Joint production and quality control in production systems with two customer classes and lost sales

This article considers a single-product, make-to-stock manufacturing system facing random demand from two customer classes with different quality cost and profit parameters. Each outgoing product is inspected and graded on the basis of quality. Each customer class can only be served from the inventory of products of certain quality grades, if any exist, and the system may reserve a fraction of the inventory of some quality grade for customers of a certain class. The problem is one of finding a product quality grading plan and production and inventory rationing policies to maximize the mean profit rate of the system. The structures of the optimal production and order admission control policy are investigated numerically for the case when a specific quality grading plan is used. Based on this investigation, some simple and efficient threshold-type control policies are proposed. From numerical results, it appears that the proposed approach of coordinated quality, production control, and inventory control achieves higher profit than other manufacturing practices, in which there is little or no coordination between the production and quality control departments.