while the strategic objectives of the public administration regarding the metro extension presents some more inhomogeneity, the new type of mobility to sustain the future growth of with some zones largely benefted and others just margin- the city. Trough the combination of the aggregate results ally. and benefts distribution maps, we were able to quanti- In conclusion, if the schematic goals of speeding up the tatively efect a change of vision for the decision-maker public transport network are actually realized, their efect from a traditional transport plan based on new “heavy” would be enormously positive and equal to that of six new underground infrastructures to a plan made of punctual high-frequency mass transit lines. Te margin of beneft of and cheaper actions homogeneously difused on the entire this scenario is such that even obtaining only a fraction of the Milanese public transport network. increase in commercial speed simulated can ensure a positive For example, the frst scenario considered the transport overall outcome. lines envisaged in the previous Milanese land use plan (PGT). Tis type of comparison is useful for testing, and poten- Tis huge plan hypothesized the creation of 6 new high- tially reorienting, decision-makers’ vision and strategies, on performance lines for a total length of 77.3km (56.1 km of which plans were founded. Also thanks to these comparative metro lines and 21.2 km of tram lines), providing one run results, City Council decided to renounce a growth based every 3 minutes per direction. In the evaluation, metro lines on new “heavy” and costly infrastructure and, nowadays, have been studied once as traditional heavy lines and once the Milanese transport authority is working on punctual as automatic lines, having a higher investment but lower interventions that are able to ensure higher overground operating costs. public transport commercial speeds. 10 Advances in Operations Research

Rescaldina Solaro Solaro Arcore Bovisio-Masciago Desio Lissone 2014 Villasanta Vimercate Paolo Beria, Rafaele Grimaldi Cesate Varedo Cerro Maggiore Limbiate Vanzaghello Legnano Concorezzo Nova Milanese Muggiò San Vittore Olona Monza Magnago Garbagnate Milanese Senago Paderno Dugnano San Giorgio su Legnano Agrate Brianza TRASPOL - LaboratorioVilla Cortese di PoliticaCanegrate dei Trasporti DairagoPolitecnico di Milano Lainate Cinisello Balsamo Caponago Castano Primo Nerviano Brugherio Piano Urbano della Mobilità Sostenibile Cusano Milanino Carugate Parabiago Arese Bollate Buscate Busto Garolfo Cormano Arconate Bussero Pogliano Milanese Bresso Novate Milanese Sesto San Giovanni Cologno Monzese Rho Baranzate Casorezzo Cernusco sul Naviglio

Vanzago Sc.: VelocizzInveruno TPL superﬁcie (TPL_V1) Robecchetto con Induno Pregnana Milanese Vimodrone Cassina de' Pecchi Pero Cuggiono Arluno Ossona Vignate Mesero Cornaredo Pioltello Santo Stefano Ticino Sedriano Marcallo con Casone Segrate Vittuone Settimo Milanese Bernate Ticino Bareggio

Milano Rodano

Bofalora sopra Ticino Corbetta

Magenta

Variations in user surplus - Origin Cusago Cesano Boscone Peschiera Borromeo Pantigliate [€ during peak hour] Cisliano Corsico

more Robeccothan sul -130.0Naviglio Cassinetta di Lugagnano -129.9 - -100.0 Albairate Trezzano sul Naviglio San DonatoMilanese Mediglia -99.9 - -70.0 Buccinasco Assago -69.9 - -40.0 Gaggiano Tribiano Vermezzo

-39.9 - -10.0 Abbiategrasso

Zelo Surrigone Rozzano San Giuliano Milanese -9.9 - 10.0 Opera Colturano Gudo Visconti 10.1 - 40.0 Dresano Zibido San Giacomo 40.1 - 70.0 Ozzero Noviglio Locate di Triulzi Melegnano 70.1 - 100.0 Rosate Basiglio Morimondo 100.1 - 130.0 Pieve Emanuele Carpiano Cerro al Lambro Lacchiarella more than +130.0 Vernate Binasco Bubbiano Calvignasco

Figure 5: Variation in consumer surplus due to the generalised speeding up of the entire overground public transport (€ in the morning peak hour; our elaboration).

Rescaldina Solaro Solaro Arcore 2014 Bovisio-Masciago Desio Lissone Villasanta Vimercate Paolo Beria, Rafaele Grimaldi Cesate Va re do Cerro Maggiore Limbiate Vanzaghello Legnano Concorezzo Nova Milanese Muggiò San Vittore Olona Monza Magnago Garbagnate Milanese Senago Paderno Dugnano San Giorgio su Legnano Agrate Brianza TRASPOL - LaboratorioVilla Cortese di PoliticaCanegrate dei Trasporti DairagoPolitecnico di Milano Lainate Cinisello Balsamo Caponago Castano Primo Nerviano Brugherio Piano Urbano della Mobilità Sostenibile Cusano Milanino Carugate Parabiago Arese Bollate Buscate Busto Garolfo Cormano Arconate Bussero Pogliano Milanese Bresso Novate Milanese Sesto San Giovanni Cologno Monzese Rho Baranzate Casorezzo Cernusco sul Naviglio

Va nza go Sc.:Inveruno Linee di Forza PGT Robecchetto con Induno Pregnana Milanese Vimodrone Cassina de' Pecchi Pero Cuggiono Arluno Ossona Vignate Mesero Cornaredo Pioltello Santo Stefano Ticino Sedriano Marcallo con Casone Segrate Vittuone Settimo Milanese Bernate Ticino Bareggio

Milano Rodano

Bofalora sopra Ticino Corbetta Variations in userMagenta surplus - Origin Cusago Cesano Boscone Peschiera Borromeo Pantigliate [€ during peak hour] Cisliano Corsico

more thanRobecco sul-130.0 Naviglio Cassinetta di Lugagnano -129.9 - -100.0 Albairate Trezzano sul Naviglio San Donato Milanese Mediglia -99.9 - -70.0 Buccinasco Assago -69.9 - -40.0 Gaggiano Tribiano Vermezzo

-39.9 - -10.0 Abbiategrasso

Zelo Surrigone Rozzano San Giuliano Milanese -9.9 - 10.0 Opera Colturano Gudo Visconti 10.1 - 40.0 Dresano Zibido San Giacomo 40.1 - 70.0 Ozzero Noviglio 70.1 - 100.0 Locate di Triulzi Melegnano Rosate Basiglio Morimondo 100.1 - 130.0 Pieve Emanuele Carpiano

Cerro al Lambro Lacchiarella more than +130.0 Vernate Binasco Bubbiano Calvignasco

Figure 6: Variation in consumer surplus due to the 6 new high-performance public transport lines envisaged by the PGT (€ in the morning peak hour; our elaboration). Advances in Operations Research 11

4.2. Te Rail Connection between Malpensa Terminal 2 and the them. In addition, models give the quantities, in terms of daily Simplon Line. Te project presented by the Lombard railway passengers, for every mode on each OD pair, allowing us to company (FerrovieNord S.p.A.) and the airport manager of calculate the users changing modes. Finally, model outputs, Milano Malpensa and Milano Linate (SEA S.p.A.) proposes as in the previous case, also included data used to correct the an extension of the existing rail tracks from Malpensa monetary transfers in the CBA. airport’s terminal 2 to Gallarate railway station, located on Overall, the output of the regional model consists of the Simplon rail line. Te aim of this new connection is to a database fle with tables of attributes (generalised cost), increase the number of direct services, both national and quantities (amount of users), and transfers (fares, tolls, and international, stopping at the airport. Due to the relocation taxes) per 238,210 origin-destination pairs and 8 (2 × 4) of actual services on the new tracks, the project allows the mode and travel purpose combinations. By means of SQL release of capacity on the Simplon rail axis, thus enabling procedures, we estimated the surplus variation using the the regional government to increase frequencies of some RoH method. Once the core calculations were done per suburban services. Tis project was the very frst application ODpair,mode,andtravelpurpose,weproceededwiththe of the regional and national guidelines, recently issued [21, aggregation of the results in 1,455 origin and destination 22]. zones, using the same zoning of the model. Te same thing Similartowhatwaspresentedforthepreviouscase, has been done for all attributes, quantities, and transfers. for the CBA assessment, we interfaced the transport model, Te simplifed model is based on 50 origin-destination pairs developedbytheLombardyRegion,withtheevaluationpro- corresponding to the relation between Malpensa airport and cedure, developed with a database and spreadsheet sofware. the main provincial capitals (and surrounding hinterlands) In this case, the transport model was developed quite recently outside of the Lombardy Region; the fnal output referred to (it was used for the frst time in 2015 to evaluate the Regional 2(2× 1) mode and travel purpose combinations; once the Program on Mobility and Transport). For this reason, in the surplus calculation was done for each of the initial 5 transport preliminary evaluation phase, a higher efort was devoted to modes,theresultswereaggregatedintheprivateandpublic debug and calibration procedures (see below). Tese opera- mode to ensure comparability with the regional model. tions were made possible by the geographical visualizations of Afer the aggregation, the obtained data of both models surplus variation efects through the interactions with a GIS have been interfaced with spreadsheet sofware for the CBA, sofware (see Section 4.2.2). and limited to regional model data, with a GIS sofware to Given that the expected efects mainly spread at the produce cartographical representations of the main variables. regional level, model zoning, user characteristics, and trans- In total, eight fnal scenarios have been evaluated through port modes presented a higher level of aggregation in com- this procedure. However, even if this number is defnitely parison with the previous case. lower than the total scenario evaluated for the mobility plan, In detail, the transport model provided the generalised we take even more care to develop ad hoc debug procedures cost components of each origin–destination (OD) pair for within the automation process. four diferent travel purposes (work, study, leisure, and Tis efort was necessary to allow a perfect interaction business trips) and, at the frst logit stage, the transport between the RoH method and the regional transport model modes considered were private and public .Tenumberof output.Infact,whilelogitaloneallowstheintroduction passengers, for every mode on each OD pair, referred to of “out-of-scale” generalised costs for nonexisting options daily movements inside the Lombardy Region and between (typically putting 9.999 in the generalised cost components), Lombardy and Switzerland. In parallel, we developed a the RoH does not. In other words, both reference and simplifed transport model on a spreadsheet, to include it in postproject scenario have to be “feasible” for every existing the evaluation of other high-speed rail passengers originating combination of transport modes and travel purpose. Oth- from other Italian regions. For the characteristics of attracted erwise,ifthatalternativebecamefeasibleduetotheproject users, in this secondary model, we considered a unique travel implementation, the RoH method will return unrealistic user purpose (leisure) and car (as driver), car (as passenger), surplus values. coach,HStrain(plusshuttlebusinterchange),andHS Tis was initially the case of some OD pairs in the train (plus Malpensa express train interchange) as available Lombardy transport model within the public mode (the use transport modes. Tis model was calibrated using a Customer of public transport was capped to a maximum travel time Satisfaction survey on Malpensa airport users realized in 2016 of 2 hours), which were “not existing” (with a conventional for SEA S.p.A. 9.999 GC associated) before the project and “existing” (with In both models, each segment of the simulated mobility is a realistic GC associated) afer. Tis produced wrong results associated with a set of calibrated � coefcients (5), including that were pointed out thanks to the transposition of the the values of time (per trip purpose and per mode). To results on a GIS sofware (other anomalies were detected ensure results comparability, in the simplifed model, we in relation to incoherent railway station connectors and considered the same value of time for leisure purposes simulated service tarifs). included in the regional transport model. Diferently from In comparison with the SUMP case, the Appraisal Sum- the elaboration presented in the previous case study, no active mary Table has been split between fnancial and economic modes were included in these simulations. Consequently, performances. Te two analyses difer for how they treat we were able to use directly generalised costs provided by user surplus and externality components (included in the models, thus ensuring the highest level of consistency with economic CBA, but not in the fnancial one). Net Present 12 Advances in Operations Research

Value (NPV) and Internal Rate of Return (IRR) have been cal- 4.2.2. Outputs and Results. In order to make the decision culated for both parts, while the Net Beneft over Investment of the regional government more transparent and informed, Ratio (NBIR) and the Beneft Cost Ratio (B/C) are indicators the outputs of the assessment have been presented in a onlyforthelatter.Inthisstage,nobudgetconstraintis homogeneous and detailed way. Documents and analyses foreseen and all actions are included. When, at latter stages, clarify all the relevant facts that should back the decisions, the available budget will be defned, these constraints can not limited to the sole aggregate CBA indicators (NPV, be managed consistently using appropriate algorithms [41]. NBIR, B/C, and IRR). As for the previous case, results were Lastly, a separate tool for Risk Analysis was implemented presented through an Appraisal Summary Table (Figure 7) to test the critical variables identifed by the Sensitivity and a Book of Maps (Figure 8). Analysis (for each scenario, investment costs, user surplus, A particular care was taken with the scenario comparison, externalities, and demand growth trends were tested). Te in order to enrich the undergoing debate between decision- term “critical variable” refers to those components for which makers and stakeholders. Interestingly, results underline a a variation of 1% of their value leads to a percentage variation series of critical aspects, common for all scenarios, that none equal to or greater than the VANe [21, 22]. of the actors had foreseen before. First, the hypothesized network reconfguration was con- 4.2.1. Scenarios. Previous to the assessment phase, public siderably benefcial for regional users that move between actors and stakeholders defned a set of 8 scenarios difering the regional capital and its hinterland, but—unexpect- in terms of simulated demand (based on, resp., a conserva- edly—airport users were associated with a loss of surplus − − tive and optimistic growth in air passengers for the period (from 0.01 to 0.04 €/day per passenger) and with a shif 2016–2025), feasible rail projects and, consequently, diferent from public transport to private car. networks and supply. Tanks to the cartographical visualization of the phe- In particular, in order to ensure faster connections nomenon (Figure 8), it was clear how this particular result between Milan and the airport, and thus possibly attracting was a direct consequence of the new path envisaged for both new demand and shifing the existing one from airport Malpensa express service. In fact, according to regional OD shuttle buses, decision-makers hypothesized to drop one matrix data, almost 67% of users direct to and coming of the two Milan stops (Milano Porta Garibaldi) from the from the airport are generated/attracted by Milan. Tus, airport express train. ensuringafasterconnectionfromMilanoCentralestation throughcancellingtheintermediatestopofMilanoPorta Besides the main aim of ensuring a faster and more Garibaldi implicates an increase in travel time, and eventually frequent connection with the airport, another political goal inthenumberofinterchanges,forthoseuserslocatedin was to demonstrate quantitatively the necessity of redesigning the southwest and northwest of Milan. Only those located or even deleting part of a correlated rail project, named in northeast areas obtain a reduction in travel time (for “Potenziamento Rho-Gallarate e Raccordo Y.” due to poten- remaining zones, thanks to the existing metro network, the tial interferences in train circulations caused by the foreseen accessibility of these two stations are equivalent). Overall, the Y-shaped fat junction. Tis fat junction was approved by the netefectforMilaneseusersisaloss in surplus in respect to national government in 2007 and inserted into the Strategic the airport connection. Infrastructure Program (PIS). Te approval process did not Secondly, the travel time reduction of 6 minutes for HS require either an assessment or preliminary design phase passengers proved to be not sufcient to promote a sensible duetothespecialconditionallowedtotheso-called“Legge modalshifinfavourofthepublictransportmode(Figure9). Obiettivo”, abrogated in 2016 (for critical aspects related to In fact, the increase in user surplus is almost completely “Legge Obiettivo” projects see [42, 43]). related to the reduction of the number of interchanges (the On the contrary, airport managers were mainly focused ratio of �Interchange on �Cost shows that the perceived cost on enlarging the catchment area of the airport through for each interchange is equal to 50 €, suggesting that this adding,tothealreadyforecastedsuburbanandregional typology of users considers a direct service more attractive supply [44], other market oriented rail services connecting than a connection similar in respect to travel time, but that the main regional and provincial Italian capitals. impliesevenjustaninterchange).Consequently,onthoseOD Table 3 lists the scenarios that emerged from the consul- pairs where a direct bus connection already exists, few users tation phase, with their main characteristics. areattractedfromthenewHSservice. Each scenario was constructed starting from a “question,” Lastly, both R 25|P 25s1 and R 25|P 25s2 scenarios, with posed by decision-makers, which summarizes the diferent a B/C ratio, respectively, of 1.07 and 1.22, show a limited contexts in which the project could be realized or not. From a improvement in consumer conditions in respect to project methodological point of view, all those services that, entirely costs. Tus, it was not entirely possible to validate the thesis or for part of their path, generate user benefts not directly of the public decision-maker on the efectiveness of the frst connected to the project under assessment were considered solution in comparison with the latter. However, this result invariants. Likewise, only the infrastructural investments is partially misleading because, due to the preliminary stage necessary to ensure the supply remodelling envisaged were of project design, evaluations utilized feasible train timetables considered. Other projects, even if not yet realized, have been only for the new services envisaged. On the contrary, possible eventually considered as invariants between the reference and interferences with the already existing services were not postproject scenarios. considered. Advances in Operations Research 13

Table 3: Project scenarios.

∗ ∗ ∗ ∗ ∗ ∗ ∗ Scenario code R 18 P 18 R 25 P 25s1 P 25s2 P 25s0 P 30 ∗∗ ∗∗ ∗∗ ∗∗ OD matrix horizon 2015 2015 2025 2025 2025 2025 2025 Infrastructure components Rail track T2 - Gallarate xx x Yfatjunction x Ysplit-leveljunction x Fourth rail track Rho-Parabiago xx x xx Fourth rail track Parabiago- Gallarate x Forecasted rail services and frequency � � � Malpensa Express (Milan – Saronno – 30 30 60 Terminal 2) � Malpensa Express (Milano – Saronno – 30 Terminal 2 - Gallarate) � � Malpensa Express (Milano – Rho – 30 15 Gallarate – Terminal 1) � � Malpensa Express (Milano – Rho – Y 30 60 junction – Terminal 2) � � � � Regional train (Bergamo – Saronno – 60 60 60 60 Gallarate) � � � Regional train (Bergamo – Saronno – 60 60 60 Gallarate – Terminal 1) � � Suburban train S9 (Albairate – Saronno) 30 30 � � � � Suburban train S9 (Albairate – Saronno – 30 30 30 30 Busto Arsizio) � Suburban train S9 (Albairate – Saronno – 30 Busto Arsizio – Gallarate – Terminal 1) � � � � Suburban train S15 (Milan – Parabiago) 30 30 30 30 � Suburban train S15 (Milan – Parabiago – 30 Gallarate – Terminal 1) HS train (Multiple Origins -Milan– Spot Spot Saronno – Terminal 2) HS train (Multiple Origins -Milan– Spot Spot Gallarate – Terminal 1) HS train (Multiple Origins -Milan–Rho Spot Spot – Y junction – Terminal 2) ∗ ∗∗ R stands for state of the art scenario, while P is associated to post-project scenario; in these scenarios, both conservative and optimistic demand was considered.

From this analysis, decision-makers decided to allow the Tis need is more and more actual, given the increasing shif progress of the infrastructural project to the next design of mobility planning practices [1] from a single infrastructure phase and, at the same time, to prepare further checks aimed to complex and consistent urban plans, to take advantage of at optimizing network supply. the benefts of policy packaging [2]. To reach this goal, once a transport model is available, it is convenient to extract the needed data from the chosen model 5. Conclusions and to adopt, depending on whether nonadditive policies are included in the simulation or not, either the Rule of Half or Cost-beneft analysis and public expenditure assessment logsum methods for consumer surplus calculation. techniques are broadly studied in literature. However, some Another objective of the paper deals with the enrichment relevant aspects of evaluation, especially related to the practi- of the outputs to allow a better evaluation. Tanks again to the cal application in complex cases and to the efective inclusion integration with a transport model, it is possible to provide a of CBA in the policy design process, remain unsolved. geographical and social distributive analysis, spatially depict- Te primary objective of this paper is to give indications ing the efects on consumer surplus, and of envisaged actions, about how to correctly evaluate, using Cost-Beneft Analysis, policies, and projects. Tis tool could potentially be applied complex urban mobility plans and infrastructural projects. also to spatially represent other variables (such as safety or 14 Advances in Operations Research

Figure 7: An example of Appraisal Summary Table organisation.

(a) (b)

Figure 8: Total variation in user surplus. (a) Scenario R 25|P 25s1; (b) scenario R 25|P 25s2.

environmental benefts). However, in order to carry out this improve the transparency and the awareness of the choices type of analysis, a deeper interaction with the transport model taken. is needed. In particular, information on the diferent paths In particular, through the description of two operative between OD pairs have to be collected from the fourth step case studies, we show evidence on how these two tools can of the transport model (“route assignment” phase). provide a signifcant support to decision-makers: by quan- A second possible output to efectively represent and titatively demonstrating how, in mature networks, smaller communicate the results of the evaluation is the Appraisal actions have a systematically higher efciency than large and Summary Table.Bothtools,byimprovingresultsreadability, expensive projects (SUMP case study) and by unearthing can help politicians, policy-makers, stakeholders, and citizens possible critical aspects of the envisaged network supply to correctly understand project and plan efects and in general (Malpensa airport rail connection case study). Advances in Operations Research 15

University and Research (MIUR), within the SIR programme (DDno.197del23gennaio2014).

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