Managing a two-stage production-inventory system with external orders for intermediate goods

In this article, we consider a two-stage production-inventory system in which the first-stage facility produces components for external orders as well as inventory replenishment. The external orders can be accepted if the first-stage capacity is not in use. End products are produced in a make-to-stock mode using components, and unmet demand due to stockout is partially backlogged. We address the problem of coordinating component inventory replenishment, component production capacity allocation, end-product production, and end-product demand control in stockout. Formulating the problem as a Markov decision process, we characterize the optimal control policies. Using numerical experiments, we examine the circumstances under which the manufacturer can realize an additional profit from accepting external orders at the first stage. We also examine the effectiveness of backlogging external orders for profit enhancement. The results show that it will not be effective if the unit-backlogging cost rate is at least 6% of the revenue generated by an external order. We present a heuristic with three linear switching functions and a state-independent threshold. Compared to the optimal policy, its average percentage performance for 48 example cases is 0.31%.