Optimal control of a single stage production system subject to random process shifts

We consider a single stage production system with Poisson demand and exponential processing times. After producing a good item, the production process can shift to an ‘out-of-control’ state with a given probability and start producing bad items. The state of the process is known only when the next stage (or customer) receives the item. Once an out-of-control process is detected, process correction is instantaneous. Customers arriving to an empty system get backlogged. In this framework, we examine FIFO (First In First Out) and LIFO (Last In First Out) issuing policies. The objective is to minimize the total expected discounted or average costs over an infinite time horizon. We characterize the structure of the optimal production policy for FIFO and LIFO, show that LIFO is better than FIFO and, in general, better than a large class of issuing policies. A numerical example illustrates that savings up to 20 percent can be obtained from using LIFO over FIFO. We also derive conditions under which maintaining zero inventory is optimal, and show that zero inventory is more likely to be optimal when either the 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.