Optimal implementation and benefits of rolling inventory

We study a warehouse management problem in which the schedule of incoming supplies and customer orders for a wide variety of products is known over a number of periods. In addition to storage at the warehouse, products can be kept in the shipping trailers (rolling inventory) parked in the warehouse yard, avoiding material handling costs but incurring trailer handling and opportunity costs. Our objective is to determine the amount of product (if any) to leave in each of the incoming trailers, so that it does not have to be stored and then reloaded for an outgoing delivery, in order to minimize overall warehousing costs. We propose three possible implementation policies and show that the search for optimal solutions can be restricted to these three basic policies without loss of generality. Using this result, we formulate the problem as an integer program, in which incoming trailers are assigned to outgoing deliveries. Under one of the proposed policies incoming trailers can only be stored in the yard directly upon arrival, with their original contents. In this case, we show that our formulation possesses the integrality property and thus the optimal solution can be easily obtained. When the three policies are considered jointly, however, this is no longer the case. Nevertheless, computational tests show that the linear programming bound is very strong and commercial integer programming solvers generate an optimal solution very quickly. In most cases, no branch-and-bound nodes are required. Finally, we perform a computational study based on realistic data provided by our industry partner to evaluate the benefits of rolling inventory, the effectiveness of the different implementation policies and the viability of our proposed solution approaches.