An enhanced dynamic programming approach to the deterministic time-dependent lot-sizing problem under shared warehousing

The lot-sizing problem for one-to-one distribution with time-dependent demand has long been studied in logistics at the operational level. Conventionally, the heuristic-based forward dynamic programming method is usually utilized for the case considering only the trade-off among operational costs, such as transportation and inventory costs. With the onset of e-commerce, many small- and medium-sized e-retailers that have insufficient volume to warrant a dedicated facility are now outsourcing warehousing and logistics services. A single warehouse today may be shared by multiple e-retailers with time-dependent space requirements. Thus, it becomes critical to incorporate the shared warehousing cost, or the rent cost, which was often considered at the tactical level into the lot-sizing problem. This paper deals with the optimal lot-sizing problem in which rent cost and other operational costs are considered jointly. Four necessary conditions for the optimal solution are identified. An enhanced forward dynamic programming approach based on the identified necessary conditions is proposed to solve this multi-objective optimization problem. The performance of the proposed approach is examined for a broad range of cost parameters and demand functions. The results indicate that the proposed approach is promising in terms of computation time and solution quality.