A stochastic model predictive control to heterogeneous rail freight car fleet sizing problem

•The rail freight car fleet size and allocation problem has been analyzed.•Demands and travelling times are treated as stochastic variables.•Interchangeability among rail freight car types is included by the model.•Model predictive control approach is used as a solution approach.

In this paper a rolling horizon approach is applied for simultaneous optimization of the rail freight car fleet size and allocation problem. Developed dynamic model of loaded and empty rail freight car flows explicitly treats state, control and station capacity constraints in presence of various freight car types under the partial substitutability among them. Demands and traveling times are considered as random variables. Proposed approach is applied to a set of test cases and it shown to be successful, ultimately providing a new managerial tool for more effective and efficient planning and analyzing rail freight car fleets.