Optimal (s,S) policies for manufacturing systems of unreliable machines in tandem

This paper studies optimal (s,S) policies for production planning in manufacturing systems of unreliable machines in tandem. The manufacturing system produces one type of product. This type of manufacturing system occurs in many applications. In our study we assume that the inter-arrival time of a demand and processing time for one product in each machine are exponentially distributed. Each machine is unreliable and is subject to a sequence of repairing processes when it is broken down. The up time and the repairing time in each phase are assumed to be exponentially distributed. We study the manufacturing system by considering each machine as an individual system with random supply and demand. The Markov Modulated Poisson Process (MMPP) is used to model the random process of supply. For each machine, we obtain the approximated optimal (s,S) policies which minimizes the average running cost of its buffer