OPTIMAL-CONTROL OF A SINGLE-STAGE PRODUCTION SYSTEM SUBJECT TO RANDOMPROCESS SHIFTS

We consider a single stage production system with Poisson demand and e xponential processing times. After producing a good item, the producti on process can shift to an ''out-of-control'' state with a given proba bility and start producing bad items. The state of the process is know n only when the next stage (or customer) receives the item. Once an ou t-of-control process is detected, process correction is instantaneous. Customers arriving to an empty system get backlogged. In this framewo rk, we examine FIFO (First In First Out) and LIFO (Last In First Out) issuing policies. The objective is to minimize the total expected disc ounted or average costs over an infinite time horizon. We characterize the structure of the optimal production policy for FIFO and LIFO, sho w that LIFO is better than FIFO and, in general, better than a large c lass of issuing policies. A numerical example illustrates that savings up to 20 percent can be obtained from using LIFO over FIFO. We also d erive conditions under which maintaining zero inventory is optimal, an d show that zero inventory is more likely to be optimal when either th e backlogging cost or arrival rate of customers is small, and when the inventory carrying cost or the processing rate or the probability of getting a good item is large.