Optimization models and methods for transportation services
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Managing transportation services efficiently is essential to both public and private sectors. This dissertation addresses three scheduling problems in modern transportation systems: the network design problem, the train dispatching problem, and the service route design problem. The transportation network design problem with service requirements designs arcs on a directed network and route commodities on the designed arcs so that i) commodities satisfy service requirements and ii) the total cost is minimized. We develop three mathematical programming models: a compact but weak arc-flow formulation, a large but strong path-flow formulation, and a hybrid formulation that uses both the arc-flow and the path-flow representations. We show that the hybrid formulation can significantly strengthen the LP formulation without introducing many variables. To find a good hybrid formulation, we develop columnization and decolumnization algorithms that uses the LP relaxation information to identify commodities that should use the path-flow representation. We also develop valid inequalities for commodities using the path-flow representation. The train dispatching problem schedules the movements of trains on scarce railroad tracks so as to improve the average velocity of trains. We develop a mathematical programming model and strengthen the model using valid inequalities. Besides, we present a heuristic to find a feasible solution quickly, which can serve as the warm-start solution to the MIP solver. For the third problem, we seek to design vehicle routes to deliver and pickup orders for a major grocery chain. We design a GRASP that can incorporate various operational requirements, including warehouse loading capacity, loading sequence, time window requirements, truck volume and weight capacities, and driver time limits. Our GRASP procedure consists of two phases: the solution construction (Phase I) and the Tabu search (Phase II). We show that the neighborhood structure of solutions is highly degenerate, which limits the solution space explored by the Tabu search. We apply the Tabu search with random variable neighborhood to increase the solution space explored.