Lot sizing with defective item under warehouse limitation and construction costs

The economic order quantity (EOQ) problem is one of the most common used models for the production planning and inventory control problems. A common and unrealistic assumption in these problems is considering prefect quality for all units. In this study, a multi-product EOQ model with imperfect items is proposed. In this system, all received products are not perfect, and imperfect items are scraped. Moreover, in this model the warehouse construction cost is considered as a part of inventory system costs. The objective of this study is to determine the optimal order quantity and reorder point of each product such that the total inventory cost is minimized. The proposed model is a development of a convex nonlinear programming problem therefore an exact algorithm is developed to solve this problem. Finally, to demonstrate the applicability of proposed procedure, a numerical problem is represented.