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