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

Abstract 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. Scope and purpose We investigate a production–inventory model under the assumptions that demand for the product is governed by a compound Poisson process, and the machine is subjected to random failures. A two-critical-number policy ( m, M ) is used to control a machine’s setups and shutdowns, namely, machine is shut down whenever the inventory level reaches M, and is resumed to operate only when the inventory level falls below the critical number m (m⩽M) . Our objective is to determine optimal control parameters which minimize system costs consisting of setup costs, inventory holding costs, and backorder costs. The problem arises in many practical situations. The results can be used by production planners to design new production systems or to reduce costs of existing systems.