Production inventory model with reworking of imperfect production, scrap and shortages

Abstract

In traditional inventory models such as the economic order quantity and the economic production quantity models, the sole objective is to minimize the total inventory-related costs, typically the holding cost and the ordering cost. These models do not consider the presence of defective products in the lot or reworking them. In an imperfect manufacturing process, the defective items are produced with the finished goods. The rework process is necessary to convert those defective items into finished goods. This paper develops a production inventory model with planned backorders for determining the optimum quantity for a single product manufactured in a single stage manufacturing system that generates imperfect quality products where a proportion of the defective products are reworked in the same cycle. Additionally, a range of real values for the proportion of defective products for which there is an optimal solution is established, and a closed form for the total cost of the inventory system is obtained. To achieve this objective, a suitable mathematical model is developed and the optimal production lot size that minimises the total cost is derived. The relevant model is built and solved, and necessary and sufficient conditions for a unique and globally optimal solution are derived. Illustrative examples are provided and numerically verified. For validation of the results, this model was coded in Microsoft® Visual Basic 6.0.