Two-stage stochastic programming approach for fleet sizing and allocating rail wagon under uncertain demand

•Proposing a scenario-based two-stage stochastic model for wagon sizing and allocating in order to maximize profit of the studied company.•The models of this research consider the possibility of renting wagons from other companies and renting wagons to other companies.•The proposed stochastic model has value added compared to deterministic model and using it recommended to decision makers.•Sensitivity analysis is used to validate the stochastic model.•In this research, the problem and all its data are derived from real-world data. In this paper, a scenario-based two-stage stochastic programming model has been developed to determine the optimal number of wagons and allocation of full and empty wagons during different time periods to optimize profit. In allocating wagons, when the wagon arrives at a station, it is not possible to reallocate the wagon at the moment of arrival, this issue has not been addressed before. In addition, the possibility of renting wagons to/from other companies is concerned in the railway planning. These two actions have not been addressed before. In this paper, firstly, the research problem is formulated in the form of an integer programming model with deterministic data. Due to the inherent uncertainty in the transportation demands of the real case study, the deterministic model has been transformed into a scenario-based two-stage stochastic programming model with recourse. Then the L-shaped method was proposed to solve the stochastic model and by using it for 34 instances, its better efficiency than CPLEX software was shown. The stochastic model was solved using the L-shaped method and the results show that the studied company should rent 749 wagons to meet the demands, and on average, the stochastic model is expected to have about 1.1% added value in the company's profit compared to the deterministic model.