Bi-level programming for supplier selection under quantity discount policy

Document Type: Article


1 Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

2 Department of Industrial Management, Faculty of Management and Accounting, Shahid Beheshti University, G.C., Tehran, Iran

3 College of Management and Accounting, Allameh Tabataba'i University, Tehran, Iran


This paper proposes two models to formulate a Supplier Selection Problem (SSP) in a single-buyer, multi-supplier two-echelon supply chain network. The model coordinates order allocation and supplier selection problems under all-unit quantity discount policy. In this way, bi-level programming is employed to obtain two models: 1) The model with buyer as a leader; 2) The model with vendor as a leader. The resulted nonlinear
bi-level programming problems are hard to solve. Therefore, Particle Swarm Optimization (PSO) algorithm is used to deal with the complexity of the model and makes it solvable. Numerical results show that the proposed model is ecient for SSP in compliance with order allocation decision making.


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