Optimization Models for Empty Railcar Distribution Planning in Capacitated Networks

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.