Two-stage stochastic programming for the railroad blocking problem with uncertain demand and supply resources

Abstract

The railroad blocking problem is classified in the tactical level of freight rail transportation problems. The objective of this problem is to determine the optimal paths for each shipment such that the railway limitations are satisfied. In this problem, the quantities of both demand and supply resource indicators are often assumed to be certain and known, but because a blocking solution is designed for a relatively long period of time, this assumption is not reasonable. In this paper, we have developed a two-stage stochastic program for this problem to consider the uncertainty inherent in demand and supply resource indicators. Due to the size and complexity of the stochastic program and the impossibility of using commercial software in even the simplest instances, two solution methods have been proposed. The first method developed is based on the L-Shaped method, and the second method is a modification of the first one that uses a new initial solution (which is obtained by adapting a side optimization model) together with the L-Shaped method. Extensive experiments on test networks show that the two methods outperform the commercial software and that the second method is superior to the first one. We finally present the application of the uncertain model and the computational results of the second method for the Railways of Iran as a real-size example, and we show that the application of the stochastic model could reduce total cost by more than 12million dollars per three-month horizon compared with the deterministic solution.