Markovian approximation for manufacturing systems of unreliable machines in tandem

This paper studies production planning of manufacturing systems of unreliable machines in tandem. The manufacturing system considered here produces one type of product. The demand is assumed to be a Poisson process and the processing time for one unit of product in each machine is exponentially distributed. A broken machine is subject to a sequence of repairing processes. 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 stochastic supply and demand. The Markov Modulated Poisson Process (MMPP) is applied to model the process of supply. Numerical examples are given to demonstrate the accuracy of the proposed method. We employ (s, S) policy as production control. Fast algorithms are presented to solve the average running costs of the machine system for a given (s, S) policy and hence the approximated optimal (s, S) policy.