A multi-objective quantity discount and joint optimization model for coordination of a single-buyer multi-vendor supply chain

Supply chain management is concerned with the coordination of different parts of the production system. Companies have realized that they must closely collaborate with the suppliers of their strategic components or products. Recently, developing integrated inventory models for the supplier selection problem has attracted a significant amount of attention amongst researchers. In these models some incentives are required from the vendors to motivate the buyer to change his (her) policies to the policy which is optimal for the entire system. Quantity discount policies are used as common incentives in the literature. However, the literature on this problem does not incorporate quantity discount into the coordination model. This paper develops a multi-objective mixed integer nonlinear programming model to coordinate the system of a single buyer and multiple vendors under an all-unit quantity discount policy for the vendors. Due to the complexity of the problem two well known meta-heuristic algorithms are proposed to solve the problem. An illustrative example is given to show the behavior of the model. Results obtained from solving the sample problems show good performance of the proposed algorithms in finding the optimal solutions.