OPTIMAL ROAD PRICING SCHEME DESIGN AGACHAI SUMALEE Submitted in accordance with the requirements for the degree of DOCTOR OF PHILOSOPHY The University of Leeds Institute for Transport Studies August 2004 The candidate confirms that the work submitted is his own and that appropriate credit has been given where reference has been made to the work of others. This copy has been supplied on the understanding that it is copy right material and no quotation from the thesis may be published without proper acknowledgement. To my late sister, Wanida Sumalee (Orn) “The flower of my heart” Acknowledgements I would like to sincerely thank my supervisors, Prof. Tony May and Dr. Simon Shepherd for their patience, support, and advice throughout this research, especially when I was in the hardest time of my life. The first time I learnt about road pricing was in Tony’s lecture when I was a Master student, and from that moment I started getting really interested in this research topic. Thanks for such a good lecture, Tony. Simon, I think we have come a long way together. Thanks for being such a good supervisor, colleague, and friend. My life and work in Leeds has been very enjoyable. I have to thank Prof. David Watling (aka Dave) for being such a good colleague, boss, friend, and travel companion. Thanks a lot, Dave. I am sure we will carry on our in-car discussion about various transport research topics for a very long time (well, also about Leeds United and Liverpool FC). Also, I have to thank my colleagues and friends at ITS and, in particular, the Network Group for supporting me in various ways throughout the last three and half years (some names to mention in particular: Dave Milne and Richard Connors). Special thanks go to Prof. Siriphong Lawphongpanich for his time and discussion on the cutting plane algorithm and optimal toll problem, to Prof. Hai Yang for suggesting a number of useful comments that help improving my thesis, to Ferri Ghahri-Saremi for his initial suggestion on the branch-tree idea, to Nick Marler for being such a nice office mate and your help on my writing. I’d like to acknowledge the financial support from the UK Department for Transport that made this research possible. Also, I want to thank Mike Goodwin and Phil Philippou who were looking after the students funded by the DfT for the last four years. I would also like to thank all participants of the survey conducted during this research. - i - Furthermore, I would like to thank Mr. David Kamnitzer at IBI group (London) for his support at the initial stage of this study and made this study possible. I am deeply indebted to my fiancée, Aya Fukushige, who is always there for me and understand me throughout the long hard period of my study. Thanks for your companion, patience and love. Also, my sincere gratitude goes to Aya’s parents who have been very supportive for both of us. My personal gratitude goes to my father, mother, brother, and sister for their moral support and encouragement. My parents always give the priority to education which really had a good influence on us and made it possible for me to pursue my PhD study. Life is so uncertain. I’d like to dedicate this thesis to my beloved sister, Wanida Sumalee (Orn), who passed away at such a young age. You are always proud of me and love me with all your heart. I am also proud of you and love you so much. Sleep well my sister. You will always be with me and our family forever. “We must be willing to let go of the life we have planned, so as to have the life that is waiting for us” “The three great essentials to achieve anything worthwhile are first, hard work; second, stick-to-it-iveness; and third, common sense.” Thomas Edison - ii - Abstract There are two main approaches to designing road pricing schemes. The first is judgmental in nature and focuses on the acceptability and practicality of the scheme. The second is based on theory concentrating on the optimality and performance of the scheme. This research aimed to integrate these two approaches into a single framework and to develop a tool to aid the decision maker in designing a practical and optimal road pricing scheme. A review of the practical design criteria and a survey with six local authorities in the U.K. were conducted to clarify the concept of the judgmental design. A simple charging scheme like a charging cordon is believed to be the most practical charging regime due to its simple structure. The decision on the boundary and structure of the cordon is based largely on public acceptability and possible adverse impacts. Road pricing is used to serve several objectives including congestion reduction, revenue generation, and increase in efficiency of the transport system. The framework for the theoretical optimal toll design problem adopted was a Stackelberg game where the travellers’ behaviour were assumed to follow the concept of Wardrop’s user equilibrium. This problem can also be formed as a Mathematical Program with Equilibrium Constraint (MPEC). After reviewing various methods for solving the MPEC problem, three possible methods (the merit function method, improved cutting plane algorithm, and Genetics Algorithm (GA) based algorithm) were developed and tested with the optimal toll problem. The GA based algorithm was found to be the most appropriate for the development of the design algorithm with practical constraints. Three different features of the judgmental design were included into the optimisation algorithm: the closed cordon formation, constraints on the outcomes of the scheme, and the allowance for multiple objectives. An algorithm was developed to find the optimal cordon with an optimal uniform toll. It is also capable of designing a scheme with multiple cordons. The algorithms for solving the constrained optimal cordon design problem and the multiobjective cordon design problem were also - iii - developed. The algorithm developed for the multiobjective problem allows the application of the posterior and progressive preference articulation approach by generating the set of non-dominated solutions. The algorithms were tested with a network of Edinburgh. The results revealed several policy implications. Adopting a judgmental cordon with a simple uniform toll may be less effective. A variable optimised toll around the judgmental cordon can generate around 70% more benefit than the optimal uniform toll. The optimised location of a cordon generated about 80% higher benefit compared to the best judgmental cordon. Additional constraints such as a maximum of total travel time decreased the level of the benefit of the scheme by 90%. Different objectives may require different designs for the charging cordon scheme. The welfare maximisation cordon should focus on those trips contributing most to the social welfare function which are mainly in the congested areas with an appropriate toll level. The revenue maximisation cordon should impose a higher number of crossing points and minimise possible diversion routes to avoid the tolls which should be high. The equity cordon should cover a wider area of the network with low toll level to ensure a good distribution of the cost and benefit to all origin-destination pairs. The algorithms developed can offer support to the decision maker in developing a charging cordon scheme by formalising the process of charging cordon design. This will increase the transferability of the technique and the transparency of the decision process. - iv - Table of Content ACKNOWLEDGEMENTS................................................................................................................. 1 ABSTRACT........................................................................................................................................III TABLE OF CONTENT .......................................................................................................................V LIST OF TABLES .............................................................................................................................IX LIST OF FIGURES ...........................................................................................................................XI CHAPTER 1 INTRODUCTION ................................................................................................... 1 1.1 TRANSPORT PROBLEMS AND EMERGENCE OF ROAD PRICING ................................................ 1 1.2 APPROACH TO DESIGNING A ROAD PRICING SCHEME............................................................ 5 1.2.1 Judgmental approach..................................................................................................... 5 1.2.2 Theoretical approach ..................................................................................................... 7 1.3 OBJECTIVES AND SCOPE OF THE RESEARCH.......................................................................... 9 1.4 STRUCTURE OF THE THESIS ................................................................................................ 10 CHAPTER 2 ROAD PRICING: FROM THEORY TO PRACTICE...................................... 14 2.1 INTRODUCTION .................................................................................................................. 14 2.2 DEVELOPMENT OF THE ECONOMIC THEORY ....................................................................... 15 2.3 ROAD PRICING AS A TRANSPORT INSTRUMENT ................................................................... 21 2.3.1 Objective of the road pricing scheme..........................................................................