Solving a multi periodic stochastic model of the rail–car fleet sizing by two-stage optimization formulation

We propose a formulation and solution procedure for optimizing the fleet size and freight car allocation under uncertainty demands. There are important interactions between decisions on sizing a rail–car fleet and utilizing that fleet. Consequently, the optimum use of empty rail–cars for demands response in the length of the time periods one of advantages the proposed model. The model also provides rail network information such as yard capacity, unmet demands, and number of loaded and empty rail–car at any given time and location. Consequently, the model helping managers or decision makers of any train company for planning and decision making. We propose two-stage solution procedure for solve rail–car fleet sizing problem. Numerical examples are given to illustrate the model and solution methodology.