Optimal replenishment and rework with multiple unreliable supply sources

We study a production-inventory system with multiple unreliable supply sour ces. Through inspection and rework, the system can improve the quality of t he units received from the supply sources. There are two interleaved decisi ons: the replenishment quantities from the sources and the inspection-rewor k quantities among the units received. We show the optimal solution to the replenishment decision can be efficiently derived from a greedy algorithm, and inspection-rework is optimally applied to a single source identified by the algorithm. Furthermore. in the case of linear cost functions, it is op timal to place orders from two supply sources, i.e., dual sourcing. The res ults extend to the infinite-horizon case, where an order-up-to policy is op timal. The model also readily adapts to situations in which the supply impe rfection takes the form of a reduced delivery quantity (yield loss).