Cooperative inventory games in multi-echelon supply chains under carbon tax policy: Vertical or horizontal?

This paper studies carbon tax policy in inventory games of multi-echelon supply chains. Four structures are considered with regard to the decision-making of supply chain mem-bers (decentralized, vertical downward cooperation, vertical upward cooperation, and hor-izontal cooperation). The purposes are to find the solutions of inventory games at each co-operation scheme, to compare strategies, and to examine the impact of the carbon tax on costs, emissions, and cooperation savings. A coordination mechanism with synchronized cycles is proposed, using cooperative game theory concepts in SC centralization. Closed-form equilibrium values were calculated for the optimal replenishment cycles, costs, and carbon emissions functions. For this intent, an algebraic method was deployed for vertical cooperation games. Though, other games were solved by an exact solution method. The numerical examples examined the impacts of the carbon tax on each structure and com -pared optimal solutions. Moreover, the impact of inventory and carbon emissions param-eters on the cost and carbon emissions savings from cooperation settings were evaluated, indicating that SCs can reduce both costs and carbon emissions through cooperation. Ad-ditionally, it was found that the carbon tax can reduce the level of carbon emissions, while simultaneously decreasing coalition costs and emissions savings. (c) 2021 Elsevier Inc. All rights reserved.