Solving a deterministic multi-product single-machine EPQ model with partial backordering, scrapped products and rework

In this paper, an economic production quantity (EPQ) inventory model with scrap and rework is developed. The inventory model is for multiple products and all products are manufactured in a single machine. Clearly, the existence of one machine results in limited production capacity and thus in shortages. Therefore, shortages are permitted and partially backordered. We show that the model of the problem is a constrained non-linear program and use the GAMS modelling language to solve it. Our objective is to minimize the joint total cost of the system and the supply cost of the warehouse space, subject to capacity, service level, and budget and warehouse space constraints. Subsequently, a nonlinear programming solver BARON is used to solve the model. At the end, a numerical example is provided to demonstrate the applicability of the model to real-world manufacturing problems. To verify the solution obtained and to evaluate the performance of MCDM (Multi-Criteria Decision Making) methods, a TUKEY test is employed to compare the means of the primary objective values, the mean values of the second objective, and the mean of the CPU time needed for solving the problem using various methods of MCDM. Also, to compare the methods, we used the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution). The results show that the Torabi-Hasini method is the most efficient method to solve the model and the solving capacities of the methods differ significantly. Finally, some conclusions and future research are discussed.