Analysis of a production/inventory system subject to random disruptions

In this paper we study an unreliable bottleneck production/inventory system with a constant production and demand rate that is subject to random disruptions. We assume that the restoration times are constant, the time between breakdowns is exponential, the production setup cost and/or setup time is positive, and excess demand is backordered. We propose an (s, S) production policy for such systems and develop expressions for the operating characteristics of the system. The properties of the policy parameters that minimize the expected total cost rate are investigated and a procedure for finding their optimal values is developed. In addition, we devise and test a simple heuristic procedure for finding near optimal production policies. The results of a numerical experiment suggest that: (i) setup cost reduction is more effective in reducing total operating cost when the production system is more reliable, (ii) setup cost reduction in unreliable production systems results in higher optimal safety stock level, and (iii) proper determination of the safety stock levels is extremely important in Just-in-Time systems, which are susceptible to disruptions.