The internal warehouse replenishment problem: the importance of storage and replenishment policies

Storing inventory in both a reserve and forward area is a way to improve the efficiency of a B2C warehouse. Due to the small size of the forward area order picking distances can be reduced, although internal replenishments from the reserve to the forward area are necessary to keep the warehouse up and running. In the warehouse literature, the organisation of a forward area is mostly studied from a tactical point of view, discussing the size of the forward area, the selection of products to store there and the number of locations to allocate to each product, also known as storage capacity. The operational implications of these decisions are often ignored or simplified, possibly resulting in (replenishment) cost underestimations. In this paper we study how the forward area could be replenished such to avoid stockouts during order picking whilst integrating practical issues that rise during the operation, e.g., limited replenishment force and time. We present the internal warehouse replenishment problem (IWRP), that determines which products to replenish, in which quantity and by which replenisher. The IWRP is solved for different sizes of a rectangular forward area and differing storage and replenishment capacities whilst considering various inventory policies and planning horizons. We consider an out-of-rack forward reserve system where picking and replenishing is performed in alternating waves. The IWRP is optimally solved using a standard mixed integer program solver. Results show how all parameters influence the objective, and reveal practical issues that should be considered when configuring the forward area. For certain parameter combinations instances were not solved within a realistic time, hence the call for a heuristic solution method.