考虑碳税和产品绿色度的闭环供应链网络Nash博弈均衡模型
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摘要
随着全球气候变暖的逐渐加剧和部分资源日渐枯竭,减少碳排放并促进资源的循环利用已成为世界范围内共同关注的热点议题之一,多数国家对温室气体排放采取了多种形式的限制措施,其中碳税是较为常见的政府政策。考虑到制造企业的生产与再制造活动是碳排放的重要来源,为应对碳税政策,制造商可对产品进行低碳技术投资来提升产品的绿色度水平。通常产品绿色度水平越高,则单位产品的碳排放量越低。故在此背景下,企业如何在增加的投资额与降低的碳排放量之间进行权衡,进而得出最优的生产/再制造与定价策略是其面临的重要决策问题。本文以变分不等式、互补理论和拉格朗日对偶理论为基础,在考虑闭环供应链网络同类成员竞争的基础上,结合制造商在产品设计过程中的绿色度决策,在政府碳税和补贴政策下建立了消费者具有低碳偏好的闭环供应链网络均衡模型。结合变分不等式的修正投影收缩算法,设计了模型求解程序。在数值算例中,分析了政府碳税和补贴、回收比例因子以及消费者低碳偏好的变化对产品绿色度决策、产量与价格决策以及企业利润的影响,进而给出相应的管理学启示。结果表明:政府一方面需合理选择补贴力度,补贴过低无法充分发挥该机制的作用,而补贴过高又影响政策效果;另一方面,政府应引导企业将回收比例设置在合理区间内,具体应结合再制造成本节约水平与产品的绿色度水平综合选取。碳税机制是一种值得推广的碳减排机制,可促使企业选择低碳生产技术减少碳排放量并使利润略有增加。尽管制造商利润随消费者低碳意识的提高而略有改善,但其更应依靠政府等外部力量来提升消费者的低碳偏好意识。本文所得结论对低碳供应链研究和政府政策设计具有一定的借鉴意义。
With the further worsening of global warming,and decreasing of some exhausting resources,reducing carbon emission and promoting resources recycling have become one of the hot issues from the world-wide scope. The majority of the countries have taken several restricted measures on the greenhouse gases,in which carbon tax is the common policies used by different government.Considering that the manufacturing and remanufacturing of production enterprises is the main source of carbon emission, the manufacturers can improve the degree of greenness for the products via investing on the low-carbon technology. In general,the higher the degree of greenness for products,the lower carbon emissions of one product. Therefore,how to balance the increase of investment and the reduction of carbon emissions,and then arrive at the optimal production,and thus to obtain the optimal strategy for the manufacturing,remanufacturing and pricing becomes the significant decision problem for the enterprises. Based on variational inequality( VI),complement theory and Lagrangian dual theory,and considering the competition between same type of the players on the supply chain network and the manufacturers' decision for the degree of greenness during the product design,we established the closed-loop supply chain network equilibrium with consumers' low-carbon preference under the carbon tax and subsidy policies of government. Furthermore,we designed the solution algorithm based on the modified projection and contraction algorithm of VI. We analyzed the impact of carbon tax and subsidies of government,recycling ratio and consumer preference for low-carbon products on the decision for the degree of product greenness,decision for production capacity and pricing,and the profit of enterprises,and further summarized the corresponding insights of the management. Several results go as follows. Firstly,on the one hand,government should set the reasonable subsidy extent because the lower and higher subsidy can both prevent the effect of the policy. On the other hand,government should provide some guidance( e. g.,combining the level of cost reduction during remanufacturing and product green degree) for the enterprises when they set the recycling ratio so that the ratio can be within the reasonable interval. Secondly,the carbon tax is a good mechanism for the carbon reduction deserved to be spread,which can render the enterprises to choose the production technologies with low-carbon emission and can improve their profits slightly. Lastly,although the profit of the enterprises can be improved with the increasing of consumer's low-carbon consciousness,this consciousness should be promoted via the external power,e. g.,the government. Results in this paper can provide some reference for the research of low-carbon supply chain and the design of government policy.
With the further worsening of global warming,and decreasing of some exhausting resources,reducing carbon emission and promoting resources recycling have become one of the hot issues from the world-wide scope. The majority of the countries have taken several restricted measures on the greenhouse gases,in which carbon tax is the common policies used by different government.Considering that the manufacturing and remanufacturing of production enterprises is the main source of carbon emission, the manufacturers can improve the degree of greenness for the products via investing on the low-carbon technology. In general,the higher the degree of greenness for products,the lower carbon emissions of one product. Therefore,how to balance the increase of investment and the reduction of carbon emissions,and then arrive at the optimal production,and thus to obtain the optimal strategy for the manufacturing,remanufacturing and pricing becomes the significant decision problem for the enterprises. Based on variational inequality( VI),complement theory and Lagrangian dual theory,and considering the competition between same type of the players on the supply chain network and the manufacturers' decision for the degree of greenness during the product design,we established the closed-loop supply chain network equilibrium with consumers' low-carbon preference under the carbon tax and subsidy policies of government. Furthermore,we designed the solution algorithm based on the modified projection and contraction algorithm of VI. We analyzed the impact of carbon tax and subsidies of government,recycling ratio and consumer preference for low-carbon products on the decision for the degree of product greenness,decision for production capacity and pricing,and the profit of enterprises,and further summarized the corresponding insights of the management. Several results go as follows. Firstly,on the one hand,government should set the reasonable subsidy extent because the lower and higher subsidy can both prevent the effect of the policy. On the other hand,government should provide some guidance( e. g.,combining the level of cost reduction during remanufacturing and product green degree) for the enterprises when they set the recycling ratio so that the ratio can be within the reasonable interval. Secondly,the carbon tax is a good mechanism for the carbon reduction deserved to be spread,which can render the enterprises to choose the production technologies with low-carbon emission and can improve their profits slightly. Lastly,although the profit of the enterprises can be improved with the increasing of consumer's low-carbon consciousness,this consciousness should be promoted via the external power,e. g.,the government. Results in this paper can provide some reference for the research of low-carbon supply chain and the design of government policy.
引文
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[15]高举红,韩红帅,侯丽婷,等.考虑产品绿色度和销售努力的零售商主导型闭环供应链决策研究[J].管理评论,2015,27(4):187-196.
[16]XI S,LEE C.A game theoretic approach for the optimal investment decisions of green innovation in a manufacturer-retailer supply chain[J].International journal of industrial engineering,2015,22(1):147-158.
[17]石平,颜波,石松.考虑公平的绿色供应链定价与产品绿色度决策[J].系统工程理论与实践,2016,36(8):1937-1950.
[18]DRAKE D,KLEINDORFER P R,WASSENHOVE L N V.Technology choice and capacity portfolios under emissions regulation[J].Production and operations management,2016,25(6):1006-1025.
[19]WANG Q,ZHAO D,HE L.Contracting emission reduction for supply chains considering market low-carbon preference[J].Journal of cleaner production,2016,120:72-84.
[20]JI J N,ZHANG Z Y,YANG L.Carbon emission reduction decisions in the retail-/dual-channel supply chain with consumer’preference[J].Journal of cleaner production,2017,141:852-867.
[21]HAMMAMI R,NOUIRA I,FREIN Y.Effects of customers’environmental awareness and environmental regulations on the emission intensity and price of a product[J].Decision sciences,2017(21).DOI:10.111/deci.12302.
[22]NAGURNEY A,DONG J,ZHANG D.A supply chain network equilibrium model[J].Transportation research:part E,2002,38(5):281-303.
[23]HAMMOND D,BEULLENS P.Closed-loop supply chain network equilibrium under legislation[J].European journal of operational research,2007,183(2):895-908.
[24]YANG G F,WANG Z P,LI X Q.The optimization of the closedloop supply chain network[J].Transportation research:part E,2009,45(1):16-28.
[25]QIANG Q,KE K,ANDERSON T,et al.The closed-loop supply chain network with competition,distribution channel investment,and uncertainties[J].Omega,2013,41(2):186-194.
[26]NAGURNEY A,CRUZ J,DONG J,et al.Supply chain networks,electronic commerce,and supply side and demand side risk[J].European journal of operational research,2005,164(2):120-142.
[27]张桂涛,胡劲松,王磊,等.考虑消费者渠道偏好的多期闭环供应链网络均衡[J].系统工程理论与实践,2016,36(2):347-362.
[28]胡劲松,徐元吉,刘芳霞,等.具有模糊需求的多商品流供应链网络均衡研究[J].控制与决策,2012,27(5):665-672.
[29]ZHANG G T,ZHONG Y G,SUN H,et al.Multi-period closedloop supply chain network equilibrium with carbon emission constraints[J].Resources,conservation&recycling,2015,104(B):354-365.
[30]MITRA S,WEBSTER C.Competition in remanufacturing and the effect of government subsidies[J].International journal of production economics,2008,111(1):287-298.
[31]QIAN G Q.The closed-loop supply chain network with competition and design for remanufactureability[J].Journal of cleaner production,2015,105:348-356.
[32]王文宾,邓雯雯,白拓,等.碳排放约束下制造商竞争的逆向供应链政府奖惩机制研究[J].管理工程学报,2016,30(2):188-194.
[33]张桂涛,胡劲松,孙浩,等.考虑产品寿命次数的多期闭环供应链网络均衡[J].信息与控制,2015,44(1):29-37.
[34]HE B S,XU Y,YUAN X M.A logarithmic-quadratic proximal prediction-correction method for structured monotone variational inequalities[J].Computational optimization and applications,2006,35(1):19-46.
[2]DU S F,HU L,SONG M.Production optimization considering environmental preference and preference in the cap-and-trade system[J].Journal of cleaner production,2016,112(20):1600-1607.
[3]BENJAAFAR S,LI Y,DASKIN M.Carbon footprint and the management of supply chains:insights from simple models[J].IEEEtransactions on automatic science and engineering,2013,10(1):99-116.
[4]栾晏.发达国家和发展中国家能源消费与碳排放控制研究[D].长春:吉林大学,2015.
[5]KUO T C,HONG I H,LIN S C.Do carbon taxes work?analysis of government policies and enterprise strategies in equilibrium[J].Journal of cleaner production,2016,139(20):337-346.
[6]张博,徐承红.开征碳税的条件及碳税的动态调整[J].中国人口·资源与环境,2013,23(6):16-20.
[7]熊中楷,张盼,郭年.供应链中碳税和消费者低碳意识对碳排放影响[J].系统工程理论与实践,2014,34(9):2245-2252.
[8]LIU B Y,HOLMBOM M,SEGERSEDT A,et al.Effects of carbon emission regulations on remanufacturing decisions with limited information of demand distribution[J].International journal of production research,2015,53(2):532-548.
[9]杨惠霄,骆建文.碳税政策下的供应链减排决策研究[J].系统工程理论与实践,2016,36(12):3092-3102.
[10]MIAO Z,MAO H,FU K,et al.Remanufacturing with trade-ins under carbon regulations[J].Computers&operations research,2018,89:253-268.
[11]MA X,HO W,JI P,et al.Coordinated pricing analysis with the carbon tax scheme in a supply chain[J].Decision sciences,2017.
[12]朱庆华,窦一杰.基于政府补贴分析的绿色供应链管理博弈模型[J].管理科学学报,2011,14(6):86-95.
[13]LIU Z L,ANDERSON T D,CRUZ J M.Consumer environmental awareness and competition in two-stage supply chains[J].European journal of operational research,2012,218(3):602-613.
[14]江世英,李随成.考虑产品绿色度的绿色供应链博弈模型及收益共享契约[J].中国管理科学,2015,23(6):169-176.
[15]高举红,韩红帅,侯丽婷,等.考虑产品绿色度和销售努力的零售商主导型闭环供应链决策研究[J].管理评论,2015,27(4):187-196.
[16]XI S,LEE C.A game theoretic approach for the optimal investment decisions of green innovation in a manufacturer-retailer supply chain[J].International journal of industrial engineering,2015,22(1):147-158.
[17]石平,颜波,石松.考虑公平的绿色供应链定价与产品绿色度决策[J].系统工程理论与实践,2016,36(8):1937-1950.
[18]DRAKE D,KLEINDORFER P R,WASSENHOVE L N V.Technology choice and capacity portfolios under emissions regulation[J].Production and operations management,2016,25(6):1006-1025.
[19]WANG Q,ZHAO D,HE L.Contracting emission reduction for supply chains considering market low-carbon preference[J].Journal of cleaner production,2016,120:72-84.
[20]JI J N,ZHANG Z Y,YANG L.Carbon emission reduction decisions in the retail-/dual-channel supply chain with consumer’preference[J].Journal of cleaner production,2017,141:852-867.
[21]HAMMAMI R,NOUIRA I,FREIN Y.Effects of customers’environmental awareness and environmental regulations on the emission intensity and price of a product[J].Decision sciences,2017(21).DOI:10.111/deci.12302.
[22]NAGURNEY A,DONG J,ZHANG D.A supply chain network equilibrium model[J].Transportation research:part E,2002,38(5):281-303.
[23]HAMMOND D,BEULLENS P.Closed-loop supply chain network equilibrium under legislation[J].European journal of operational research,2007,183(2):895-908.
[24]YANG G F,WANG Z P,LI X Q.The optimization of the closedloop supply chain network[J].Transportation research:part E,2009,45(1):16-28.
[25]QIANG Q,KE K,ANDERSON T,et al.The closed-loop supply chain network with competition,distribution channel investment,and uncertainties[J].Omega,2013,41(2):186-194.
[26]NAGURNEY A,CRUZ J,DONG J,et al.Supply chain networks,electronic commerce,and supply side and demand side risk[J].European journal of operational research,2005,164(2):120-142.
[27]张桂涛,胡劲松,王磊,等.考虑消费者渠道偏好的多期闭环供应链网络均衡[J].系统工程理论与实践,2016,36(2):347-362.
[28]胡劲松,徐元吉,刘芳霞,等.具有模糊需求的多商品流供应链网络均衡研究[J].控制与决策,2012,27(5):665-672.
[29]ZHANG G T,ZHONG Y G,SUN H,et al.Multi-period closedloop supply chain network equilibrium with carbon emission constraints[J].Resources,conservation&recycling,2015,104(B):354-365.
[30]MITRA S,WEBSTER C.Competition in remanufacturing and the effect of government subsidies[J].International journal of production economics,2008,111(1):287-298.
[31]QIAN G Q.The closed-loop supply chain network with competition and design for remanufactureability[J].Journal of cleaner production,2015,105:348-356.
[32]王文宾,邓雯雯,白拓,等.碳排放约束下制造商竞争的逆向供应链政府奖惩机制研究[J].管理工程学报,2016,30(2):188-194.
[33]张桂涛,胡劲松,孙浩,等.考虑产品寿命次数的多期闭环供应链网络均衡[J].信息与控制,2015,44(1):29-37.
[34]HE B S,XU Y,YUAN X M.A logarithmic-quadratic proximal prediction-correction method for structured monotone variational inequalities[J].Computational optimization and applications,2006,35(1):19-46.