The Optimal Production and Quality Policy for the Vendor in a Trade

摘要

Arranging an inspection schedule for the production process or taking inspection or burn-in to screen out defective items before items are shipped are three techniques that are widely used by the vendor in a production lot such that the defective percentage in an outgoing batch satisfies the purchaser's acceptable quality limit (AQL) specified in the contract between them. Due to the costs of inspection and restoration for production process, two types of inspection error, and high cost of burn-in, how to utilize these three techniques simultaneously such that the outgoing batch satisfies AQL with low cost is a challenge of the vendor. The main purpose of this paper is to investigate the optimal inspection schedule and the optimal mixed policy of inspection and burn-in. More specifically, by using the criterion of maximizing the expected profit that the vendor makes in this trade, a nonlinear programming is built to determine (a) the number of inspections undertaken in the production process, (b) the times at which the production process is inspected, (c) the total number of items that the vendor should produce (or the production run time), (d) a certain proportion of items should be inspected, some others should be put in burn-in, and the remaining items will receive no treatment, and (e) the optimal burn-in time.