On a production-inventory model for deteriorating items subject to an imperfect process

This paper considers a production-inventory model for deteriorating items subject to an imperfect production process. A product is to be manufactured in cycles on a system that is assumed to be in an in-control state at the beginning of a production run. The demand rate of the product is assumed to be fairly stable and known. For each production cycle, the production is run for a predetermined amount of time during which items produced are used to meet the demand and to build inventories. Items produced in this state are subject to a constant rate of deterioration. After a production run is completed, the system will be kept idle until all on-hand inventories are depleted. Since no shortages are allowed, a new production run will begin only when the inventory level reaches to zero. During a production run, the production system may shift at random from an in-control state to an out-of-control state. Subsequently, items produced in the out-of-control state are subject to a higher deterioration rate than those units produced during the in-control state. The objective of the model is to determine a production uptime so as to minimize the expected total cost per unit time including the setup, the inventory holding, and the deterioration cost. The time-to-shift of the productions system and the time-to-deterioration of an item are assumed to be exponentially distributed. A closed-form solution of a near optimal production uptime is derived.