Equilibrium pricing, routing and order quantity decisions in a three-level supply chain

Document Type : Research Paper


1 Department of Industrial Engineering, KHATAM University, Tehran, Iran

2 Department of Industrial Engineering, K. N. Toosi University of Technology, Tehran, Iran


In this paper, a supply chain, including a manufacturer, a distributor and some retailers, is considered. The manufacturer produces a single product and outsources distribution operations to a distributor in order to deliver products demanded by retailers. Each retailer has a time window to receive the products and faces the Newsvendor problem with stochastic demand. The manufacturer aims to serve retailers providing that the maximum lateness doesn’t exceed a predetermined value. All players in the supply chain are willing to maximize their own profit. The model simultaneously includes pricing, order quantity and routing decisions. First, the manufacturer announces the whole sale price, then the distributor declares the unit transportation cost to the retailers, and finally each retailer decides on the amount of his order quantity. The profit functions of the players are formulated and linearized; then the solution is determined in three stages using game theory. Finally, a numerical example is presented and the equilibrium decisions of the players are determined using GAMS software.


Main Subjects

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  • Receive Date: 29 June 2019
  • Revise Date: 07 August 2019
  • Accept Date: 13 August 2019
  • First Publish Date: 24 October 2019