Production-Inventory Systems with Unreliable Machines

Abstract

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.

Cost and quality of service analysis of production systems based on the cumulative downtime

“…Typical questions addressed here regard lot and inventory sizing, layout design, and production and maintenance scheduling. For example, Berg (1994) presents a method for the computation of a number of shop-floor metrics, namely the servicelevel to customers expected, the inventory stocked, the machines and repairmen utilization, and the shutdown policies. The optimization of the preventive maintenance strategies is addressed in a large number of papers that have appeared during the recent years based on joint production and maintenance models and reliability theory, e.g., Rolstandas (1995), Yucesan (2000), Hong (2003), Ajodhya (2004) and Chelbi (2004).…”

A simulation optimisation approach for inventory management decision support based on incomplete information

“…They derive a closed form solution for the steady-state distribution of the inventory level and computed system performance measures. Berg, Posner, and Zhao (1994) extend the model of Posner and Berg (1989) in which only one machine is considered. They studied the performance of production systems that consist of a number of machines, each producing the same type of item and obtained the stationary distribution of the inventory process for different assumptions on the random behaviour of the production, demand and reliability processes.…”

Optimal Imperfect Production Inventory Model under Joint Effect of Machine Breakdowns and System Reliability

“…The first policy considers that the production of an interrupted lot will not be resumed after a breakdown (i.e., the no resumption or NR policy), while the second assumes that the production of an interrupted lot resumed immediately after production is restored and if the current on-hand inventory is below a certain threshold level (i.e., the abort-resume or AR policy). In the article [8],it was follows that a broad class of production-inventory systems 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.…”