Using genetic algorithm approach to solve a multi-product EPQ model with defective items, rework, and constrained space

The Economic Production Quantity (EPQ) model is often used in the manufacturing sector to assist firms in determining the optimal production lot size that minimizes overall production-inventory costs. There are some assumptions in the EPQ model that restrict this model for real-world applications. Some of these assumptions are (1) infinite space of warehouse, (2) all of the produced items are perfect, and (3) only one type of goods is produced. In this paper, we develop the EPQ model by assuming that each produced lot contains some imperfect items and scraps. In addition, we have more than one kind of products along with warehouse space limitations. Under these conditions, we formulate the problem as a non-linear programming model and propose a genetic algorithm to solve it. At the end, we present a numerical example to illustrate the applications of the proposed methodology and identify the optimal value of the parameters of the genetic algorithm.