Optimization Models for Empty Railcar Distribution Planning in Capacitated

Optimization Models for Empty Railcar Distribution Planning in Capacitated Networks A Dissertation Presented By Ruhollah Heydari to The Department of Mechanical and Industrial Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the field of Industrial Engineering Northeastern University Boston, Massachusetts January 2016 ABSTRACT Because of spatial and temporal imbalances in the supply and demand of empty railcars/cars in freight transportation systems, empty equipment repositioning is inevitable. As the owners of rail network, trains and railcars, railway carriers charge their customers based on the days and the miles that a railcar is under load. Hence the cost of shipping empty cars to customers as well as the opportunity cost of extra inventory in customer facilities is on the railway’s shoulder. A reverse routing strategy suggesting to return the empty cars to the place they were loaded, imposes a 50% empty movement in a car cycle while a reload strategy suggesting to reload the cars at the point they become empty has 0% empty movement. The first strategy is good for frequent shippers only and still is too costly and the idealistic second strategy is not usually feasible because of the supply- demand imbalances. In this research we develop two formulations for the Empty Railcar Distribution problem, both aiming to minimize the total setup costs, total transportation costs, and total shortage penalties under supply limitation, demand satisfaction, customer preferences and priorities, and network capacity constraints. We first formulate the problem as a path-based capacitated network flow model. Contrary to the traditional path-based formulations, the path connecting each supply- demand pair is given by an external application called Trip Planner which is defined on top of a time-space network. Another application called Pseudo Path Generator then generates alternative paths for each supply-order pair. Then we formulate the problem as an arc-based capacitated multi-commodity network flow model where contrary to the path-based model, the car routing and car distribution decisions are integrated in a single model. The path-based formulation is more practical for the United States railroads since in US railroad industry car routing and car distribution decisions are separated from each other and usually made by different departments while the integrated arc-based formulation is close to the Swedish Railway System. Both models are complex and because of the huge number of constraints and integer decision variables are hard to solve. The models are implemented in Java and solved using Concert Technology of the IBM CPLEX solver. We also develop an Iterative Relaxation and Rounding Heuristic using Initial Basis for the path-based model. The comparison of path-based and arc-based formulations in both capacitated and uncapacitated modes confirmed the efficiency of the heuristic from both run time and solution quality perspectives. II ACKNOWLEDGEMENTS I express my sincere gratitude and appreciation to my PhD advisor, Prof. Melachrinoudis of Northeastern University, for his encouragement, guidance, and continuous support over the years of my graduate studies, not only in research but also in other aspects of student life in the United States. I thank Dr. Kubat and Dr. Turkcan from Northeastern University and Dr. Pranoto from Norfolk Southern Railway for being part of my PhD committee and providing me with their valuable comments on this research. I would also like to thank Dr. Clark Cheng of Norfolk Southern for encouraging me to choose my Dissertation topic in the area of Car Distribution Problems; Fabio Colombo from Universita degli Studi di Milano, Italia (Team OR at UNIMI) for providing me with their group's 2011 RAS competition results; Nilay Roy from Research Computing Center of Northeastern University for his hours of technical support on distributed computing; Lisa O'Neill, Director of Graduate Student Services, for her endless support throughout my educational life at Northeastern University, and all other faculty, staff and friends who were always there when I needed their support. I am indebted to my family for their relentless support and encouragement, during my graduate studies. And I want to express my greatest gratitude to them and specially to my mom whose patience, love, and praying has always been with me. Finally I will dedicate this work to my mom. Thank you maman! III LIST OF TABLES Table 2-1 A comparison among current models used by railway carriers and our model ............. 25 Table 3-1 Parameters used to calculate the cost coefficients ......................................................... 49 Table 3-2 Demand node priorities based on customer priorities ................................................... 49 Table 3-3 Illustration of customer profiles .................................................................................... 51 Table 3-4 Model assumptions ........................................................................................................ 55 Table 4-1 Mathematical notation ................................................................................................... 58 Table 5-1 Notation for the arc-based formulation ......................................................................... 96 Table 5-2 Permitted flows vs leak in the customer level ............................................................... 99 Table 6-1 Networks used for verification and validation of the models and the solution procedures ..................................................................................................................................................... 113 Table 6-2 Customers’ demand for a one-week time horizon ....................................................... 118 Table 6-3 Available supply of different pools in each yard ......................................................... 119 Table 6-4 Performance measures (optimal assigned cars; optimal objective value) for different models for two scenarios with different shortage penalties ......................................................... 128 Table 6-5 Different models, variable setup and algorithms to solve them .................................. 129 Table 6-6 Parameters used to generate case example for sensitivity analysis ............................. 135 Table 6-7 Parameters used to generate case examples for computational complexity calculations ..................................................................................................................................................... 143 IV LIST OF FIGURES Figure 3-1 An itinerary for a flight trip .......................................................................................... 27 Figure 3-2 Underlying networks used in the railroad optimization models ................................... 33 Figure 3-3 The time-space network (a) and its associated multigraph (b) ..................................... 37 Figure 3-4 Time-space block-train network associated to Figure 3-2(f) ....................................... 38 Figure 3-5 Time-space resource-constrained block network (colors for visualization) ................. 41 Figure 3-6 Time-space resource-constrained block network (the main representation) ................ 42 Figure 3-7 Customers on time-space resource-constrained block network .................................. 43 Figure 3-8 Bipartite supply-demand multigraph ............................................................................ 44 Figure 3-9 Costs on the time space network .................................................................................. 49 Figure 3-10 Classifying fleet for empty railcar distribution .......................................................... 54 Figure 4-1 Shortage cost function .................................................................................................. 62 Figure 4-2 Car distribution model in three different modes .......................................................... 64 Figure 4-3 An arc-train network with only one path between any O-D pair (a-1) can be transformed to a resource-constrained bipartite graph (a-2), while the one with more than one path (b-1) is transformed to a bipartite multigraph (b-2). .............................................................. 68 Figure 4-4 Lattice path of length four in in ℤퟐ .............................................................................. 70 Figure 4-5 Six lattice paths and their associated permutation words ............................................ 71 Figure 4-6. A trip plan and its associated pseudo paths when a) no delay is permitted, and b) a maximum delay of two days is acceptable ..................................................................................... 75 Figure 5-1 Delay arcs in the customer level .................................................................................. 98 Figure 5-2 Permitted flow vs leak in customer level ..................................................................... 99 Figure 5-3 Dealing with delay arc flow using a new variable ..................................................... 101 Figure 6-1 Static networks associated with the Tiny and Supper Tiny Networks: a) physical rail network, b) train network, c) blocking plan and d) block to train assignment ............................. 113 Figure 6-2 Static networks associated with the Medium Network: a) physical rail network, b) train network and c) blocking

Load more