Solving a deterministic multi product single machine EPQ model withpartial 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 shortages. Therefore, shortages are permitted and partially backordered. We show that the model of the problem is a constrained non-linear program and use GAMS modelling language to solve it. Our objectiveis to minimize the joint total cost of the system and the supply cost of warehouse space, subject to capacity, service level, budget and warehouse space constraints. Subsequently, a nonlinear programming solver BARON is used to solve the model. At the end, numerical examples are provided to demonstrate the applicability of the model in real-world manufacturing problems.To verify the solution obtained and to evaluate the performance of MCDM (Multi Criteria Decision Making) methods , TUKEY test is employed to compare the means of the primary objective values, the mean values of the second objective , and the mean needed CPU time of solving the problem using various methods of MCDM. Also, To compare the methods we used TOPSIS (Technique for Order Preference by Similarity to Ideal Solution). The results show that torabi-hasini method is the most efficient method to solve the model and the solution qualities of the methods differ significantly. Finally, some conclusions and future researches are included.