A Hybrid Mathematical and Decision-Making Model to Determine the Amount of Economic Order considering the Discount

Abstract

Suppliers are one of the most important parts of the supply chain, whose performance indirectly has a significant impact on customer satisfaction. Because customer demands are different from organizations, organizations have to consider different criteria for selecting their suppliers. In recent years, many studies in this field have been conducted using various criteria and methods. The main purpose defined in this research is to develop a model for simultaneous item ordering systems in real business conditions. In this research, a model is developed by considering the two objectives of minimizing overall costs and maximizing the amount of products ordered from different suppliers based on their weight value. Weights are calculated based on different criteria using the fuzzy analytic hierarchy process method for each supplier in different periods. Then, due to the multiobjective nature of the model, the proposed model has been solved by using the epsilon constraint in GAMS and nondominated sorting genetic algorithm II in MATLAB software. Considering the simultaneous order of inventory of multiproduct with several suppliers in several periods of time in discrete space with discount is one of the contributions of this research. To validate the proposed model, the results of the exact solution are compared with the meta-heuristic solution. Comparison results and assessment metrics indicate that the results of the proposed solution approach with an error of less than 1% had good performance. The results show that the system cost increases, by increasing the amount of discount, because of the increase in the amount of demand. Therefore, with a 30% increase in the discount, the system costs will increase to 36,496 units. Also, with a 20% reduction, the cost reduction will be reduced to 14,170 units.