Economic production quantity models for deteriorating/imperfect products and service with rework

•The paper considers a production system, which is not perfect, produces imperfect items.•The items are assumed to be deteriorated over time.•Two mathematical models considering different features of production and inventory are proposed.•Approximated optimal solutions are obtained.•Illustrative examples are provided for demonstrating the solution procedure.

In this paper, two economic production quantity (EPQ) models are proposed for deteriorating/imperfect items with rework process. The production process is imperfect, and imperfect quality items are reworked to become serviceable. At the same time, the remaining good quality items may deteriorate. The inspection of deteriorated items is also imperfect, so that deteriorated items may be sold to customers, which will create negative impact on corporate image. In the first model, a single production-rework plant system is considered. The optimal production times and the economic production quantities are obtained analytically. In the second model, a system that consists of n production plants and one rework plant is considered. A solution procedure is developed in order to obtain the optimal operating cost. Numerical examples are provided to compare the performance of the two systems.