Modeling and optimization of the multi-objective single-buyer multi-vendor integrated inventory problem with multiple quantity discounts

This paper deals with a multi-objective integrated inventory model to coordinate a two-stage supply chain including a single buyer and multiple vendors. the earlier work on the problem is limited to considering only one type of discount. this paper extends the problem under the multiple quantity discount environment. we try to minimize the system cost, number of defective items, number of late delivered items and maximize the total purchasing value. numerical examples are presented to provide some insights into the proposed model and di erent discount schemes. results obtained from sensitivity analysis show that changes in unit prices have a relatively large e ect on the objective function; as the upper bounds of discount intervals are reduced, the value of objective function decreases. it is also seen that the order quantity from the suppliers increases as the number of suppliers o ering all unit quantity discounts increases. in addition, we use a solution approach that is not used by previous studies on this problem, and the obtained results show that the de algorithm, proposed in this study, outperforms the pso proposed by kamali et al. [1] in both solution quality and computational time.