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

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