Warehouse space capacity and delivery time window considerations in dynamic lot-sizing for a simple supply chain

This paper studies a single item, two-echelon dynamic lot-sizing model with delivery time windows, early shipment penalties, and warehouse space capacity constraints. The two-echelon system consists of a warehouse and a distribution center. The underlying problem is motivated by third party logistics and vendor management inventory applications in the computer industry where delivery time windows are typically specified by the distribution center under the terms of a supply contract. The capacity of the warehouse is limited. This constraint should be considered explicitly because the finished products are expensive items (such as computer equipment and peripherals), and they have to be stored in the warehouse in an appropriate climate before they are shipped to the distribution center. Studying the optimality properties of the problem, the paper provides a polynomial time algorithm for computing its solution. The optimal solution includes: (i) the replenishment plan specifying “when, and in what quantities, to replenish the stock at the third-party warehouse,” and (ii) the dispatch plan specifying “when, and in what quantities, to release an outbound shipment to the distribution center, and in which order to satisfy the demands.” The algorithm is based on dynamic programming and requires O(T³) computational complexity.