Analysis of a production–inventory system with machine breakdowns and shutdowns

This paper deals with a production–inventory system which consists of an unreliable machine and a storage. A two-critical-number policy is used to control a machine's setups or shutdowns. Apart from the intentional shutdowns, the machine is subjected to random failures which must be repaired to make it operational again. The demand process for a product is a compound Poisson process. We assume that the demand-size distributions are arbitrary and unsatisfied demand is backlogged rather than lost. We first present a reasonable condition to ensure the existence of the steady-state distribution of the inventory process, and then derive an expression of steady-state distribution. Based on it, we further obtain a cost expression for a special case of the exponentially distributed demand sizes. Finally, the numerical results reveal some relations between the optimal policy parameters and the system's parameters.