Optimizing the loading of double stack trains under uncertain container availability

This paper contributes to the literature on the operations management of double stack trains by introducing a new, real-world research problem that arises when loading trains at marine container terminals with on-dock rail service. Specifically, in this research we model the reality that containers that need to be loaded on railcars can be unavailable at the time of loading, while optimizing the assignment of railcars to hubs and trains, and containers to railcars. To this end, we propose a two stage stochastic program that aims to minimize the number of well cars used when container availability is uncertain (first stage) while also maximizing their space utilization when taking corrective actions (second stage). For its solution, a tailored integer L-shaped solution method is presented. Algorithmic performance and managerial insights are highlighted in a series of numerical experiments. Findings include: 1) The proposed L-shaped method is superior compared to a state-of-the-art commercial solver (up to 5 times faster in our experiments). 2) It is beneficial for the rail manager to prioritize making available 40-foot containers versus 20-foot containers. 3) The higher the probability of container availability in the second stage, the more well cars should be made available in the first stage.