A Simultaneous Magnanti-Wong Method to Accelerate Benders Decomposition for the Metropolitan Container Transportation Problem

In most Australian cities, container ports are located close to the city, with transportation to and from the port facilitated by trucks. Recently, with a view to reducing container-truck induced city congestion and pollution, state and federal governments have begun championing a modal switch to short-haul rail for these transportation tasks. In this paper, we describe a metropolitan container transportation problem arising from this context that seeks to effectively leverage both modes of transport from a least-cost perspective. We propose a mathematical programming formulation and develop a new modified Benders decomposition method for the problem. We show that the simultaneous Magnanti-Wong method finds Pareto-optimal cuts by solving an augmented version of the subproblem that exploits subproblem dual-degeneracy without destroying its underlying structure. Computational results demonstrate the effectiveness of this routine over the performance of commercial solver implementations of the mathematical programming formulation.