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The growth in online shopping and third party logistics has caused a revivalof interest in finding optimal solutions to the large scale in-transit freightconsolidation problem. Given the shipment date, size, origin, destination, anddue dates of multiple shipments distributed over space and time, the problemrequires determining when to consolidate some of these shipments into oneshipment at an intermediate consolidation point so as to minimize shippingcosts while satisfying the due date constraints. In this paper, we develop amixed-integer programming formulation for a multi-period freight consolidationproblem that involves multiple products, suppliers, and potential consolidationpoints. Benders decomposition is then used to replace a large number of integerfreight-consolidation variables by a small number of continuous variables thatreduces the size of the problem without impacting optimality. Our results showthat Benders decomposition provides a significant scale-up in the performanceof the solver. We demonstrate our approach using a large-scale case with morethan 27.5 million variables and 9.2 million constraints.

A Redesigned Benders Decomposition Approach for Large-Scale In-Transit Freight Consolidation Operations