Two-echelon supply chain with production disruption and controllable deterioration considering carbon emission under Stackelberg game approach

Department of Mathematics, Sidho-Kanho-Birsha University, Purulia, West Bengal 723104, India

^* Corresponding author: gcmahata.skbu@gmail.com, gourmahata@yahoo.co.in

Received: 30 November 2023
Accepted: 22 March 2024

Abstract

This paper considers a two-echelon supply chain consisting of a manufacturer and a retailer in which the manufacturer faces a random production disruption risk. The manufacturer replenishes the unproduced items to fulfil the retailer’s order from the secondary market at a higher price. To attract more customers, this paper considers a customer’s demand dependent on product selling price, stock level, and freshness level of the fresh items. Furthermore, this paper considers preservation technology investment (PTI) to mitigate the deterioration rate of the items and carbon tax regulation to curb down carbon emissions revealed from the supply chain activities. The Stackelberg game approach with a leader–follower relationship is used considering the manufacturer as a leader and the retailer as a follower. Several theorems are developed to illustrate the concavity of the profit function and to find out the optimal solutions in which the objective is to maximize the manufacturer’s total profit subject to the minimum total cost that the retailer is willing to incur. Several numerical examples are presented to illustrate the proposed models and the obtained results are compared for with and without carbon tax policy. Finally, sensitivity analysis with some key managerial insights is given to demonstrate the model. The results show that a product’s freshness level influences consumers’ decision to buy more, and that’s why the freshness level is an important competitive tool to increase sales as well as the supply chain’s total profit.