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

Li-E Yu

Ekoloji, 2019, Issue 107, Pages: 813-828, Article No: e107096


Download Full Text (PDF)


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.


carbon emission reduction, vertical and horizontal cooperation, bullwhip effect, cost allocation scheme


  • Akshit S, Nishikant MI, Syed A, Nagesh S, Ravi S (2015) Cloud computing technology: Reducing carbon footprint in beef supply chain. Int. J. Prod. Econ. 164: 462-471.
  • Bonney M, Jaber MY (2011) Environmentally responsible inventory models: non-classical models for a non-classical era. Int. J. Prod. Econ. 133: 43-53.
  • Bouchery Y, Ghaffari A, Jemai Z, Dallery Y (2012) Including sustainability criteria into inventory models. Eur. J. Oper. Res. 222: 229-240.
  • Barari S, Agarwal G, Zhang WJ, Mahanty B, Tiwari MK (2012) A decision framework for the analysis of green supply chain contracts: an evolutionary game approach. Expert Syst. Appl. 39: 2965-2976.
  • Battini D, Persona A, Sgarbossa F (2014) A sustainable EOQ model: theoretical formulation and applications. Int. J. Prod. Econ. 149: 145-153.
  • Bazan E, Jaber MY, Zanoni S (2015) Supply chain models with greenhouse gases emissions, energy usage and different coordination decisions. Appl. Math. Model. 138: 5131-5151.
  • Chen X, Benjaafar S, Elomri A (2013) The carbon-constrained EOQ. Eur. J. Oper. Res. 41: 172–179.
  • Cao J, Zhang XM, Zhou GG (2015) Supply chain coordination with revenue-sharing contracts considering carbon emissions and governmental policy making. Environ. Prog. Sustain. Energy 35: 479-488.
  • Cheng YW, Mu D, Zhang Y (2017) Mixed carbon policies based on cooperation of carbon emission reduction in supply chain. Discrete Dyn. Nat. Soc. 2017: 4379124.
  • Driessen Th (1988) On cores of subconvex games and permutationally convex games. Methods Oper. Res. 60: 313–323.
  • Disney SM, Farasyn I, Lambrecht M, Towill DR, Velde WV (2006) Taming the bullwhip effect whilst watching customer service in a single supply chain echelon. Eur. J. Oper. Res. 173: 151–172.
  • Dincer K, Brian S (2014) Integrated inventory control and transportation decisions under carbon emissions regulations: LTL vs. TL carriers. Transp. Res. E 68: 14-38.
  • Du SF, Zhu JA, Jiao HF, Ye WY (2015) Game-theoretical analysis for supply chain with consumer preference to low carbon. J. Prod. Res. 53: 3753-3768.
  • Devika K, Jafarian A, Hassanzadeh A, Khodaverdi R (2016) Optimizing of bullwhip effect and net stock amplification in three-echelon supply chains using evolutionary multi-objective meta heuristics. Ann. Oper. Res. 242: 457–487.
  • Dai R, Zhang JX, Tang WS (2017) Cartelization or cost-sharing? Comparison of cooperation modes in a green supply chain. J. Clean. Prod. 156: 159-173.
  • Dong HJ, Dai HC, Geng Y, Fujita T, Liu Z, Xie Y, Wu R (2017) Exploring impact of carbon tax on China’s CO2 reductions and provincial disparities. Renew. Sust. Energ. Rev. 77: 596-603.
  • Elena PB, Angel AJ, Javier F, Barry BB (2015) Horizontal cooperation in road transportation: a case illustrating savings in distances and greenhouse gas emissions. Int. Trans. Oper. Res. 22: 585–606.
  • Granot D, Huberman G (1982) The relationship between convex games and minimum cost spanning tree games: a case for permutationally convex games. SIAM J. Algebra Discrete Methods. 3: 288–292.
  • Ghosh D, Shah J (2012) A comparative analysis of greening policies across supply chain structures. Int. J. Prod. Econ. 135: 568-583.
  • Gao J, Zhou WL (2015) Coordinating supply chains to reduce carbon emissions that of a retailer and a supplier. Environ. Eng. Manag. J. 14: 1857-1863.
  • Ghosh D, Shah J (2015) Supply chain analysis under green sensitive consumer demand and cost sharing contract. Int. J. Prod. Econ. 164: 319-329.
  • Harris FW (1913) How many parts to make at once. Management. 10, 135–136: 152.
  • Hua G, Cheng TCE, Wang S (2011) Managing carbon footprints in inventory management. Int. J. Prod. Econ. 132: 178-185.
  • He P, Zhang W, Xu XY, Bian YW (2015) Production lot-sizing and carbon emissions under cap-and-trade and carbon tax regulations. J. Clean. Prod. 103: 241-248.
  • He LF, Zhao DZ, Xia LJ (2015) Game theoretic analysis of carbon emission abatement in fashion supply chains considering vertical incentives and channel structures. Sustainability 7: 4280-4309.
  • Jira C, Toffel MW (2013) Engaging supply chains in climate change. Manuf. Serv. Oper. Manag. 15: 559–577.
  • Judith T, Michela C, Richard JB (2013) Cooperation and game-theoretic cost allocation in stochastic inventory models with continuous review. Eur. J. Oper. Res. 231: 567–576.
  • Kuo TC, Hong IH, Lin SC (2016) Do carbon taxes work? Analysis of government policies and enterprise strategies in equilibrium. J. Clean. Prod. 139: 337-346.
  • Lou GX, Xia HY, Zhang JQ (2015) Investment strategy of emission-reduction technology in a supply chain. Sustainability. 7: 10684-10708.
  • Li H, Wang CX, Shang M, Ou W (2017) Pricing, carbon emission reduction, low-carbon promotion and returning decision in a closed-loop supply chain under vertical and horizontal cooperation. Int. J. Environ. Res. Public Health. 14: 1332.
  • Meca A, Jimmer J, Garcia-Jurado I, Borm P (2004) Inventory games. Eur. J. Oper. Res. 156: 127-139.
  • Presley K, Wesseh J, Lin BQ, Atsagli P (2017) Carbon taxes, industrial production, welfare and the environment. Energy. 123: 305-313.
  • Rivers N, Schaufele B (2015) Salience of carbon taxes in the gasoline market. J. Environ. Econ. Manag. 74: 23-36.
  • Vincent H, Laurent B (2015) The carbon-constrained EOQ model with carbon emission dependent demand. Int. J. Prod. Econ. 164: 285-291.
  • Wahab MIM, Mamun SMH, Ongkunaruk P (2011) EOQ models for a coordinated two-level international supply chain considering imperfect items and environmental impact. Int. J. Prod. Econ. 134: 151-158.
  • Wei J, Zhao J, Li YJ (2015) Price and warranty period decisions for complementary products with horizontal firms’ cooperation/noncooperation strategies. J. Clean. Prod. 105: 86-102.
  • Wang QP, Zhao DZ, He LF (2016) Contracting emission reduction for supply chains considering market low-carbon preference. J. Clean. Prod. 120: 72-84.
  • Yang L, Zheng CS, Xu MH (2014) Comparisons of low carbon policies in supply chain coordination. J. Syst. Sci. Syst. Eng. 23: 342-361.
  • Yang L, Zhang Q, Ji JN (2017) Pricing and carbon emission reduction decisions in supply chains with vertical and horizontal cooperation. Int. J. Prod. Econ. 191: 286–297.
  • Zhang CT, Liu LP (2013) Research on coordination mechanism in three-level green supply chain under non-cooperative game. Appl. Math. Model. 37: 3369-3379.