Supply Chain Vertical and Horizontal Cooperation for Carbon Emission Reduction Considering Bullwhip Effect under the Carbon Tax Scheme

Considering the bullwhip effect, in a two-echelon supply chain consisting of one single supplier and multiple retailers, the vertical and horizontal cooperation game for carbon emission reduction is analyzed under carbon tax scheme. This paper investigates four different decision models: decentralized decision, vertical cooperation, horizontal cooperation and vertical and horizontal cooperation. After analyzing and comparing the optimal solutions of different models, it is found that the vertical and horizontal cooperation is always a dominant strategy for the supply chain in terms of both of cost and carbon emissions. Then, the collaborative condition of the vertical and horizontal cooperation game is analyzed. The result shows that the higher the fixed construction cost of warehouse is, the stronger the cooperation motivation of supply chain members is. However, the higher carbon tax rate will hinder the cooperation and bring greater carbon emissions. Furthermore, a cost allocation scheme is proposed based on proportion rule to achieve Pareto improvement for supplier and retailers. Although the vertical and horizontal cooperation cost game is not necessarily concave, it is permutationally concave game.