Production-Inventory Systems with Unreliable Machines

A broad class of production-inventory systems is studied in which a number of producing machines are susceptible to failure following which they must be repaired to make them operative again. The machines' production can also be stopped deliberately due to stocking capacity limitations or any other relevant considerations. The interplay between the processes involved, namely, production, demand, and failure/repair or reliability, in conjunction with the shutdown policy used, determine the inventory accumulation process and possible shortages. We first obtain the stationary distribution of the inventory process for different assumptions on the random behavior of the production, demand, and reliability processes. By employing level-crossing techniques, a mathematical analysis is carried out for a "core" model, which then serves the role of the nucleus for the study of a wide range of models. We compute performance measures that characterize the operation of the production-inventory system with respect to its service-level to customers, expected inventory stocked, machines' utilization, repairmen utilization, and so on. A numerical illustration is provided which shows the effect of machine breakdowns on service and inventory levels.