The load planning problem for double-stack intermodal trains

This paper presents a general methodology that addresses the load planning problem for intermodal trains. We propose a model that can deal with single- or double-stack railcars as well as arbitrary containers-to-cars matching rules. Moreover, we model weight and center of gravity constraints, stacking rules and technical loading restrictions associated with specific container types and/or contents. We propose an integer linear programming (ILP) formulation whose objective is to choose the optimal subset of containers and the optimal way of loading them on outbound railcars so as to minimize the resulting loading cost. An extensive numerical study is conducted. It shows that ignoring center of gravity constraints and containers-to-cars matching rules may lead to an overestimation of the train capacity and to select load plans that are not feasible in practice. We also show that we can solve realistic instances to optimality in reasonable computational time using a commercial ILP solver.