Integrated production–inventory models for imperfect production processes under inspection schedules

This paper deals with inventory models that unify the inventory problems of raw materials and finished products for a single product imperfect manufacturing system. The product is manufactured in batches, and raw materials are jointly replenished from outside suppliers. The system is assumed to deteriorate during the production process. As a result, some proportion of defective items is produced. The defective items are reworked at some cost either before or after a sale. Periodic inspections at equally spaced times and restorations of the production process are used to operate the system. The objective is to minimize the expected total cost for the system. A solution procedure is developed to find a near optimal solution for the basic model. The analysis is extended to various cases where the defect rate is a function of the set-up cost, the proportion of defective items is not constant, or the inventory system has a limited capacity for raw materials.