Economic production quantity in an imperfect manufacturing process with synchronous and asynchronous flexible rework rates

We present inventory models to schedule an imperfect manufacturing process where a proportion of the items are defective. The proportion is known; and the production is followed by a 100% inspection. The manufacturer implements a rework strategy to rectify the defective items. Since the rework can be implemented on a number of plans, a flexible rework rate is presented. The flexible rework offers the manufacturer the selection of the rework rate, which can be different from the production rate, and also the selection of the rework process itself, which can be asynchronous and synchronous. Under the asynchronous rework, the defective items are kept until the completion of the production lot; while, under the synchronous rework, the defective items are reworked as soon as they are produced. A linear rework cost function of the rework rate is assumed. The objective of this paper is to develop mathematical models to determine the optimal lot sizes and backorders for different assumptions about the rework rate and the rework process. It has been proven that the rework strategy and the rework rate influence the lot size and the backorder, especially for large values of the defective proportion.