Optimal lot-sizing and joint replenishment strategy under a piecewise linear warehousing cost structure

In the general lot-sizing replenishment problem, warehousing costs are considered as part of the inventory holding cost. When decision makers need warehouse space to store their products, they generally think about the warehousing cost as included in the inventory cost. In this study, we investigate an optimal lot-sizing and replenishment problem under a piecewise linear warehousing cost structure. Theoretical analysis of the optimality structure of a model of multiple stock-keeping units with joint inventory costs is conducted, and an effective search algorithm is proposed. Based on our random experiments, we demonstrate that our search algorithm outperforms the approach that the existing literature offers as solution.