Inventory analysis of an unreliable production-inventory system

This paper deals with a production-inventory system in which there are a machine consisting of multiple unreliable units and a storage facility of fixed capacity. The product produced is stored in the storage facility. The demand process for product is a compound Poisson process. Assume that the demand-size distributions are arbitrary, and the unsatisfied demand is backlogged rather than lost. The main purpose of this paper is to prove an existence theorem on the stationary distribution of the slack capacity and to derive an expression of its stationary distribution function.