Optimal Integrated Ordering and Production Policy in a Supply Chain With Stochastic Lead-Time, Processing-Time, and Demand

This paper seeks the optimal integrated ordering and production control in a supply chain by minimizing the expected sum of material and product holding costs and demand backordering costs subject to finite capacitated warehouses. With the assumptions of exponential replenishment lead-times, exponential processing-times, Poisson demand arrivals, and at most one outstanding order with its size changeable at any time, it is shown that the optimal integrated policy can be characterized by two monotonic switching curves. The optimal ordering decision follows a set of order-up-to-point policies, while the optimal production decision follows a set of base-stock policies. Based on the monotonic and asymptotic properties of the switching curves, a simple linear switching threshold policy is proposed, which performs extremely well in the experiments. The key assumptions are then relaxed and numerical examples illustrate that the main structural properties of the optimal policy are preserved.