The load planning and sequencing problem for double-stack trains

This paper addresses the integrated load planning and sequencing problem (LPSP) for double-stack trains. This decision problem occurs in intermodal terminals and consists in assigning containers from a storage area to slots on railcars of outbound trains and in determining the loading sequence of the handling equipment. Even though this a relevant operational problem, it has seen no attention in the operations research literature so far. Prior models either focus on single-stack railcars or treat the load planning and sequencing separately. By extending prior work on load planning, we propose four integer linear programming formulations differing in the number of constraints and variables. An extensive numerical study identifies two formulations that perform best in our setting with respect to the number of optimal solutions found in a given time limit and average solution time. With these formulations, we solve instances with up to 50 containers with a commercial general-purpose solver in less than 20 minutes. A case study based on real data provided by the Canadian National Railway Company highlights that the LPSP can reduce the number of container handlings in intermodal terminals compared to sequential solutions by on average 11.3% and 16.5% for gantry cranes and reach stackers, respectively