Optimal Inventory Levels for an Unreliable Manufacturing System: Necessary and Sufficient Conditions for a Zero-Inventory Policy to be Optimal

Abstract

Abstract We consider a manufacturing system subject to occasional failures. The commodity produced by the system has a constant demand. Costs are incurred for either exceeding or not meeting demand. What is the optimal production policy? We show that there is an optimal inventory level towards which the production should always be aimed. An explicit expression is obtained for this optimal inventory level. Whenever the the failure rate of the system is small or the repair rate high, or, under some conditions, the cost of positive inventories is large or that or negative inventories small or the maximum production rate high or the demand rate small, (there are critical numbers for each), the optimal inventory policy is of the Zero-inventory type, i.e., no inventory should be maintained