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

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.