Simultaneous determination of the optimal production–inventory and product inspection policies for a deteriorating production system

Abstract

In this paper, we attempt to find a method for the optimization of production–inventory and product inspection policies for deteriorating production systems. Taking advantage of the nature of a deteriorating production system, a strategy would be not to inspect the first s items of the batch. Therefore, an inspection policy which disregards the first s (DTF-s) items of the batch is proposed. Under the DTF-s policy, we do not inspect the first s produced items but inspect only those items from the (s+1)th till the end of the production run. The objective of this study was the joint determination of the production lot size and the inspection policy s, resulting in a minimization of the expected average cost per unit time. Based on this model, the underlying conditions necessary for the existence of an optimal policy are given. Two commonly used inspection strategies, no inspection and full inspection are discussed. Under both inspection strategies, an optimal production–inventory lot is bounded by the traditional economic quantity. The case of full inspection is shown to be an extension of previously reported results. The option of investing in the process of quality improvement is also discussed. Finally, numerical examples are given to illustrate the method and its advantages in the conclusion. Scope and purposeThis paper considers the relationship between production, inventory and inspection in a deteriorating production system which may transit from the “in-control” state to the “out-of-control” state after a period of operation. Once the transition to the “out-of-control” state has occurred, it is assumed that some percentage of the items produced are defective or of substandard quality. However, in many cases, defects in a defective item can only be identified by an inspection process which carries an inspection cost. Those inspected items which are found to be defective are reworked at some cost before being shipped. On the other hand, defective items which are not inspected will be passed to the customer, incurring a much larger warranty cost. In order to operate such a system economically, tradeoffs among production setup, inventory, inspection and defective cost must be analyzed. Deterioration of the production system is an inherent process in all manufacturing industries. An understanding of the relationship among production, inventory and inspection for such systems will help managers to maintain efficient and economic control of operations.