Supply chain optimization policy for a supplier selection problem: a mathematical programming approach

Most supplier selection models consider the buyer’s viewpoint and maximize only the buyer’s profit. This does not necessarily lead to an optimal situation for all the members of a supply chain. Coordination models have been developed to optimize the entire supply chain and align the decisions between its entities. Little research has been done on the application of these models in the supplier selection problem. Here, a combination of a supplier selection model and a co-ordination model in a centralized supply chain is considered. In the proposed model, the buyer selects the right supplier and order an appropriate quantity. The suppliers split the buyer ordered quantities into small lot sizes and deliver them over multiple periods. The objective function is to minimize the total cost of the supply chain. A nonlinear mathematical model is proposed for the problem. The total cost of the supply chain includes the costs of the buyer and the suppliers. The nonlinear model is transformed into a concave minimization problem and solved by considering the specific characteristics of the problem. Finally, the proposed model is illustrated by a numerical example.