A three-echelon supply chain coordination with quantity discounts for multiple items

This study derives an integrated model for three-echelon supply chain (i.e. single-supplier, single-vendor and multi-retailer) to minimise the joint costs of all participants associated with holding costs, ordering costs, and purchasing costs. We particularly emphasise that quantity discounts and joint replenishment policies can be utilised as coordination mechanisms among all parties. In addition, a linearisation approach and mixed integer method are developed not only to obtain an executable integer solution for a finite planning horizon problem but also to simplify the conventional multiple-step procedure used in the quantity discount. The result indicates that the coordination and consolidation of orders can lead to the total cost reduction. Finally, a numerical example is given to illustrate the benefits of orders coordination and consolidation.