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


1 Department of Industrial Engineering, Amirkabir University of Technology, 424 Hafez Avenue, 1591634311, Tehran, Iran

2 Department of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran


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 consider only one type of discount. This paper extends the problem under the multiple quantity discount environment. We try to minimize the system cost, the number of defective items, the number of late delivered items and maximize the total purchasing value. Numerical examples are presented to provide some insights about the proposed model and different discount schemes. Results obtained from sensitivity analysis show that changes in unit prices have a relatively large effect on the objective function and as the upper bounds of discount intervals are reduced, the value of objective function decreases. It also seen that the order quantity from the suppliers increases as the number of suppliers offering all unit quantity discount 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.