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A Study on Pupils Transportation

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A Study on Pupils Transportation Journal of Traffic and Logistics Engineering Vol. 6, No. 1, June 2018 A Study on Pupils Transportation Roberto Montemanni and Luca Maria Gambardella Dalle Molle Institute for Artificial Intelligence (IDSIA) University of Applied Sciences of Southern Switzerland (SUPSI) CH-6928 Manno, Switzerland Email: {roberto, luca}@idsia.ch Abstract—The Swiss Municipality of Capriasca was in In the context depicted above, we were given Origin- need of reorganizing the pupils transportation service for Destination (OD) matrices for pupils for the four phases the local primary school and to evaluate different strategic of a school day (transportation is eventually provided also changes to the current organization. This paper describes for the lunch break). For example, the morning requests the problem and the requirements of the Municipality for school start are presented in Table I. For each request together with the tools we developed for the study. The resulting solutions, later adopted by the Municipality, are an origin (), a destination 푑푒푠푡() and the number of also described. pupils are given. Notice that OD matrices changes for the different day times. The Municipality was interested in Index Terms—computer science applications, tranportation, estimating: combinatorial optimization 1. At an operational level, how many private buses would have been necessary to provide the service; I. INTRODUCTION 2. At a strategic level, what was the impact on The Municipality of Capriasca is located in the transportation costs if some, or even all the school southern part of the Italian-speaking Canton Ticino, locations were moved to Tesserete, the central town Switzerland (see Fig. 1). The municipality covers a of the Municipality (see Fig. 3). This last request was relatively large territory of 36.35km2 mainly in the motivated by an already forecasted long-term mountains (see Fig. 2) and is the results of a merger consequence of the merging process mentioned between year 2001 and 2008 of several previously before. independent municipalities, with approximately 6300 The rest of the paper provides further details of the inhabitants in total (year 2011). problem, describes the approach we developed to answer One of the services provided by the Municipality is the questions above, and finally presents our findings and primary education, involving approximately 300 pupils discusses them. for a total of 15 classes, three for each of the five levels of the local elementary education [1]. A side-service offered II. SOLUTION APPROACH to the families is the transportation of pupils from the area The tool we developed is based on mixed integer linear where they live to school and back, for a total of four programming (MILP) and incorporates private buses journeys per day, covering morning school start and end routes to complement public buses and pedobuses in order at 8:15 and 11:30, respectively, and afternoon start and to serve all pupils with an acceptable quality-level. The end at 13:15 and 16:30, respectively [5]. Due to the engine is described in the rest of this section. Travel times relatively recent merging process, in 2011 (the time of the were estimated from Google Maps study presented in this paper) classrooms were spread (www.google.com/maps/), the timetable for public buses among five different school locations (see Fig. 3). The was available online (www.ffs.ch), while the Municipality transportation had been previously run by a private provided the pedobus service timetable. company, but due to the increase of the number of The approach we developed is based on the following inhabitants, and by some changes of Federal regulations, considerations: the previous plan was not economically sustainable for the 1. The geographic configuration of the area is shaped scholastic year 2011-12. The Council decided then to like a star, with the town of Tesserete in the center. open a call for a new contract, and in parallel launched For this reason, Tesserete is used as a hub where initiatives to incentivize a sustainable lifestyle, pupils can change transportation mode or connecting incorporating also public buses into the system and from one bus to another; especially the so-called green zones, where a walk-to- 2. The time horizon for pupils transportation is very school systems, called pedobus [2], was implemented for restricted. A hard constraint is imposed such that pupils leaving close enough to their school. Public bus each transportation cannot take more than 30 lines (blue, red, azure, yellow), pedobus green zones minutes. On top of this, minimizing the travel time is (green lines) and actual location of classrooms are important, since it is a direct measure for the quality depicted in Fig. 3 [3]. of service; 3. Pupils cannot change transportation more than one, in order to keep the quality of service at an Manuscript received February 21, 2018; revised June 1, 2018. acceptable level; ©2018 Journal of Traffic and Logistics Engineering 6 doi: 10.18178/jtle.6.1.6-10 Journal of Traffic and Logistics Engineering Vol. 6, No. 1, June 2018 4. Pupils with the same origin and destination will (villages/quarters) touched by route 푘∈퐾, the arrival k travel together. This is important to avoid complains time is indicated as 푇 . A set of requests R, representing from the families about discriminations; i 5. Given the current transportation requests and their group transportation requests as in Table I, is also given. scattered nature around the territory, bus capacity is For each request ∈푅, the origin and destination locations not a problem, since in no reasonable solution it are indicated with () and 푑푒푠푡() respectively. Tesserete exceeds that of a typical large bus (55 seats). is referred to as h푢푏 in the formulation, and connection We decided to work with a set covering-like model (see, times between 2 and 10 minutes are allowed in there. A for example [7]) where each column represents a route of constraint on the maximum number of private buses to a bus (private or public) or a pedobus route. Such a choice hire, regulated based on parameter 푁푟푃푟푣퐵푢푠푠푒푠, is was motivated by the observation that pedobus and public imposed. The aim was to use this parameter to propose buses routes are given, while feasible private buses routes alternative solutions using a different number of private are limited in number due to the very tight time buses (eventually larger or smaller). The target of the constraints, combined with the overall limited number of optimization is to provide a fair service to all the families, roads available in such a mountain region. so the worst-case travel time was identified as a good The first step was therefore to generate, by inspection, objective function. The following binary variables are all possible reasonable private bus routes. Routes typically used in the model: serve more than one school, exploiting the fact that school 1 푓 푟표푢푡푒 푘 ∈ 퐾 푠 푠푒푙푒푐푡푒푑 locations are close to each other, and a few minutes time 푧 = { 푘 0 표푡ℎ푒푟푤푠푒 flexibility is tolerated for pupils. In total approximately 1 푓 푟푒푞푢푒푠푡 푠 푝푐푘푒푑 푢푝 푏푦 푟표푢푡푒 푘 ∈ 퐾: 표푟푔() ∈ 푘 250 (depending on the time of the day) were identified, 푥푘 = { covering public buses, pedobus and possible private buses, + 0 표푡ℎ푒푟푤푠푒 with the latter repeated several times with slightly shifted 1 푓 푟푒푞푢푒푠푡 푠 푝푐푘푒푑 푢푝 푏푦 푟표푢푡푒 푘 ∈ 퐾: 푑푒푠푡() ∈ 푘 푥푘 = { starting times. − 0 표푡ℎ푒푟푤푠푒 Formally, the problem we modeled can be described as follows. A set K of transportation routes is given, with the A further free variable is also present: routes by private bus identified as 퐾 ⊆퐾. For each stop P 훿 = 푚푎푥푚푢푚 푡푚푒 푠푒푟푣푐푒 표푣푒푟 푎푙푙 푟푒푞푢푒푠푡푠 TABLE I. REQUESTS FOR THE MORNING SCHOOL START. The resulting mixed integer linear programming imposes that requests can only use active buses; formulation (it contains some abuse of notation) is constraints (5) and (6) state that each request has to be presented in (1)-(8), served by some transportation (the starting and ending can The objective function (1) minimizes the maximum coincide when only one transportation mode is used). travel time among all requests. Constraints (2) are used to Inequalities (7) impose constraints on transportation store in 훿 the maximum difference between arrival and changes in the hub Tesserete. Constraint (8) finally starting time of all requests; constraints (3) and (4) ©2018 Journal of Traffic and Logistics Engineering 7 Journal of Traffic and Logistics Engineering Vol. 6, No. 1, June 2018 imposes a limit on the number of private buses instances treated. For more general models and implemented in the solution. approaches for school transportation we refer the The resulting model can be solved in a few seconds by interested reader to [6]. common solvers, due to the intrinsic small size of the min 훿 (1) 푘 푘 푘 푘 푠. 푡. 훿 ≥ ∑ (푇푑푒푠푡()푥−) − ∑ (푇표푟()푥+) ∀ ∈ 푅 (2) 푘∈퐾:푑푒푠푡()∈푘 푘∈퐾:표푟()∈푘 푘 푥+ ≤ 푧푘 ∀ ∈ 푅, ∀푘 ∈ 퐾: 표푟푔() ∈ 푘 (3) 푘 푥− ≤ 푧푘 ∀ ∈ 푅, ∀푘 ∈ 퐾: 푑푒푠푡() ∈ 푘 (4) 푘 ∑ 푥+ = 1 ∀ ∈ 푅 (5) 푘∈퐾:표푟()∈푘 푘 ∑ 푥− = 1 ∀ ∈ 푅 (6) 푘∈퐾:푑푒푠푡()∈푘 푘 ℎ 푘 ℎ 푥− + 푥+ ≤ 1 ∀ ∈ 푅, ∀푘, ℎ ∈ 퐾: 표푟푔() ∈ 푘, 푑푒푠푡() ∈ ℎ, 푘 ≠ ℎ, 푇ℎ푢푏 − 푇ℎ푢푏 ∉ [2;8] (7) ∑ 푧푘 ≤ 푁푟푃푟푣퐵푢푠푠푒푠 (8) 푘∈퐾푝 Figure 1. The Municipality of Capriasca within Central Europe. Figure 2. Schematic road network of the villages and quarters covered in the study. both in the morning and in the afternoon. The III. EXPERIMENTS AND RESULTS routing/matching model described in the previous section A. Bus Fleet Dimensioning and Routing was run and in a few seconds was able to provide feasible transportation/matching plans. The first request was to dimension the fleet of private The solutions found were using three private buses, but buses necessary to integrate the public buses available, in inspecting the tours we realized that there were margins of order to operate the transportation of pupils, keeping an improvements since public transportation was not fully accepting level of quality of service.
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