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The Train Unit Shunting Problem with Reallocation

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The Train Unit Shunting Problem with Reallocation The Train Unit Shunting Problem with Reallocation Master Thesis Econometrics & Management Science Specialization Operations Research & Quantitative Logistics F.E. Wolfhagen Student number: 362063 First supervisor: Dr. T. Dollevoet Second supervisor: Prof. dr. D. Huisman Supervisor NedTrain: Ir. B. Huisman Erasmus School of Economics Erasmus University Rotterdam The Netherlands March 23, 2017 Abstract This thesis is concerned with formulating the Train Unit Shunting Problem (TUSP) with Reallo- cation (TUSP-R) as an MIP and solving it using exact solution methods. The TUSP has been formulated as an MIP in several different ways in previous works, but reallocation was never in- corporated. Exactly solving the TUSP-R proved to be very challenging, so a method using a combination of the exact solution method row generation and the heuristic method tabu search was developed which solved the real life instances for shunting yard Utrecht OZ in acceptable solution times. The instances for a simplified version of Kleine Binckhorst were solved up to a certain problem size; hereafter the computation times became too long for practical use. Our method performs best for problem instances with diverse train types and relatively many different services on a LIFO style shunting yard layout. This keeps the size of the constraint matrix of the initial problem without crossing constraints relatively small compared to other types of problem instances. 2 Preface This thesis was written for partial fulfillment of the graduation requirements of the master pro- gramme Econometrics and Management Science, with a specialization in Operations Research and Quantitative Logistics at Erasmus School of Economics. I was engaged in the research and writing from October 2016 till March 2017. This research was undertaken on request of NedTrain, where I did an internship during the course of the project. As shunting yard capacity is becoming a more and more urgent topic, the need for an exact formulation for the TUSP-R arose. The research is part of the challenging task to integrate all aspects of the shunting problem, thus also service activities, in one MIP. It also serves as reference, justification, and mathematical background for the current methods used by NedTrain to determine shunting yard capacity. There are a few people without whom I would never have finished this thesis. First of all, I am very grateful to the great guidance I received from dr. Dollevoet from the Econometric de- partment at Erasmus School of Economics. As my supervisor, he provided me with very useful feedback and helped me across bumps along the way. I always left our meetings feeling more mo- tivated and confident than before. His relaxed attitude and precise evaluation of my work greatly contributed to its quality. I also want to thank professor Huisman, who is my second supervisor. His experience at NS is a valuable addition to the critical evaluation of my work. Besides the people in Rotterdam, I would like to thank NedTrain and especially Bob Huisman -a different mister Huisman- for providing me with the opportunity to write my thesis at the Maintenance Development department. I thoroughly enjoyed working there and many of my kind colleagues were readily available to help me out whenever I needed it. Bob, our discussions on the topic provided me with many valuable insights and alternative viewpoints which helped me try new approaches when I was stuck and brought me further in the process. Besides Bob, Roel van den Broek and Demian de Ruijter also deserve a special thank you for their help. Furthermore, I am very grateful and owe a great deal to my parents for their support during the writing of this thesis and my entire studies. Without them, all of this would never have been possible. Lastly, I would like to thank my friend Elise den Dekker for her moral support during the last phase of the process. I hope you enjoy reading it, and I advise you to take your time for the mathematical formula- tions in this thesis. They can be rather complex and potentially frustrating, I know all about it, but definitely have a certain charm to them. - Floor Wolfhagen, March 2017 3 Contents List of Tables 6 List of Figures 7 1 Introduction 8 2 Literature Review 13 2.1 Motion-Planning Puzzles and their Complexity . 13 2.2 General Shunting Problems . 13 2.3 Train Unit Shunting Problem . 14 3 Problem description 18 3.1 General terminology . 18 3.2 General notation . 21 3.3 Complexity . 22 4 MIP Formulation 23 4.1 Initial formulation . 24 4.2 Final formulation . 28 4.2.1 Resolving non-linearity issues . 33 4.3 Extensions . 34 4.3.1 Free tracks extension . 34 4.3.2 LIFO tracks on both sides of diagonal track extension . 39 4.3.3 Flexible maximum train unit reallocation length . 39 4.3.4 Coupling and decoupling . 42 5 Solution Approach 45 5.1 Row generation heuristic . 45 5.2 Consideration of column generation . 47 6 Data 50 7 Results 54 7.1 Results Utrecht OZ .................................... 54 7.2 Results Kleine Binckhorst ................................ 57 7.3 Comparison results Utrecht OZ and Kleine Binckhorst ................ 61 8 Discussion 64 4 9 Conclusion 65 9.1 Further Research . 66 Bibliography 68 Appendices 70 A Notation 70 A.1 Overview variables initial formulation . 70 A.2 Overview variables final formulation . 70 A.3 Overview notation extensions . 71 B MIP formulation used for obtaining the computational results 73 5 List of Tables 1.1 Example: arriving and departing times and types of trains 1-8 . 10 3.1 Set overview . 21 3.2 Parameter overview . 21 4.1 Crossing overview LIFO track . 26 4.2 Crossing overview free tracks . 35 6.1 Train unit lengths . 51 6.2 Track lengths for shunting yard Kleine Binckhorst .................. 52 6.3 Characteristics of data set for shunting yard Kleine Binckhorst ........... 52 6.4 Track lengths for shunting yard Utrecht OZ ...................... 53 6.5 Characteristics of data set for shunting yard Utrecht OZ ............... 53 7.1 Solved instances and computation times of different solution methods Utrecht OZ . 54 6 List of Figures 1.1 Railway map of the Netherlands, 2016 . .8 1.2 Map of Kleine Binckhorst ................................9 1.3 VIRM -4.......................................... 10 1.4 SLT -6........................................... 10 1.5 Example: need for reallocation . 11 1.6 Rush Hour instance with solution steps . 11 3.1 Relations schedules, services, events, compositions, train units, and carriages . 19 4.1 Example track layout only LIFO tracks . 23 4.2 Crossing possibilities LIFO tracks . 27 4.3 Example track layout only free tracks . 34 4.4 Crossing possibilities free tracks . 37 4.5 Example track layout LIFO tracks on both sides of the diagonal track . 39 4.6 Example track layout varying drive back distance . 40 6.1 Simplified structure of Kleine Binckhorst ....................... 52 6.2 Map of Utrecht OZ .................................... 53 7.1 Overview objective values solutions NR-MIP, RG, and TS-RG, Utrecht OZ .... 55 7.2 Overview computation times TS-RG for different settings, Utrecht OZ ....... 56 7.3 Overview objective values TS-RG for different settings, Utrecht OZ ......... 56 7.4 Overview number of solved instances OPG, SAR, and TS-RG, Kleine Binckhorst . 57 7.5 Overview average number of reallocations and computation time TS-RG, Kleine Binckhorst ........................................ 58 7.6 Overview average number of iterations TS-RG, Kleine Binckhorst ......... 59 7.7 Overview number of solved instances with zero reallocations OPG and TS-RG, Kleine Binckhorst .................................... 60 7.8 Overview results number of solved instances and average number of reallocations different settings TS-RG, Kleine Binckhorst ...................... 61 7.9 Overview average number of reallocations TS-RG, Kleine Binckhorst and Utrecht OZ 62 7.10 Overview average computation times TS-RG, Kleine Binckhorst and Utrecht OZ . 62 7 Spoorkaart ool ch es rffum quert Wa Us UithuizenUithuizermeedenRood t Baflo m m m Winsum edu ppersum 2016 Bedu St Lo AppingedaDelfzijl WesDelfzijl aven Sauwerd www.spoorkaart2016.nl H p y haburen k lingen nr g n Groningen arlingen einum H Har FranekerDro D warden Noord ijpsker idhor ammin e Westereen u LeeuC HurdegarypFeanwaldenD BuitenpostGr Z Groningen Mantgum Den Helder Sneek Noord Leeuwarden Den Helder Zuid Sneek wolde Bovenkarspel Flora Groningen pemeer Oost Nieuweschans Anna Paulowna IJlst ener Europapark oogezand-Sappemeeruidbroekheemdanschoten er Krops MartenshoekH Sap Z e Bovenkarspel- Workum Sc Wi Bad We L Grootebroek Enkhuizen Schagen Hindeloopen Haren Koudum-Molkwerum Veendam Grou - 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