A dynamic model for inventory lot sizing and outbound shipment scheduling at a third-party warehouse

This paper presents a model for computing the parameters of an integrated inventory replenishment and outbound dispatch scheduling policy under dynamic demand considerations. The optimal policy parameters specify (i) how often and in what quantities to replenish the stock at an upstream supply chain member (e.g., a warehouse), and (ii) how often to release an outbound shipment to a downstream supply-chain member (e.g., a distribution center). The problem is represented using a two-echelon dynamic lot-sizing model with pre-shipping and late-shipping considerations, where outbound cargo capacity constraints are considered via a stepwise cargo cost function. Although the paper is motivated by a third-party warehousing application, the underlying model is applicable in the general context of coordinating inventory and outbound transportation decisions. The problem is challenging due to the stepwise cargo cost structure modeled. The paper presents several structural properties of the problem and develops a polynomial time algorithm for computing the optimal solution.