Suppliers ranking by cross-efficiency evaluation in the presence of volume discount offers

The performance of each supply chain is significantly related to the performance of the suppliers. Due to the multiple criteria nature of the supplier selection problem, data envelopment analysis (DEA), as a multiple criteria decision-making tool, seems to be an appropriate method. This paper specifically focuses on the supplier selection problem when the suppliers offer volume discounts to encourage the purchase of large volumes. However, in all the papers which deal with the volume discount concept in DEA models, each decision-making unit (DMU) is free to decide which outputs and inputs to emphasise that in turn cause to have many efficient DMUs. Therefore, the main purpose of this study is to use the cross-efficiency method when suppliers offer volume discounts. A numerical example demonstrates the application of the proposed method.