A Solvable Case of Emergency Supply Chain Scheduling Problem with Multi-stage Lead Times

We consider a capacitated multi-stage operations scheduling problem encountered in a real life supply chain for disaster relief, consisting of component suppliers, a packaging contractor, local distribution centers, and many customer demand points. Each customer order has a due date and can be fulfilled by either existing inventory at distribution centers or a new assembly operation at the packaging contractor. The problem is to find a production and distribution schedule to minimize the total tardiness in fulfilling the customer orders, which is computationally a difficult problem, especially when supply chain lead time is involved. In this paper, we present a polynomial time algorithm that solves this problem optimally when the order sizes are identical. The proposed solution process is based upon decomposition, and is demonstrated step-by-step through a numerical example. Future extensions of this study are also discussed.