Understanding and Optimising Carsharing Systems Sisi Jian

Home , Carsharing, GoGet, Ute (vehicle)

Understanding and Optimising Carsharing Systems

Sisi Jian

A thesis presented in fulfilment of the requirements for the degree of

Doctor of Philosophy

School of Civil and Environmental Engineering

The University of New South Wales

August 2017

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Carsharing, as an alternative to private vehicle ownership, has spread worldwide in recent years due to its potential of reducing congestion, improving auto utilisation rates and limiting the environmental impact of emissions releases. Along with its growth, the flexibility of carsharing systems also brings complex problems to the operators.

One dominant challenge in carsharing systems is to ensure the supply of vehicles can meet the demand of users in a cost-effective manner. This requires accurately predicting users' demand and optimally relocating vehicles in response to demand variations. The two principal areas of this thesis are methods to estimate demand and optimally relocate fleet.

From the demand side, this study models users’ vehicle selection and utilisation patterns. Focusing on vehicle selection behaviour, a spatial hazard-based model (SHBM) is proposed to investigate the impacts of users’ socio-demographic attributes and fleet characteristics on their choice set formation behaviour in selecting vehicles. The modelling is achieved by regarding “distance to carsharing vehicle” as a random variable analogous to the duration in conventional hazard-based models. Data collected from the Australian carsharing company GoGet are utilised to calibrate the models. The accelerated failure time model with a log-logistic distribution is found to provide the best fit. Upon making a vehicle selection, users then decide the amount of consumption to allocate to each selected vehicle type. This process involves making multiple discrete choices of continuous amounts and is modelled by the multiple discrete-continuous extreme value (MDCEV) modelling framework. Three MDCEV models considering travel time, mileage, and monetary expenditure as the continuous

i consumption constraints are developed to estimate the impacts of a set of socio- demographic attributes on user’s vehicle choice and capture the satiation effect with increasing the consumption for each vehicle type. An efficient simulation procedure is applied to evaluate the performance of the three MDCEV models. The results indicate travel time, mileage and expenditure affect users’ vehicle usage pattern in the same way. The findings from these two demand models can be referred to by the operators when determining the most efficient allocation of resources within carsharing systems.

From the operation side, the research develops and solves novel models for the vehicle stock imbalance problem in one-way carsharing systems. Previous studies have proposed relocation methods to handle it, but the interdependence between demand and supply has never been considered. The thesis proposes two relocation models to link demand and supply. Both incorporate a discrete choice model (DCM) in an integer linear programming (ILP) model to account for the interaction. The difference between them lies in the DCMs. In the first model, the DCM does not assume users’ demand to be elastic to vehicle availability. The ILP model solves optimal relocation decisions and updates vehicle availability for each station; the DCM then coupled with the updated vehicle availability changes users’ trip demand reciprocally. Built on the first model, the second model extends the DCM by including vehicle availability as a parameter directly affecting demand. In this new framework, demand and supply are linked by vehicle availability: it is the output of the ILP model and at the same time the input of the DCM. The nonlinearity of the DCM is further linearised through a linearisation approach. Both models are tested in the GoGet network. The results reveal if there is a strong interdependence between demand and supply, the supply has a critical impact on system profit.

The core contribution of this thesis is to take the first attempt to understand and optimise carsharing systems considering the interdependency of demand and supply comprehensively.

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Acknowledgements

I will never forget the lucky Skype call I received four years ago when I was studying at Singapore. Yes, that’s the interview call from my supervisor Dr. Vinayak Dixit, and that Skype call led me to the world of research and changed my life entirely. I am so fortune to have Vinayak to be my supervisor. I can hardly find proper words to express how much it means to me for his academic suggestions, career advices, constructive criticisms, and giving me precious opportunities to see the world. Also, I would like to express my most sincere thanks to my supervisor Prof. Travis Waller, for providing so many invaluable suggestions and inspiring me to pursue the happiness of research.

PhD study is a tough process, but I am so grateful to have the most lovely colleagues in our group sharing the gains and frustrations during the entire process.

Specially, I would like to thank Dr. Taha Hossein Rashidi and Dr. David Rey for their fantastic advices on my researches. I would like to thank Dr. Kasun Wijayaratna for all those long talks, and his kind advices not only on researches, but also on my life in

Australia. I would also like to thank Ms Maria Lee and Ms Sylvia Brohl for providing incredible assistance in dealing with so many paper works. I wish to also thank Dr.

Zhitao Xiong, Xun Li, Chenyang Li, Xiang Zhang, and Tao Wen for wines and hot pots. Good wines and delicious food are the best medicines to relieve the tensions from work. Furthermore, I would like to thank Mr. Bruce Jeffreys and Ms. Rachel Moore from GoGet for providing the data to support my research, and the Australian Research

Council for their support under Linkage Grant.

Finally, I am so lucky to have the greatest husband who always supports me and tolerates me with his love, understanding, and patience. Also, I would like to thank

iv my parents for their selfless love and understanding my decision of studying abroad. I wish to also thank my two cats for accompanying me all the time and bringing me so much happiness. My dearest family always give me the light when I am in shadow.

List of Relevant Publications

The following provides a list of the journal and conference publications that have contributed towards the development of the thesis.

Peer-reviewed journal publications

1. Jian, S., Rashidi, T.H., Wijayaratna, K.P. and Dixit, V.V., 2016. A Spatial Hazard-Based analysis for modelling vehicle selection in station-based carsharing systems. Transportation Research Part C: Emerging Technologies, 72, pp.130-142. 2. Jian, S., Rey, D., Dixit, V., 2016. Dynamic Optimal Vehicle Relocation in Carsharing Systems Accepted for publication in the 2016 Transportation Research Record: Journal of the Transportation Research Board. 3. Jian, S., Rashidi, T.H., and Dixit, V., 2017. An analysis of carsharing vehicle choice and utilization patterns using multiple discrete-continuous extreme value (MDCEV) models. Transportation Research Part A: Policy and Practice, 103, pp.362-376.

Papers submitted and under review

4. Jian, S., Rey, D., and Dixit, V. An Integrated Supply-Demand Approach to Solving Optimal Relocations in Carsharing Systems. In review with Networks and Spatial Economics.

Peer-reviewed conference papers

5. Jian, S., Rey, D., and Dixit, V., 2016. Dynamic Optimal Vehicle Relocation in Carsharing Systems. In proceedings of the 95th Transportation Research Board Annual Meeting, Washington, D.C., 10 - 14 January 2016. 6. Jian, S., Rashidi, T.H., Wijayaratna, K. P., and Dixit, V., 2015. Hazard-based modelling of vehicle selection in carsharing systems. In proceedings of the 94th Transportation Research Board Annual Meeting, Washington, D.C., 11 - 15 January 2015 7. Dixit, V., Trieu, J., Jian, S., and Li, X., 2014. Value of travel time savings for carsharing users in Sydney, presented at Australian Institute of Traffic Planning and Management (AITPM) National Conference, Adelaide, Australia, 28 - 31 July 2014

Table of Contents

Abstract ...... i Acknowledgements ...... iv List of Relevant Publications ...... vi Table of Contents ...... vii List of Figures ...... x List of Tables...... xii Chapter 1 Introduction ...... 1 1.1 Background and Motivations ...... 1 1.2 Research Context ...... 5 1.3 Contributions ...... 10 1.4 Organisation ...... 11 Chapter 2 Literature Review of Carsharing Related Researches ...... 17 2.1 The History and Growth of Carsharing ...... 17 2.2 The Benefits of Carsharing ...... 19 2.3 Demand Modelling...... 22 2.3.1 Mode choice modelling ...... 22 2.3.2 User behaviour modelling ...... 25 2.4 Operation Strategies ...... 30 2.4.1 Carsharing system types ...... 30 2.4.2 Vehicle relocation models – user-based relocation ...... 32 2.4.3 Vehicle relocation models – operator-based relocation ...... 36 2.4.4 Strategic system designs ...... 46 2.5 Research Gaps ...... 49 Part I Demand Estimation ...... 53 Chapter 3 A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems ...... 55 3.1 Introduction ...... 55 3.2 State of the Art of SHBM Modelling Framework ...... 58 3.3 Model Formulation and Methodology ...... 59 3.3.1 Parametric hazard-based models in survival analysis ...... 59

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3.3.2 Concept of the acceptable walking distance ...... 63 3.3.3 Performance measures of model comparison ...... 65 3.4 Data Collection and Preparation ...... 66 3.5 Results and Analysis ...... 71 3.6 Concluding Remarks ...... 80 Chapter 4 An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using Multiple Discrete-Continuous Extreme Value (MDCEV) Models ...... 83 4.1 Introduction ...... 83 4.2 State of the Art of MDCEV Modelling Framework ...... 86 4.3 Model Formulation and Methodology ...... 87 4.3.1 MDCEV model of carsharing fleet choice and utilisation ...... 88 4.3.2 Simulation procedure for MDCEV model ...... 92 4.3.3 Performance metrics for model comparison ...... 93 4.4 Data Preparation and Summary ...... 95 4.4.1 Vehicle type definition ...... 95 4.4.2 Correlations between travel time, mileage and expenditure ...... 97 4.4.3 Parameters considered in baseline utility functions ...... 101 4.5 Results and Analysis ...... 103 4.5.1 MDCEV estimation results ...... 103 4.5.2 Simulation and comparison results ...... 110 4.6 Policy Implications ...... 113 4.7 Concluding Remarks ...... 117 Part II Operation Optimisation ...... 119 Chapter 5 Dynamic Optimal Vehicle Relocation ...... 121 5.1 Introduction ...... 121 5.2 Problem Statement and Formulation ...... 123 5.3 Description of Case Study Network ...... 131 5.4 Sensitivity Analysis and Results Discussions ...... 134 5.5 Concluding Remarks ...... 142 Chapter 6 Optimal Relocations in Demand Responsive Carsharing Systems ...... 145 6.1 Introduction ...... 145 6.2 Integrated Supply-Demand Model ...... 148

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6.3 Linearisation ...... 154 6.4 Sensitivity Analysis and Results Discussions ...... 156 6.5 Concluding Remarks ...... 169 Chapter 7 Conclusions and Future Researches ...... 171 7.1 Summary and Conclusions ...... 171 7.2 Future Researches ...... 175 Bibliography ...... 178

List of Figures

Figure 1:1 Thesis structure ...... 12

Figure 2:1 Global trends of carsharing; source: Shaheen and Cohen (2016) ...... 19

Figure 2:2 Trip tracks for different carsharing system types ...... 31

Figure 3:1 Summary of research contributions in Chapter 3 ...... 57

Figure 3:2 Schematic explaining choice set formation of carsharing users ...... 64

Figure 3:3 Distribution of GoGet usage data considering a 2km radius ...... 70

Figure 3:4 Cumulative survival probability pattern for log-logistic model ...... 74

Figure 3:5 Hazard pattern for log-logistic model ...... 75

Figure 4:1 Summary of research contributions in Chapter 4 ...... 85

Figure 4:2 Kernel density distribution of travel time ...... 98

Figure 4:3 Kernel density distribution of travel mileage ...... 99

Figure 4:4 Kernel density distribution of monetary expenditure ...... 99

Figure 4:5 Kernel density distribution of mileage/travel time ratio ...... 100

Figure 4:6 Comparison of vehicle usage pattern in CBD and non-CBD areas (measured by average expenditure (AU dollar)) ...... 115

Figure 4:7 Comparison of vehicle usage pattern for Australian and non-Australian users (measured by average expenditure (AU dollar)) ...... 116

Figure 5:1 Summary of research contributions in Chapter 5 ...... 123

Figure 5:2 Locations and capacities of GoGet vehicle pods ...... 131

Figure 5:3 System profit over capacity and one-way trip price in low-demand scenario (total demand = 6086) ...... 135

Figure 5:4 System profit over capacity and one-way trip price in medium-demand scenario (total demand = 10356) ...... 136

Figure 5:5 System profit over capacity and one-way trip price in high-demand scenario (total demand = 28237) ...... 136

Figure 5:6 The numbers of trips for different demand and capacity scenarios ...... 140

Figure 6:1 Framework of the integrated supply-demand model ...... 146

Figure 6:2 Summary of research contributions in Chapter 6 ...... 147

Figure 6:3 System profit over 푅표 and 훽 when capacity = 198 in low-demand scenario ...... 159

Figure 6:4 System profit over 푅표 and 훽 when capacity = 198 in medium-demand scenario ...... 159

Figure 6:5 System profit over 푅표 and 훽 when capacity = 198 in high-demand scenario ...... 160

Figure 6:6 The numbers of trips over one-way trip prices for different 훽 values in three demand scenarios when capacity = 198 ...... 163

Figure 6:7 System profit over one-way trip prices for different 훽 values and capacities in the low-demand scenario ...... 167

Figure 6:8 The numbers of trips over one-way trip prices for different β values and capacities in the low-demand scenario ...... 168

Figure 7:1 Final remarks of the thesis ...... 174

List of Tables

Table 2:1 Summary of studies on carsharing demand modelling ...... 28

Table 2:1 Summary of studies on carsharing demand modelling (continued) ...... 29

Table 2:2 Summary of studies on user-based relocation methods ...... 35

Table 2:3 Summary of studies on operator-based relocation methods ...... 43

Table 2:3 Summary of studies on operator-based relocation methods (continued) ... 44

Table 2:3 Summary of studies on operator-based relocation methods (continued) ... 45

Table 2:4 Summary of studies on strategic system design methods ...... 48

Table 3:1 Summary of the variables used in the models ...... 67

Table 3:2 Correlations between variables ...... 69

Table 3:3 Parameter estimation results for four models ...... 72

Table 3:4 Calculation results of BIC of four models ...... 73

Table 4:1 Summary of number of vehicle types chosen by users ...... 96

Table 4:2 Hourly rates for all membership plans and vehicle types (Australian dollar per hour) ...... 97

Table 4:3 Means and medians of continuous variables ...... 98

Table 4:4 Correlation estimation results of travel time, mileage and monetary expenditure ...... 100

Table 4:5 Summary of vehicle fleet usage in three months ...... 101

Table 4:6 Summary of variables used in the models ...... 102

Table 4:7 Parameter estimation results for baseline utility ...... 104

Table 4:8 Parameter estimation results for baseline constants ...... 107

Table 4:9 Parameter estimation results for satiation parameters (훾) ...... 109

Table 4:10 Comparison of normalised RMSE and correct ratios for simulation results ...... 111

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Table 4:11 Comparison of observed data and MDCEV model simulation results for percentage of users choosing vehicle type ...... 112

Table 4:12 Comparison of observed data and MDCEV model simulation results for means and medians of each vehicle type ...... 113

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Chapter 1. Introduction

Chapter 1 Introduction

1.1 Background and Motivations

Mobility is a major life force of the modern society. Commuters take trains and buses to go to work. Families drive cars to visit relatives and friends. Consumers need trucks to deliver food and other necessities. Mobility also accelerates the development of economy and technology. Public transport offers mobility to the masses of labour.

Private vehicles add to the mode choice and also provide convenience for users. The advent to aircrafts have facilitated globalisation, economic prosperity, and a connected society. Improvements in mobility have shortened the time and resources necessary to distribute new knowledge and eased the communication between individuals. These have further boosted the immense technological and scientific development leading to further growth of the society as a whole.

Admittedly, a continual improvement in mobility is attractive. However, people’s excessive desire for mobility has led to serious repercussions in our cities.

The widespread use of private cars has resulted in traffic congestion and excessive delays, compromising the benefits of mobility. The increasing number of cars on road has generated greater road infrastructure costs as well as maintenance and management costs. Furthermore, greenhouse gas emissions caused by vehicle fuel consumption have become one of the major threats to the environment. As for the case of Australia, the road transport was estimated to produce 12% of all greenhouse gas emissions in

2012 (Green Vehicle Guide, 2017). The problem is even worse in developing countries such as China, India and Mexico. These countries are experiencing rapid urbanisation

Chapter 1. Introduction

and economic growth. Consequently, private vehicle affordability has increased, but the current transport systems cannot adapt to the sudden influx of cars onto the road network. People from these countries are suffering from severe congestion and poor air quality due to outdated road infrastructure, lack of sense of adhering to traffic regulations, and large numbers of low fuel-efficient cars on road.

Facing these issues, transport authorities have proposed several regulations to reduce the number of vehicles on road. For example, congestion pricing has been applied to many major cities to relieve congestion on arterial roads. In some

“megacities” in China, governments have established restriction measures to only allow certain vehicles to use the urban roads. Beijing bans vehicles with even and odd- numbered license plates on alternate days. Shanghai does not allow vehicles with nonlocal license plates to drive on flyovers during rush hours. These regulations can reduce traffic congestion and pollution for local transport network, but may raise inequity concerns. Furthermore, implementing these schemes will also produce high management costs. Advocating travellers to utilise public transport is another approach to mitigate congestion and pollution. However, public transport in most cities has been found to be restrictive by travellers due to its poor service coverage and schedule inflexibility. Governments have invested heavily into the construction of rail facilities, modified existing road infrastructure to enhance public transport accessibility, and introduced more supply of public transport vehicles as a means to increase frequency and improve connectivity. Moreover, the worldwide uptake of electric vehicles can curb air pollution, but may not fundamentally reduce the number of vehicles on road.

Under such circumstances, additional mobility modes are required in order to meet travellers’ aspirations for convenience, reliability, sustainability, and

Chapter 1. Introduction

affordability simultaneously. Recently, the concept of shared mobility has emerged as a response to these challenges. It is defined as an innovative transport strategy that enables travellers to get access to transport modes, such as cars and bicycles, in a short- term on an “as-needed” basis (Shaheen et al., 2015). With shared mobility, seamless and convenient mobility becomes more affordable, which can yield travel cost savings for the users. Travellers no long need to purchase a vehicle. Instead, they purchase on- demand mobility. The reduction in vehicle ownership can be anticipated, along with the potential for a decline in traffic congestion and improvement in air quality. In addition, the door-to-door on-demand services of shared mobility can be complementary to public transport, improving the accessibility for travellers. In some suburban areas with poor public transport coverage, shared mobility can fulfil the first- and-last mile needs and connect those areas with the public transport networks.

The rising penetration of the Internet and smartphones has boosted the uptake of shared mobility in the past decade. Multiple shared mobility options have evolved, such as on-demand ride-hailing, carsharing, carpooling, and bikesharing. These options are and will continue to change our current mobility patterns. The focus of this thesis is to understand the uptake of shared mobility services as well as to forecast the changes in mobility patterns due to the uptake, specifically investigating carsharing.

In carsharing systems, carsharing operators are the mobility providers who offer a fleet of vehicles at different locations. Carsharing users have the freedom to rent vehicles within the fleet on a short-term basis, usually by the hour or by the minute, paying only for the time they use the vehicles and the mileage they drive without the costs of purchasing and maintaining vehicles.

Chapter 1. Introduction

From the perspective of individual travellers, carsharing systems offer travellers greater flexibility than public transport, reduce their travelling costs compared to private vehicles, and yet provide them a comparable travel experience to that of using a private vehicle. From the perspective of transport networks, empirical evidence has shown that carsharing has a positive impact on reducing vehicle ownership and has the potential to relieve congestion, lower emissions, and increase auto utilisation rates (Cervero et al., 2007a, Prettenthaler and Steininger, 1999). The latest report by Martin and Shaheen (2016) verified the positive impact of carsharing on reducing vehicle ownership. In their three-year study on one-way carsharing services of five major cities in North America, it was estimated that 2% to 5% of carsharing users sold their cars, and 7% to 10% decided to not purchase a new car. In addition to directly reducing car ownership, the study also indicated that the mileage reduced by carsharing was greater than that created by carsharing, resulting in a reduction of annual vehicle miles by 10 million to 29 million per city investigated.

This decrease in mileage further removed 5.5 to 12.7 metric tons of emissions per vehicle per year.

These attractive features of carsharing have led to an increasing presence of carsharing programmes in urban transport systems. As reported by Shaheen and Cohen

(2016), the number of customers engaged in the global carsharing market had grown exponentially during the last decade. At the same time, the number of vehicles provided by carsharing operators had also increased exponentially to meet the rising demand. By 2014, carsharing was operating in 33 countries and an estimated 1,531 cities with approximately 4.8 million users sharing over 104,000 vehicles. The benefits and increased uptake of carsharing are evident. However, it is important to understand

Chapter 1. Introduction

the decision-making process of travellers in their consideration of carsharing as a viable mode. Enhanced knowledge of this behaviour has the potential to assist transport planners and engineers to further develop carsharing programmes and policies to amplify benefits of the shared mobility options.

1.2 Research Context

For carsharing to generate more significant social benefits and truly improve sustainability, it is essential to further its usage. Creating a mode shift towards carsharing is difficult, but it can be eased by having a greater understanding of the factors which affect the demand for carsharing. As a mobility provider, vehicles in a carsharing system are the tools that help users achieve utility. A carsharing operator usually provides a variety of vehicles with different manufacturers and body types to satisfy users’ diverse travel demand. Determining the optimal composition of fleet at a profit is the key to attract more users and increase service usage. To solve this problem, one needs to understand users’ vehicle selection process and vehicle usage patterns.

Users’ vehicle selection process is the decision process undertaken by an individual to select a specific vehicle given a choice of vehicles within a carsharing fleet. The choice set of carsharing vehicles is very large. Taking the largest carsharing company in Australia, GoGet, as an example, it operates over 1000 vehicles across the

Greater Sydney area. Users will follow two steps to make the vehicle selection decisions. First, users screen the alternatives and come up with a small and manageable choice set. Second, they make their selection from options considered in the choice set.

Chapter 1. Introduction

How we form the choice set is an important consideration. Users’ cognitive capacity for screening and filtering alternatives from a choice set based on a predominant factor is an essential component of the first step of vehicle selection behaviour (Rashidi and

Mohammadian, 2012). Accessibility to carsharing vehicles dictates the utilisation of carsharing facilities. Thus, the distance to the carsharing vehicle is considered to be the critical factor affecting the choice set formation of vehicle selection. Understanding users’ acceptable walking distance is helpful for operators to optimise the locations of vehicle stations and vehicle placement across the stations. Thus, this thesis attempts to answer:

“What is the acceptable walking distance to a vehicle pod for users who select to travel using a carsharing vehicle?”

In addition to the walking distance to a vehicle pod, other factors such as users’ socio-demographic attributes and vehicle manufacturers and body types will also play important roles in affecting users’ vehicle selection. Modelling the impacts of these factors on vehicle selection can imply users’ preferences towards different vehicle types and further help operators identify the favourable vehicles to be included in carsharing systems. This leads to the second research questions of this thesis:

“What factors influence users’ selection of vehicles?”

Upon making a vehicle selection, users then decide how to allocate their limited travel budget to the chosen vehicle types. The vehicle types are discrete alternatives. The limited travel budget is a continuous variable. Since users are charged by travel time and mileage in carsharing systems, the budget can be the total planned travel time, mileage or monetary expenditures during a certain time period. Carsharing

Chapter 1. Introduction

usage patterns involve users’ making multiple discrete choices of the continuous amount of budget. This decision process is again influenced by users’ socio- demographic attributes and vehicle characteristics. Understanding their vehicle utilisation patterns will tell operators whether users are willing to spend more on luxury cars or economic cars, whether they prefer to drive for longer periods of time with large cars or small cars, and whether they like to use vans or utility vehicles to move large items. These findings will provide insights for carsharing operators assisting in planning optimal fleet compositions across different geographic locations.

Two more questions are studied regarding vehicle utilisation patterns:

“Which of the three continuous variables (travel time, mileage, expenditure) most significantly influences vehicle usage patterns?”

“How do users allocate the limited budget to the selected vehicle types?”

Estimating consumers’ demand is the first step to increase carsharing usage.

The next step should emphasise on improving the operation of carsharing systems in order to provide higher levels of services to satisfy users. Along with the expansion of carsharing industry, carsharing operating models have also evolved from “simple-to- operate” to “flexible-to-use”. Different types of carsharing systems have been proposed and implemented to meet users’ diverse demand, which inevitably increases the complexity of carsharing operating models.

Traditionally, carsharing operators require users to return the vehicles to the origins where they initially picked up the vehicles. This type of carsharing system is referred to as a round-trip system. It is straight forward to operate these systems since operators can plan the vehicle stock for each station based on the demand distribution

Chapter 1. Introduction

and keep the stocks balanced as vehicles are always returned (Jorge and Correia,

2013a). However, it is not always convenient for users who need to only travel one- way. Along with the increasing competition within the carsharing industry, some operators developed one-way carsharing systems that allow users to return the vehicles to any vehicle pods (carsharing vehicle stations). These one-way systems provide more flexibility to users and have the potential to attract more trips. Autolib’s carsharing system in France is a notable one-way carsharing programme: the company operates a fleet of more than 1,800 electric vehicles and possesses about 65,000 members (Kanter,

2013). The program Car2go is another successful one-way carsharing programme.

Car2go implements a station-less one-way carsharing system that allows users to pick up and return vehicles at any place within a certain area (Firnkorn and Müller, 2011),

This type of station-less one-way carsharing system is also defined as the free-floating carsharing system. The operations of Car2go in Seattle, U.S., have shown that the average number of daily rentals increased from less than 1 rental per vehicle per day to approximately 5 rentals per vehicle per day after operating the pilot programme for one year (Seattle Department of Transportation, 2014).

These cases support the claim that one-way carsharing systems tend to better satisfy the needs of the customer than round-trip systems. Though there are potential benefits for the customer, the flexibility of one-way carsharing complicates the management of the services from an operational perspective. The main challenge is to ensure the supply of carsharing vehicles can meet the demand of carsharing users.

Since travellers’ demands are not necessarily uniformly distributed across urban networks, carsharing vehicle stocks can become spatially and temporally imbalanced.

This may influence vehicle availability and result in situations where users’ pick-up

Chapter 1. Introduction

reservations cannot be fulfilled due to a lack of vehicles and users’ parking needs cannot be satisfied due to surplus vehicles. Such poor accessibility may considerably impair the profitability of one-way carsharing systems. Hence, it is critical to dynamically relocate vehicles to mitigate vehicle stock imbalance. Relocation operations represent an increase in operational costs which could potentially be compensated with the revenues earned from the increased demand for one-way trips or, in turn, could reduce benefits. A failure example is the Honda Diracc carsharing system in Singapore. At first, the system attracted a substantial number of users; but as more users joined in, the relocation process became more complex. Eventually, the project failed to maintain high accessibility, and ceased operating after six years

(Brook, 2008). This underlines the necessity to conduct an integrated supply and demand cost-benefit analysis before introducing one-way carsharing services.

Furthermore, it should be noted that user demand is elastic to both trip cost and the available supply of vehicles in carsharing networks. Increasing trip price can bring operators high revenue earned from a single trip, but will also reduce users’ willingness to utilise carsharing services. More vehicles available in vehicle pods can ensure the reliability and accessibility of carsharing services, but may induce high costs of purchasing vehicles and maintaining parking spaces. Understanding how demand responses to trip price and vehicle supply and how profit changes over these two factors can help operators determine the most profitable development plans.

Conversely, it should be noted that the demand is not only elastic to vehicle supply, but also can change the availability of vehicles and further change the vehicle stock distribution. Thus, it is important to consider the mutual effects between demand and supply when evaluating the profitability of a carsharing system and determining

Chapter 1. Introduction

relocation strategies. By integrating supply and demand in the cost-benefit analysis, this research attempts to answer two more questions:

“How does demand and supply interact in one-way carsharing systems?”

“How do vehicle availability and trip price influence one-way carsharing system profits?”

1.3 Contributions

This thesis undertakes an integrated demand and supply analysis of carsharing systems.

To the best of the author’s knowledge, this research contains the first attempt to understand and optimise carsharing systems comprehensively considering the interdependency of demand and supply. The core contributions of this thesis can be summarised as follows:

• Introduce a spatial hazard-based modelling framework to model carsharing

users’ vehicle selection behaviour. (Chapter 3)

o Investigate the importance of users’ attributes and fleet characteristics

on vehicle choice set formation behaviour.

o Identify the acceptable walking distance to gain access to a carsharing

vehicle.

• Apply multiple discrete-continuous extreme value (MDCEV) models to

analyse carsharing users’ vehicle utilisation patterns. (Chapter 4)

Chapter 1. Introduction

o Three MDCEV models considering travel time, mileage, and monetary

expenditure as the continuous consumption constraints are developed.

o An efficient simulation procedure is undertaken to compare the three

models to determine the best-fit approach.

• Propose an optimisation model considering the interdependency between

demand and supply when analysing the profitability of one-way carsharing

systems. (Chapter 5)

o Integrate an integer programming model with a discrete choice model

to maximise the profit for carsharing operators who provide both one-

way and round-trip services. The profit considers the revenues earned

by trip demand as well as the costs associated with vehicle relocations.

• Incorporate an optimisation model with a discrete choice model that includes

vehicle availability as a variable directly affecting users’ mode choice

behaviour (Chapter 6)

o Extend the method proposed in Chapter 5 and use vehicle availability

to link demand and supply in one-way carsharing systems.

o Linearise the constraints of the discrete choice model.

1.4 Organisation

This section describes the structure of this thesis and summarises the content of each chapter. This study explores carsharing systems from two aspects: demand estimation and operation optimisation. The demand estimation part places emphasis on users’

Chapter 1. Introduction

demand for carsharing vehicles. Two demand models are developed to estimate users’ vehicle selection behaviour and vehicle utilisation patterns. The operation optimisation part focuses on cost-benefit analysis of introducing one-way trip service to carsharing systems. Two optimisation models are developed to capture the interdependency of demand and supply. Figure 1:1 presents a summary of this research and categorises the four models into two parts.

Figure 1:1 Thesis structure

These four models compose the four main chapters of this thesis. In addition, a comprehensive literature review is documented in Chapter 2 and concluding remarks are presented in Chapter 7. The following paragraphs briefly describe the content of each chapter.

Chapter 2 Literature Review: This chapter reviews the developing history of carsharing and different carsharing systems, studies on demand estimations, and one- way carsharing relocation approaches. The demand estimation researches mainly focused on characterising carsharing users and modelling their mode choice behaviour between carsharing and other transport modes. Studies with respect to one-way

Chapter 1. Introduction

carsharing operation mainly emphasised solving the vehicle stock imbalance problem through user-based and operator-based relocation strategies, as well as optimal system design approaches. Research gaps are identified after reviewing current studies: most of them did not consider the impact of supply when estimating user demand or incorporate demand variation when modelling relocation strategies, although the interdependency between demand and supply has been pointed out by some studies.

Chapter 3 Modelling Vehicle Selection Behaviour: This chapter attempts to investigate the importance of users’ attributes and fleet characteristics on choice set formation behaviour in selecting vehicles using a spatial hazard-based model (SHBM).

In the SHBM, “distance to a vehicle” is considered as the prospective decision criteria that carsharing users follow when evaluating the set of alternative vehicles. This variable is analogous to the duration in a conventional hazard-based model. In addition, user socio-demographic attributes, vehicle characteristics, land use type of the trip origin, etc., collected from the Australian carsharing company GoGet are utilised to parameterise the shape/scale/location parameters of the hazard functions. A number of forms of parametric SHBMs are tested to determine the best fit to the data.

The accelerated failure time model with a log-logistic distribution was found to provide the best performance. The estimation results of the coefficients of the parameters can provide a starting point for carsharing organisations to optimise their vehicle pod locations and types of vehicles available at different pods, to maximise the usage.

Chapter 1. Introduction

Chapter 4 Modelling Vehicle Utilisation Patterns. Carsharing users’ vehicle choice behaviour involves choosing multiple vehicle types simultaneously and allocating continuous amounts of budget to the chosen vehicle types. The multiple discrete- continuous extreme value (MDCEV) modelling framework is applied to capture the process of allocating continuous amounts to discrete alternatives. Three MDCEV models considering travel time, mileage, and monetary expenditure as the continuous consumption constraints are developed. The three models estimate the impacts of a set of socio-demographic attributes on user’s vehicle choice and capture the satiation effect with increasing the consumption for each vehicle type. An efficient simulation procedure is applied to obtain the simulated results of the three models. The simulated results are compared to the observed data provided by GoGet carsharing company using normalised RMSE and correct ratio to determine the best-fitted model. The results suggest that travel time, mileage and monetary expenditure are equally important in determining which vehicles to choose, and affect users’ vehicle utilisation patterns in the same way. These findings can provide insights to carsharing operators on deciding the optimal fleet composition to be deployed to different areas.

Chapter 5 Dynamic Optimal Vehicle Relocation. The main challenge faced by one- way carsharing systems is the vehicle stock imbalance problem due to the uneven distribution of user demand. This chapter attempts to address this problem by proposing an optimisation model that integrates with a discrete choice model. The model accounts for the interdependent relationship between carsharing demand and supply. User demand is influenced by the availability of carsharing vehicles while the demand changes vehicle availability as well as vehicle stock distribution. The model

Chapter 1. Introduction

determines the optimal relocation decisions to maximise the profit for carsharing operators that offer both one-way and round-trip services. The model is tested using

GoGet carsharing network to evaluate the impacts of different pricing and capacity policies on the system profit in different travel demand scenarios. The results indicate that the one-way trip price has a more significant impact on system profit than vehicle pod capacity. Furthermore, the maximum profits occur at different prices of one-way trips with different travel demand profiles.

Chapter 6 Optimal Relocations in Demand Responsive Carsharing Systems. This chapter is an extension and improvement of the method proposed in Chapter 5. The discrete choice model cited by Chapter 5 does not consider vehicle availability as a factor that could directly influence the elasticity in demand. To evaluate the impact of the interaction between demand and supply more directly, a discrete choice model that includes vehicle availability as a parameter directly affecting users’ mode choice behaviour is introduced and incorporated within the optimisation formulation. The incorporation of a discrete choice model with the integer linear programming formulation leads to a nonlinear model. A linearisation scheme is proposed to reformulate it. The model is also tested in GoGet network. A sensitivity analysis on total travel demand, one-way trip price, system capacity and vehicle availability coefficient is undertaken to evaluate their impacts on system profit. The results reveal that the pattern of profit over trip price varies among scenarios with different vehicle availability coefficients, which is inconsistent with the upward parabola pattern of profit over trip price observed from the previous model in Chapter 5. It can be concluded that the interdependence between demand and supply should be considered

Chapter 1. Introduction

when setting relocation plans and pricing strategies in one-way carsharing systems. If there is a strong interaction between demand and supply, the supply of carsharing vehicle fleet has a more critical impact on system profit.

Chapter 7 Conclusions and Future Researches. This final chapter presents the conclusions and contributions of this thesis. The future directions of this research are also discussed in this chapter.

Chapter 2. Literature Review of Carsharing Related Researches

Chapter 2 Literature Review of Carsharing Related

Researches

This chapter reviews the studies related to carsharing. First, the history of the development of carsharing is introduced, followed by summarising the benefits of carsharing systems. Then, studies regarding carsharing demand modelling are categorised into mode choice modelling and user behaviour modelling, and are reviewed in Section 2.3. Section 2.4 places the emphasis on the operation of one-way carsharing systems. Initially, different types of carsharing systems are introduced and compared. Then, studies with respect to two types of vehicle relocation strategies and system design approaches are described. Finally, the research gaps identified in the literature are presented in Section 2.5.

2.1 The History and Growth of Carsharing

The concept of carsharing emerged in 1948 when the earliest carsharing organisation known as “Sefage” (Schweizer Selbstfahrergemeinschaft) was founded in Zurich,

Switzerland (Shaheen et al., 1998). “Sefage” was initially motivated by the affordability of sharing cars for individuals who could not afford purchasing a car.

Later in the 1970s, several other experiments of carsharing appeared, e.g. “Procotip” in France in 1971 and “Witkar” in Netherlands in 1973 (Shaheen and Cohen, 2007).

These early carsharing systems remained in small scale but discontinued after a few years’ operation. More successful and large-scaled carsharing organisations were

Chapter 2. Literature Review of Carsharing Related Researches

launched until the mid-1980s. These included the two oldest and largest carsharing programmes: “Mobility CarSharing” begun in 1987 in Switzerland with over 20,000 members and “StattAuto” begun in 1988 in Berlin with 4,000 members (Shaheen et al., 1998).

Following Europe, carsharing started in North America in the 1980s with two pilot experiments: “Mobility Enterprise” undertaken by Purdue University, and

“Short-Term Auto Rental (STAR)” operated in San Francisco, California (Shaheen et al., 2006). Although these two programmes exited the market after two to three years’ operation, they promoted the concept of carsharing to the public, evaluated the feasibility of implementing carsharing, and collected the market’s response to carsharing. Such initial demonstration programmes are common during the worldwide expansion of carsharing. They were launched to test carsharing operations and evaluate new markets. Many of these programmes discontinued after a short period, but most were replaced by permanent carsharing services (Shaheen and Cohen, 2007). After the exits of these two pilot projects, carsharing re-emerged in North America in 1994 with the launch of Auto-Com (later CommunAuto) and experienced a notable increase in the number of carsharing organisations between 1999 and 2001 (Shaheen et al., 2006).

Along with the rapid growth in North America, carsharing also spread to Asia

(Japan and Singapore) in 1997, Australia in 2003, and South America in 2009

(Shaheen and Cohen, 2013). As reported by Shaheen and Cohen (2016), carsharing was operating in 33 countries and an estimated 1,531 cities with approximately 4.8 million users sharing over 104,000 vehicles by October 2014. Figure 2:1 presents the global trends of carsharing industry over the last decade. The number of customers engaged in the global carsharing market had grown exponentially during the last

Chapter 2. Literature Review of Carsharing Related Researches

decade and reached approximately 5 million by 2014. At the same time, the number of vehicles provided by carsharing operators had also increased exponentially to meet the rising demand and was estimated to be hundreds of thousands by 2014.

Figure 2:1 Global trends of carsharing; source: Shaheen and Cohen (2016)

2.2 The Benefits of Carsharing

Reviewing the history of the carsharing industry, it can be found that affordability motivated its emergence, and convenience boosted its global expansion. Besides these benefits brought to individual travellers, studies have shown that carsharing also has positive impacts on urban society by reducing vehicle ownership (Barth and Todd,

1999), which can further reduce congestion, provide more equitable access to private transport and limit the environmental impact of emissions release (Duncan, 2011).

Chapter 2. Literature Review of Carsharing Related Researches

Carsharing offers the user the choice to forego ownership of a vehicle as he or she will still have access to a private vehicle when it is necessary for specific trip purposes. As a result, this has the potential to reduce the number of vehicles travelling within the overall networks. Martin et al. (2010) studied the impact of carsharing on household vehicle holdings in North America and presented that the average number of vehicles per household dropped from 0.47 to 0.24 for those households utilising carsharing. The study also suggested that carsharing has removed 90,000 to 130,000 vehicles from the road at an aggregate level. The latest three-year study on one-way carsharing services of five major cities in North America also demonstrated the mileage reduced by carsharing has exceeded the mileage created by it, resulting in a decrease in annual vehicle mileage by 10 million to 29 million miles per city investigated (Martin and Shaheen, 2016). A vast amount of literature has highlighted the advantages of carsharing programmes (Stillwater et al., 2009b, Duncan, 2011,

Jorge and Correia, 2013a, Shaheen and Cohen, 2013).

For further information about carsharing, Shaheen and Cohen (2013) provided the latest overview of the state of practice of carsharing and its impact on transportation systems. The main advantages can be summarised as follows:

• Reducing travel costs to individual users: Carsharing provides an option to

reduce the fixed costs associated with car ownership, such as insurance,

registration and service costs (Katzev, 2003). Thus, it can encourage savings,

and allocate income more efficiently at an individual user level.

• Alleviating traffic congestion: As mentioned before, carsharing reduces the

need for private vehicle ownership which in turn reduces the number of

vehicles traversing the network and consequently decreases the vehicle

Chapter 2. Literature Review of Carsharing Related Researches

kilometres travelled (VKT) (Martin et al., 2010, Shaheen and Cohen, 2013).

Currently, this advantage can be enhanced with the advent of autonomous

vehicles. As studied by Fagnant and Kockelman (2014), each shared

autonomous vehicle can replace around eleven conventional vehicles owing to

its potential to overcome carsharing barriers (i.e. users’ travelling to access

available vehicles).

• Lowering travel related energy usage and greenhouse gas emissions: The

reduction of vehicle ownership due to carsharing can bring about

environmental benefits of mode shift, vehicle production, and parking

infrastructure savings. The decrease in vehicle kilometres travelled (VKT) with

carsharing members also implies the reduction of fuel consumption and

greenhouse gas emissions (Chen and Kockelman, 2016). Chen and Kockelman

(2016) reported that carsharing members have reduced their individual travel-

related energy use and greenhouse gas emissions by 51% after joining a

carsharing scheme. This has contributed to approximately 5% savings at the

aggregate level in the U.S.

• Improving accessibility to private vehicle usage: With carsharing schemes,

socially sustainable transport systems can be achieved because lower-income

earners can now potentially access private vehicles, whereas without

carsharing schemes it would not be financially feasible (Wachs and Taylor,

1998).

• Improved parking conditions: A reduction in car ownership will reduce the

demand for off and on street parking of private vehicles.

Chapter 2. Literature Review of Carsharing Related Researches

2.3 Demand Modelling

Literature has suggested the need for carsharing as a mode of transport within the urban environment (Stillwater et al., 2009b, Ciari et al., 2013, Jorge and Correia, 2013a,

Shaheen and Cohen, 2013). For carsharing to create more significant social benefits and truly improve sustainability, it is essential to understand what factors affect the demand for carsharing to further its usage. From the perspective of carsharing operators, it is also critical to determine the most efficient allocation of resources to satisfy users’ demand. As a result, there is a growing body of literature modelling carsharing users’ demand patterns.

Jorge and Correia (2013a) presented a comprehensive literature review regarding demand modelling approaches for carsharing programmes. The paper highlighted that demand estimation is difficult due to the interdependency of vehicle availability and the number of trips. Most studies have adopted regression models, stated-preference surveys, and data mining techniques to study the characteristics of users of carsharing programmes (Catalano et al., 2008, Stillwater et al., 2009b,

Morency et al., 2011, Schmöller et al., 2015, Jorge et al., 2015a). These studies can be mainly categorised into mode choice modelling and user behaviour modelling.

2.3.1 Mode choice modelling

Stated preference techniques and discrete choice models are the most widely- applied methods to model users’ mode choice behaviour among carsharing and other transport modes. Catalano et al. (2008) utilised the survey data and stated preference techniques. They found that users’ model choice behaviour were affected by travel

Chapter 2. Literature Review of Carsharing Related Researches

time, travel cost, parking time, and the number of cars available to household members.

Le Vine et al. (2014b) analysed travellers’ preference on round-trip carsharing, point- to-point carsharing, and other transport modes using the survey data from London.

They suggested that point-to-point carsharing could attract three to four times more users compared to round-trip carsharing. Travellers of commuting trips would use point-to-point carsharing more frequently than round-trip carsharing. Le Vine et al.

(2014a) focused more specifically on grocery shopping trips and concluded that one- way carsharing was more likely to be chosen when the amount of time that travellers spent on the way was longer and when the grocery shopping frequency was lower.

Efthymiou et al. (2013) applied an ordered logit model to investigate the willingness of young people (aged 18 to 35) in Greece to join carsharing schemes. Efthymiou and

Antoniou (2016) extended their research through a hybrid choice and latent variable model and captured the effect of people’s satisfaction of current travel patterns on their choice of carsharing. More recently, Kim et al. (2017) also considered the impact of satisfaction of current travel patterns when modelling travellers’ mode choice behaviour. They further captured the effect of the uncertainty of shared car availability by developing a random-regret minimisation-based hybrid choice model.

Besides Kim et al. (2017), several other researchers also found out the dependency between carsharing vehicle availability and its demand from the findings of mode choice modelling. De Luca and Di Pace (2015) undertook a survey on travellers who commuted within the metropolitan area of Salerno, Italy, to model the mode choice behaviour, and evaluate the feasibility of implementing inter-urban carsharing programmes. The results suggested that inter-urban commuters’ mode choice behaviour was significantly affected by travel cost, access time to carsharing

Chapter 2. Literature Review of Carsharing Related Researches

services, travellers’ gender, age, trip frequency, car availability and whether the trip was home-based. The impacts of carsharing service accessibility and availability were highlighted from the study. Later in 2016, Ciari et al. (2016) also confirmed such dependency between carsharing demand and service availability and station location through a binary logistic model.

Travellers’ choice of electric vehicles (EVs) when using carsharing services have also attracted researchers interests. Zoepf and Keith (2016) modelled users’ propensity towards hybrid electric vehicles(HEVs), plug-in electric vehicles (PEVs) and battery electric vehicles (BEVs) through a stated preference survey on members of Zipcar, the largest carsharing operator in North America. They implied that carsharing users preferred HEVs, and the utility of EVs decreased when the reserved travel distance increased. The negative impact of distance on selecting EVs was also reported by Wielinski et al. (2016): Carsharing users preferred to use hybrid vehicles when the travel distance was above 24 kilometres. Besides, Cartenì et al. (2016) studied people’s willingness to use EVs in carsharing services based on a survey undertaken in Salerno, Italy. They first modelled travellers’ choice of switching from private cars to carsharing services, then evaluated the effect of having EVs in the fleet on travellers’ mode switching behaviour. The estimation results indicated that the possibility of using EVs could increase the probability of switching from private cars to carsharing services.

Simulation techniques are another widely applied approaches to model travellers’ mode choice. Ciari et al. (2013) used an activity-based simulation tool to investigate travellers’ mode choice. The simulation model was validated using the customer data of Mobility Switzerland. Balac et al. (2015) applied the multi-agent

Chapter 2. Literature Review of Carsharing Related Researches

simulation tool (MATSIM) and found that carsharing fleet size and the availability of cars had the potential to increase the usage in both round-trip and one-way carsharing systems. Moreover, one-way carsharing could generate approximately three times more trips than round-trip carsharing.

2.3.2 User behaviour modelling

As for user behaviour modelling, Stillwater et al. (2009a), Morency et al.

(2012), and De Lorimier and El-Geneidy (2013) studied the impacts of factors such as the built environment and users’ socio-demographic attributes on carsharing demand through regression models. It should be noted that De Lorimier and El-Geneidy (2013) pointed out the size of a carsharing station was the key to its usage, which revealed the direct impact of carsharing supply on its demand. Correia et al. (2014) also focused on the impact of carsharing stations. They considered the flexibility of users’ choice on those stations: users might not always select the closest carsharing station, instead they might use the second or even the third closest station if there was no vehicle available in the closest station. Their findings reflected the impact of the information of station vehicle stocks on users’ station choice, and implied the complexity of users’ vehicle selection process.

Besides regression models, Habib et al. (2012) and Costain et al. (2012) utilised the hazard-based modelling framework to explore users’ behaviour regarding carsharing membership duration. Habib et al. (2012) found users’ intention to remain to be a carsharing member decreased as the membership duration increased. Users’ membership duration would not necessarily be influenced by increasing the inventory

Chapter 2. Literature Review of Carsharing Related Researches

of carsharing stations, but the monthly frequency of usage would be increased by doing so. Costain et al. (2012) concluded that monthly carsharing subscription rates had a negative impact on users’ membership duration, while perceived savings had a positive impact. They also formulated several regression models to investigate users’ usage frequency, vehicle type choice and analyse users’ attitudes towards the environment and the safety.

Morency et al. (2011) established the typology of carsharing users using the transaction data provided by CommunAuto, a carsharing company in Montreal,

Quebec, Canada. Data mining techniques were used to categorise members based on their temporal units which could represent their behaviour. The results were consistent with the aim of the short-term rental principle of carsharing: the majority of members used carsharing with low frequency (0.4 uses of the programme per week on average) and travelled short distances using the services (14.3 kilometres per week on average).

The attribute of travelling short distances of carsharing users was also reflected by the survey developed by Kopp et al. (2015). They compared the mobility behaviour of free-floating carsharing users to non-carsharing users through a smartphone-based survey in Germany. They found carsharing users had a significantly higher education level and income than non-carsharing users. Their mobility behaviour was found to be more purpose-oriented and more flexible.

Focusing on the motivations of using carsharing, Schaefers (2013) applied the qualitative means-end chain analysis method and summarised four motivational patterns of using carsharing: value-seeking, convenience, lifestyle, and environmental consciousness.

Chapter 2. Literature Review of Carsharing Related Researches

Furthermore, Leclerc et al. (2013) studied carsharing users’ behaviour from the perspective of trip characteristics, such as trip stop locations and trip chain attributes.

Their findings revealed that carsharing trip chains contained more trips compared to typical car trips. Those carsharing trips were shorter and served mainly for non- working purposes.

The literature regarding carsharing demand modelling is summarised in Table

2:1.

Chapter 2. Literature Review of Carsharing Related Researches

:1 Summary of studies on carsharing demand modelling studies of demand carsharing on Summary :1 Table2

Chapter 2. Literature Review of Carsharing Related Researches

Table 2:1 Summary of studies on carsharing demand modelling (continued) studies of demand carsharing on Summary Table2:1

Chapter 2. Literature Review of Carsharing Related Researches

2.4 Operation Strategies

Along with the expansion of the carsharing industry, carsharing operating models have also evolved from “simple-to-operate” to “flexible-to-use”. Different types of carsharing systems have been proposed and implemented to meet users’ diverse demand, which inevitably increases the complexity of carsharing operating models.

Under such circumstances, several research efforts have been focused on building effective relocation and system design strategies to solve operation problems. This section will review the literature around the advantages and shortcomings of different types of carsharing systems, followed by the strategies and algorithms proposed to optimise carsharing operations.

2.4.1 Carsharing system types

Based on vehicle returning policies, carsharing systems can be categorised into three major types: round-trip (also called two-way in some papers), one-way, and free- floating carsharing systems. The degree of flexibility of these three systems increases in ascending order.

Both round-trip and one-way trip carsharing systems are station-based systems.

Carsharing vehicles are distributed in several stations or vehicle pods with limited capacity across a certain operation area. In round-trip system, users are required to return the rented vehicles to the same stations where they pick them up as shown in

Figure 2:2. This form of carsharing systems is simple for operators to maintain, but not always convenient for travellers who only want to go one-way. Therefore, round- trip systems are best suited for leisure, shopping and sporadic trips.

Chapter 2. Literature Review of Carsharing Related Researches

Figure 2:2 Trip tracks for different carsharing system types

A more flexible system is the one-way carsharing which allows users to return their vehicles to any carsharing stations close to their destinations. The flexibility of one- way carsharing systems is better suited to users who only need to make one-way trips.

Furthermore, as presented in Figure 2:2, given a certain origin-destination pair, the total driving mileage might be reduced by half in one-way systems compared to round- trip systems. Therefore, one-way systems have the potential to capture a substantially larger market share than round-trip systems. The market attractiveness of one-way carsharing systems has encouraged a number of carsharing companies to provide one- way services to users, such as Autolib in France (Autolib, 2017), Zipcar in U.S.

(Zipcar, 2017), and Communauto in Canada (Communauto, 2017).

Evolved from station-based one-way systems, free-floating carsharing systems further improve the flexibility of vehicle return. In free-floating systems, users can pick up and return vehicles at any place, not restricted to stations, within a certain area

Chapter 2. Literature Review of Carsharing Related Researches

(Firnkorn and Müller, 2011). One notable free-floating system is the programme

Car2go implemented in U.S. Its pilot program in Seattle, U.S. has experienced an average number of daily rentals increased from less than 1 rental per vehicle per day to approximately 5 rentals per vehicle per day after operating one year (Seattle

Department of Transportation, 2014).

2.4.2 Vehicle relocation models – user-based relocation

Along with the benefits of one-way carsharing systems (both station-based and station-less), the flexibility of such systems also brings more complex problems to the operators. One dominant challenge is rectifying imbalanced vehicle stocks. The source of the vehicle stock imbalance can be attributed to the non-uniformity in the spatio- temporal distribution of the demand, potentially leading to the aggregation of vehicles over time and space. This problem could induce an expensive operational strategy that could potentially impair profitability. For example, the one-way carsharing system

Honda Diracc system in Singapore attracted a large number of users right after it launch; but eventually failed to maintain high accessibility as more users joined, and ceased operating after six years (Brook, 2008).

Under such circumstances, several research efforts have been focused on building effective relocation strategies for one-way carsharing systems. Those strategies are mainly categorised into user-based and operator-based relocation approaches. The basic concept of user-based relocation is to make use of price incentives to encourage users to relocate vehicles. One strategy proposed by Di

Febbraro et al. (2012), Cepolina and Farina (2012) and Clemente et al. (2013) is to ask

Chapter 2. Literature Review of Carsharing Related Researches

users to drive vehicles to designated locations by offering them discounts. In their models, users could choose to drop off their vehicles in their desired zones or the zones with a shortage of vehicles suggested by the system. Di Febbraro et al. (2012) and

Clemente et al. (2013) also offered the users a discount if they were willing to end trips in the suggested zones. However, a major issue with such strategy is the uncertain acceptance probabilities that the users will agree to drop off at the proposed destinations given certain discount and distance. Thus, it is difficult for operators to know users’ decisions in advance and further take control of vehicle stocks over the operation time.

Another method to implement user-based relocation is to encourage joint and split trips based on vehicle stock distribution (Barth et al., 2004, Uesugi et al., 2007).

This method requires several users who are willing to start and end trips from the same stations to share one vehicle if the origin station is lacking vehicles and the destination station has excessive vehicles. On the contrary, if the origin station has an oversupply of vehicles and the destination station has a shortage, the method will recommend users to drive separate vehicles.

Furthermore, dynamic pricing schemes have also been developed to influence the distribution of user demand and further control vehicle stocks (Waserhole and Jost,

2012, Jorge et al., 2015b). This approach is based on the fact that users’ travel demand is elastic to travel cost. In such schemes, lower trip prices would be offered to encourage trips from stations with excessive vehicles to stations with inadequate numbers of vehicles; whereas higher trip price would be given to reduce the number of trips from unsaturated stations to oversaturated stations.

Chapter 2. Literature Review of Carsharing Related Researches

An overview of user-based relocation studies is presented in Table 2:2. These studies emphasised that user-based relocation has the advantage of not increasing operation costs since no extra staff needs to be hired to relocate vehicles. However, depending purely on users can be unreliable since users might not be sensitive to the price incentives provided by the operators. Owing to this reason, this study will focus on operator-based relocation, which is more reliable.

Chapter 2. Literature Review of Carsharing Related Researches

based relocation methods basedrelocation

Table 2:2 Summary of studies of use on Summary Table2:2

Chapter 2. Literature Review of Carsharing Related Researches

2.4.3 Vehicle relocation models – operator-based relocation

Operator-based relocation requires extra staff to redistribute vehicles between stations. Relocation staff either drive carsharing cars from one station to another or use car transporters to relocate carsharing cars. Compared to user-based relocation, operator-based relocation is more reliable because the relocation activity is controlled by the operators. Nevertheless, this type of relocation will incur extra costs associated with vehicle relocation and generate more greenhouse gas emissions due to additional vehicle trips. Facing these potential disadvantages, many studies have concentrated on minimising relocation costs or maximising system profits. Optimisation and simulation techniques are the two major methods applied to solve these problems.

Barth and Todd (1999) developed a hybrid discrete-event and time-stepped simulation model based on the queuing theory to evaluate the performance of three relocation strategies in one-way carsharing systems. The performance was assessed via indicators including total average waiting time, total queue length, and number of relocations. They found the relocation strategies became more effective if more complete user demand information could be provided. Repoux et al. (2015) also applied the event-based simulation model to compare different relocation strategies based on several performance indicators. The indicators of their study were demand loss, station and vehicle states, and largest vehicle shortage.

Kek et al. (2006) formulated a time-stepping simulation model to test the effectiveness of two relocation strategies: 1) move vehicles to the stations with shortest travel time, and 2) relocate vehicles from the stations with surplus vehicles to the stations with shortages. The performance indicators of their model included zero vehicle time, full-port time, and number of relocations. The model was tested using

Chapter 2. Literature Review of Carsharing Related Researches

operational data from the Honda ICVS system in Singapore. The proposed relocation strategies were proved to effectively reduce the operation costs, the number car parking lots required, and the number of staff needed. Kek et al. (2009) extended their research and introduced a three-phase optimisation-trend-simulation (OTS) decision support system for relocation operations. The system contained an optimiser, a trend filter, and a relocation simulator. The optimiser was a mixed integer linear programming (MILP) model with the objective to minimise overall system costs. The outputs of this optimiser were vehicle activity and staff activity. These outputs served as the input of the trend filter and were further translated to a set of operating parameters through several heuristics. Those operating parameters, such as staff strength, shift hours, decision of relocation strategies, and relocation thresholds, were the input to the relocation simulator developed by Kek et al. (2006). The simulator then evaluated the performance of the whole system using three indicators, i.e. zero- vehicle time, full-port time and number of relocations. The authors also tested the performance of this system using Honda ICVS operational data and concluded that its performance was better than their previous model.

Fan et al. (2008) and Fan (2014) developed a multi-stage stochastic programming model to optimise dynamic vehicle allocation of one-way carsharing systems. The model considered demand uncertainty by presupposing that only the demand for the first day was known in advance, while the demand for the next day was stochastic. They suggested that the managers of carsharing companies had full operational control of which vehicle reservations to accept or refuse and only the trips helping to balance vehicle stocks should be accepted. The model solved the optimal vehicle supply at each station at the beginning of the day and the optimal relocation

Chapter 2. Literature Review of Carsharing Related Researches

trips to be performed at the end of the day. Fan et al. (2008) applied the Monte Carlo sampling method to solve the proposed model. Later, Fan (2014) highlighted that ignoring demand uncertainty would incur higher operation costs in one-way carsharing systems.

Nair and Miller-Hooks (2011) also considered the uncertainty of demand. They formulated a stochastic mixed integer programming (MIP) model aiming to solve optimal vehicle relocation plans in order to satisfy the most near-future demand. In their model, the demand was calculated based on historical information. Relocation decisions were determined based on demand as well as the number of vehicles and free parking spaces at each station. The main contribution of this paper is the consideration of demand stochasticity. The model was experimented in Singapore. The authors found that demand uncertainty had a strong impact on relocation costs and service level. Later, Nair et al. (2013) applied this model to the bikesharing system operated by Ve´lib’ in Paris, France. Also focusing on demand variation, Jorge et al. (2012) incorporated the uncertainty in demand in the previous proposed model by de Almeida

Correia and Antunes (2012). They concluded that demand variation would impair the performance of relocation strategies.

Jorge et al. (2014) developed an optimisation model to solve relocation decisions to maximise the total profits of one-way carsharing systems. They applied the model to Lisbon, Portugal and used a simulation model to compare two relocation policies, and found that both policies could increase system profits. More recently,

Jorge et al. (2015a) utilised an optimisation model to assess the profitability of introducing one-way carsharing services in an existing round-trip system. The model provided a rationale for whether a one-way trip should be accepted with the purpose

Chapter 2. Literature Review of Carsharing Related Researches

of maximising total profit. They applied the model to Boston, U.S. and confirmed the profitability of adding one-way services in all scenarios.

Wang et al. (2010a), (2010b) incorporated the demand forecasting into their relocation model. They proposed a microscopic traffic simulation model to simulate the road network of Clementi, Singapore. A focus-forecasting model was built to forecast users’ demand for carsharing. The forecasted demand served as the input for the inventory-replenishing model, which further solved the optimal relocation.

Nourinejad and Roorda (2014) built a dynamic vehicle relocation model to determine the optimal relocation, reservation time and fleet size for one-way carsharing systems. The model consisted of a vehicle relocation optimisation model to find the optimal relocations, and a parking inventory optimisation model to determine when relocations should be conducted. A static benchmark model was developed to be compared to the solutions of the dynamic model. The dynamic relocation model was applied to Autoshare in Canada, and the results revealed that increasing reservation time could reduce fleet size.

More recently, Nourinejad et al. (2015) put their focus on the optimisation of rebalancing relocation staff. They argued that although the imbalanced distribution of vehicles in one-way carsharing systems could be addressed by employing rebalancing operators to drive the vehicles from unpopular stations to popular stations, the relocation staff themselves would become imbalanced. Aiming at rebalancing the staff, they developed two integrated multi-travelling salesman formulations to assign relocation actions to relocation staff and determine the optimal fleet and staff size.

Similar relocation staff rebalancing problem was also studied by Smith et al. (2013), and Lee and Park (2013b), (2013a). Smith et al. (2013) developed an optimisation

Chapter 2. Literature Review of Carsharing Related Researches

strategy to route the rebalancing staff and vehicles. Lee and Park (2013b) and (2013a) applied a genetic algorithm to optimise the operation sequence of relocation staff with the objective of minimising relocation cost.

Electric vehicles (EVs) have been widely utilised in one-way carsharing systems. When dealing with the vehicle stock imbalance problem in electric vehicle sharing systems, one should also consider the battery recharging requirements.

Bruglieri et al. (2014) proposed a mixed integer linear programming (MILP) model to address the vehicle relocation problem in an electric vehicle sharing system. They accounted for the EV recharging problem through a constraint of the maximum distance travelled by EV. The objective of this model was to maximise the total number of served relocation requests. The solution gave the optimal schedule and route for relocation staff. Later, Bruglieri et al. (2017) argued that this model did not consider the economic sustainability, so they modified the model by changing the objective to maximise the total system profit. They associated each served relocation request with a revenue and each utilised staff with a cost, and the profit was given by the difference between the total revenues and total costs. Both models were tested in the city of Milan, Italy.

Boyacı et al. (2015) developed a multi-objective MILP model for electric vehicle sharing systems. The two objectives are maximising the operator’s net benefit as well as the user’s net benefit. They considered the recharging problem of EV by including a fixed EV charging period after an EV was returned to the station. The model solved the optimal relocation plan, fleet size, number of parking spaces in stations, number and location of stations required. More recently, Boyacı et al. (2017) also built a multi-objective MILP model aiming at maximising the total number of

Chapter 2. Literature Review of Carsharing Related Researches

served trip requests and minimising the total relocation costs in one-way electric vehicle sharing systems. Unlike typical multi-objective problems converted multiple objective functions to a single function through variable weights, they applied a hierarchical approach to ensure the objective were satisfied following their importance order for the decision makers. They put users’ demand as the most important objective to guarantee high service level. The model was solved by a clustering algorithm.

Another perspective on EV comes from Cao et al. (2016), who proposed a vehicle relocation threshold determining method to plan relocations in electric vehicle sharing systems. The threshold provided the reference of whether relocations should be performed between stations. They tested the method using data from EVCard system in Shanghai, China. Marouf et al. (2014) focused on the technology to redistribute EVs. They presented an automatic parallel parking controller and platooning system to redistribute EVs automatically.

In the context of free-floating carsharing systems, Weikl and Bogenberger

(2015a) and (2015b) proposed an optimisation and rule-based approach to determine optimal relocation operations. They categorised the carsharing operation area into several zones with a historical shortage or surplus of vehicles. They also generated a demand indicator based on historical booking data. The zone categorisation and demand indication provided the input of the optimisation model and determined the optimal number of vehicles in each zone during each time interval. Once the real-time bookings were triggered, the number of vehicles in each zone changed and the method further solved the inter-zonal or intra-zonal relocation decisions based on the deviation of the current number of vehicles and the optimal number of vehicles in the zones.

Also focusing on free-floating carsharing systems, Herbawi et al. (2016) proposed to

Chapter 2. Literature Review of Carsharing Related Researches

use shuttles to relocate vehicles in free-floating carsharing systems. Their objectives were to maximise the number of vehicles that could be carried within a given time interval and to minimise the total duration of relocating those vehicles using shuttles.

An evolutionary algorithm was developed to solve their model.

An overview of researches studying operator-based relocation methods could be found in Table 2:3.

Chapter 2. Literature Review of Carsharing Related Researches

basedmethods relocation

operator

Table 2:3 Summary of studies of on Summary Table2:3

Chapter 2. Literature Review of Carsharing Related Researches

based(continued) methods relocation

Table 2:3 Summary of studies of operator on Summary Table2:3

Chapter 2. Literature Review of Carsharing Related Researches

based(continued) methods relocation

Table 2:3 Summary of studies of operator on Summary Table2:3

Chapter 2. Literature Review of Carsharing Related Researches

2.4.4 Strategic system designs

In addition to relocation approaches, strategic system design is another method to control the supply and demand distribution in one-way carsharing systems.

Researchers usually formulated optimisation or simulation models to solve the optimal fleet size, number of carsharing stations, and locations of stations in order to avoid or mitigate vehicle stock imbalance problem in one-way carsharing systems.

de Almeida Correia and Antunes (2012) developed a mixed integer programming model to select the sites for carsharing stations and determine the size of selected stations. Rather than performing relocations, they focused more on optimally designing carsharing networks that ‘naturally’ circumvented the occurrence of vehicle stock imbalance situations. In their study, relocation was considered only at the end of the day. Three trip selection schemes were considered: 1) controlled service scheme, i.e. the operator had the full control over trip selection; 2) full service scheme, i.e. all trips requested by customers must be satisfied; and 3) conditional service scheme, i.e. a hybrid of the first two schemes that the operator did not have the obligation to accept all trips between stations, but could only reject the requests when there were no vehicles available at the pick-up stations. All the models were tested in a case study in Lisbon, Portugal. The results showed that the controlled service scheme would yield the highest profits. The results also suggested that the operation costs could be reduced by choosing the appropriate number of vehicle pods, the optimal locations and sizes of vehicle pods. Correia et al. (2014) expanded this model by considering the flexibility of user’s choice on carsharing stations. They assumed that if users had the information of vehicle availability of stations, they might switch to the

Chapter 2. Literature Review of Carsharing Related Researches

second or the third closest station. The results reflected the positive impact of information on total profit and efficiency of carsharing fleet.

George and Xia (2011) determined the optimal fleet size in one-way carsharing systems through a closed queueing network model. They derived the asymptotic behaviour of vehicle availability with respect to fleet size. They then proposed several vehicle balancing methods based on it. The authors further maximised the total system profit via an optimisation model and its approximation. Fanti et al. (2014) applied the framework proposed by George and Xia (2011) to electric vehicle sharing systems.

They considered three types of EVs: fully charged, partially charged and out of charge.

They also developed an optimisation model to solve the optimal fleet size with the objective of maximising profit. More recently, Hu and Liu (2016) expanded the closed queueing network to a mixed queueing network to make the previous framework more general. In this mixed queueing network, carsharing stations and routes were considered as nodes in the closed queueing network, while carsharing users and stations constructed the open queueing network. Moreover, the authors incorporated the road congestion in the new framework and designed the optimal fleet size and parking capacities jointly.

The summary of strategic system design studies is presented in Table 2:4.

Chapter 2. Literature Review of Carsharing Related Researches

Table 2:4 Summary of studies on strategic system design system methods studies of strategic on Summary Table2:4

Chapter 2. Literature Review of Carsharing Related Researches

2.5 Research Gaps

The interdependency between demand and supply in carsharing systems has been highlighted by the literature review paper by Jorge and Correia (2013a). Such interdependency plays an important role when decision makers set up carsharing operation plans and growth strategies. However, reviewing carsharing related studies in Section 2.3 and 2.4, most studies did not consider the impact of supply when estimating user demand or incorporate demand variation when modelling relocation strategies. Only a few studies have accounted for the inter-relationship between supply and demand.

Reviewing studies on demand estimation, Kim et al. (2017), De Luca and Di

Pace (2015), Ciari et al. (2016), Balac et al. (2015), De Lorimier and El-Geneidy

(2013), and Correia et al. (2014) investigated the impacts of fleet size, locations of carsharing stations and vehicle availability on users’ mode choice behaviour and usage patterns. Their findings confirmed the significant influence of carsharing facilities on user demand. Moreover, these results revealed the fact that carsharing demand estimation should be constrained by the supply of carsharing systems.

The supply of carsharing systems not only refers to the fleet size, station locations and size, but also relates to the types of vehicles provided to the users.

Popular vehicle types will attract more users to join carsharing systems and increase the frequency of using carsharing services. Therefore, it is important for decision makers to accurately predict the vehicle types that carsharing users prefer and the amounts of budget they are willing to allocate to the different vehicle types. However, there has been limited research into understanding and characterising users’ vehicle selection behaviour and vehicle utilisation patterns.

Chapter 2. Literature Review of Carsharing Related Researches

With respect to the imbalance distribution of vehicle supply in one-way systems, studies mainly focused on proposing relocation strategies or optimal system designs to solve this problem. However, most relocation models assumed deterministic demand either generated based on historical data or obtained via simulation models. A few studies accounted for the impact of demand variation on relocation strategy performance. Kek et al. (2009), Wang et al. (2010a) and (2010b) incorporated a demand forecasting model in their relocation optimisation model. Fan et al. (2008),

Nair and Miller-Hooks (2011), Nair et al. (2013), Jorge et al. (2012) and Jorge et al.

(2015b) considered stochastic demand when building relocation optimisation models.

These studies have shown that demand variation would influence the performance of relocation models. However, the interaction between demand and relocation decisions are not fully investigated.

Furthermore, it should be noted that users’ travel demand for carsharing services is influenced by the available supply of carsharing vehicles. Demand, on the one hand, generates the revenues for carsharing operators; Relocation, on the other hand, induces extra costs to them. These two factors contribute in determining the profit of carsharing systems. Hence, the interdependency between demand and supply in one-way carsharing systems makes the relocation strategies and profitability analysis more complex.

To sum up, two major research gaps have been identified through literature review. First, users’ vehicle selection behaviour and vehicle utilisation patterns have never been fully understood and characterised. Second, the interdependency between demand and supply in one-way carsharing systems has never been incorporated when making relocation strategies and profitability analysis. The following chapters will

Chapter 2. Literature Review of Carsharing Related Researches

attempt to bridge these gaps and discuss from two major parts: demand estimation and operation optimisation.

Chapter 2. Literature Review of Carsharing Related Researches

Part I. Demand Estimation

Part I Demand Estimation

A carsharing system is a mobility provider for travellers. It usually provides a fleet of various types of vehicles to meet users’ diverse travel demands. For example, a user making commuting trips will only need an economic small car, whereas a user moving to a new house will require a large van. Providing adequate coverage of vehicles is essential to further users’ usage of carsharing services. This involves determining the types of vehicles preferred by users and the optimal composition of the fleet at a profit.

The first part of this thesis aims to help carsharing operators understand users’ demand and preferences for vehicles. The demand estimation in this part differs from the previous studies in that it focuses especially on the demand for carsharing vehicles.

This demand modelling is constrained by the supply of vehicles.

Part I contains two chapters. Chapter 3 investigates carsharing users’ vehicle selection behaviour. A spatial hazard-based modelling framework is proposed to evaluate the importance of vehicle locations, users’ sociodemographic attributes and fleet characteristics on their choice set formation behaviour in selecting vehicles.

Further to this vehicle selection problem, Chapter 4 applies the multiple discrete- continuous extreme value modelling framework to model users’ vehicle fleet choice and utilisation patterns within carsharing systems. The model accurately predicts the vehicle types that carsharing users prefer, and the amounts of budget they are willing to allocate to the different vehicle types. These two chapters together construct the demand estimation part of this thesis.

Part I. Demand Estimation

This part draws heavily from the following peer-reviewed journal paper and under-review article:

Chapter 3 – Jian, S., Rashidi, T.H., Wijayaratna, K.P. and Dixit, V.V., 2016.

A Spatial Hazard-Based analysis for modelling vehicle selection in station-

based carsharing systems. Transportation Research Part C: Emerging

Technologies, 72, pp.130-142.

Chapter 4 – Jian, S., Rashidi, T.H., and Dixit, V. An Analysis of Carsharing

Vehicle Choice and Utilisation Patterns Using Multiple Discrete-Continuous

Extreme Value (MDCEV) Models. In review with Transportation Research

Part A: Policy and Practice

Chapter 3. A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems

Chapter 3 A Spatial Hazard-Based Analysis for Modelling

Vehicle Selection in Station-Based Carsharing Systems

3.1 Introduction

As introduced in Chapter 2, the benefits of reducing congestion, improving auto utilisation rate, and limiting the environmental impact of emissions release have boosted the worldwide uptake of carsharing. Thus, it is critical to understand what factors affect the demand for carsharing to further its usage. Demand is dependent on trip attributes such as: trip purpose, duration of the trip, time of day and week and also the vehicle selected out of the available choices. Jorge and Correia (2013a) presented a comprehensive literature review regarding demand modelling approaches for carsharing programmes. The paper highlighted that demand estimation is difficult due to the interdependency of vehicle availability and the number of trips. Furthermore, there has been limited research into understanding and characterising the impacts of the supply of vehicles on users’ demand within modelling frameworks. In order to evaluate carsharing programmes effectively, the demand for and the supply provided must be accurately determined.

Chapter 2 has introduced that carsharing systems can be categorised into station-based and free-floating systems based on facility configurations. Free-floating systems allow users to pick up and drop off a car freely in a defined zone without any fixed positioning. Station-based systems provide users with multiple predefined “pick up and drop off” vehicle pods (Firnkorn and Müller, 2011). Station-based systems are

Chapter 3. A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems less flexible for the consumer but more widely adopted by carsharing operators. This chapter focuses on station-based carsharing systems and aims to advance the existing literature by investigating users’ vehicle selection behaviour.

Users’ vehicle selection is a significant factor in determining the most efficient allocation of resources within a carsharing program. Vehicle selection is users’ decision process to select a specific vehicle given a choice of vehicles within a carsharing fleet. By understanding vehicle selection process, programmes can optimise the vehicle utilisation within the fleet. In particular, this study attempts to answer two questions:

“How far is an acceptable walking distance when users make decisions on using carsharing vehicles?”

“What factors influence users’ selection of vehicles?”

The process of vehicle selection is a discrete choice process for an individual when utilising carsharing. The choice set of carsharing vehicles is usually very large.

Users will follow two steps to make the decision. First, users screen the alternatives and come up with a small and manageable choice set. Second, they make their selection from options considered in the choice set. How we define the choice set is an important consideration and the focus of this study.

Users’ cognitive capability for screening and filtering alternatives from a choice set is usually based on a critical or influential factor. This factor is an essential component of the first step of vehicle selection behaviour (Rashidi and Mohammadian,

2012). Accessibility to carsharing facilities dictates the utilisation of carsharing facilities. An individual will not choose carsharing services if the time travels to

Chapter 3. A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems carsharing vehicles is beyond his or her acceptable access time. Since most carsharing users walk to get access to a carsharing vehicle, the main factor affecting the choice set of vehicles is considered to be the “distance to the carsharing vehicle within a specific carsharing facility”. A spatial hazard-based model (SHBM) has been formulated to model vehicle selection behaviour using data provided by GoGet, an

Australian carsharing company. The SHBM is applied instead of a discrete choice model because it is more consistent with users’ vehicle selection process than discrete choice models. In this specific case, SHBM can account for the critical factor of screening and filtering process, whereas discrete choice models cannot. The modelling was achieved by considering the “distance to the carsharing vehicle” as a random variable analogous to the duration in conventional hazard-based models (HMBs). A number of parametric forms of HBMs were tested to determine the best fit to the data set. The two major contributions of this study are summarised in Figure 3:1: We introduce an analytical modelling structure for modelling demand for carsharing with a focus on vehicle selection, and apply a choice set formation technique that has been previously applied to a housing search problem (Rashidi and Mohammadian, 2012).

Figure 3:1 Summary of research contributions in Chapter 3

The remainder of this chapter has been structured in the following manner. Section 3.2 provides a detailed literature review discussing the recent studies regarding to the applications of SHBMs within the field. The modelling framework and analysis

Chapter 3. A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems methodology of the SHBM is explained within Section 3.3. The collection and preparation of the data used to formulate the model are discussed in Section 3.4. This is followed by Section 3.5 which presents the results and analysis of the modelling.

Finally, the implications of the results are highlighted within Section 3.6.

3.2 State of the Art of SHBM Modelling Framework

Literature has shown that choice set formation has an impact on the parameter estimation of behavioural choice models (Ben-Akiva and Lerman, 1985, Timmermans and Golledge, 1990, Rashidi and Mohammadian, 2012).

Rashidi and Mohammadian (2012) presented a detailed review of approaches to choice set formation. It has historically been classified into two approaches: 1) random selection out of the universal choice set; and 2) consideration of the entire universal choice set. The two approaches contained weaknesses in developing accurate behavioural models. Rashidi and Mohammadian (2012) and Manski (1977) argued that the most critical element within choice set formation was developing an appropriate filtering/screening method. The decision process can be completed in two phases: initially the hazard model determines a filtered choice set identifying the probabilistically relevant alternatives and then a secondary choice model determines the alternative with the greatest utility from this filtered choice set (Rashidi and

Mohammadian, 2012). The study presented within this paper attempts to achieve the first step of this process through the use of the SHBM, a relatively new technique that has had a few applications within literature (Rashidi and Mohammadian, 2012,

Rogerson et al., 1993, Pellegrini and Grant, 1999). The model considers “distance to

Chapter 3. A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems the carsharing vehicle” as a random variable analogous to the duration of a HBM to construct the choice set of the vehicle selection decision.

3.3 Model Formulation and Methodology

The parametric hazard-based models used in this study are introduced in this section.

To begin with, the various types of parametric models are described, followed by a presentation of the constraints related to the problem. Finally, the criterion of selecting among a set of parametric models are introduced.

3.3.1 Parametric hazard-based models in survival analysis

Survival analysis is generally defined as a variety of statistical techniques for analysing positive-valued random variables (Miller Jr, 2011). The variable can be the duration until the occurrence of a certain event. The event can be death or disease in the medical area, failure in the engineering area, etc. As discussed in Section 3.2, the duration can be interchangeable with distance without losing the generality of survival analysis. In this study, the event of interest is where the vehicle is selected, and the random variable is the distance taken to make the selection.

In survival analysis, the length of a duration spell for a subject is represented by a continuous random variable 푇. This continuous variable follows a probability density function (PDF), 푓(푡), and a corresponding cumulative density function (CDF),

퐹(푡). The probability of failing sometime before time 푡 is equal to the CDF, 퐹(푡):

Pr(푇 ≤ 푡) = 퐹(푡) (3.1)

Chapter 3. A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems

where 푡 denotes the elapsed time since the entry to the state at time zero.

The survival function is defined as the probability of survival at time 푡, denoted by 푆(푡), can be written as:

푆(푡) = Pr(푇 > 푡) = 1 − 퐹(푡) (3.2)

As the slope of the CDF is the PDF, 푓(푡) can be expressed as follows:

Pr⁡(푡 ≤ 푇 ≤ 푡 + ∆푡) 휕퐹(푡) 휕(1 − 퐹(푡)) 푓(푡) = lim = = ∆푡→0 ∆푡 휕푡 휕푡 (3.3) 휕푆(푡) = − 휕푡

where ∆푡 is a very small time interval.

The hazard rate is defined as the probability of failure in the interval (푡, 푡 + Δ푡) given that it has survived until time 푡. Let 휃(푡) denote the hazard rate, then we have:

푓(푡) 푓(푡) −휕푆(푡)/휕푡 푆′(푡) 휃(푡) = = = = (3.4) 1 − 퐹(푡) 푆(푡) 푆(푡) 푆(푡)

Using the fact that:

푔′(푥) 휕푙푛푔(푥) = (3.5) 푔(푥) 휕푥

Equation (3.4) can be rewritten as:

−휕푙푛푆(푡) 휃(푡) = (3.6) 휕푡

In practice, one can first assume the shape of the hazard rate, and then derive the survival function based on the hazard rate using Equation (3.6) as follows:

Chapter 3. A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems

푡 푆(푡) = exp [− ∫ 휃(푢)푑푢] (3.7) 0

Most applications of survival analysis concentrate on parametric hazard-based models that analyse the data with the output of the duration to the failure. Regarding parametric hazard-based models, there are two categories: the accelerated failure time

(AFT) models and the proportional hazards (PH) models (Rashidi and Mohammadian,

2015). The AFT models consider a linear relationship between the log of the survival time and the covariates considered, while the PH models assume that absolute differences in covariates imply proportionate differences in the hazard rate at a specific time.

In parametric models, the underlying distribution of the survival duration is usually assumed to be a certain known probability distribution, such as exponential,

Weibull, log-logistic, and lognormal distributions. Cox (1959) first employed the

Weibull distribution and proposed a Weibull baseline hazard model. Since then, the

Weibull hazard-based model has been most frequently used in the studies of duration modelling (Yamamoto and Kitamura, 2000, Rashidi and Mohammadian, 2012, Hasan et al., 2013, Haque and Washington, 2015). It presents a flexible functional form that can capture monotonically increasing or decreasing hazard function. However, it should be noted that the hazard function might not be monotonic in some cases, which requires testing non-monotonic distributions for the parametric hazard models. Log- logistic and lognormal hazard-based models are developed to account for the non- monotonic distributions.

Chapter 3. A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems

In this study, we examine AFT models, and test both monotonic functions (i.e.

Weibull and exponential distributions) and non-monotonic functions (i.e. log-logistic and lognormal distributions) to determine the best fitted parametric hazard model.

As mentioned before, AFT models consider a linear relationship between the log of the survival time and the covariates. Thus, the general form of AFT models is formulated as follows:

푙푛(푡푗) = 푥푗훽푥 + 푧푗 (3.8)

For individual j,⁡푥푗 represents explanatory variables, 훽푥 denotes the vector of coefficients, and 푧푗 is the error with density 푓(. ), which determines the regression model. By letting 푓(. ) be the extreme-value density, the Weibull and exponential parametric hazard models are obtained. By ensuring 푓(. ) follows a logistic distribution, the log-logistic hazard model is formulated. Similarly, by setting 푓(. ) to be a normal distribution, we obtain the lognormal hazard model.

For AFT models, exp⁡(−푥푗훽푥) is defined as the acceleration parameter. If exp⁡(−푥푗훽푥) equals to one, time passes at its normal rate and the failure will occur at the expected duration. If exp⁡(−푥푗훽푥) is larger than 1, time is accelerated, that is, the failure is expected to occur earlier. If exp⁡(−푥푗훽푥) is smaller than 1, then time is decelerated, which means the failure will occur later than expected.

Using Equations (3.7) and (3.8), and the probability density functions of different distributions, we rewrite the survival functions of these four distributions as follows:

Exponential survival function: 푆(푡) = exp[−exp⁡(−푥푗훽푥)푡푗] (3.9)

Chapter 3. A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems

푝 Weibull survival function: 푆(푡) = exp[−exp⁡(−푝푥푗훽푥)푡푗 ] (3.10)

−1 Log-logistic survival function: 1/훾 (3.11) 푆(푡) = (1 +[exp⁡(−푥푗훽푥)푡푗] )

ln(푡푗) − 푥푗훽푥 Lognormal survival function: 푆(푡) = 1 − 휙 ( ) (3.12) 휎

where 푝 is the scale parameter of the Weibull distribution, 훾 is the shape parameter of the log-logistic distribution, 휎 is the scale parameter of the lognormal distribution, 푥푗 represents the vector of covariates, and 훽푥 is the vector of coefficients.

3.3.2 Concept of the acceptable walking distance

In the context of this particular study, the hazard-based models are used to understand the formation of the vehicle choice set. Thus, 푡 represents the distance between the user’s origin and the available carsharing vehicle. However, the critical acceptable walking distance for each type of vehicle is not known, only that it falls within some interval of the distance between the selected vehicle and all the unselected vehicles of that type.

Figure 3:2 helps explain the concept. As shown in Figure 3:2, there are 7 types of carsharing vehicles available for users to select. Vehicles from different types have different attributes, while vehicles with the same type are exactly the same vehicles only with different distances from the origin of the user. As the carsharing network usually covers large urban areas, the vehicles from the same type are distributed sparsely with relatively long distances between each other. Since users will only

Chapter 3. A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems consider the closest vehicle of each type of vehicle, there is only one vehicle from each type included in this data set.

Figure 3:2 Schematic explaining choice set formation of carsharing users

In this example, we assume that Vehicle 1 is selected by the user, but it does not mean that the distance to Vehicle 1 is the acceptable walking distance of Type 1 vehicles.

Instead, the critical acceptable walking distance of the vehicle type that is selected is somewhere farther than the distance of Vehicle 1, but closer than the second closest vehicle of that type (Vehicle 1’). Therefore, the probability of Type 1 vehicles being selected can be represented by the difference between the survival function of the selected vehicle and the second closest vehicle. For the type of vehicle that is selected in this trip, the probability being selected can be written as:

PrS(푡 ≤ 푡∗ < 푡′) = 푆(푡) − 푆(푡′) (3.13)

Chapter 3. A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems

where 푡′ denotes the distance of the second closest vehicle, and 푡 represents the distance of the selected vehicle.

As for the rest of the types of vehicles that are not selected, the acceptable walking distance is somewhere between the origin of the user and the distance of the vehicle. So, for these types of vehicles, the probability being selected can be written as:

PrNS(0 ≤ 푡∗ < 푡) = 1 − 푆(푡) = 퐹(푡) (3.14)

Equations (3.13) and (3.14) take into account the inclusion of the acceptable walking distance, and are used to formulate the maximum likelihood estimation model.

3.3.3 Performance measures of model comparison

We develop four different hazard models in this research, therefore, it is necessary to compare the goodness of fit across these four models. The Bayesian

Information Criterion (BIC) is utilised to select the best-fitted hazard-based model. It is the criterion for model selection among a finite set of parametric models. The model with lower BIC value is considered to have a better fit. The formulation of BIC is:

퐵퐼퐶 = −2 × ln(푙푖푘푒푙푖ℎ표표푑) + ln⁡(푁) × 푘 (3.15)

where 푘 denotes the number of the parameters estimated, and 푁 is the number of observations.

Chapter 3. A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems

3.4 Data Collection and Preparation

The dataset used to undertake this research was graciously provided by GoGet, which is an Australian carsharing company founded in 2003 operating throughout Sydney,

Melbourne, Brisbane, and Adelaide. Anonymous carsharing trip data of the Sydney region obtained between January 1st, 2012 and June 9th, 2012 was utilised for the development of the SHBM. At the time of data collection, GoGet operated a round- trip station-based carsharing system, and there were 55 GoGet vehicle pods (carsharing facilities) located in Sydney CBD area containing a total of 208 vehicles. The recorded data considered 23642 trips completed by 3081 users across the six-month period of data collection. The dataset includes a wide range of anonymous user-related, vehicle- related, and trip-related variables, which are described in Table 3:1. These variables are selected specific to the aim of the research: understanding the vehicle selection within carsharing programmes.

Chapter 3. A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems

Table 3:1 Summary of the variables used in the models

Percentage Std. of Binary ID Variable Mean Definition Dev. variable = 1

1 user_age (year) 39.60 10.86 - Age of user Binary variable: =1, user owns 2 user_car_ownership - - 20.90 a car; =0, otherwise Binary variable: =1, user uses user_how_often_use_ the car at least once a week; 3 - - 34.79 the_car =0, user rarely uses the car, i.e. less than once a week. Binary variable: =1, user uses user_main_way_to_ 4 - - 58.33 public transit to work; =0, work otherwise Binary variable: =1, user's 5 user_landuse_binary - - 67.87 origin land use type is

residential; =0, otherwise User Binary variable: =1, user lives user_live_near_ 6 - - 70.11 near dedicated parking pod; dedicated_parking =0, otherwise Binary variable: =1, user's 7 dl_country - - 79.10 driving license country is Australia; =0, otherwise Binary variable: =1, user owns 8 plan_binary - - 26.74 a frequent usage membership plan; =0, otherwise Binary variable: =1, user uses 9 booking_method - - 11.46 mobile phone to book a car; =0, otherwise Binary variable: =1, the 10 car_manufacture - - 11.55 manufacturer of the car is Alfa Romeo, =0, otherwise

Binary variable: =1, the car is 11 car_body_type - - 18.86 MPV or Electric vehicle; =0,

the car is hatchback Vehicle 12 car_age (year) 3.30 0.74 - Age of GoGet car Binary variable: =1, the car is 13 pet_friendly - . 7.82 pet friendly; =0, otherwise trip_travel_time 14 0.21 0.55 - Total travel time of each trip (hours)

Trip Number of times user has used 15 usage 3.07 10.04 - a vehicle

User-level variables (variable ID 1 to 9 shown in Table 3:1) were extracted directly from the anonymous user information provided by GoGet. The information regarding the users’ age, car ownership and usage and journey to work were obtained. Eight out

Chapter 3. A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems of the nine user level variables were binary in nature. The variable user_landuse_binary identifies if the land use of the origin is residential or not. This classification is based on the land use zoning map obtained from the NSW Department of Premier and Cabinet, Office of Environment and Heritage (NSW GOVERNMENT

ENVIRONMENT AND HERITAGE, 2014). Among all the users, 67.87% are originating from residential areas, 25.12% from commercial or industrial areas, and

7.01% from public services or recreational area. The variable user_live_dedicated_parking is extracted from the survey responses conducted by

GoGet. The variable captures whether a member believes that they have a dedicated parking spot near them.

The variable plan_binary divides users into frequent user group and infrequent user group. At the time of data collection, GoGet provided five membership plans to users with different monthly rates and trip rates: GoFrequent, GoOccasional, GoStarter,

GoBusiness, and GoStudent. The variable plan_binary equal to 1 indicating the user is on GoFrequent plan. It has the lowest trip rate and the highest monthly service subscription rate. It is more suitable for users who use carsharing services frequently.

Vehicle-related variables include the manufacturer, body type, vehicle age, and pet option of the vehicles. Four manufacturers, Toyota, Hyundai, Alfa Romeo and

Suzuki, supply the fleet of 208 GoGet vehicles being studied. The hourly rates that

GoGet charge users for driving cars with different manufacturers are different. Out of all the manufacturers, the hourly rate charged for using Alfa Romeo vehicles is the highest as this is deemed to be a luxury vehicle. The other manufacturers have equal rate and the hourly rate is AU$2 (AU$1 = US$0.75 [29/08/2016]) lower than the rate of Alfa Romeo. As a result, a car_manufacturer variable is generated as a binary

Chapter 3. A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems variable that if the manufacturer is Alfa Romeo it equals 1, and 0, otherwise. The variable pet_friendly identifies whether the vehicle is pet friendly. Trip-level attributes consist of trip travel time, denoted by trip_travel_time, and the number of times that each user selects each vehicle, denoted by usage.

Table 3:2 presents the correlation between the 15 variables. Though the majority of the correlation coefficients are less than 0.15, there are several correlations that should be noted. Variables user_how_often_use_the_car (3) and plan_binary (8) have a weakly positive correlation of 0.22 indicating that frequent carsharing users tend to also be private vehicle users. The variable car_body_type (11) are negatively correlated with car_manufacturer (10), car_age (12) and pet_friendly (13). This shows that vehicles with special body types are mostly older vehicles and not pet- friendly compared to hatchbacks.

Table 3:2 Correlations between variables

ID 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

1 1.00

2 0.11 1.00

3 0.06 0.10 1.00

4 -0.02 -0.06 -0.07 1.00

5 -0.15 0.07 0.08 0.04 1.00

6 -0.05 0.06 -0.05 0.07 -0.03 1.00

7 0.15 0.13 0.04 -0.01 0.01 -0.06 1.00

8 0.11 -0.04 0.22 0.00 -0.12 -0.07 0.02 1.00

9 -0.11 -0.04 0.05 0.00 0.01 0.03 0.00 0.14 1.00

10 0.01 0.01 0.01 0.00 0.00 -0.01 0.01 0.00 0.00 1.00

11 -0.01 0.01 -0.01 -0.02 -0.02 0.00 0.00 0.00 0.00 -0.22 1.00

12 0.00 0.03 0.02 0.00 0.01 0.01 0.02 0.00 -0.01 -0.11 -0.21 1.00

13 -0.01 0.00 -0.01 0.00 -0.01 -0.01 0.01 0.02 0.01 -0.16 -0.20 -0.09 1.00

14 0.02 0.01 -0.02 -0.01 -0.02 0.01 -0.03 -0.01 -0.01 0.00 -0.01 -0.01 0.00 1.00

15 0.01 -0.03 0.05 0.04 0.03 -0.03 0.02 0.01 0.02 -0.09 -0.14 -0.06 -0.11 -0.03 1.00

Chapter 3. A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems

GoGet provided the Euclidean distance between a user’s residence and each carsharing vehicle pod. Furthermore, it is also important to note that a maximum travel distance catchment of two kilometres that an individual would travel to a vehicle pod was assumed within this study. This assumption was made to complete an initial screening of the data to determine feasible travel distances between the origin and the vehicle pods. As walking is the dominant access/egress mode to GoGet vehicles, the application of Euclidean distance offered a reasonable estimate for distances less than

2 kilometres. Figure 3:3 presents the distribution of the observed GoGet usage data considering the two-kilometre origin to vehicle pod radius. The figure shows a high proportion of users located within one kilometre of the vehicle pod (62% of the total data set) with the usage decreasing as the distance increases. In addition, the total catchment considers 80% of the data set. Accordingly, the use of the two-kilometre catchment was deemed as a valid initial screening criterion to obtain realistic modelling.

Figure 3:3 Distribution of GoGet usage data considering a 2km radius

In addition, the GoGet booking system only provides users with the information of available vehicles upon booking. Thus, within the modelling

Chapter 3. A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems framework, it is assumed that the user can only select vehicles that are available at the time of utilisation, which narrows the choice set.

3.5 Results and Analysis

The four hazard-based models were estimated using the statistical analysis software package SAS 9.4. Table 3:3 shows the results of parameter estimation. The signs of the coefficients, except dl_country and car_manufacturer_binary, are consistent in all models.

In this case, the coefficient of car_manufacturer_binary is statistically significant for the monotonic distributions (exponential and Weibull), marginally significant for the log-logistic distribution and insignificant for lognormal distribution.

The coefficient of dl_country is statistically significant for the monotonic distributions

(exponential and Weibull) and statistically insignificant for the non-monotonic distributions (log-logistic and lognormal). This may suggest that the monotonic distributions might be anchoring their flexibility on these two variables and creating biases. Therefore, the non-monotonic distributions are more favourable functional forms.

Chapter 3. A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems

Table 3:3 Parameter estimation results for four models for estimation results Parameter Table3:3

Chapter 3. A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems

As discussed in Section 3.3, the BIC metric is employed to select the best-fitted hazard- based model. With Equation (3.15), we obtain Table 3:4 showing the results of BIC of all four models. The BIC value for the model with log-logistic distribution is 61380.67, which is the smallest among all the models. It can be concluded that the log-logistic distribution provides the best hazard-based model among the four distributions considered for this study, and as such log-logistic spatial hazard-based model is used for further analysis.

Table 3:4 Calculation results of BIC of four models

Exponential Weibull Log-logistic Lognormal Log likelihood value -31367.11 -31344.32 -30596.28 -30695.03 Number of observations 63933 63933 63933 63933 Number of parameters 16 17 17 17 BIC 62911.27 62876.76 61380.67 61578.18

The hazard-based model with log-logistic distribution is further examined. The estimated CDF is employed to simulate the distance between a GoGet user and his or her selected vehicle. Figure 3:4 shows the simulated results for the cumulative survival probability with log-logistic distribution. The general pattern is monotonically decreasing, which is consistent with observations.

Chapter 3. A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems

Figure 3:4 Cumulative survival probability pattern for log-logistic model

Table 3:3 presents the parameter estimation results of log-logistic distribution. As shown in the table, the 훾 parameter of log-logistic distribution is smaller than 1, meaning that the shape of the log-logistic hazard model is not monotonic. The hazard rate will first increase to a certain value and then decrease as the distance between the user and the vehicle increases.

Figure 3:5 plots the pattern of the hazard value over the distance to the vehicle

The pattern confirms the non-monotonic interpretation of the 훾 parameter for the log- logistic distribution. In Figure 3:5, the hazard value first increases as the distance increases. When the distance is approximately 0.2 kilometres, the hazard value starts to fall. This can be explained that when the walking distance is within 0.2 kilometres, users are not affected by the distance to the vehicle. Another reason might be that only

20% of the vehicles are within the 0.2-kilometre radius, so users do not have enough

Chapter 3. A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems choices for the vehicles within 0.2 kilometres. When the distance is larger than 0.2 kilometres, the impact of the distance on users’ vehicle selection behaviour becomes more significant. Users prefer to select vehicles that are nearer to their original locations, which satisfies the initial assumption and common sense of carsharing vehicle selection.

Figure 3:5 Hazard pattern for log-logistic model

Before discussing the results of the parameter estimation, it should be noted that in the

AFT models, the effect of covariates is facilitated by incorporating a negative sign for the parameters within the formulation. In other words, if the coefficient (훽푥) of the covariate is estimated to have a negative value, the expected time to failure decreases and the probability of failure increases. In the context of the vehicle selection, this means that an individual with a larger value of the covariate tends to choose a vehicle with a shorter distance between the origin and the vehicle pod. Conversely, if 훽푥 of a

Chapter 3. A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems covariate is positive, an increase in the value of the covariate increases the expected time to failure. This means that an individual with a higher value of this type of covariate tends to accept a greater distance between the origin and the vehicle pod.

The parameter estimates for the log-logistic distribution shows that most of the parameters listed are statistically significant at a 95% confidence level except the binary variable dl_country. Among the parameters, the coefficients of all the vehicle related parameters are negative. The binary car manufacturer variable has a negative coefficient which indicates that people who select a non-luxury (as defined in Section

3.4) carsharing vehicle (i.e. not an Alfa Romeo) have the tendency to commute longer to the vehicle pod. This finding can be explained by the fact that the rate of these luxury vehicles is higher than other normal vehicles. Carsharing is reported to be more popular among individuals with lower incomes who might value lower transportation costs more than the extra aesthetic and comfort based utility of the vehicles (Costain et al., 2012). Thus, users are more willing to select vehicles with lower hourly rates at the expense of walking longer distances.

Furthermore, the car body type variable also has a negative coefficient estimate suggesting that users who select hatchback vehicles are more likely to travel longer distances to the vehicle pods, whereas users who choose multi-purpose vehicles

(MPVs) or electric vehicles have higher probability to travel shorter distances to find a vehicle. This can be explained by the general household characteristics of carsharing users. Celsor and Millard-Ball (2007) indicated that the more common users of carsharing facilities are from single occupant households. In general, this category of user will not have the requirement to use a large vehicle or an MPV as this group of people normally do not need to transport more than a few people. In addition, Cervero

Chapter 3. A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems et al. (2007b) found that carsharing vehicles are mostly utilised for short-term journeys which do not require the use of large vehicles. So even if the hatchback is relatively far away from the origin, the user will be inclined to hire it over a MPV or a larger vehicle. With respect to the electric vehicles, since electric vehicles are not as common as conventional petroleum vehicles, users might prefer petroleum vehicles regardless of the distance to the vehicle pod due to familiarity.

The variable pet_friendly is found to have a negative coefficient, suggesting that pet friendliness is not an extra benefit for most carsharing users. This is intuitive in that pet owners who are regularly travelling with their pet generally own pet friendly car. The negative correlation between pet_friendly and car_body_type also helps explain the result: pet-friendly vehicles are more likely to be hatchbacks, and the majority vehicles provided by GoGet are hatchbacks.

It is interesting to note that the age of the car also has a negative coefficient, meaning that as the age of the vehicle increases users’ willingness to travel farther to the vehicle will reduce significantly. This is an intuitive result as the common perception of users is that newer vehicles are more reliable, and as such it is valuable to walk a greater distance to obtain a better vehicle.

It is clear that car ownership also has a negative coefficient, suggesting that users who own a car are more willing to select vehicles that are closer to them. In other words, people not owning a car but intending to use a carsharing service have higher probability to travel a greater distance to the vehicle pod. People who own a car have the choice to not use a carsharing vehicle if the distance to the vehicle pod is too great.

But for those people who do not own a car, they might not have any alternative except using carsharing vehicles if they absolutely need to make use of a private vehicle. This

Chapter 3. A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems result is consistent with the result of the binary variable user_main_way_to_work. The coefficient of this variable is positive meaning that users who use public transport to travel to work originate farther from the vehicle pod. This category of user may not own a private vehicle, but more importantly do not have access to a vehicle during work hours. As a result, if they need to complete a trip requiring a private vehicle during that time, they may be forced to travel a greater distance to the vehicle pod.

In addition, the plan_binary variable has a negative coefficient suggesting that frequent users of carsharing services tend to select vehicles within shorter distances from their origin. This may be attributed to the scenario where people who live near or have easy access to carsharing vehicles are more likely to be involved with a frequent use carsharing plan, due to the convenience of the vehicle pod locality relative to their residence.

Observing the positive coefficients, the covariate usage has a positive sign indicating that users prefer to walk farther for cars that they have selected and used multiple times. This is also a logical outcome in that users value the reliability and familiarity of the vehicle more than the distance to the vehicle. Considering a similar rationalization, users that have greater carsharing trip lengths tend to select vehicles located further away from their origin. Again, this could be attributed to the fact that when the user is planning a longer trip, they are more likely to choose a car that is more suitable to the purpose of the trip and familiar to the user regardless of the distance to the car.

Increased usage of cars (user_how_often_use_the_car_binary) by a user suggests an increase in the distance between the origin and the vehicle pod when selecting a carsharing vehicle. This is a contrasting result to what was observed with

Chapter 3. A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems the car ownership variable even though this variable indication is attributed to the ownership of a private vehicle. There are a few explanations for this result: initially owners of private vehicles are less likely to use carsharing facilities, as a result there is no utility for people to be originated within the vicinity of the carsharing services.

However, when they do need to use the services they will need to travel further to gain access to the facility. Furthermore, within Australia, carsharing vehicles have priority parking spaces throughout built up CBD areas where parking is a premium and accordingly users’ may find it more convenient to use the carsharing facilities ahead of using their own private vehicles.

The users’ age also has a positive coefficient implying the older a user, the farther his or her origin is to the vehicle pod. Elderly users may not own a private vehicle and also may have more leisure time, as a result distance to the vehicle pod is either inevitable or does not impact their utility as much as younger users.

Variables linked to characteristics of the users’ origins prior to using the carsharing facilities present positive coefficients (user_landuse_binay and user_live_near_dedicated_parking). This suggests that people originating from residential zones, living in a suburban environment, tend to travel farther to gain access to a carsharing vehicle as these trips may involve a greater level of planning relative to those happening situated in commercial and industrial zones. It can also be explained that users from commercial and industrial zones, who live in an urban environment, have a greater mode choice (access to taxis and public transport) reducing their tendency to walk large distances to use carsharing facilities. Further, residing near a dedicated GoGet parking area increases the incentive to access

Chapter 3. A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems carsharing services and results in users’ willingness to travel greater distances to make use of the facilities.

Interestingly, the variable booking_method_binary is found to have a positive coefficient and is statistically significant. The variable takes the value of one if the booking is done using a mobile application and zero if other methods are used. The statistically significant positive coefficient indicates that people are willing to travel farther to access the carsharing vehicles when using the mobile application, which reflects their flexibility to access the vehicles based on real time information about other transportation options.

3.6 Concluding Remarks

This study presented a behavioural model to achieve a greater understanding of users’ selecting vehicles within a carsharing programme. The study attempted to answer two questions: “How far is an acceptable walking distance when users make decisions on using carsharing vehicles?” and “What factors influence users’ selection of vehicles and are there any patterns or trends associated within these factors?” An answer to these two questions enable the researcher to model the choice set formation behaviour as a probabilistic process which is a function of distance and a set of identified covariates.

As the vehicle selection process is complicated, a choice set formation methodology based on a SHBM was developed using a rich dataset from the Australian carsharing company GoGet. The SHBM considered “distance to the carsharing vehicle” as a non-negative random variable analogous to the duration of conventional HBMs.

Chapter 3. A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems

The results from the modelling contain a number of negatively and positively correlated covariates which can provide trends and patterns that could potentially be used to guide policies of carsharing programmes. Positive coefficient estimates imply that as the value of the independent variable increases users tend to travel a farther distance to select a carsharing vehicle. Negative coefficient estimate, on the other hand, indicate the opposite where an increase in the variable means that users favour to travel a shorter distance to select the vehicle.

The user age, frequency of usage of cars, users’ main way to work, booking method and users’ land use type have positive coefficients. These results indicate that elderly users, users taking public transport to work, users with frequent usage of cars, users using mobile phones to book a trip, and users from residential areas tend to originate farther to the vehicle pods. The number of times a user selects a specific

GoGet vehicle and trip travel time also have positive coefficients. This demonstrates that users value familiarity with the vehicle and age of the vehicle over the walking distance to the vehicle from the origin.

On the other hand, users’ car ownership and plan type variables have negative coefficient estimates. This demonstrates that the vehicles located within a shorter distance to the origin have a higher probability of being selected by the users who own a car and the users who join a frequent use carsharing plan. The variables car manufacturer, car body type, car age and whether the car is pet friendly also have negative coefficient estimates. This may suggest that the luxury vehicles, vehicles with specific body type, old cars, and vehicles that allow for carrying pets along do not have enough incentive to users compared to those newer vehicles and vehicles with lower

Chapter 3. A Spatial Hazard-Based Analysis for Modelling Vehicle Selection in Station-Based Carsharing Systems hourly rates and smaller sizes. These conventional vehicles are more likely to be selected even if they are further away from the users.

Based on these trends, carsharing organisations can optimise their vehicle pod locations to centre on the catchments containing these user classes, in order to maximise the usage of the systems and boost the overall popularity of the schemes.

The increase in use of carsharing systems has created questions for transportation agencies to provide and manage existing parking locations for carsharing systems to increase their use, and influence car ownership. The model presented in this chapter will help carsharing operators understand how users formulate the vehicle selection choice set, and predict the probability of a vehicle being selected together with the advanced discrete choice model being formulated in the next step.

Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models

Chapter 4 An Analysis of Carsharing Vehicle Choice and

Utilisation Patterns Using Multiple Discrete-Continuous

Extreme Value (MDCEV) Models

4.1 Introduction

The previous chapter proposed a spatial hazard-based analysis to model carsharing users’ vehicle selection process. The model identified the impacts of a set of user attributes and vehicle characteristics on users’ vehicle selection behaviour in carsharing systems. The findings provide a starting point for operators to optimise the locations of stations and vehicle placement across the stations. Further to this vehicle selection problem, it is important for decision makers to accurately predict the vehicle types that carsharing users prefer and the amounts of budget they are willing to allocate to the different vehicle types. These questions have not yet been studied according to the literature review in Chapter 2. This study aims to bridge the research gap by modelling users’ vehicle fleet choice and utilisation patterns within carsharing systems.

The modelling results can help operators determine the most profitable vehicle acquisition plans and the optimal fleet sizes to be deployed to different areas for each vehicle type.

Carsharing users select different vehicle types for different occasions. For example, attending a meeting during a workday may only require a hatchback, but a user moving to a new house may require a van or a utility vehicle. In this study, a user’s vehicle selection record is defined as his or her “vehicle fleet choice”. Upon

Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models making a vehicle selection, users will decide the amounts of budget to allocate to each of the chosen vehicle types. This scenario involves making multiple discrete choices of continuous amounts. The vehicle types are the discrete alternatives. The budget is the continuous variable to be allocated to the discrete alternatives. A recent development of the multiple discrete continuous extreme value (MDCEV) modelling framework proposed by Bhat (2005) provides an applicable method to address the carsharing fleet choice and utilisation problem. The MDCEV model was formulated based on the utility maximisation theory. It estimates the impacts of attributes on decisions concerning the allocation of continuous amounts of budget to multiple discrete alternatives. It also captures the diminishing nature of the marginal utility with increasing consumptions (Pinjari et al., 2009).

In carsharing networks, the discrete alternatives are vehicle types, mainly classified by body type and manufacturers. With respect to the continuous budget constraint, since users are charged by the travel time and the mileage, users might decide the utilisation patterns constrained by travel time, mileage or monetary expenditure. With the purpose of identifying the most accurate fleet usage patterns, we develop three MDCEV models with time (time-MDCEV), mileage (mileage-MDCEV) and monetary expenditure (expenditure-MDCEV) as the continuous budget constraint.

To compare the performance of the three models, we use the forecasting procedure presented by Pinjari and Bhat (2010a) to obtain simulated results, and compare the simulated results of the three models to the observed data using two performance metrics, i.e. normalised RMSE and correct ratio. Furthermore, since the expenditure of each carsharing trip is composed of travel time expenditure and mileage expenditure, it is possible to compare the aggregate measure of the expenditure (using simulation

Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models results of the expenditure-MDCEV model) with the decomposed measure of the expenditure (calculated by combining the simulation results of the time-MDCEV and mileage-MDCEV models).

The major contributions of the study are summarised in Figure 4:1. First, we apply the MDCEV methodology to model carsharing vehicle fleet choice and the usage of different vehicle types to understand how users allocate travel time, mileage and monetary expenditure to multiple types of vehicles. Then, we simulate users’ choice and usage of vehicles based on the calibrated MDCEV models, and compare the simulation results of time-MDCEV, mileage-MDCEV and expenditure-MDCEV models to the observed data to identifying the actual behaviour of users’ fleet choice and utilisation patterns.

Figure 4:1 Summary of research contributions in Chapter 4

The remainder of the chapter is organised as follows. Section 4.2 reviews the studies that discussed and applied MDCEV models. Section 4.3 describes MDCEV modelling framework as well as MDCEV simulation algorithm and comparison procedure.

Section 4.4 presents the collection and preparation of the dataset used to calibrate the models. This is followed by the results analysis and discussions in Section 4.5, and the sensitivity analysis of key variables and policy implications in Section 4.6. The last section summarises the major findings of this study and conclusions are highlighted.

Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models

4.2 State of the Art of MDCEV Modelling Framework

The MDCEV modelling framework has been employed within several fields by a number of researches since its emergence. Bhat (2005) developed a MDCEV model to estimate discretionary time-use decisions on how consumers allocated continuous amount of time to participate in multiple activities. Based on this study, Pinjari et al.

(2009) formed a joint mixed MNL-MDCEV structure to analyse the residential self- selection effects in the time-use model. Pinjari and Bhat (2010b) extended the time- use study and introduced the nested structure of the MDCEV model. Castro et al.

(2012) argued the limitation of MDCEV model was that it only considered a single linear resource constraint, and accommodated multiple constraints in the MDCEV model to handle this limitation. In their modified model, multiple budget constraints, such as money, time, and capacity, could be considered simultaneously. The multiple constrained MDCEV model was applied to time-use decisions where individuals allocated both their monetary and time budget to multiple activities. Besides,

Copperman and Bhat (2007), Kapur and Bhat (2007), Spissu et al. (2009), Chikaraishi et al. (2010), Wang and Li (2011) have also applied MDCEV models to analyse time- use behaviour.

In the field of transportation, Ahn et al. (2008) applied an MDCEV model to estimate the impacts of adding alternative fuel passenger vehicles on consumers’ demand patterns for conventional passenger vehicles. Rajagopalan and Srinivasan

(2008) utilised an MDCEV model to integrate the mode choice and mode usage at the household level. Still focusing on household behaviour, Bhat and Sen (2006) used an

MDCEV model to analyse the household vehicle type holdings and usage patterns.

Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models

Later in 2009, they furthered the study by formulating a nested model structure that incorporated an MDCEV model as the upper level to model vehicle usage and an MNL model as the lower nest to model vehicle type choice (Bhat et al., 2009). Pinjari (2011) extended the study on household vehicle holdings and usage and proposed a general class of MDCEV models based on generalised extreme value error specifications.

More recently, You et al. (2014) incorporated the MDCEV model with a larger activity-based travel demand model to build a household vehicle fleet mix model system.

With respect to the model performance, Pinjari and Bhat (2010a) proposed an efficient forecasting procedure for MDCEV models. This forecasting procedure was used by Jäggi et al. (2013) to determine the accuracy of the forecasting of the MDCEV models on household fleet choice and usage. They compared the forecasted results of

MDCEV models and a random model to the observed results using the performance metrics, residual and hit ratio. The results indicated that the MDCEV models performed better than a completely random model.

The review of the literature on MDCEV modelling framework confirms the feasibility of applying it to modelling carsharing vehicle fleet choice and utilisation patterns. The next section will describe the model formulation in detail.

4.3 Model Formulation and Methodology

This section first restates the derivation of the MDCEV model based on Bhat (2005) and Bhat (2008), then describes the simulation procedure of MDCEV models

Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models developed by Pinjari and Bhat (2010a), and finally proposes two performance measures which are used to compare the three MDCEV models built in this study.

4.3.1 MDCEV model of carsharing fleet choice and utilisation

The utility structure of the MDCEV model proposed by Bhat (2005) is based on the utility structure developed by Kim et al. (2002), which used a generalised variant of the translated Constant Elasticity of Substitution (CES) direct utility function.

Assume an individual can allocate budget 퐸 to 퐾 alternatives. In our case, 퐸 can be the expenditure budget, the travel time budget, or the mileage budget. The alternatives are different carsharing vehicle types. Let 푥푘 be the consumption quantity on vehicle type 푘 (푘 = 1,2, … , 퐾). The total consumptions across 퐾 vehicle types are subject to the budget constraint as follows:

퐾

∑ 푥푘 ≤ 퐸 (4.1) 푘=1

Kim et al. (2002) defines the utility that an individual accrues for allocating the consumption quantity 푥푘 to each of the alternative 푘 to be as follows:

퐾

훼푘 푈(푥) = ∑ 휓푘(푥푘 + 훾푘) (4.2) 푘=1

Where 휓푘 , 훼푘 and 훾푘 are parameters associated with vehicle type 푘 . 휓푘 represents the baseline marginal utility (the marginal utility at the point of zero

Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models

consumption) for vehicle type 푘. The random utility function of 휓푘 given by Bhat

(2005) is as follows:

′ 휓푘 = exp(훽 푧푘 + 휀푘) (4.3)

Where 푧푘 is a set of attributes that characterise the alternative 푘 and the decision makers, i.e. carsharing users in our case, and 훽′ are the parameters that determine the impacts of the observed attributes on alternative 푘. 휀푘 is a standard

Gumbel error term that captures the unobserved characteristics influencing the baseline utility for alternative 푘.

훼푘 is the satiation parameter that reduces the marginal utility with increasing the consumptions of vehicle type 푘. It controls the satiation effect by exponentiating the consumption quantity.

훾푘 controls the translation and determines if corner solutions (an individual does not spend budget on any alternative) or interior solutions (an individual needs to spend budget on all alternatives) are allowed. Furthermore, 훾푘 also controls the satiation effect by translating the consumption quantity. Higher 훾푘 values indicate less satiation effects with respect to the consumption of 푥푘.

By combining Equations (4.2) and (4.3), the overall random utility function of the MDCEV model can be written as:

퐾

′ 훼푘 푈(푥) = ∑ exp(훽 푧푘 + 휀푘)(푥푘 + 훾푘) (4.4) 푘=1

Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models

In the context of carsharing, each user aims to maximise the random utility

(Equation (4.3)) subject to the binding linear budget constraint presented in Equation

(4.1).

The optimal consumption and the probability function can then be derived by forming the Lagrangian and applying the Kuhn-Tucker (KT) conditions. As presented by Bhat (2005), the Lagrangian function is:

퐾 퐾

′ 훼푘 퐿 = ∑ exp(훽 푧푘 + 휀푘)(푥푘 + 훾푘) − 휆 [∑ 푥푘 − 퐸] (4.5) 푘=1 푘=1

where 휆 is the Lagrangian multiplier associated with the budget constraint.

Bhat (2005) specifies an extreme value distribution for 휀푘 assuming that the error is independent from 푧푘 and is independently distributed across alternatives. Under such assumption, the probability function is written as:

푀 푀 1 ∏푀 푒푉푖 푖=1 ( ) (4.6) 푃(푥2, 푥3, … , 푥푀, 0,0, … ,0) = [∏ 푐푖] [∏ ] [ 퐾 푉 푀] 푀 − 1 ! 푐푖 (∑ 푒 푘 ) 푖=1 푖=1 푘=1

1−훼푖 where 푐푖 = ( ), and 푀 is the number of vehicle types chosen by the user. 푥푖+훾푖

Reviewing the probability expression (Equation (4.6)), if each individual chooses only one alternative, the model will collapse to the standard form of the multinomial logit (MNL) model. Indeed, the MDCEV model is the generalisation of the MNL model for the situations where multiple choices of continuous amounts are allowed (Castro et al., 2012).

Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models

Bhat (2008) redefines the utility function (Equation (4.4)) to be Equation (4.7) with the purpose of highlighting the roles of the three parameters and accounting for the inter-relationships between them. The roles of 훾푘, 훼푘, and 휓푘 do not change in this new utility function.

퐾 훼푘 훾푘 ′ 푥푘 푈(푥) = ∑ exp(훽 푧푘 + 휀푘) {( + 1) − 1} (4.7) 훼푘 훾푘 푘=1

Bhat (2005) and Bhat (2008) claimed that it is very difficult to estimate both

훾푘 and 훼푘 simultaneously because they both determine the slope of the indifference curves at the corner points. Thus, they suggested to estimate one parameter once and set the other parameter to be a fixed value. This leads to 훾-profile and 훼-profile

MDCEV configurations. 훾-profile estimates the value of 훾푘 for each alternative and sets 훼푘 to be 0 for all alternatives. Whereas in 훼-profile, the 훾푘 values are constrained to be 1 for all alternatives, and the satiation parameters 훼푘 differ across alternatives.

In this study, we test the 훾-profile and estimate the parameters using the R code provided by the SimTRAVEL Research Lab (The SimTRAVEL Research Lab, 2016).

The program “MDCEV Estimation_No Outside Good” is applied. The MDCEV utility function for 훾-profile is rewritten as:

퐾 ′ 푥푘 푈(푥) = ∑ 훾푘exp(훽 푧푘 + 휀푘)ln⁡( + 1) (4.8) 훾푘 푘=1

Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models

4.3.2 Simulation procedure for MDCEV model

In this study, we test three carsharing fleet choice and utilisation models with monetary expenditure, travel time and travel mileage as the budget constraint, respectively. It is interesting to compare the three models to identify the best-fitted model to better understand users’ vehicle utilisation patterns. However, since the three constraints have different scales and units, the log-likelihood results cannot be used to compare the models. Therefore, we undertake the simulation procedure based on the parameter estimation results, and compare the simulated results of the three models to the observed data to evaluate the goodness-of-fit of the three models.

The simulation procedure applied in this study uses an algorithm for simulating

훾-profile MDCEV models proposed by Pinjari and Bhat (2010a). Initially, the baseline utility values for all alternatives are calculated based on the model parameter 훽′, the input data and the error term 휀푘. The random numbers used for 휀푘 in the R code are from a Halton sequence developed by Halton (1960). In the second step, the alternatives are sorted in the descending order of their baseline utility values, and the first alternative is assumed to be chosen. Then, the algorithm checks if the alternative with the second highest baseline utility is chosen by verifying the KT conditions for other unchosen alternatives. If the KT conditions are met, the algorithm stops and only the first alternative is chosen. Otherwise, the algorithm continues by choosing the second alternative. The algorithm keeps including the next alternative until either the

KT conditions are verified or the number of chosen alternatives reaches the maximum number 퐾. Then, the budget allocated to each of the chosen alternative is calculated using the adjusted baseline utility of the previous steps along with the parameter 훾.

Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models

4.3.3 Performance metrics for model comparison

To evaluate the goodness-of-fit of the three models and compare the performance of the simulation results, the performance metrics applied in this study are normalised root-mean-square-error (RMSE) and correct ratio.

RMSE is used to measure the residuals between the simulated results and the observed data. RMSE aggregates these residuals into a single metric to assess the accuracy of model prediction. The following equation is the formula to calculate

RMSE.

The RMSE of a model prediction with respect to the estimated variable is defined as the square root of the mean squared error:

∑푁 (푦 − 푓 )2 푅푀푆퐸 = √ 푛=1 푛푘 푛푘 (4.9) 푘 푁

Where 푅푀푆퐸푘 is the RMSE for vehicle type 푘, 푦푛푘 is the observed value for individual 푛 with respect to vehicle type 푘, 푓푛푘 is the simulated value for individual 푛 with respect to vehicle type 푘 . Since the three constraints time, mileage and expenditure have different scales and units, the RMSE value needs to be normalised be comparable. Equation (4.10) calculates normalised RMSE based on Equation (4.9).

푅푀푆퐸푘 푁표푟푚푎푙푖푠푒푑⁡푅푀푆퐸푘 = (4.10) 푦̅̅푘̅

where 푦̅̅푘̅ is the average of the observed value for vehicle type 푘 across all observations.

Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models

The overall normalised RMSE for all vehicle types is the sum of the normalised

RMSE of each vehicle type:

퐾 푁표푟푚푎푙푖푠푒푑⁡푅푀푆퐸 = ∑ (푁표푟푚푎푙푖푠푒푑⁡푅푀푆퐸푘) (4.11) 푘=1

Correct ratio evaluates the accuracy of the prediction of multiple discrete choices. For each pair of observation and simulation result, it is calculated using

Equation (4.12).

푁푐표푟푟푒푐푡⁡푝푟푒푑푖푐푡푒푑⁡푐ℎ표푖푐푒푠 퐶표푟푟푒푐푡⁡푅푎푡푖표 = (4.12) 푁푎푙푡푒푟푛푎푡푖푣푒푠

Where 푁푐표푟푟푒푐푡⁡푝푟푒푑푖푐푡푒푑⁡푐ℎ표푖푐푒푠 is the number of correctly predicted alternatives, and 푁푎푙푡푒푟푛푎푡푖푣푒푠 is the number of all alternatives. For example, given alternatives A1, A2, A3, A4, a user selects A1 and A2 in the observed data. The simulation result shows that the user chooses A1, A2, A3. This means the model predicts the choice of A1, A2, A4 correctly, but the choice of A3 incorrectly. Thus, the correct ratio of this comparison pair is equal to 3/4.

Correct ratio is calculated for each observation and instance pair separately, and the average correct ratio of all instances and observations is taken.

Lower normalised RMSE and higher correct ratio indicate better performance of the model, and therefore can reflect the behaviour of carsharing users’ fleet choice behaviour and utilisation more accurately.

Furthermore, besides comparing the simulation results for the three MDCEV models, it is also interesting to compare the simulated expenditure directly obtained

Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models from the expenditure-MDCEV model to the monetary expenditure results calculated jointly using the travel time and mileage simulation results. Since trip expenditure is equal to the sum of the travel time cost and mileage cost, the expenditure can be calculated by the equation below:

′ 푡 푑 퐸푘 = 푃푘푇푘 + 푃푘 퐷푘 (4.13)

′ where 퐸푘 is the expenditure for vehicle type 푘 calculated by the simulated

푡 푑 travel time 푇푘 and mileage 퐷푘 spent on vehicle type 푘. 푃푘 and 푃푘 are the unit prices

′ of time and mileage travelled using vehicle type 푘. 퐸푘 can be calculated for each of the individual, and the joint simulation results can be compared to the three MDCEV models to determine the best fitted model.

4.4 Data Preparation and Summary

Data used for developing the carsharing vehicle choice and utilisation model was provided by GoGet, an Australian carsharing company. Three-month anonymous carsharing trip data collected between March 1st, 2016 and May 31st, 2016 was utilised.

The data considered all trips completed by 17,215 carsharing users in the three months.

4.4.1 Vehicle type definition

Within the three-month data collection period, there were 11 vehicle types provided by GoGet for users to choose, i.e. Audi A1, Audi A3, Toyota Corolla Hatch,

Toyota Yaris Hatch, Toyota Hiace, Toyota Hilux, Toyota RAV4, Hyundai Accent,

Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models

Hyundai i30 Wagon, Hyundai I-MAX, and Kia Carnival. The 11 vehicle types were further classified into 7 categories: Toyota hatchback, Hyundai hatchback, Audi, van, ute, SUV and people mover. The classification process was based on body type and manufacturer: initially, the 11 vehicle types were grouped into 5 body types, i.e. van

(Toyota Hiace), ute (Toyota Hilux), SUV (Toyota RAV4), people mover (Hyundai I-

MAX and Kia Carnival), and hatchback (Audi A1, Audi A3, Toyota Corolla Hatch,

Toyota Yaris Hatch, Hyundai Accent, and Hyundai i30 Wagon); then, the hatchbacks were further classified into three sub-categories by manufacturer, i.e. Audi hatchback,

Toyota hatchback, and Hyundai hatchback. These 7 vehicle types were the 7 alternatives in the MDCEV models developed in this study. Table 4:1 presents the distribution of number of vehicle types chosen by carsharing users. In the three-month period, approximately 30% of users have used no less than two types of vehicles, which confirms the multiple discreteness of carsharing users’ vehicle choice patterns.

Table 4:1 Summary of number of vehicle types chosen by users

Number of chosen Frequency Percentage vehicle types 1 12,159 70.63% 2 3,822 22.20% 3 997 5.79% 4 202 1.17% 5 30 0.17% 6 5 0.03% Total 17,215 100.00%

It should also be noted that GoGet charges users by hour and kilometre. The mileage rate is the same for all 7 types of vehicles and for all users, which is AU$0.4 per kilometre (AU$1=US$0.74 [14/06/2016]). The hourly rates vary among different vehicle types and membership plans. Regarding membership plans, there are five

Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models major plans with different monthly service subscription rates and hourly rates for users to choose. The five membership plans are GoFrequent, GoOccasional, GoStarter,

GoBusiness, and GoStudent. The plan GoFrequent has the lowest trip rate and the highest monthly service subscription rate. It is more suitable for users who use carsharing services frequently. GoStarter has no monthly service subscription rate but the highest trip rate. GoBusiness is offered only to business users and GoStudent is exclusive to student users. These two membership plans do not charge monthly service subscription rate and provide the same trip rate as GoFrequent. For each membership plan, Audi, van, SUV, and people mover charge the same rate, which is higher than the rate of Toyota hatchback, Hyundai hatchback and ute. The detailed hourly rates for all plans and seven vehicle types are summarised in Table 4:2.

Table 4:2 Hourly rates for all membership plans and vehicle types (Australian

dollar per hour)

Toyota Hyundai People Audi Van Ute SUV hatchback hatchback mover

GoFrequent 6.35 6.35 8.35 8.35 6.35 8.35 8.35 GoOccasional 9.30 9.30 11.30 11.30 9.30 11.30 11.30 GoStarter 10.45 10.45 14.45 14.45 10.45 14.45 14.45 GoBusiness 6.35 6.35 8.35 8.35 6.35 8.35 8.35 GoStudent 6.35 6.35 8.35 8.35 6.35 8.35 8.35

4.4.2 Correlations between travel time, mileage and expenditure

As mentioned in Section 4.1, this study considers travel time, mileage, and monetary expenditure to be the three variables that might affect carsharing users’ vehicle choice and utilisation patterns. The means and medians of the three variables

Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models are presented in Table 4:3. The means of all three variables are considerably larger than the medians, indicating the substantial skewness in travel time, mileage and monetary expenditure. The kernel density distributions of these three variables are plotted in Figures 4:2 to 4:4. The distributions are highly consistent. All three variables are centrally distributed.

Table 4:3 Means and medians of continuous variables

Variable Mean Median

Travel time (hour) 176.43 72 Travel mileage (km) 19.53 9 Monetary expenditure (AU dollar) 250.86 116.78

Figure 4:2 Kernel density distribution of travel time

Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models

Figure 4:3 Kernel density distribution of travel mileage

Figure 4:4 Kernel density distribution of monetary expenditure

In addition to sharing similar distributions, these three variables are also highly correlated. First, the expenditure of each carsharing trip is composed by the travel time expenditure and the mileage expenditure. Thus, the variable monetary expenditure is highly dependent on the other two variables, i.e. travel time and mileage. Furthermore, travel time and mileage are positively correlated in carsharing trips. Figure 4:5 plots

Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models the distribution of the mileage to travel time ratio. The ratio is also centrally distributed, showing the consistency of travel time and mileage relationship among carsharing users.

Figure 4:5 Kernel density distribution of mileage/travel time ratio

The highly-correlated relationship between these three variables is also confirmed by the correlation estimation results as shown in Table 4:4.

Table 4:4 Correlation estimation results of travel time, mileage and monetary

expenditure

Travel Travel Monetary Time Mileage Expenditure

Travel Time 1

Travel Mileage 0.8969* 1

Monetary Expenditure 0.9557* 0.9420* 1

Since these three variables are not independent, it is not reasonable to combine them as three complementary constraints in a single MDCEV model. If we aim to

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Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models understand the importance of these three variables in users’ decision making process, a better way is to formulate three MDCEV models considering travel time, mileage and monetary expenditure as the budget constraint separately, and identify the best fitted model.

In these three MDCEV models, the total travel time, mileage, and monetary expenditure spent during the three months by each user on the 7 vehicle types were calculated to be the aggregation of the expenditure, time, and mileage across all the trips made by each car type by the user. Table 4:5 presents the summary of the vehicle fleet usage in the dataset. Toyota hatchback is the most used vehicle type, followed by van, SUV and Hyundai hatchback. Ute and People move are least used.

Table 4:5 Summary of vehicle fleet usage in three months

Toyota Hyundai People Audi Van Ute SUV hatchback hatchback mover Average travel time 13.69 1.22 0.80 1.64 0.18 1.57 0.42 (hour)

Average Mileage 119.02 10.19 9.22 15.89 1.61 16.11 4.38 (km)

Average expenditure 163.65 14.35 13.17 26.06 2.28 24.62 6.73 (Australian dollars)

Percentage of users 77.55% 11.86% 7.07% 23.59% 3.25% 12.80% 2.03% choosing vehicle type

4.4.3 Parameters considered in baseline utility functions

The carsharing trip data includes a wide range of anonymous user-related socio-economic and demographic variables, which are described in Table 4:6. These

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Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models variables are selected specific to the aims of the study. Among them, only variable Age is a continuous variable, the rest of the variables are categorical variables. Variable

Driving license country represents if the user holds a local driving license. Variable

Insurance plan tells if the user chooses to reduce the insurance excess fee, which further reveals the risk attitude of the user. Variable Income level was generated based on the median income level of the region where the user located. Variable Originate from CBD area shows the attribute of the origin of the trip. Variable Membership plan shows the plan that the user joins, and the five plans has been described in Section

4.4.1.

Table 4:6 Summary of variables used in the models

Variable Percentage Mean Std. Dev. Age in years - 37.17 10.21

Driving license country Australian driving license 77.72% - - Non-Australian driving license 22.28% - -

Insurance plan Reduce excess fee 54.34% - - Standard plan 45.66% - -

Income level Low income (Household weekly 29.36% - - income < $600) Medium income (Household weekly 40.89% - - income between $600 to $1500) High income (Household weekly 25.11% - - income >$1500)

Membership plan GoFrequent 13.80% - - GoOccasional 20.67% - - GoStarter 53.01% - - GoBusiness 5.25% - - GoStudent 7.27% - - Originate from CBD area 12.70% - -

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Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models

4.5 Results and Analysis

This section will first present the estimation results of the three MDCEV models, followed by the comparison results based on the simulation algorithm.

4.5.1 MDCEV estimation results

Model estimation results of the time-MDCEV, mileage-MDCEV and expenditure-MDCEV models are presented in Tables 4:7, 4:8 and 4:9. Toyota hatchback is considered as the base alternative in the estimations of the three models.

Reviewing the t-statistic results for the estimated parameters, the majority of them are statistically significant, and those insignificant parameters are marked in grey in these three tables.

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Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models

Parameter estimation results for baseline for estimation utility results Parameter Table 4:7 Table4:7

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Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models

It should be noted that the MDCEV model structure applied in this study contains the baseline utility and the satiation parameter 훾 . The baseline utility specifies the marginal utility of a certain vehicle type at the point of zero consumption. A set of attributes are included in the baseline utility for each type of vehicle to estimate their impacts on users’ preference of the vehicle type. It can be found from Table 4:7 that the influences of the parameters on different vehicle types are highly consistent among the three models. The signs and the magnitudes of the coefficients of the parameters do not vary among across the three models, only that the statistical significance of a few parameters changes. This finding indicates that carsharing users’ vehicle consumption patterns are consistent with respect to travel time, mileage, and monetary expenditure.

In general, users with high income are less likely to choose utility vehicles, such as van and ute. This can be explained that high-income users mostly utilise carsharing vehicles for leisure and business, and they do not often need vehicles with special body types for purposes like moving. Among the three types of hatchbacks, high-income users show the preference for luxury vehicle (Audi), and are less willing to choose Hyundai hatchbacks, which is intuitively consistent with the expectation. On the contrary, users with low income have the preference for van, ute and people mover over Toyota hatchback, implying that low-income users utilise carsharing vehicles more for special purposes like moving to new places or travelling with a large group of people, than for business and commuting.

The results also present that users originating from CBD areas are less willing to choose van and ute compared to Toyota hatchback. This is mainly because small vehicles are easier to park in CBD areas, and those utility cars are usually located near

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Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models to appliance and furniture companies which are far away from CBD areas. These users are also more likely to choose Audi over Toyota hatchback. This can be explained by the abovementioned findings with respect to the income: people living in CBD areas usually have higher income and therefore have higher chance to choose luxury vehicle

(Audi).

Age also has an impact on user’s vehicle selection: younger users are more likely to choose Audi over economic hatchback than elderly users. This is consistent with the common sense that younger people like to experience the better acceleration performance of luxury cars. Younger users also prefer to use van. Their proclivity towards utility vehicles can be explained that they have higher probability to rent accommodations, and thus use utility vehicles for moving more often than elderly users.

Furthermore, local users are found to use van and ute more often, and drive

SUV and people mover less often than foreigners. This is because foreign users are less likely to choose utility vehicles for the purposes like moving large furniture and appliances, while they are more likely to use large vehicles to travel around.

Users paying extra fee to reduce insurance excess show higher preference for large vehicles (people mover and van) over normal vehicle types, which is in consistence with the common sense that people tend to become more careful when driving unfamiliar vehicle types.

In addition, carsharing membership plans have significant impacts on the selection for vehicle types. Generally, frequent carsharing users choose economic hatchback more often than other vehicle types, whereas users on other plans such as

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Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models starter plan, business plan and student plan prefer other types of vehicles except SUV over Toyota hatchback. The opposite vehicle choice behaviours of these two groups of carsharing members reflect the two major purposes of joining carsharing programmes. Users on frequent membership plan needs to pay the highest monthly service subscription rate and the lowest trip rate. These users regard carsharing as one of their major transport modes. They usually utilise carsharing vehicles for commuting trips and grocery shopping trips. As a result, they choose to use economic small cars more often. On the contrary, users on starter, business and student plans use carsharing services less frequently. Carsharing serves as a complement to their day-to-day transport modes. Thus, they tend to choose vehicles with specific characteristics to satisfy different trip purposes.

Table 4:8 Parameter estimation results for baseline constants

expenditure- time-MDCEV mileage-MDCEV MDCEV Vehicle Type Coefficient Coefficient Coefficient (t-stat) (t-stat) (t-stat) Hyundai hatchback -1.753(-9.723) -1.986(-12.210) -1.825(-10.153) Audi -2.611(-10.413) -2.678(-12.290) -2.692(-10.707) Van -1.503(-10.882) -1.597(-13.240) -1.587(-11.541) Ute -4.376(-13.400) -4.743(-15.450) -4.447(-13.609) SUV -1.750(-9.082) -1.536(-9.763) -1.831(-9.468) People mover -4.095(-8.997) -4.654(-10.280) -4.170(-9.153)

The results of baseline constants in Table 4:8 provide an implication of the inherent preferences and the marginal utilities for different vehicle types. The baseline constants of all six alternatives except the base one are negative across all three models, indicating users’ preference on the base alternative, Toyota hatchback, over other

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Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models vehicle types. Besides Toyota hatchback, the orders of the baseline constants for the three MDCEV models only perform slightly different from each other. For time and expenditure MDCEV models, van has the highest baseline utility, meaning that van has the greatest baseline preference when users allocate travel time and monetary expenditure. In the mileage-MDCEV model, SUV has the highest baseline constant and van has the second highest baseline constant. This difference reflects users’ different choice behaviours regarding time, expenditure and mileage consumptions.

Users prefer to allocate more time and expenditure but less mileage to van compared to SUV. This is consistent with the purposes of using these two types of vehicles.

Normally users use van to move large items resulting in longer time to move those items. As for SUV, users mostly choose it to travel, and hence lead to longer mileage.

In contrast with van, another utility vehicle ute has the lowest baseline constants in all three models, indicating that users do not like to use ute. It is found that Hyundai hatchback has higher baseline utility compared to another small vehicle Audi. This illustrates carsharing users’ preference on economic vehicles over luxury vehicles.

Furthermore, people mover has the second lowest baseline utility reflecting users’ low interest towards large vehicles. Referring to these findings, operators could consider to reduce the number of utes operated in the network and add more vans to meet users’ high preference for vans. In the case of small vehicles, economic vehicles, like Toyota and Hyundai, are preferable by users, suggesting operators to consider carefully before putting more luxury cars in the network. With respect to large vehicles, SUVs are better choices than people movers when setting up acquiring plans.

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Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models

Table 4:9 Parameter estimation results for satiation parameters (휸)

expenditure- time-MDCEV mileage-MDCEV MDCEV Vehicle Type Coefficient Coefficient Coefficient (t-stat) (t-stat) (t-stat) Toyota hatchback 21.455(22.731) 194.400(23.370) 220.835(25.516) Hyundai hatchback 7.281(18.303) 49.740(20.330) 84.955(18.422) Audi 10.802(14.725) 115.300(15.800) 202.126(14.148) Van 10.115(21.114) 81.840(23.500) 178.771(20.072) Ute 6.939(8.402) 50.810(9.272) 83.218(8.489) SUV 9.404(20.170) 80.990(22.270) 161.972(19.660) People mover 25.700(8.158) 292.200(8.024) 536.851(7.252)

The satiation parameter 훾 determines the satiation effect with the consumption of each vehicle type. A higher satiation parameter suggests that carsharing users are less likely to get satiated with the consumption of that vehicle type, and are willing to drive it more. The order of the satiation parameters for all three MDCEV models are nearly the same, except the order of Hyundai hatchback and ute in mileage-MDCEV model is the different from the other two models. In time-MDCEV and expenditure-MDCEV models, Hyundai hatchback has higher satiation parameters than ute, while in mileage-

MDCEV model, the satiation parameter of ute is slightly higher than Hyundai hatchback.

Overall, people mover has the highest satiation parameter, whereas another large vehicle type SUV has low satiation parameter. This is because the multi-purpose feature of people mover can meet most of users’ driving requirements, so that users are less easily to get bored with driving it. On the contrary, SUV is neither as large capacitated as people mover nor as easy-driving as small hatchbacks, and thus has high satiation effect. Toyota hatchback also has high satiation parameter. This can be

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Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models attributed to the high reputation and reliability of Toyota in Australia. As reported in

September 2016, Toyota has nearly double market share compared to Hyundai in

Australia (CarAdvice, 2016). Audi also has higher satiation parameter than Hyundai hatchback, which can be due to the extraordinary driving experience of Audi. For the two utility vehicles, van has higher satiation parameter than ute, confirming people’s preference of van over ute.

4.5.2 Simulation and comparison results

This section will compare the three models and identify the best-fitted MDCEV model for carsharing vehicle choice and utilisation. The comparison procedure has been presented in Sections 4.3.2 and 4.3.3. Since expenditure is composed of travel time expenditure and mileage expenditure, we calculate the decomposed expenditure by combining the simulation results of the time-MDCEV and mileage-MDCEV models. Then we compare the simulated results of time consumption, mileage consumption, aggregate expenditure consumption, and decomposed expenditure consumption to the observed data. The normalised root-mean-square error (RMSE) and correct ratio are used as the performance metrics to determine the best-fitted model as presented in Table 4:10. Normalised RMSE can reflect the fitness of the continuous prediction and correct ratio can evaluate the performance of the discrete choice of the models.

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Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models

Table 4:10 Comparison of normalised RMSE and correct ratios for simulation

results

Simulation results Normalised RMSE Correct ratio

time-MDCEV model 66.48 81.02% mileage-MDCEV model 66.57 80.92% expenditure-MDCEV model 66.02 80.91% decomposed simulated expenditure 133.17 80.61%

In general, both normalised RMSE values and correct ratios of the three MDCEV models are fairly consistent. Aggregate expenditure model has the lowest normalised

RMSE, and time-MDCEV model has the highest correct ratio. However, the differences of these two performance measures among the three models are too slight to determine the best-fitted model. Instead, the comparison results reflect that travel time, mileage and monetary expenditure are equally important in determining which vehicles to choose, and these three variables affect users’ vehicle utilisation patterns in the same way. This finding is also in line with the observed distributions of these three variables as discussed in Section 4.4.2: the distributions of travel time, mileage and expenditure are highly consistent.

As for the decomposed expenditure model, it is an expectable result that it has higher normalised RMSE than the travel time and mileage models, because this decomposed expenditure is calculated using the simulation results of time-MDCEV and mileage-MDCEV models and therefore is supposed to perform no better than these two models. The comparison between the decomposed and aggregate expenditure models is more valuable. As shown in Table 4:10, the normalised RMSE of the decomposed expenditure model is higher than the aggregate model, which is an

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Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models indicative of the bad performance of the decomposed model compared to the aggregate one. Therefore, rather than predicting users’ travel time and mileage usage separately to get an intuition of budget allocation, it is more accurate to treat travel time and mileage expenditures as a whole.

In addition to these two performance measures, Table 4:11 compares the vehicle type distributions of the four simulation results to the observed data. As shown in Table 4:11, the differences in the percentage of users choosing each vehicle type in the observed data and the simulated time, mileage, and expenditure consumptions are quite small. This confirms that the proposed three MDCEV models as well as the decomposed expenditure model can accurately predict carsharing users’ discrete choices of vehicles types.

Table 4:11 Comparison of observed data and MDCEV model simulation results

for percentage of users choosing vehicle type

Toyota Hyundai People Audi Van Ute SUV hatchback hatchback mover Observed consumption 77.55% 11.85% 7.06% 23.58% 3.25% 12.77% 2.03%

Simulated travel time 77.33% 14.38% 6.80% 21.86% 2.80% 14.65% 1.75%

Difference 0.21% 2.53% 0.25% 1.72% 0.44% 1.87% 0.29% Simulated mileage 77.05% 14.46% 6.84% 23.98% 2.44% 14.47% 1.38%

Difference 0.50% 2.61% 0.21% 0.39% 0.81% 1.70% 0.65% Aggregate simulated 77.20% 14.50% 6.96% 22.11% 2.82% 14.56% 1.83% expenditure Difference 0.35% 2.65% 0.09% 1.47% 0.43% 1.78% 0.21% Decomposed simulated 79.00% 15.42% 7.38% 24.53% 3.04% 15.84% 1.85% expenditure Difference 1.45% 3.57% 0.33% 0.95% 0.20% 3.07% 0.19%

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Table 4:12 compares the means and medians of the observed and the simulated usage of each vehicle type. The differences of means and medians between the observed data and the simulated results are fairly small for these four models, implying that these models can closely replicate users’ continuous consumption allocation patterns of vehicles.

Table 4:12 Comparison of observed data and MDCEV model simulation results

for means and medians of each vehicle type

Toyota Hyundai People Audi Van Ute SUV hatchback hatchback mover time-MDCEV (hour) Observed mean 13.69 1.22 0.80 1.64 0.18 1.57 0.42 Simulated mean 13.49 1.29 0.68 2.14 0.22 1.48 0.23 Normalised difference 0.01 0.05 0.18 0.23 0.18 0.06 0.83 Observed median 5.50 0.00 0.00 0.00 0.00 0.00 0.00 Simulated median 5.00 0.00 0.00 0.00 0.00 0.00 0.00 Normalised difference 0.09 0.00 0.00 0.00 0.00 0.00 0.00 mileage-MDCEV (km) Observed mean 119.02 10.19 9.22 15.89 1.61 16.11 4.38 Simulated mean 121.35 10.31 6.91 21.30 1.56 13.10 1.90 Normalised difference 0.02 0.01 0.25 0.34 0.03 0.19 0.57 Observed median 42.00 0.00 0.00 0.00 0.00 0.00 0.00 Simulated median 41.16 0.00 0.00 0.00 0.00 0.00 0.00 Normalised difference 0.02 0.00 0.00 0.00 0.00 0.00 0.00 Expenditure-MDCEV (AU dollar) Observed mean 163.65 14.35 13.17 26.06 2.28 24.62 6.73 Simulated mean 164.04 15.96 10.56 32.65 2.80 21.19 3.65 Normalised difference 0.00 0.10 0.25 0.20 0.19 0.16 0.84 Observed median 69.00 0.00 0.00 0.00 0.00 0.00 0.00 Simulated median 65.75 0.00 0.00 0.00 0.00 0.00 0.00 Normalised difference 0.05 0.00 0.00 0.00 0.00 0.00 0.00 Decomposed expenditure Observed mean 163.65 14.35 13.17 26.06 2.28 24.62 6.73 Simulated mean 163.29 15.09 10.52 34.17 2.56 21.97 3.35 Normalised difference 0.00 0.05 0.25 0.24 0.11 0.12 1.01 Observed median 69.00 0.00 0.00 0.00 0.00 0.00 0.00 Simulated median 63.87 0.00 0.00 0.00 0.00 0.00 0.00 Normalised difference 0.07 0.00 0.00 0.00 0.00 0.00 0.00

4.6 Policy Implications

The modelling results and findings discussed in the previous section can provide insights to carsharing operators on deciding the optimal fleet composition to be

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Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models deployed to different areas. A carsharing operator normally operates a set of vehicles across a relatively large metropolitan area. The whole network usually consists of several sub-areas with different characteristics. Taking GoGet Sydney as an example, it operates over 1000 vehicles across the Greater Sydney area. Some vehicles are located in CBD areas with high population and workforce density, some are distributed in suburban areas with poor public transport coverage. Users living in CBD areas and suburban areas will have different preference for vehicle types. The proposed MDCEV models have captured the impact of users’ origin on their vehicle choice patterns via the binary variable Originate from CBD area. Changing the value of this variable to be 1 or 0, one can predict the potential usage of each vehicle type in CBD and non-

CBD areas. Figure 4:6 presents the sensitivity analysis results of variable Originate from CBD area in expenditure-MDCEV model. Only expenditure-MDCEV model is tested because time, mileage and expenditure influence users’ vehicle utilisation pattern in the same way. The variable Originate from CBD area is set to be 1 across all users to test the vehicle usage in CBD areas and set to be 0 for all users to predict the usage for non-CBD areas. As shown in Figure 4:6, users from CBD areas rent

Toyota hatchback, Audi, SUV and people mover more often than suburban areas, whereas users from suburban areas spend more money on Hyundai hatchback and utility vehicles. When distributing vehicles to the network, carsharing operator should allocate most of the luxury cars to CBD area, and most of the utility vehicles to non-

CBD areas. Furthermore, to maximise vehicle utilisation and user ridership given limited carsharing parking spaces in each area, the operator can also refer to the usage pattern presented in this table to determine the number of each type of vehicle to be placed in that area.

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200

180

160

140

120

100

60 verage verage ExpenditureDollar) (AU

A 40

0 Toyota Hyundai People Audi Van Ute SUV hatchback hatchback mover CBD 172.78 14.68 15.96 19.31 1.81 22.43 3.89 Non-CBD 162.78 16.14 9.58 34.74 2.98 21.01 3.62

Figure 4:6 Comparison of vehicle usage pattern in CBD and non-CBD areas

(measured by average expenditure (AU dollar))

Moreover, Sydney has a diverse and dynamic ethnic mix with 31.7% of the population born overseas (Regional Development Australia Sydney, 2017). Benefiting from such society, GoGet carsharing services have attracted a number of users from different countries. As presented in Table 4:6, 22.28% of carsharing users hold non-Australian driving licenses. These foreign users show different preferences on vehicles from local users according to the modelling results. This finding is also valuable to be referred by the operator with respect to fleet deployment. People from different countries tend to live concentratedly in certain areas. For instance, East Asian and South East Asian are found to live concentratedly in the northern and south-western parts of Sydney. They also like to live surrounding train lines or around university areas due to the large population of Asian international students. Middle Eastern population clusters are often found in western areas of Sydney. The remainder of Sydney are predominantly

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Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models inhabited by local Australians, especially in the northern and southern coastlines, the eastern suburbs and the far-western and far-southwestern Sydney (MapSydney, 2017).

Based on this fact, a sensitivity analysis is undertaken on the variable Driving license country to compare vehicle usage patterns of local Australians and foreign users.

Expenditure-MDCEV model is also applied for the analysis. The results are presented in Figure 4:6. Local users tend to use utility vehicles more often and large vehicles less often than foreign users. Thus, carsharing operator could allocate more large vehicles to northern, southern-western and western Sydney, and more utility vehicles to the rest parts of Sydney.

180

160

140

120

100

verage verage ExpenditureDollar) (AU 0 A Toyota Hyundai People hatchbac hatchbac Audi Van Ute SUV mover k k Australian 164.24 15.99 10.57 34.12 3.07 19.65 3.23 Non-Australian 163.25 15.88 10.49 28.16 1.95 26.16 4.97

Figure 4:7 Comparison of vehicle usage pattern for Australian and non-

Australian users (measured by average expenditure (AU dollar))

In addition to these two tested variables, carsharing operator could also obtain policy implications from other variables. For example, they could optimise the fleet composition in education and commercial areas based on the results of membership

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Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models plan variables. The proposed models help operators understand users’ various demand on vehicle types based on their sociodemographic characteristics, and are beneficial for operators to design optimal fleet composition in different areas.

4.7 Concluding Remarks

This chapter attempted to accurately model carsharing users’ vehicle choice behaviour and utilisation patterns. Unlike traditional single discrete choice scenarios, carsharing users’ vehicle choice process involves making multiple discrete choices of continuous amounts of consumptions, such as travel time, travel mileage and monetary expenditure. To handle with these multiple discrete and continuous features, the

MDCEV modelling framework was applied. Three MDCEV models considering travel time, mileage and expenditure as the budget constraint were developed, and a simulation procedure and several performance metrics were applied to determine the most accurate vehicle usage patterns for carsharing users.

The three MDCEV models estimated the impacts of a set of user-related attributes on decisions concerning the allocation of the budget to multiple vehicle types, and captured the diminishing nature of the marginal utility with increasing consumptions. The parameter estimation results for the three models were quite consistent. The results indicated that users’ income, age, origin location, membership plan, insurance plan, and driving license country had impacts on the choice for some of the vehicle types. Based on these findings, carsharing operators are able to understand users’ various demand on vehicle types via their sociodemographic characteristics, and further design optimal fleet composition in different areas. The

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Chapter 4. An Analysis of Carsharing Vehicle Choice and Utilisation Patterns Using MDCEV Models satiation parameter estimation results suggest the decision makers to reduce the number of utes and Hyundai hatchbacks in the network and add more people movers,

Toyota hatchbacks and Audi hatchbacks.

Regarding the comparison results of the three models, they perform consistently well in predicting both the discrete choices and the continuous allocations.

This finding reflects that travel time, mileage and monetary expenditure have the same importance in determining which vehicles to choose, and affect users’ vehicle utilisation patterns in the same way.

The findings in this chapter can help carsharing operators understand the demand for different vehicle types of users from different areas and backgrounds. This is essential for decision makers to determine the optimal fleet compositions that can maximise vehicle utilisation and user ridership in different areas of a carsharing network.

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Part II. Operation Optimisation

Part II Operation Optimisation

The previous two chapters construct the first part of this thesis: modelling users’ demand and preference for vehicles of station-based carsharing systems. The demand estimations are constrained by the supply of vehicles. Part II will focus on the supply side of carsharing systems and develop optimal operation mechanisms for carsharing systems that account for the interaction between demand and supply.

Introducing one-way carsharing services to a traditional round-trip system can attract a substantially larger market demand but will incur extra costs associated with vehicle relocations. As highlighted in Section 2.5, user demand is influenced by the available supply of vehicles in the carsharing networks. Conversely, the demand can change the availability of vehicles and further change vehicle stock distribution. Thus, it is important to consider the mutual effect between demand and supply when evaluating the profitability of a carsharing system and determining relocation strategies.

The related research gaps identified in Section 2.5 are bridged by two novel optimisation models that integrate a carsharing demand model. These two models are discussed in Chapter 5 and Chapter 6 respectively. Furthermore, Part II draws heavily from the following peer-reviewed journal paper and under-review article:

Chapter 5 – Jian, S., Rey, D. and Dixit, V., 2016. Dynamic Optimal Vehicle

Relocation in Carsharing Systems. Transportation Research Record: Journal

of the Transportation Research Board, (2567), pp.1-9.

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Chapter 6 – Jian, S., Rey, D., and Dixit, V. An Integrated Supply-Demand

Approach to Solving Optimal Relocations in Carsharing Systems. In review

with Networks and Spatial Economics

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Chapter 5. Dynamic Optimal Vehicle Relocation

Chapter 5 Dynamic Optimal Vehicle Relocation

5.1 Introduction

The flexibility of one-way carsharing systems can attract more users, but yield more complex operation problems to the operators. One dominant challenge is to ensure the supply of carsharing vehicles can meet the demand of carsharing users. Since travellers’ demands are not necessarily uniformly distributed across urban networks, carsharing vehicle stocks can become spatially and temporally imbalanced. This may influence vehicle availability and result in situations where users’ pick-up reservations cannot be fulfilled due to a lack of vehicles and users’ parking needs cannot be satisfied due to surplus vehicles. Such poor accessibility may considerably impair the profitability of one-way carsharing systems. Hence, it is critical to dynamically relocate vehicles to rectify and anticipate vehicle imbalance. Relocation operations represent an increase in operational costs which could potentially be compensated with the revenues earned from the increased demand for one-way trips or, in turn, could reduce profits.

Under such circumstances, several research efforts have been focused on building effective relocation strategies or optimal system designs for one-way carsharing systems. A detailed literature review with respect to one-way carsharing relocation methods can be found in Section 2.4, where we found most relocation models did not consider the impact of demand variation on the availability of carsharing vehicles as well as vehicle stock distribution. However, Jorge and Correia

(2013b) claimed that demand variation will influence the performance of relocation strategies. Furthermore, it should be noted that users’ travel demand for carsharing

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services is influenced by the available supply of carsharing vehicles. Demand, on the one hand, brings about the revenues to carsharing operators; Relocation, on the other hand, generates extra costs to them. These two factors contribute in determining the profits of carsharing systems. Hence, the interdependency between demand and supply in one-way carsharing systems makes the profitability analysis more complex.

An attractive solution to this logistical challenge is to undertake an integrated supply and demand cost-benefit analysis before introducing one-way carsharing services to the existing round-trip carsharing systems. This chapter proposes an approach that incorporates an integer linear programming (ILP) model with a discrete choice model (DCM) with constant results of utility functions. The ILP model is formulated to maximise the profit for carsharing operators. It solves the optimal supply decisions for the carsharing systems and updates vehicle availability across carsharing stations. The DCM considers the elasticity of users’ travel demand towards trip cost and trip travel time. Coupled with the updated vehicle availability, the choice model determines the demand for one-way and round-trip carsharing reciprocally. These two models work together to account for the interaction between supply and demand in carsharing systems.

Since the demand and the availability of vehicles are influenced by their interdependency as well as by trip cost and vehicle availability, a systematic sensitivity analysis on total travel demand, one-way trip price, and vehicle pod capacity is conducted to evaluate their impacts on the carsharing system profits. Figure 5:1 summarises the research contributions of Chapter 5.

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Figure 5:1 Summary of research contributions in Chapter 5

The rest of this chapter is structured as follows. A detailed description of the research problem and the methodology are presented in Section 5.2. The Sydney carsharing network case study is presented in Section 5.3 followed by the results of the sensitivity analysis in Section 5.4. Finally, the major findings of this chapter are presented Section

5.5.

5.2 Problem Statement and Formulation

The problem addressed in this chapter can be restated as follows. A carsharing operator that is currently operating round-trip carsharing services wants to introduce one-way carsharing services to its original carsharing network. The updated carsharing services may attract more travel demand for carsharing but at the same incur additional relocation costs to maintain balanced vehicle stocks.

The demand for one-way and round trips is determined by vehicle availability, trip travel time and travel cost. The demand is assumed to be reactive to the changes in vehicle availability. The operator aims to maximise the profit for this updated carsharing network by making optimal relocation decisions.

Furthermore, the following assumptions are made for this problem:

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1. We assume discrete time steps during which decisions are made.

2. All the vehicles are available at the initial time step of each day.

3. Users can only make a trip request when a vehicle is available and all

carsharing trip requests are accepted by the operator.

4. The total travel demand of each origin-destination (OD) pair at each time

step is known and constant. However, the operator does not know the

demand for one-way and round trips in advance. Each user has three travel

mode options: one-way carsharing (OW), round-trip carsharing (RT), and

other transport infrastructure (TI). User’s choice is influenced by trip cost,

trip travel time, and the availability of vehicles. A constraint is included to

account for vehicle availability. The multinomial logit (MNL) model

proposed by Catalano et al. (2008) is applied to account for the impacts of

trip price and travel time. The motivation of using Catalano et al. (2008)’s

model is its consistency with general cases. As reviewed in Section 2.3,

travellers’ mode choice behaviour among carsharing and other transport

modes has been investigated by a few studies. Among them, Le Vine et al.

(2014a)’s research only focused on grocery shopping trip. Ciari et al.

(2013)’s study assumed an unlimited number of cars available at the

stations, which is not realistic for our case. Catalano et al. (2008)’s study

result is more applicable to general cases, and therefore is adopted in the

model formulation part. The MNL model includes travel time, travel cost,

parking time, and number of household cars as the parameters that

influence travellers’ mode choice behaviour.

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5. If a vehicle is used for a round trip, the parking space for that vehicle is

reserved until this trip ends; while if a vehicle is used for a one-way trip,

its parking space is available during the booked period.

6. Carsharing users are assumed to be charged by travel time.

An ILP formulation to maximise carsharing operators’ profits is proposed based on the above assumptions. We next introduce the mathematical notation used throughout the chapter.

Sets

Let 퐺 = (푁, 퐴) be a complete graph, where 푁 is a set of nodes and 퐴 is a set of arcs, i.e. 퐴 ≡ {(푖, 푗): 푖, 푗 ∈ 푁, 푖 ≠ 푗}. Let 푇 be the set of time steps in the operation period, and 푇∗ be the set of time steps excluding the first time step.

Decision variables

푟푖푗,푡 ∈ ℤ: Number of vehicles relocated from node 푖 to 푗 at time 푡, ∀푖, 푗 ∈ 푁:⁡푖 ≠

푗, ∀푡 ∈ 푇;

푣푖,푡 ∈ ℤ: Number of vehicles available at node 푖 at time 푡, ∀푖 ∈ 푁, ∀푡 ∈ 푇;

푂푊 푑푖푗,푡 ∈ ℤ: Number of users booking one-way trips from node 푖 to 푗 at time 푡, ∀푖, 푗 ∈

푁:⁡푖 ≠ 푗, ∀푡 ∈ 푇;

푅푇 푑푖푗,푡 ∈ ℤ: Number of users booking round trips from node 푖 to 푗 at time 푡, ∀푖, 푗 ∈

푁:⁡푖 ≠ 푗, ∀푡 ∈ 푇.

Parameters

푅표: Price rate per time step for one-way trips;

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푅푟: Price rate per time step for round trips;

퐶푚: Cost of maintaining a vehicle per time step driven;

퐶푟: Labour cost of relocating a vehicle per time step driven;

푆푖: Capacity of node 푖, ∀푖 ∈ 푁;

퐷푖푗,푡: Total travel demand from node 푖 to 푗 at time 푡, ∀푖, 푗 ∈ 푁:⁡푖 ≠ 푗, ∀푡 ∈ 푇;

휏푖,푗: Travel time from node 푖 to 푗 (in number of time steps), ∀푖, 푗 ∈ 푁:⁡푖 ≠ 푗;

푤푖: Time round-trip user spends at destination node 푖, ∀푖 ∈ 푁;

푅푇 휓푖,푗 : Probability that a user travelling from node 푖 to 푗 chooses RT among RT, OW and TI, ∀푖, 푗 ∈ 푁:⁡푖 ≠ 푗;

푂푊 휓푖,푗 : Probability that a user travelling from node 푖 to 푗 chooses OW among RT, OW and TI, ∀푖, 푗 ∈ 푁:⁡푖 ≠ 푗;

푇퐼 휓푖,푗: Probability that a user travelling from node 푖 to 푗 chooses TI among RT, OW and

TI, ∀푖, 푗 ∈ 푁:⁡푖 ≠ 푗;

푃푇: Parking time of each trip;

푁퐶퐴푅: Number of household cars for each user;

훽푡푡: Coefficient for travel time;

훽푡푐: Coefficient for travel cost;

훽푝푡: Coefficient for parking time;

훽푛푐: Coefficient for number of household cars for each user;

훽푐푠: Alternative specific constant for carsharing;

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훽푡푖: Alternative specific constant for other transport infrastructure.

We have the following equations to determine users’ mode choice. The utility functions are given by Catalano et al. (2008).

푅푇 푒푈푖,푗 푅푇 ∀푖, 푗 ∈ 푁:⁡푖 ≠ 푗; (5.1) 휓푖,푗 = 푂푊 푅푇 푇퐼 푒푈푖,푗 + 푒푈푖,푗 + 푒푈푖,푗

푂푊 푒푈푖,푗 푂푊 ∀푖, 푗 ∈ 푁:⁡푖 ≠ 푗; (5.2) 휓푖,푗 = 푂푊 푅푇 푇퐼 푒푈푖,푗 + 푒푈푖,푗 + 푒푈푖,푗

푅푇 푈푖,푗 = ⁡ 훽푡푡(휏푖,푗 + 휏푗,푖 + 푤푗) + 훽푡푐푅푟(휏푖,푗 + 휏푗,푖 + 푤푗) ∀푖, 푗 ∈ 푁:⁡푖 ≠ 푗; (5.3) + 훽푝푡푃푇 + 훽푛푐푁퐶퐴푅 + 훽푐푠

푂푊 푈푖,푗 = ⁡ 훽푡푡휏푖,푗 + 훽푡푐푅표휏푖,푗 + 훽푝푡푃푇 + 훽푛푐푁퐶퐴푅 ∀푖, 푗 ∈ 푁:⁡푖 ≠ 푗; (5.4) + 훽푐푠

푇퐼 푈푖,푗 = 훽푡푡휏푖,푗 + 훽푡푐퐶푚휏푖,푗 + 훽푝푡푃푇 + 훽푡푖 ∀푖, 푗 ∈ 푁:⁡푖 ≠ 푗; (5.5)

Objective function

푂푊 푅푇 max⁡Π = ∑ ∑ ∑ (푑푖푗,푡 )( 푅표 − 퐶푚)휏푖,푗 + ∑ ∑ ∑ (푑푖푗,푡)( 푅푟 푡∈푇 푖∈푁 푗∈푁,푗≠푖 푡∈푇 푖∈푁 푗∈푁,푗≠푖

(5.6) − 퐶푚)(휏푖,푗 + 휏푗,푖 + 푤푗) − ∑ ∑ ∑ (푟푖푗,푡) (퐶푟 푡∈푇 푖∈푁 푗∈푁,푗≠푖

+ 퐶푚)휏푖,푗

Subject to

푣푖,0 = 푆푖 ∀푖 ∈ 푁; (5.7)

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∗ 푣푖,푡 ≤ 푆푖 ∀푖 ∈ 푁, ∀푡 ∈ 푇 ; (5.8)

푣푖,푡 = 푣푖,푡−1 − ∑ 푟푖푗,푡−1 푗∈푁,푗≠푖

+ ∑ 푟푗푖,푡−1−휏푗,푖 푗∈푁,푗≠푖

푂푊 − ∑ 푑푖푗,푡−1 푗∈푁,푗≠푖 ∀푖 ∈ 푁, ∀푡 ∈ 푇∗; (5.9) + ∑ 푑푂푊 푗푖,푡−1−휏푗,푖 푗∈푁,푗≠푖

푅푇 − ∑ 푑푖푗,푡−1 푗∈푁,푗≠푖

+ ∑ 푑푅푇 푖푗,푡−1−(휏푖,푗+휏푗,푖+푤푗) 푗∈푁,푗≠푖

푅푇 푅푇 푑푖푗,푡 ≤ 퐷푖푗,푡휓푖,푗 ∀푖, 푗 ∈ 푁:⁡푖 ≠ 푗, ∀푡 ∈ 푇; (5.10)

푂푊 푂푊 푑푖푗,푡 ≤ 퐷푖푗,푡휓푖,푗 ∀푖, 푗 ∈ 푁:⁡푖 ≠ 푗, ∀푡 ∈ 푇 (5.11)

푅푇 푅푇 ∑ 푑푖푗,푡 = 푚푖푛 { ∑ (퐷푖푗,푡휓푖,푗 )⁡⁡⁡,⁡⁡⁡ ⁡푣푖,푡 푗∈푁,푗≠푖 푗∈푁,푗≠푖 ∀푖 ∈ 푁, ∀푡 ∈ 푇 (5.12)

푂푊 − ∑ 푑푖푗,푡 } 푗∈푁,푗≠푖

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푂푊 푂푊 ∑ 푑푖푗,푡 = 푚푖푛 { ∑ (퐷푖푗,푡휓푖,푗 )⁡⁡⁡,⁡⁡⁡ 푣푖,푡 푗∈푁,푗≠푖 푗∈푁,푗≠푖 ∀푖 ∈ 푁, ∀푡 ∈ 푇 (5.13)

푅푇 − ∑ 푑푖푗,푡} 푗∈푁,푗≠푖

푂푊 푑푖푗,푡 ≥ 0, integer ∀푖, 푗 ∈ 푁:⁡푖 ≠ 푗, ∀푡 ∈ 푇; (5.14)

푅푇 푑푖푗,푡 ≥ 0, integer ∀푖, 푗 ∈ 푁:⁡푖 ≠ 푗, ∀푡 ∈ 푇; (5.15)

⁡푟푖푗,푡 ≥ 0, integer ∀푖, 푗 ∈ 푁:⁡푖 ≠ 푗, ∀푡 ∈ 푇; (5.16)

푣푖,푡 ≥ 0, integer ∀푖 ∈ 푁, ∀푡 ∈ 푇; (5.17)

The objective function (5.6) maximises the profit over the operation period for carsharing operators. The profit is equal to the difference between the revenues earned by users’ trips and the costs caused by vehicle maintenance and relocations.

Constraints (5.7) ensures that the number of vehicles at node 푖 at the initial time step is equal to its capacity. Constraints (5.8) guarantees that the number of vehicles at node 푖 at time 푡 will not exceed its own capacity. Constraints (5.9) is a flow conservation constraint. It specifies that the number of vehicles available at node 푖 at time 푡 equals to the number of vehicles available at the previous time step minus all the outbound relocation trips, one-way and round trips at the previous time step, and plus all the inbound relocation trips, one-way and round trips at the previous time step.

Constraints (5.10) and (5.11) ensure that the number of one-way and round trips are less than or equal to their travel demand determined by the MNL model. Here, the demand for one-way or round trips equals to total travel demand multiplied by the

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probability that they are chosen by travellers. Constraints (5.12) and (5.13) determine that the numbers of one-way and round trips equal to the minimum of their travel demand and the number of vehicles left for select. These two constraints make the model nonlinear. To linearise the model, constraints (5.12) and (5.13) can be rewritten as:

푅푇 푅푇 ∑ 푑푖푗,푡 ≤ ∑ (퐷푖푗,푡휓푖,푗 ) ∀푖 ∈ 푁, ∀푡 ∈ 푇 (5.18) 푗∈푁,푗≠푖 푗∈푁,푗≠푖

푅푇 푂푊 ∑ 푑푖푗,푡 ≤ 푣푖,푡 − ∑ 푑푖푗,푡 ∀푖 ∈ 푁, ∀푡 ∈ 푇 (5.19) 푗∈푁,푗≠푖 푗∈푁,푗≠푖

푂푊 푂푊 ∑ 푑푖푗,푡 ≤ ∑ (퐷푖푗,푡휓푖,푗 ) ∀푖 ∈ 푁, ∀푡 ∈ 푇 (5.20) 푗∈푁,푗≠푖 푗∈푁,푗≠푖

푂푊 푅푇 ∑ 푑푖푗,푡 ≤ 푣푖,푡 − ∑ 푑푖푗,푡 ∀푖 ∈ 푁, ∀푡 ∈ 푇 (5.21) 푗∈푁,푗≠푖 푗∈푁,푗≠푖

Since equations (5.18) and (5.20) are interchangeable with constraints (5.10) and (5.11), equations (5.18) and (5.20) are discarded. Then, constraints (5.12) and

(5.13) can be linearised by equations (5.19) and (5.21). These two equations are then combined as one equation as follows:

푅푇 푂푊 ∑ 푑푖푗,푡 + ∑ 푑푖푗,푡 ≤ 푣푖,푡 ∀푖 ∈ 푁, ∀푡 ∈ 푇 (5.22) 푗∈푁,푗≠푖 푗∈푁,푗≠푖

Finally, constraints (5.14) to (5.17) set the domains for the decision variables.

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5.3 Description of Case Study Network

We apply the proposed optimisation model to GoGet Sydney carsharing network to evaluate its performance and undertake sensitivity analysis. GoGet is Australia’s largest carsharing company (GoGet Carshare, 2013). It is currently operating round- trip services and planning to introduce one-way carsharing services to its existing carsharing network. At the time of data collection, there were 37 frequently-used vehicle pods located around Sydney urban areas containing 198 vehicles in total. The distribution of these 37 vehicle pods is presented in Figure 5:2. The vehicle pods with larger symbols have higher capacities. It is clear from Figure 5:2 that the majority of

GoGet vehicle pods are located around urban areas with high population densities. We assume that the locations and capacities of these current vehicle pods remain unchanged after the introduction of one-way trip services.

Figure 5:2 Locations and capacities of GoGet vehicle pods

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The study focuses on the AM peak operation period (from 7:00 AM to 10:00 AM). To reduce calculation time, the three-hour period is expressed in 12 time steps with 15 minutes per time step.

The data required to apply the model are: the potential origin-destination (OD) travel demand matrix, trip travel time matrix, parking times, and the number of household cars for each user. Regarding the travel demand matrix, we use Sydney AM peak OD travel demand matrix obtained from EMME, a travel demand forecasting software (Emme, 2016), to determine the total travel demand for each vehicle pod at each time step. Sydney AM peak OD travel demand matrix contains the OD demand between all travel zones within Sydney. We use ArcGIS 10.3, a software to manage geographic data (ArcGIS Desktop, 2017), to associate GoGet vehicle pods with their corresponding travel zones. The total number of trips generated by all travellers during

AM peak in GoGet operating area is 80930. However, only a proportion of these trips can be carsharing trips, because among all travellers, only GoGet users can choose to use GoGet carsharing services. Therefore, for each OD pair, we consider a proportion of the total OD travel demand to be the potential carsharing travel demand. In this way, the total travel demand from vehicle pod 푖 to 푗 equals to a certain proportion of the travel demand from pod 푖’s corresponding travel zone to pod 푗’s corresponding travel zone. The demand multiplied by a proportion can be a non-integer. To ensure travel demands are integers, we round the proportioned demands to the nearest integers.

Three demand scenarios with proportions equal to 0.15, 0.2, and 0.4 are tested in this study. The total travel demands with these three proportions are equal to 6086, 10356, and 28237. These three scenarios represent low-demand, medium-demand and high- demand cases, respectively.

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The trip travel times are computed by dividing the OD route distance by the average driving speed. The OD route distance is calculated using ArcGIS 10.3

Network Analyst geoprocessing tool. The average driving speed is assumed to be 30 kilometres per hour because all the vehicle pods are located in urban areas with high traffic flows and all the trips are generated during AM peak period with low average driving speed. The travel times of one-way and relocation trips are equal to the travel times of corresponding OD pairs. The travel time of a round trip is the sum of the travel time from the origin to the destination, the time the user spends at the destination, and the travel time from the destination back to the origin. The time users spending at the destination is assumed to follow a normal distribution with mean equals to 1 time step and variance equals to 1. Both travel times and waiting times are in number of time steps.

The parking time of each trip is assumed to be 0 to simplify the problem. This is reasonable since carsharing vehicles have dedicated parking spaces, so the time of finding parking spaces is negligible. The number of household cars for each user is also assumed to be 0 as the majority of carsharing users do not own a car. The rest of the parameters are set as follows:

푅푟 (price rate per time step for round trips): AU$2 per 15 min (AU$1=US$0.74

[14/06/2016]), which is the average rate of GoGet trips;

퐶푚 (cost of maintaining a vehicle per time step driven): AU$0.5 per 15 min;

퐶푟 (cost of relocating a vehicle per time step driven): AU$1.5 per 15 min, which is the lowest hourly salary in Sydney;

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The values of the coefficients involved in the utility functions are set based on the MNL model proposed by Catalano et al. (2008). In their model, the unit of time is minute, whereas the unit in this study is 15 minutes. We multiply the coefficient for travel time 훽푡푡 and parking time 훽푝푡 in their model by 15 to make the model applicable to this study. Furthermore, in their model, the unit of travel cost is Euro, while the unit of travel cost in this study is Australian dollar. To make the model applicable, we multiply the coefficient for travel cost 훽푡푐 by 0.72 (AU$1= €0.72 [14/06/2016]). The values of the coefficients in the MNL model are set as follows:

훽푡푡 (Coefficient for travel time): -0.3908;

훽푡푐 (Coefficient for travel cost): -0.2082;

훽푝푡 (Coefficient for parking time): -1.6155;

훽푛푐 (Coefficient for number of household cars for each user): -2.6054;

훽푐푠 (Alternative specific constant for carsharing): 1.4833;

훽푡푖 (Alternative specific constant for other transport infrastructure): 1.1489.

The one-way trip price 푅표 and the vehicle pod capacity 푆푖 are considered as sensitivity analysis parameters to study the impacts of one-way trip price and pod capacity on system profit, and to understand the interdependent relationship between demand and supply in carsharing systems.

5.4 Sensitivity Analysis and Results Discussions

The ILP model was solved by the commercial package CPLEX (IBM-ILOG, 2016), a mixed integer linear programming (MILP) optimiser for solving linear and integer

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models. The model was implemented on an Intel (R) Core (TM) i7-6600U processor

@2.60 GHz 2.81 GHz, 12.0 GB RAM computer with a Windows 10 64-bit operating system. 90 scenarios were generated with total travel demand equal to 6086, 10356, and 28237, one-way trip price 푅표 changing from 3 to 12 with a discretisation step of

1, and capacity inflating from the original capacity to 1.5 and 2 times larger than it.

Since the times that round-trip users spend at destinations were randomly generated, we solved 5 instances for each of the scenario to achieve statistical convergence. Every instance was solved to optimality. The average running time for all instances was 7.83 seconds, and the standard deviation was 3.71 seconds. The results of system profits of three demand scenarios are demonstrated in Figures 5:3, 5:4, and 5:5.

Figure 5:3 System profit over capacity and one-way trip price in low-demand

scenario (total demand = 6086)

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Figure 5:4 System profit over capacity and one-way trip price in medium-

demand scenario (total demand = 10356)

Figure 5:5 System profit over capacity and one-way trip price in high-demand

scenario (total demand = 28237)

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As shown in Figures 5:3, 5:4, 5:5, for a given capacity, the system profit as a function of 푅표 can be described by an approximate upward parabolic profile with a unique maximal profit observed for some optimal one-way price. The unique maximal profit occurs at different 푅표 among the three demand scenarios. In the high-demand scenario as presented in Figure 5:5, the maximal profit is obtained when 푅표 is AU$8 per 15 minutes, which is 4 times higher than the round-trip price. This profile can be explained by the observation that higher 푅표 leads to higher revenues obtained from one-way trips. Since the number of available vehicles is limited, the optimisation model assigns more vehicles to one-way trips with higher unit price in order to maximise the profit. As 푅표 increases, the profit eventually decreases because the demand for one-way trips is also determined by the discrete choice model. As presented in the utility function (Equation (5.4)), the price of one-way trip 푅표 has a negative impact on one-way trip demand. Therefore, when the value of 푅표 is too high, much fewer users are likely to choose one-way trips, and tend to choose round trips and other transport modes, which results in a lower system profit. According to the

Figure 5:5, the maximum profit occurs when 푅표 is around AU$8/15min, which is approximately 4 times higher than 푅푟.

In contrast, in the low-demand and medium-demand scenarios as illustrated in

Figure 5:3 and Figure 5:4, the one-way trip prices 푅표 that yield the maximal profits are much lower compared to the high-demand scenario. The optimal 푅표 in low- demand scenario is between AU$4 to 5 per 15 minutes, and in medium-scenario is

AU$5. This is mainly because when the total demand is very low, a small increase in one-way trip price will lead to a significant reduction in total demand for carsharing trips. The system profit is equal to the product of the unit profit earned by a single trip

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and the total number of served trips. In these two demand scenarios, although higher one-way trip prices can yield higher unit profits, the increased unit profits cannot compensate the huge reduction in carsharing demand. As a result, the maximal system profits occur when the one-way trip prices are only slightly higher than the round-trip price.

These results can be referred by the decision makers when they are planning for the price of one-way trips. In the areas with high travel demand, high one-way trip prices can be set to obtain high system profits. Whereas, in the areas with low travel demand, the better way is to set one-way trip prices to be profitable but close to the round-trip price in order to attract more carsharing demands.

Figures 5:3, 5:4, and 5:5 also indicate that system profit keeps increasing as the capacity increases. This is because one-way and round-trip demands are dependent on the vehicle availability. Higher capacity indicates that users can access to more vehicles, so that more trips can be made. Furthermore, when carsharing demand remains the same, the larger number of vehicles also reduces the number of relocation trips, which results in lower relocation costs. Therefore, the carsharing company can gain more profits as the capacity increases. However, the trend of profit over capacity varies among different demand scenarios. When the total travel demand is higher than the current capacity (high-demand scenario in Figure 5:5), the profit will increase continuously at the same speed when the capacity increases. On the contrary, when the total travel demand is near to or lower than the capacity (low-demand and medium- demand scenario in Figures 5:3 and 5:4), the profit will not keep increasing when the capacity inflates to a certain extent. As shown in Figures 5:3 and 5:4, the profit increases when the capacity inflates from 198 to 286. However, the profit almost

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remains unchanged when the capacity increases from 286 to 396. This is because the demand has reached the upper limit in these two scenarios and current capacity can serve all the trips requested. Thus, inflating capacity cannot contribute to higher system profit.

The carsharing operators could gain insights into this result. If the travel demand is relatively high, the company can expand its capacity to capture more trips after evaluating the trade-off between the costs of inflating capacity and the profits obtained from the increased number of trips. In turn, if the travel demand is low, increasing capacity will not lead to higher profit but induce more setting up costs.

Moreover, Figures 5:3, 5:4 and 5:5 also indicate that the impact of one-way trip price on system profit is more significant than the impact of vehicle pod capacity.

To further understand how the profit reacts to the capacity and the one-way trip price, we plot the numbers of one-way trips, round trips and all trips for different scenarios in Figure 5:6.

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The analysis of Figure 5:6 reveals that in low-demand and medium-demand scenarios, the number of one-way trips keeps decreasing as 푅표 increases, which can be explained by the negative impact of one-way trip price on user demand. The number of round trips keeps increasing as 푅표 increases. This is mainly because as 푅표 increases, more users who are originally willing to use one-way services cannot afford those one-way trips, and switch to book round trips. According to the Figure 5:6, the decreasing speed of one-way trips is higher than the increasing speed of round trips, which leads to the reduction in the total number of carsharing trips when one-way trip price increases.

In the high-demand scenario, the number of one-way trips initially increases and then falls. This is different from low-demand and medium-demand scenarios. This is because when the demand is high enough, the optimisation model has the freedom to accept more one-way trips and fewer round trips to generate higher revenues.

Initially, even though the one-way trip price is higher than the round-trip price, the one-way trip option is still an attractive option. However, when 푅표 is larger than AU$4 per 15 minutes, fewer users are willing to accept the price of one-way trips and tend to choose round trips or other transport modes. Therefore, the number of one-way trips performs in this pattern, and the pattern of round trips is exactly the opposite to one- way trips.

Figure 5:6 also depicts that as capacity increases, the numbers of one-way and round trips increases due to the higher vehicle availability. However, the increase speeds of the numbers of carsharing trips are smoother in low-demand and medium- demand scenarios than high-demand scenario. This because when the total travel demand is low, expanding the capacity to an extent will not lead to any more demand for carsharing trips. In contrast, when the total travel demand is high, inflating capacity

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can result in a significant increase in carsharing trip requests. This finding is consistent with the pattern of profit over capacity as discussed in the previous paragraphs.

5.5 Concluding Remarks

One-way carsharing systems have been adopted by an increasing number of carsharing operators for their potential to attract larger demands. The major issue raised in such systems is the imbalance in vehicle stock distribution. This issue is complex to solve due to the interdependency between demand and supply in carsharing systems: the demand for carsharing trips is dependent on vehicle availability as well as travel time and travel cost, and the demand further influences vehicle availability. Therefore, it is necessary to understand how demand and supply interact with each other. This chapter presented an ILP model to evaluate the profitability for carsharing operators who offer both one-way and round-trip carsharing services. The model solved the imbalanced vehicle stock problem by providing optimal relocation decisions accounting for demand’s reaction through a discrete choice model.

The optimisation model was tested on GoGet carsharing network in Sydney’s urban areas using realistic travel demand matrix. The optimisation model run relatively quickly on a large urban area, therefore no potential issues are foreseen to implement this method on larger networks. A sensitivity analysis on travel demand, one-way trip price, and network capacity were undertaken to understand the impacts of price elasticity and capacity on the profitability.

The results suggest that one-way trip price influences the system profit by affecting carsharing trip demand and availability for different types of trips. The

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optimal one-way trip price that yields the maximum of profit varies in different demand scenarios. When the total travel demand is low, the maximal system profits occur at low one-way trip prices that are close to the round-trip price. As the total travel demand increases, the system profits reach the maximum at higher one-way trip prices.

With respect to network capacity, it changes the profit by influencing vehicle availability. Furthermore, the impact of vehicle pod capacity on system profit is not as significant as that of the price of one-way trips.

Based on these trends, decision makers could get insight when setting one-way trip prices to maximise profits. They should also evaluate the trade-off between the costs of inflating network capacity and the revenues of more trips captured by higher vehicle availability.

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Chapter 6. Optimal Relocations in Demand Responsive Carsharing Systems

Chapter 6 Optimal Relocations in Demand Responsive

Carsharing Systems

6.1 Introduction

This chapter is an extension and improvement of the method proposed in Chapter 5.

In the previous chapter, we proposed an approach that incorporates an integer linear programming (ILP) model with a discrete choice model (DCM) with constant results of the utility functions. The ILP model solves the optimal supply decisions for the carsharing system and updates vehicle availability; the DCM together with the updated vehicle availability, reciprocally, determines users’ trip demand. These two models work together to account for the interaction between demand and supply in carsharing systems. However, it should be noted that the choice model cited by Chapter 5

(Catalano et al. (2008)’s model) does not consider vehicle availability as a factor that could directly influence the elasticity in demand. The integrated approach treats vehicle availability as a constraint to incorporate the impact of vehicle availability on trip demand. But if we aim to understand the interaction between demand and supply in carsharing systems, the best solution is to incorporate the ILP model with a choice model that assumes users’ demand to be directly elastic to vehicle availability.

Chapter 6 overcomes the limitation of the previous model. A refined integrated formulation for one-way carsharing optimisation is built based on the model proposed in Chapter 5. In the new integrated supply-demand model, vehicle availability is the output of the ILP model and serves as the input of the DCM simultaneously. In this

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way, user demand is directly responsive to vehicle availability. User demand and vehicle supply are linked by vehicle availability. The framework of this approach is illustrated in Figure 6:1.

Figure 6:1 Framework of the integrated supply-demand model

However, another difficulty arises in the integrated supply-demand model due to the nonlinearities induced by the integration of the DCM. In the previous model, the DCM only contains variables such as travel time, travel cost, parking time and number of household vehicles. The inputs of these variables are known in advance and thus the probability of choosing different travel modes can be calculated in advance. Whereas in the new integrated model, the DCM contains another variable vehicle availability.

Vehicle availability is the decision variable in both the ILP model and the DCM. The value of this variable is only known for the initial state and keeps changing in the following operation time steps. Since the probability functions of the DCM are

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nonlinear, including those functions as constraints leads to the nonlinearity of the whole optimisation model.

With respect to the solution methods for nonlinear models, Branch and Bound,

Outer-Approximation, Generalised Benders and Extended Cutting Plane have been widely applied to solve mixed integer nonlinear programming (MINLP) models, but typically require intensive computational resources (Grossmann, 2002). In some cases,

MINLP formulations can be linearised and converted into mixed integer linear

Programming (MILP) models, often at the expense of auxiliary decision variables. The

MILP models can be conveniently solved using robust methods such as LP-based branch and bound method and implemented in codes such as CPLEX and XPRESS

(Grossmann, 2002). In this study, we apply the linearisation techniques to the present integrated logistical problem. To the authors’ best knowledge, this study is the first to use linearisation method to solve the MINLP model that integrates with a discrete choice model. Figure 6:2 summarises the research contributions of Chapter 6.

Figure 6:2 Summary of research contributions in Chapter 6

The chapter is organised as follows. Section 6.2 presents the extended integrated supply-demand model derived from the ILP model developed in Chapter 5. Then, the linearisation method of the model is described in Section 6.3. The sensitivity analysis

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on Sydney carsharing network is presented in Section 6.4. Finally, the major findings obtained in this study are highlighted in Section 6.5.

6.2 Integrated Supply-Demand Model

The context of the problem addressed in this chapter remains the same as Chapter 5. It involves the introduction of one-way trip services to the existing round-trip carsharing services, while keeping the locations and the number of carsharing vehicle pods unchanged. The added one-way services may attract more travel demand for the current carsharing system. The demand is elastic vehicle availability, travel cost and travel time. The demand also influences vehicle availability and changes the distribution of vehicle stocks in the network. Hence, the updated carsharing services may also incur extra relocation costs to balance the vehicle stocks in the network. The objective of this integrated supply-demand model is to determine the optimal relocation decisions in order to maximise the profit for the updated carsharing network.

The assumptions made for this problem is also consistent with Section 5.2, except

Assumption 4. Below is the new assumption for Chapter 6:

The total travel demand of each origin-destination (OD) pair at each time step is known and constant, however, the operator does not know the demand for one-way and round trips in advance. Each user has three travel mode options: one-way carsharing (OW), round-trip carsharing (RT), and other transport infrastructure (TI).

Users’ choice is influenced by trip cost, trip travel time, and the number of vehicles available in carsharing vehicle pods. A multinomial logit (MNL) model is applied to account for the impacts of trip cost, travel time, and the number of vehicles available

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on users’ demand. The parameters of the MNL model include trip travel time (in number of time steps), travel cost, parking time, the number of household cars for each user, and the number of vehicles available in carsharing vehicle pods. The major difference between this assumption and Assumption 4 in Chapter 5 is the introduction of the variable vehicle availability in the MNL model.

The mathematical formulation is presented as follows. Compared to the formulation built in Chapter 5, the sets, decision variables and objective function remain unchanged. The difference lies in the parameters and corresponding constraints.

First, the probabilities of choosing RT, OW and TI are changed to be time dependent.

This is because these probabilities are determined by the number of vehicles available in this new model, and the number of vehicles available in each vehicle pod keeps updated over time steps. Second, a new parameter 훽 is added to represent the coefficient for the number of vehicles available in the MNL model. Changes are also made to the utility functions and constraints containing these parameters. The complete formulation is presented below and the changes are marked in bold.

Sets

Decision variables

푟푖푗,푡 ∈ ℤ: Number of vehicles relocated from node 푖 to 푗 at time 푡, ∀푖, 푗 ∈ 푁:⁡푖 ≠

푗, ∀푡 ∈ 푇;

푣푖,푡 ∈ ℤ: Number of vehicles available at node 푖 at time 푡, ∀푖 ∈ 푁, ∀푡 ∈ 푇;

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푂푊 푑푖푗,푡 ∈ ℤ: Number of users booking one-way trips from node 푖 to 푗 at time 푡, ∀푖, 푗 ∈

푁:⁡푖 ≠ 푗, ∀푡 ∈ 푇;

푅푇 푑푖푗,푡 ∈ ℤ: Number of users booking round trips from node 푖 to 푗 at time 푡, ∀푖, 푗 ∈

푁:⁡푖 ≠ 푗, ∀푡 ∈ 푇.

Parameters

푅표: Price rate per time step for one-way trips;

푅푟: Price rate per time step for round trips;

퐶푚: Cost of maintaining a vehicle per time step driven;

퐶푟: Cost of relocating a vehicle per time step driven;

푆푖: Capacity of node 푖, ∀푖 ∈ 푁;

퐷푖푗,푡: Total travel demand from node 푖 to 푗 at time 푡, ∀푖, 푗 ∈ 푁:⁡푖 ≠ 푗, ∀푡 ∈ 푇;

휏푖,푗: Travel time from node 푖 to 푗 (in number of time steps), ∀푖, 푗 ∈ 푁:⁡푖 ≠ 푗;

푤푖: Time round-trip user spends at destination node 푖, ∀푖 ∈ 푁;

푹푻 흍풊,풋,풕: Probability that a user travelling from node 풊 to 풋 at time 풕 chooses RT among RT, OW and TI, ∀풊, 풋 ∈ 푵:⁡풊 ≠ 풋, ∀풕 ∈ 푻;

푶푾 흍풊,풋,풕 : Probability that a user travelling from node 풊 to 풋 at time 풕 chooses OW among RT, OW and TI, ∀풊, 풋 ∈ 푵:⁡풊 ≠ 풋, ∀풕 ∈ 푻;

푻푰 흍풊,풋,풕 : Probability that a user travelling from node 풊 to 풋 at time 풕 chooses TI among RT, OW and TI, ∀풊, 풋 ∈ 푵:⁡풊 ≠ 풋, ∀풕 ∈ 푻;

푃푇: Parking time of each trip;

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푁퐶퐴푅: Number of household cars for each user;

휷: Coefficient for 풗풊,풕;

훽푡푡: Coefficient for travel time;

훽푡푐: Coefficient for travel cost;

훽푝푡: Coefficient for parking time;

훽푛푐: Coefficient for number of household cars for each user;

훽푐푠: Alternative specific constant for carsharing;

훽푡푖: Alternative specific constant for other transport infrastructure.

We apply the following equations to determine users’ mode choice. The utility functions are formulated based on the MNL model proposed by Catalano et al. (2008).

The model includes travel time, travel cost, parking time, and number of household cars as the parameters that influence travellers’ mode choice behaviour. However, it does not consider the impact of carsharing vehicle availability on travellers’ choice.

Therefore, to accommodate the impact of vehicle availability, we introduce the variable, the number of vehicles available 푣푖,푡, and its corresponding coefficient, 훽, to the previous model as follows. It should be noted that the value of 훽 cannot be determined owing to the lack of data. In order to test the impact of vehicle availability on trip demand and system profit, a sensitivity analysis on 훽 is undertaken in Section

6.4.

푹푻 ∀푖, 푗 ∈ 푁:⁡푖 ≠ 풆푼풊,풋,풕 푹푻 (6.1) 흍풊,풋,풕 = 푶푾 푹푻 푻푰 풆푼풊,풋,풕 + 풆푼풊,풋,풕 + 풆푼풊,풋 푗, ∀푡 ∈ 푇;

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푶푾 ∀푖, 푗 ∈ 푁:⁡푖 ≠ 풆푼풊,풋,풕 푶푾 (6.2) 흍풊,풋,풕 = 푶푾 푹푻 푻푰 풆푼풊,풋,풕 + 풆푼풊,풋,풕 + 풆푼풊,풋 푗, ∀푡 ∈ 푇;

푹푻 푼풊,풋,풕 = ⁡ 휷풕풕(흉풊,풋 + 흉풋,풊 + 풘풋) ∀푖, 푗 ∈ 푁:⁡푖 ≠ + 휷풕풄푹풓(흉풊,풋 + 흉풋,풊 + 풘풋) + 휷풑풕푷푻 (6.3) 푗, ∀푡 ∈ 푇;

+ 휷풏풄푵푪푨푹 + 휷풄풔 + 휷풗풊,풕

푶푾 푼풊,풋,풕 = ⁡ 휷풕풕흉풊,풋 + 휷풕풄푹풐흉풊,풋 + 휷풑풕푷푻 + 휷풏풄푵푪푨푹 ∀푖, 푗 ∈ 푁:⁡푖 ≠ (6.4) + 휷풄풔 + 휷풗풊,풕 푗, ∀푡 ∈ 푇;

푇퐼 푈푖,푗 = 훽푡푡휏푖,푗 + 훽푡푐퐶푚휏푖,푗 + 훽푝푡푃푇 + 훽푡푖 ∀푖, 푗 ∈ 푁:⁡푖 ≠ 푗; (6.5)

Objective function

(6.6) − 퐶푚)(휏푖,푗 + 휏푗,푖 + 푤푗) − ∑ ∑ ∑ (푟푖푗,푡) (퐶푅 푡∈푇 푖∈푁 푗∈푁,푗≠푖

+ 퐶푚)휏푖,푗

Subject to

푣푖,0 = 푆푖 ∀푖 ∈ 푁; (6.7)

∗ 푣푖,푡 ≤ 푆푖 ∀푖 ∈ 푁, ∀푡 ∈ 푇 ; (6.8)

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푣푖,푡 = 푣푖,푡−1 − ∑ 푟푖푗,푡−1 푗∈푁,푗≠푖

+ ∑ 푟푗푖,푡−1−휏푗,푖 푗∈푁,푗≠푖

푂푊 − ∑ 푑푖푗,푡−1 푗∈푁,푗≠푖 ∀푖 ∈ 푁, ∀푡 ∈ 푇∗; (6.9) + ∑ 푑푂푊 푗푖,푡−1−휏푗,푖 푗∈푁,푗≠푖

푅푇 − ∑ 푑푖푗,푡−1 푗∈푁,푗≠푖

+ ∑ 푑푅푇 푖푗,푡−1−(휏푖,푗+휏푗,푖+푤푗) 푗∈푁,푗≠푖

푹푻 푶푾 ∑ 풅풊풋,풕 + ∑ 풅풊풋,풕 ≤ 풗풊,풕 ∀풊 ∈ 푵, ∀풕 ∈ 푻; (6.10) 풋∈푵,풋≠풊 풋∈푵,풋≠풊

푹푻 푹푻 풅풊풋,풕 ≤ 푫풊풋,풕흍풊,풋,풕 ∀풊, 풋 ∈ 푵:⁡풊 ≠ 풋, ∀풕 ∈ 푻; (6.11)

푶푾 푶푾 풅풊풋,풕 ≤ 푫풊풋,풕흍풊,풋,풕 ∀풊, 풋 ∈ 푵:⁡풊 ≠ 풋, ∀풕 ∈ 푻; (6.12)

푂푊 푑푖푗,푡 ≥ 0, integer ∀푖, 푗 ∈ 푁:⁡푖 ≠ 푗, ∀푡 ∈ 푇; (6.13)

푅푇 푑푖푗,푡 ≥ 0, integer ∀푖, 푗 ∈ 푁:⁡푖 ≠ 푗, ∀푡 ∈ 푇; (6.14)

⁡푟푖푗,푡 ≥ 0, integer ∀푖, 푗 ∈ 푁:⁡푖 ≠ 푗, ∀푡 ∈ 푇; (6.15)

푣푖,푡 ≥ 0, integer ∀푖 ∈ 푁, ∀푡 ∈ 푇; (6.16)

The objective function (6.6) and constraints (6.7) to (6.9), (6.13) to (6.16) are consistent to the model in Chapter 5. The explanations of these equations can be

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referred to Section 5.2. Constraints (6.10) determines that the numbers of one-way and round trips could not exceed the number of vehicles available at each vehicle pod.

Constraints (6.11) and (6.12) ensure that the numbers of one-way and round trips are less than or equal to their travel demand determined by the MNL model. Here, the demand for one-way or round trips equals to total travel demand multiplied by the probability that they are chosen by travellers.

Compared to the previous model in Chapter 5, constraints (6.11) and (6.12) lead to the major difference. These two constraints reflect the impact of vehicle availability on users’ demand through the MNL model. Since the decision variable 푣푖,푡 is involved in the MNL model, these two constraints are nonlinear. The next section will describe the linearisation of the nonlinear model.

6.3 Linearisation

푅푇 It should be noted that constraints (6.11) and (6.12) are not linear because 휓푖,푗,푡 and

푂푊 휓푖,푗,푡 are obtained from two utility functions containing the decision variable 푣푖,푡. To

푅푇 푂푊 linearise these two constraints, the main idea is to decompose 휓푖,푗,푡 and 휓푖,푗,푡 by introducing a binary variable 푥푖,푡,푏 , ∀푖 ∈ 푁, ∀푡 ∈ 푇, ∀푏 ∈ 푆푖 , and two parameters

푅푇 푂푊 푅푇 휓푖,푗,푡,푏 and 휓푖,푗,푡,푏, ∀푖, 푗 ∈ 푁:⁡푖 ≠ 푗, ∀푡 ∈ 푇, ∀푏 ∈ 푆푖. 휓푖,푗,푡,푏 represents the probability that a user travels from node 푖 to 푗 at time 푡 chooses RT among RT, OW and TI when

푂푊 the number of vehicles available at node 푖 is equal to 푏. Similarly, 휓푖,푗,푡,푏 denotes the probability that a user travels from node 푖 to 푗 at time 푡 chooses OW among RT, OW and TI when the number of vehicles available at node 푖 is equal to 푏. Here, 푏 is a parameter changing from 0 to the capacity of the corresponding vehicle pod. In this

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way, the equations of these two parameters involve the parameter 푏 instead of incorporating with the variable 푣푖,푡 as shown in Equation (6.17) to (6.21):

푅푇 ∀푖, 푗 ∈ 푁:⁡푖 ≠ 푒푈푖,푗,푡,푏 푅푇 (6.17) 휓푖,푗,푡,푏 = 푂푊 푅푇 푇퐼 푈푖,푗,푡,푏 푈푖,푗,푡,푏 푈푖,푗 푒 + 푒 + 푒 푗, ∀푡 ∈ 푇, ∀푏 ∈ 푆푖;

푂푊 ∀푖, 푗 ∈ 푁:⁡푖 ≠ 푒푈푖,푗,푡,푏 푂푊 (6.18) 휓푖,푗,푡,푏 = 푂푊 푅푇 푇퐼 푈푖,푗,푡,푏 푈푖,푗,푡,푏 푈푖,푗 푒 + 푒 + 푒 푗, ∀푡 ∈ 푇, ∀푏 ∈ 푆푖;

푅푇 푈푖,푗,푡,푏 = ⁡ 훽푡푡(휏푖,푗 + 휏푗,푖 + 푤푗) ∀푖, 푗 ∈ 푁:⁡푖 ≠ + 훽푡푐푅푟(휏푖,푗 + 휏푗,푖 + 푤푗) + 훽푝푡푃푇 (6.19) 푗, ∀푡 ∈ 푇, ∀푏 ∈ 푆푖; + 훽푛푐푁퐶퐴푅 + 훽푐푠 + 훽푏

푂푊 푈푖,푗,푡,푏 = ⁡ 훽푡푡휏푖,푗 + 훽푡푐푅표휏푖,푗 + 훽푝푡푃푇 + 훽푛푐푁퐶퐴푅 ∀푖, 푗 ∈ 푁:⁡푖 ≠ (6.20)

+ 훽푐푠 + 훽푏 푗, ∀푡 ∈ 푇, ∀푏 ∈ 푆푖;

푇퐼 푈푖,푗 = 훽푡푡휏푖,푗 + 훽푡푐퐶푚 ∗ 휏푖,푗 + 훽푝푡푃푇 + 훽푡푖 ∀푖, 푗 ∈ 푁:⁡푖 ≠ 푗; (6.21)

Binary variable 푥푖,푡,푏 is introduced to decide if 푏 is equal to 푣푖,푡. We let 푥푖,푡,푏 =

푅푇 ∑ 푅푇 1, if 푏 = 푣푖,푡; otherwise 푥푖,푡,푏 = 0. Then, 휓푖,푗,푡 is replaced by 푏휖푆푖(푥푖,푡,푏휓푖,푗,푡,푏), and

푂푊 ∑ 푂푊 푅푇 휓푖,푗,푡 is replaced by 푏휖푆푖(푥푖,푡,푏휓푖,푗,푡,푏). In this way, we make sure that 휓푖,푗,푡 is equal

푅푇 푂푊 푂푊 to 휓푖,푗,푡,푏 and 휓푖,푗,푡 is equal to 휓푖,푗,푡,푏 only when 푏 is equal to 푣푖,푡. Constraints (6.11) and (6.12) can then be replaced by the following linear constraints:

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푅푇 푅푇 ∀푖, 푗 ∈ 푁:⁡푖 ≠ 푑푖푗,푡 ≤ 퐷푖푗,푡 ∑(푥푖,푡,푏휓푖,푗,푡,푏) (6.22) 푏휖푆푖 푗, ∀푡 ∈ 푇;

푂푊 푂푊 ∀푖, 푗 ∈ 푁:⁡푖 ≠ 푑푖푗,푡 ≤ 퐷푖푗,푡 ∑(푥푖,푡,푏휓푖,푗,푡,푏) (6.23) 푏휖푆푖 푗, ∀푡 ∈ 푇;

푣푖,푡 = ∑(푏푥푖,푡,푏) ∀푖 ∈ 푁, ∀푡 ∈ 푇; (6.24) 푏휖푆푖

∑ 푥푖,푡,푏 = 1 ∀푖 ∈ 푁, ∀푡 ∈ 푇; (6.25) 푏휖푆푖

This method linearises the demand constraints by decomposing the decision variable into the product of a binary variable and a parameter. The decomposition method enumerates the several states of the MNL model because of the discrete nature of the number of available vehicles. It can be generally applied with good rigor in this type of problems that use a time-space network.

6.4 Sensitivity Analysis and Results Discussions

The case study is tested on GoGet Sydney carsharing network, the same as the one used in the previous optimisation study in Chapter 5. The context settings of the case study can be referred to Section 5.3.

The sensitivity analysis undertaken in Chapter 5 focused on total travel demand, one-way trip price, and vehicle pod capacity. Total travel demand dictates the elasticity of system profit to one-way trip price and system capacity. One-way trip price determines users’ travel demand. Vehicle pod capacity represents the supply of

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carsharing vehicle fleet. The findings in Chapter 5 give insights to how demand and supply influence carsharing system profits. The sensitivity analysis in this chapter aims to investigate how carsharing demand interacts with its supply, and how this interaction affects the system profits.

As mentioned in Section 6.2, we use vehicle availability to link demand and supply. Vehicle availability, representing the supply of vehicles in each pod, on one hand determines travel demand, on the other hand is affected by travel demand.

Therefore, we can understand how the interdependency between supply and demand influences the profit by investigating the impact of vehicle availability on the profit.

We introduce the number of vehicles available 푣푖,푡 and its corresponding coefficient 훽 to Catalano et al. (2008)’s model to accommodate the impact of carsharing vehicle availability on travellers’ choices. The significance of the impact is determined by the value of 훽. Thus, the study on the interdependency between supply and demand is interchangeable with the sensitivity analysis on the coefficient 훽. Therefore, we add the sensitivity analysis on the coefficient 훽 to the previous study on total travel demand, one-way trip price, and vehicle pod capacity.

In this sensitivity analysis, we utilise the three demand scenarios created in

Section 5.3 to test the impact of demand on system profit. For each scenario, we test three capacity conditions by changing capacity to be equal to the original capacity, 1.5 times and 2 times higher than the original capacity. To test the three scenarios with respect to the influences of one-way trip price and vehicle availability, we change one- way trip price 푅표 from 3 to 12 with a discretisation step of 1, and test six different values of 훽, i.e. 0, 0.2, 0.4, 0.6, 0.8, and 1 of the absolute value of the trip cost coefficient (|훽푡푐|).

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The waiting times of round trip users spend at destinations were randomly generated by a normal distribution with mean equal to 1 time step and standard deviation equal to 1 time step. We solved 5 instances for each scenario to achieve statistical convergence. The model was solved by the commercial package CPLEX

(IBM-ILOG, 2016), implemented on an Intel (R) Core (TM) i7-6600U processor

@2.60 GHz 2.81 GHz, 12.0 GB RAM computer with a Windows 10 64-bit operating system. Every instance was solved to optimality. The average running time is 24.45 seconds and the standard deviation of the running time is 31.73 seconds.

6.4.1 Impacts of one-way trip price and vehicle availability on system profit under different demand scenarios

Three demand scenarios are tested in this study to evaluate how system profit reacts to one-way trip price and vehicle availability under different travel demand situations. The results of how profit changes over one-way trip price and the coefficient of vehicle availability when there is no capacity inflation (capacity = 198 vehicles) are illustrated in Figures 6:3, 6:4, and 6:5.

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Figure 6:3 System profit over 푹풐 and 휷 when capacity = 198 in low-demand

scenario

Figure 6:4 System profit over 푹풐 and 휷 when capacity = 198 in medium-

demand scenario

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Chapter 6. Optimal Relocations in Demand Responsive Carsharing Systems

Figure 6:5 System profit over 푹풐 and 휷 when capacity = 198 in high-demand

scenario

For the three demand scenarios, we regard the case when 훽 is equal to 0 as the base case. Under the base case, vehicle availability is not included as a factor in the MNL model (Equations (6.17) - (6.21)), and thus has no direct impact on users’ travel demand. This base case is the replication of the problem solved in Chapter 5. As shown in Figures 6:3 to 6:5, the patterns of profits over one-way trip price under the base case of the three demand scenarios are consistent with the results observed in Section 5.4.

For a given coefficient of vehicle availability, system profit changes as one-way trip price changes. The maximal system profit of each of the demand scenario occurs at different one-way trip prices, showing that the changing pattern of system profit over

푅표 is dependent on total travel demand. The explanation of such pattern can be referred to Section 5.4.

For each demand scenario, Figures 6:3 to 6:5 report that the pattern of how profit changes against one-way trip price varies among different values of 훽. In the

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low-demand scenario as presented in Figure 6:3, the profit reaches the maximum when

푅표 is between AU$3 to 5 per 15 minutes with 훽 equal to 0, whereas the maximal profit is obtained at 푅표 around AU$6 to 7 per 15 minutes when 훽 increases to |훽푡푐|.

Compared to the base case, the maximal profit occurs at higher values of one-way trip price as 훽 increases. Similar conclusions can be withdrawn from the medium-demand and high-demand scenarios. In the medium-demand scenario, the maximal profit is observed at 푅표 around AU$5 when 훽 is equal to 0, while at 푅표 around AU$8 when 훽 is equal to |훽푡푐|. In the high-demand scenario, the optimal 푅표 that leads to the maximal profit increases from AU$8 to AU$11 when 훽 increases from 0 to |훽푡푐|. The higher the value of 훽, the higher the optimal one-way trip price occurs. This change in the impact of one-way trip price on profit can be explained by the introduction of vehicle availability in the utility functions (Equations (6.19) (6.20)). Unlike the base case, 훽 has a positive value meaning that vehicle availability has a positive impact on users’ travel demand for carsharing trips. As 훽 increases, the impact of vehicle availability on demand increases and the impact of one-way trip price on demand becomes less significant. When 훽 increases to an extent, the positive impact of vehicle availability on demand can nearly offset the negative impact caused by trip cost. Therefore, the demand will not decrease sharply as one-way trip price increases, and the profit will not decrease as one-way trip price keeps increasing.

In fact, the ratio of |훽푡푐| over 훽 can be defined as travellers’ value of vehicle availability (VOVA). For instance, when the coefficient of vehicle availability 훽 is set to be 0.4 multiplied by the coefficient of travel cost |훽푡푐|, the ratio of |훽푡푐| over 훽 is equal to 2.5, then travellers’ value of vehicle availability is AU$2.5 per vehicle. As

VOVA increases, more disutility caused by trip cost can be compensated. As a result,

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travellers become less sensitive to one-way trip price and more elastic to vehicle availability. Such changes of demand over 푅표 are revealed in Figure 6:6. Each row in

Figure 6:6 plots how the numbers of one-way trips, round trips, and the total number of trips change over 푅표 and 훽 for a certain demand scenario.

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three demand scenarios when capacity 198 = demand scenarios three

valuesin

휷

way trip prices for different different for way prices trip -

one over trips of numbers The 6:6 Figure

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Chapter 6. Optimal Relocations in Demand Responsive Carsharing Systems

As shown in Figure 6:6, with the same coefficient of vehicle availability, the trends of trips changing over one-way trip price perform differently depending on the total travel demand. This finding is consistent with Chapter 5. The explanations of these trends can be found in Section 5.4.

However, in each demand scenario, the decreasing curve of one-way trips, the increasing curve of round trips, and the decreasing curve of all trips become smoother as 훽 increases. This is because when 훽 is small, one-way trip price dominantly influences users’ travel demand for one-way trips at this stage. But when 훽 reaches a certain value, the impact of one-way price on trip demand is no longer dominant. The demands for one-way and round trips are less elastic to one-way trip price. As 푅표 increases, the number of one-way trips decreases slightly and stops decreasing when the coefficient of vehicle availability is large enough to offset the negative impact of trip cost on travel demand. The number of round trips also increases much slightly as

훽 becomes larger. This is due to two reasons: 1) round trips bring lower revenues compared to one-way trips. When 훽 is large enough, travel demand for one-way trips will not decrease as 푅표 increases. The optimisation model will allocate more vehicles to serve one-way trips to obtain higher revenues, and as a result leave fewer vehicles for round trips. 2) As 훽 increases, one-way trip demand is more sensitive to vehicle availability. As presented in the utility functions (Equations (6.19) (6.20)), accepting fewer round trips can guarantee more vehicles available in vehicle pods, and therefore attract higher one-way trip demand.

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6.4.2 Impacts of vehicle pod capacity on system profits

We next undertake the sensitivity analysis on vehicle pod capacity for the low- demand scenario to evaluate the impact of capacity on system profit. The results are shown in Figure 6:7.

Two major findings can be concluded from the results. First, capacity always has a positive impact on profit with different vehicle availability coefficients. The profit keeps increasing as the capacity increases. This is because higher capacity allows users to access to more vehicles and ensures higher vehicle availability. More trips can be made and therefore higher profit is gained. This result is consistent with the previous study in Chapter 5 without considering the impact of vehicle availability in the MNL model.

The second finding is that the changes in the pattern of profit over one-way trip price among different values of 훽 also appear when the capacity is inflated. The including of vehicle availability in the utility function increases the impact of capacity on system profit. When travellers’ VOVA is small (low value of 훽), the increase in profit with higher capacity is not as significant as the increase caused by higher one- way trip price. However, as VOVA becomes larger, the impact of capacity becomes more significant on system profit. This is because demand is less sensitive to trip price and more sensitive to vehicle supply when VOVA is larger. Higher capacity can guarantee more vehicles available at the initial time step, as a result attracts more carsharing demands and increases the system profit more significantly.

We plotted the numbers of one-way trips, round trips, and total trips over 푅표 with these three capacities in Figure 6:8 to further understand how profit reacts to 푅표

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and 훽 with different capacities. As shown in Figure 6:8, the trends of the number of trips with higher capacities (capacity = 286 and 396) are similar as with the original capacity (capacity = 198). These similar trends explain why the profit has the same pattern with different capacities. Also in Figure 6:8, the number of trips increased owing to capacity inflation becomes larger when the value of 훽 increases. This explains the second finding observed from Figure 6:7.

Inspired from the impacts of travel demand, capacity, one-way trip price, and coefficient of vehicle availability on system profit, decision makers should consider the interdependency of demand and supply when setting pricing strategies. If there is a strong interaction between demand and supply, the supply of carsharing vehicle fleet becomes more critical in determining system profit. To ensure sufficient vehicle supply, decision makers can inflate current vehicle pod capacity and formulate more efficient relocation strategies. But they should consider the trade-off between the costs of network expansion, relocation operations, and the potential revenues brought by these changes.

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demandscenario

the low the

and capacities andcapacities

values

휷

way trip prices for different different prices for trip way

- Figure 6:7 System profit over one profit over System 6:7 Figure

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Chapter 6. Optimal Relocations in Demand Responsive Carsharing Systems

demandscenario

way trip prices for different β values and capacities in different low the values β for and way prices capacities trip

of trips over one over trips of

numbe

The Figure 6:8 6:8 Figure

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Chapter 6. Optimal Relocations in Demand Responsive Carsharing Systems

6.5 Concluding Remarks

The study proposed in Chapter 5 considered the interaction between demand and supply when formulating the relocation model, however, the model did not accommodate vehicle supply as a factor directly determining users’ travel demand. In this chapter, we extended the aforementioned model by including vehicle availability as a parameter affecting users’ mode choice behaviour within the discrete choice model. In this way, users’ travel demand is assumed to be elastic to vehicle availability.

Vehicle availability links supply and demand by integrating the relocation optimisation model with the discrete choice model. This leads the extended model to be nonlinear. To deal with the nonlinearity, this chapter introduced new binary variables and parameters to decompose the nonlinear terms of the model. Linearising the constraints of the discrete choice model is the major contribution of this paper. The proposed linearisation method can be generally applied to linearise models incorporating discrete choice models as constraints.

The model was tested on the carsharing network of GoGet in the metropolitan area of Sydney using realistic operation data. A sensitivity analysis on total travel demand, one-way trip price, system capacity, and vehicle availability coefficient was undertaken to provide a thorough understanding of the impacts of price elasticity, system capacity, and interaction between demand and supply on system profitability.

The results reveal that the impact of one-way trip price on profit varies as the coefficient of vehicle availability changes. When the coefficient of vehicle availability is small, the demand is more sensitive to the one-way trip price, and the maximal profit occurs at lower one-way trip price. When the coefficient keeps increasing, travellers’

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value of vehicle availability (VOVA) increases and the impact of one-way trip price on travellers’ demand is no longer dominant. Instead, the demand is more elastic to vehicle availability. Therefore, increasing one-way trip price can only reduce the demand slightly. As a result, the optimal one-way trip price that yields the maximal system profit appears at a larger value. This result is different from the previous sensitivity analysis which does not accommodate vehicle availability as a parameter in the discrete choice model. The difference in profit patterns suggests if supply has a significant impact on demand, demand is less sensitive to trip price, and higher trip price will generate more profits. With respect to system capacity, the result indicates that capacity always has a positive impact on profit, and the impact is getting more significant when demand is more sensitive to vehicle availability.

The main conclusion we can withdraw from this chapter is that the interdependence between demand and supply should be taken into consideration when setting relocation plans and pricing strategies in one-way carsharing systems. If there is a strong interaction between demand and supply, the supply of carsharing vehicle fleet becomes more critical in determining system profit. To improve profit, decision makers should ensure sufficient vehicle supply by inflating current vehicle pod capacity or formulating more efficient relocation strategies.

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Chapter 7 Conclusions and Future Researches

7.1 Summary and Conclusions

This thesis undertook a comprehensive demand and supply analysis of carsharing systems. Two demand estimation models were applied to understand carsharing users’ vehicle selection behaviour and vehicle utilisation patterns. Two optimisation models were developed to optimally relocate vehicles in response to demand variations in one- way carsharing systems. The four models solved the research questions identified in

Section 1.2, and explored the interdependence of demand and supply in carsharing systems.

Demand estimation formed the first part of this thesis with the emphasis on understanding users’ demand for carsharing vehicles. First, a spatial hazard-based model (SHBM) was applied to estimate users’ vehicle selection behaviour. The distinctiveness of carsharing users’ vehicle selecting process from normal discrete choice selection inspired the author to utilise SHBM instead of a normal discrete choice model. As the number of vehicles for users to select is substantial, users will first form a smaller choice set of vehicles based on the walking distance to the vehicles, and then make the selection within the smaller choice set. The SHBM could capture users’ filtering process through a function of walking distance and a set of identified covariates. Calibrating the model through a rich dataset from the Australian carsharing company GoGet, a 200-metre walking distance threshold was identified. Within 200 metres, the distance to the vehicle could not affect users’ preference towards the vehicle significantly; whereas above 200 metres, users’ willingness to select the

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vehicle decreases significantly as the distance increases. This result implies that the distribution of vehicles in carsharing systems influences the demand for using this transport mode.

Chapter 4 furthered the research of vehicle selection with a focus on the allocation of continuous budget of the chosen vehicle types. Multiple discrete- continuous extreme value (MDCEV) modelling framework was applied to understand users’ vehicle utilisation patterns. Three types of budget were considered: travel time, mileage, and monetary expenditure. A set of user socio-demographic attributes were included in the baseline utility functions to identify their impacts on the allocation of budget to different vehicle types. The models were again calibrated using GoGet operational data. The results reflect that travel time, mileage and expenditure affect users’ vehicle usage patterns in the same way. Besides, users with different backgrounds and living areas differ significantly in vehicle utilisation patterns.

The findings in Chapters 3 and 4 reveal that the demand for vehicles is significantly influenced by the locations and characteristics of vehicles. In other words, the demand is dependent on the deployment of vehicles in carsharing networks.

Furthermore, users behave heterogeneously when selecting vehicles and allocating budget to the selected vehicles. Such heterogeneity is highly depending on users’ backgrounds, such as age, income level and living areas.

Chapters 5 and 6 constructed the second part of this thesis: optimising the operation of carsharing systems. These two chapters focused especially on the carsharing systems that provide both one-way and round-trip services. This type of system has vehicle stock imbalance issue. In contrast with previous studies which solved optimal relocation strategies, the two optimisation models developed in this

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thesis considered the interdependency between demand and supply in carsharing systems when making relocation decisions and maximising system profit. The two optimisation models incorporated a discrete choice model to account for the demand elasticity. The first model did not regard vehicle availability as a factor which directly affected user demand. Instead, the model included a vehicle availability constraint to account for the impact of vehicle supply on travel demand. The second model included a vehicle availability variable in the discrete choice model so that vehicle supply could directly change trip demand. In this model, demand is responsive to vehicle supply and demand will change the distribution of vehicle supply in reverse. This interdependent relationship is achieved by the variable vehicle availability. This variable is the output of the optimisation model and the input of the discrete choice model. In this way, demand and supply in carsharing networks are linked. Chapter 6 also proposed a method to linearise the nonlinearity problem caused by the responsive demand constraints. The linearisation method can be applied to solve integer programming models that incorporated with general discrete choice models.

Sensitivity analysis on total travel demand, one-way trip price, carsharing vehicle pod capacity, and importance of vehicle availability were undertaken in GoGet network. The results suggest that one-way trip price influences the system profit by affecting carsharing trip demand and availability for different types of trips. The optimal one-way trip prices that yield the maximal profits increase as the total travel demand increases. With respect to network capacity, if we do not consider vehicle availability as a key factor that influences travel demand, the impact of vehicle pod capacity on system profit is not as significant as that of the price of one-way trips.

Whereas, if there is a strong interdependent relationship between trip demand and

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vehicle supply, the profit will be significantly influenced by the vehicle pod capacity.

Furthermore, the optimal one-way trip prices that lead to maximal profits will occur at higher values if the impact of vehicle availability on travel demand becomes larger.

Figure 7:1 concludes the final remarks withdrawn from the thesis. The demand estimation part highlights that carsharing users’ demand for vehicles is dependent on the locations and characteristics of vehicles. This reflects the significant impact of vehicle supply on demand, and inspires the operation optimisation studies to account for such impact when generating demand matrix for the optimisation models. The optimisation models proposed in the second part of the thesis then consider a demand responsive carsharing network. The results of the optimisation models further confirm that the supply of carsharing vehicles will influence the demand and then the system profit.

Figure 7:1 Final remarks of the thesis

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Chapter 7. Conclusions and Future Researches

7.2 Future Researches

The research presented in this thesis takes the initial step to explore carsharing systems from both a user demand and vehicle supply perspective comprehensively. Starting from this research, several future research questions are worth investigating.

The model presented in Chapter 3 helps carsharing operators understand how users form the vehicle selection choice set. Furthered from this model, a secondary discrete choice model can be developed to predict the probability of a vehicle being selected within the choice set. These two models can further be integrated with an optimisation model aiming to optimally select the locations and types of vehicles in the carsharing programmes given a set of candidate vehicles. The SHBM together with the secondary discrete choice model can predict the probability of a vehicle’s selection, given its location and characteristics. The objective of the optimisation model can be maximising the carsharing ridership by maximising the sum of the probability of vehicles being selected by users given a budget constraint. The integrated model can determine which vehicle locations and vehicle types can enhance the overall popularity of carsharing schemes.

Focusing on the parameters studied in the SHBM, “distance to the carsharing vehicle” is treated as the key factor in vehicle selection process. Further extensions to this research can be investigating the impacts of some other key factors such as trip purpose and trip destination.

With respect to the vehicle utilisation study presented in Chapter 4, the performance metrics of the MDCEV models can be improved. Currently, we apply normalised RMSE and correct ratio to compare different models. These two metrics

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can identify the best-fitted model among several models, but cannot reflect if the performance of a single model is good or not. In other words, if we only propose one

MDCEV model, the two metrics cannot be used to evaluate its performance. Therefore, more generalised performance measures are required to evaluate MDCEV models.

Furthermore, since MDCEV models estimate the behaviours of both discrete choice and continuous allocation, the performance measures should account for the performance of these two aspects.

Another limitation of the MDCEV models in Chapter 4 lies in the estimation of budget. In this study, the budget of an user is calculated to be the sum of the observed expenditure on all vehicle types of the user. However, the actual budget can be more than the observed total expenditure. In order to estimate the accurate budget, a future direction can be conducting a survey of carsharing users to obtain their budget.

This will improve the estimation accuracy of the MDCEV models.

In the operation optimisation part, owing to the lack of data, this study cited a multinomial logit model from literature to serve as the choice model to influence carsharing trip demand. However, the model itself does not consider vehicle availability as a factor that could influence the elasticity in demand. To overcome this limitation, we added a vehicle availability factor and undertook a sensitivity analysis on the coefficient of vehicle availability. Further study could concentrate on conducting a stated preference survey to determine the exact coefficient of vehicle availability.

Finally, since the testing network is limited, the optimisation solver CPLEX can solve the models in a short time. However, if we enlarge the carsharing network,

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heuristic algorithms are required to shorten the computing time, which can also be a focus of future work.

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