Analysis of a production-inventory system with unreliable production facility

The general purpose of this research is to incorporate the element of machine imperfection into production-inventory models. Most existing production-inventory models simply ignore the reliability factor, thereby tacitly assuming perfectly reliable systems. Machine failures, however, do occur and could be very disruptive-particularly in a highly automated production environment. In the model studied in this work, we consider a relatively simplified production situation: one machine, constant production rate, and a compound Poisson demand process for the product; but we superimpose the reliability feature comprising the machine failure process and the ensuing repair actions. For this situation we derive an explicit closed form solution for the steady-state distribution of the inventory level, and this result is then used to compute system performance indices of interest related to service levels to customers and machine utilization. Some numerical results demonstrate the effect of the reliability parameters on these performance indices.