A multi-product green supply chain under government supervision with price and demand uncertainty

محورهای موضوعی : Mathematical Optimization

Ashkan Hafezalkotob ¹ (Department of Industrial Engineering, Industrial Engineering College, Islamic Azad University, South Tehran Branch, Entezari Alley, Oskoui Alley, Choobi Bridge, Tehran, 1151863411, Iran)
Soma Zamani ² (Department of Industrial Engineering, Industrial Engineering College, Islamic Azad University, South Tehran Branch, Entezari Alley, Oskoui Alley, Choobi Bridge, Tehran, 1151863411, Iran)

تاریخ دریافت : 1399/07/17 تاریخ پذیرش : 1399/07/17 تاریخ انتشار : 1399/03/12

کلید واژه: Green supply chain . Bi, level programming problem . Uncertainty . Game theory . Genetic algorithm,

چکیده مقاله :

In this paper, a bi-level game-theoretic model is proposed to investigate the effects of governmental financial intervention on green supply chain. This problem is formulated as a bi-level program for a green supply chain that produces various products with different environmental pollution levels. The problem is also regard uncertainties in market demand and sale price of raw materials and products. The model is further transformed into a single-level nonlinear programming problem by replacing the lower-level optimization problem with its Karush–Kuhn–Tucker optimality conditions. Genetic algorithm is applied as a solution methodology to solve nonlinear programming model. Finally, to investigate the validity of the proposed method, the computational results obtained through genetic algorithm are compared with global optimal solution attained by enumerative method. Analytical results indicate that the proposed GA offers better solutions in large size problems. Also, we conclude that financial intervention by government consists of green taxation and subsidization is an effective method to stabilize green supply chain members’ performance.

منابع و مأخذ:

Aiyoshi E, Shimizu K (1981) Hierarchical decentralized systems and its new solution by a barrier method. IEEE Tran Syst Man Cybern 11:444–449
Awudu I, Zhang J (2013) Stochastic production planning for a biofuel supply chain under demand and price uncertainties. Appl Energy 103:189–196
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(3):2965–2976
Bard JF (1983) An algorithm for solving the general bilevel programming problem. Math Oper Res 8:260–272
Bard J, Falk J (1982) An explicit solution to the multi-level programming problem. Comput Oper Res 9:77–100
Bard JT, Moore JT (1990) The mixed integer linear bilevel programming problem. Oper Res 38:911–921
Barnes JH (1982) Recycling: a problem in reverse logistics. J Macromark 2(2):31–37
Basu R, Wright JN (2008) Total supply chain management. Butterworth-Heinemann, London
Bazaraa MS, Sherali HD, Shetty CM (2006) Nonlinear programming: theory and algorithms, 3rd edn. Wiley, Hoboken, pp 113–114
Bertsimas D, Thiele A (2006) A robust optimization approach to inventory theory. Oper Res 54(1):150–168

Bianco L, Caramia M, Giordani S (2009) A bilevel flow model for hazmat transportation network design. Transp Res C Emerg 17(2):175–196
Bowen FE, Cousin PD, Lamming RC, Faruk AC (2001) The role of supply management capabilities in green supply. Prod Oper Manag 10(2):174–189
Bracken J, McGill J (1973) Mathematical programs with optimization problems in the constraints. Oper Res 21:37–44
Candler W, Townsley R (1982) A linear two-level programming problem. Comput Oper Res 9:59–76
Carter CR, Ellram LM (1998) Reverse logistics—a review of the literature and framework for future investigation. Bus Logist
19(1):85–102
Chang MS, Tseng YL, Chen JW (2007) A scenario planning approach for the flood emergency logistics preparation problem under uncertainty. Transp Res E Logist 43(6):737–754
Chen YJ, Sheu JB (2009) Environmental-regulation pricing strategies for green supply chain management. Transp Res E Logist 45(5):667–677
Chen Y, Jin GZ, Kumar N, Shi G (2013) The promise of Beijing: evaluating the impact of the 2008 Olympic Games on air quality. J Environ Econ Manag 66(3):424–443
Coello CAC (2005) An introduction to evolutionary algorithms and their applications. Advanced distributed systems. Springer, Berlin
Colson B, Marcotte P, Savard G (2005) Bilevel programming: a survey. 4OR-Q J Oper Res 3:87–107
Colson B, Marcotte P, Savard G (2007) An overview of bilevel optimization. Ann Oper Res 153:235–256
Drumwright M (1994) Socially responsible organisational buying: environmental concern as a noneconomic buying criterion. J Market 58(8):1–19
Esmaeilzadeh A, Taleizadeh AA (2016) Pricing in a two-echelon supply chain with different market powers: game theory
approaches. J Ind Eng Int 12:119
Esogbue AO (1999) Cluster validity for fuzzy criterion clustering. Comput Math Appl 37(11–12):95–100
Fenglan L (2010) An analysis of the dynamic game model between government and enterprises of green supply chain. In: International conference on management and service science (MASS), pp 1–4
Fleischmann M (2001) Quantitative models for reverse logistics. Springer, Berlin
Gan XH, Sethi SP, Yan HM (2005) Channel coordination with a riskneutral supplier and a downside-risk-averse retailer. Prod Oper Manag 14(1):80–89
Gendreau M, Marcotte P, Savard G (1996) A hybrid Tabu_Ascent algorithm for the linear bilevel programming problem. J Global Optim 9:1–14
Ghaffari M, Hafezalkotob A, Makui A (2016) Analysis of implementation of Tradable Green Certificates system in a competitive electricity market: a game theory approach. J Ind Eng Int 12(2):185–197
Gong Y, Tang J, Chen J (2007) A dynamic game analysis on the incomplete information in enterprises’ reverse logistics. In:
International conference on transportation engineering, pp 533–538
Hafezalkotob A (2015) Competition of two green and regular supply chains under environmental protection and revenue seeking policies of government. Comput Ind Eng 82:103–114
Hafezalkotob A (2017) Competition, cooperation, and coopetition of green supply chains under regulations on energy saving levels. Transp Res Part E 97:228–250
Hafezalkotob A, Mahmoudi R (2017) Selection of energy source and evolutionary stable strategies for power plants under financial intervention of government. J Ind Eng Int 13(3):357–367
Hansen B, Jaumard B, Savard G (1992) New branch and bound rules for linear bilevel programming. SIAM J Sci Stat Comput 13:1194–1217
Haupt RL, Haupt SE (2004) Practical GAs, 2nd edn. Wiley, New Jersey
Herskovits J, Leontiev A, Dias G, Santos G (2000) Contact shape optimization: a bilevel programming approach. Struct Multidiscip Optim 20:214–221
Hu L, Cao Y, Cheng C, Shao H (2002) Sampled-data control for timedelay systems. J Franklin Inst 339:231–238
Ilyas SZ, Khattak AI, Nasir SM, Qurashi T, Durrani R (2010) Air pollution assessment in urban areas and its impact on human health in the city of Quetta, Pakistan. Clean Technol Environ Policy 12:291–299
Inderfurth K, de Kok AG, Flapper SDP (2001) Product recovery in stochastic remanufacturing system with multiple reuse options. Eur J Oper Res 133:130–152
Kalyanmoy D (2001) Multi-objective optimization using evolutionary algorithms. Wiley, New York
Katsaliaki K, Mustafee N, Kumar S (2014) A game-based approach towards facilitating decision making for perishable products: an example of blood supply chain. Expert Syst Appl 41(9):4043–4059
Kiesmuller GP, Scherer CW (2003) Computational issues in a stochastic nite horizon one product recovery inventory model. Eur J Oper Res 146(3):553–579
Klausner M, Hendrickson CT (2000) Reverse logistics strategy for product take-back. Interfaces 30:156–165
Koh A (2007) Solving transportation bi-level programs with differential evolution. In: 2007 IEEE congress on evolutionary
computation (CEC-2007), pp 2243–2250
Kumar S, Luthra S, Haleem A (2013) Customer involvement in greening the supply chain: an interpretive structural modeling methodology. J Ind Eng Int 9:6
Lee JY, Schwarz LB (2007) Leadtime reduction in a (Q, r) inventory system: an agency perspective. Int J Prod Econ 105:204–212
Leung SCH, Tsang SOS, Ng WL, Wu Y (2007) A robust optimization model for multi-site production planning problem in an uncertain environment. Eur J Oper Res 181(1):224–238
Li H, Wang Y (2007) A GA for solving a special class of nonlinear bilevel programming problems. In: Shi Y, Albada G, Dongarra J, Sloot P (eds) Computational science AI ICCS 2007, Lecture notes in computer science, vol 4490, pp 1159–1162
Li H, Wang Y (2011) An evolutionary algorithm with local search for convex quadratic bilevel programming problems. Appl Math Inf Sci 5(2):139–146
Li H, Zhang A, Zhao M, Xu Q (2005) Particle swarm optimization algorithm for FIR digital filters design. Acta Electron Sin
33(7):1338–1341
Li S, Murat A, Huang W (2009) Selection of contract suppliers under price and demand uncertainty in a dynamic market. Eur J Oper Res 198(3):830–884
Liang TF (2008) Integrating production-transportation planning decision with fuzzy multiple goals in supply chains. Int J Prod Res 46(6):1477–1494
Liu, M., Ye, H., Qi, X., Shui, W. (2008). Analysis on trilateral game of green supply chain. In: Logistics: the emerging frontiers of transportation and development in China, pp 575–581
Mahmoudi R, Hafezalkotob A, Makui A (2014) Source selection problem of competitive power plants under government intervention: a game theory approach. J Ind Eng Int 10:59
Maiti SK, Roy SK (2016) Multi-choice stochastic bi-level programming problem in cooperative nature via fuzzy programming approach. J Ind Eng Int 12:287
Mitra S, Webster S (2008) Competition in remanufacturing and the effects of government subsidies. Int J Prod Econ 111(2):287–298

Mulvey JM, Vanderbei RJ, Zenios SA (1999) Robust optimization of large-scale systems. Oper Res 43(2):264–281
Murphy PR, Poist RF, Braunschweig CD (1994) Management of environmental issues in logistics: current status and future
potential. Transp J 34(1):48–56
Paul S, Wahab MIM, Cao XF (2014) Supply chain coordination with energy price uncertainty, carbon emission cost, and product return. Int Ser Oper Res Manag Sci 197:179–199
Petrovic D, Roy R, Petrovic R (1999) Supply chain modeling using fuzzy sets. Int J Prod Econ 59(1–3):443–453
Pohlen TL, Farris MT (1992) Reverse logistics in plastics recycling. Int J Phys Distrib Logist Manag 22(7):35–47
Popescu I (2007) Robust mean–covariance solutions for stochastic optimization. Oper Res 55(1):98–112
Rezaee MJ, Yousefi S, Hayati J (2017) A multi-objective model for closed-loop supply chain optimization and efficient supplier selection in a competitive environment considering quantity discount policy. J Ind Eng Int 13:199
Richter K, Dobos I (1999) Analysis of EOQ repair and waste disposal problem with integer setup. Int J Prod Econ 59:463–467
Richter K, Weber J (2001) The reverse Wagner/Whitin model with variable manufacturing and remanufacturing cost. Int J Prod Econ 71:447–456
Roberts S (2013) Have the short-term mortality effects of particulate matter air pollution changed in Australia over the period 1993–2007? Environ Pollut 182:9–14
Santoso T, Ahmed S, Goetschalckx M, Shapiro A (2005) A stochastic programming approach for supply chain network design under uncertainty. Eur J Oper Res 167(1):96–115
Sarkis J, Cordeiro J (2001) An empirical evaluation of environmental efficiencies and firm performance: pollution prevention versus end-of pipe practice. Eur J Oper Res 135:102–113
Savard G, Gauvin J (1994) The steepest descent direction for nonlinear bilevel programming problem. Oper Res Lett
15:265–270
Savaskan RC, Van Wassenhove LN (2006) Reverse channel design: the case of competing retailers. Manage Sci 52(1):1–14
Savaskan RC, Bhattacharya A, Van Wassenhove LN (2004) Closedloop supply chain models with product remanufacturing. Manage Sci 50(2):239–252
Schultmann F, Frohling M, Rentz O (2006) Fuzzy approach for production planning and detailed scheduling in paints manufacturing. Int J Prod Res 44(8):1589–1612
Seuring S, Mu¨ller M (2008) From a literature review to a conceptual framework for sustainable supply chain management. J Clean Prod 16(15):1699–1710
Sheu JB (2011) Bargaining framework for competitive green supply chains under governmental financial intervention. Transp Res E Logist 47:573–592
Sheu JB, Chou YH, Hu CC (2005) An integrated logistics operational model for green-supply chain management. Transp Res E Logist 41(4):287–313
Sokolova MV, Caballero AF (2009) Modeling and implementing an agent-based environmental health impact decision support system. Expert Syst Appl Part 2 36(2):2603–2614
Sokolova MV, Caballero AF (2012) Evaluation of environmental impact upon human health with DeciMaS framework. Expert Syst Appl 39(3):3469–3483
Srivastava SK (2007) Green supply-chain management: a state-ofthe-art literature review. Int J Manag Rev 9(1):53–80
Stackelberg HV (1952) The theory of the market economy. Oxford University Press, Oxford
Szymankiewicz J (1993) Going green: the logistics Dilemma. Logist Inf Manag 6(3):36–43
Tolga Kaya T, Kahraman C (2011) An integrated fuzzy AHPELECTRE methodology for environmental impact assessment.
Expert Syst Appl 38(7):8553–8562
Tsay AA (2002) Risk sensitivity in distribution channel partnerships: implications for manufacturer return policies. J Retail 78:147–160
Valipour M (2014) Application of new mass transfer formulae for computation of evapotranspiration. J Appl Water Eng Res 2(1):33–46
Valipour M (2016a) How much meteorological information is necessary to achieve reliable accuracy for rainfall estimations? Agriculture 6(4):53
Valipour M (2016b) Variations of land use and irrigation for next decades under different scenarios. Irriga Braz J Irrig Drain
1(1):262–288
Valipour M, Banihabib ME, Behbahani MR (2013a) Comparison of the ARMA, ARIMA, and the autoregressive artificial neural network models in forecasting the monthly inflow of Dez dam reservoir. J Hydrol 476:433–441
Valipour M, Mousavi M, Valipour R, Rezaei E (2013b) A new approach for environmental crises and its solutions by computer modeling. In: The 1st international conference on environmental crises and its solutions, at Kish Island, Iran
Valipour M, Gholami Sefidkouhi MA, Raeini-Sarjaz M (2017) Selecting the best model to estimate potential evapotranspiration with respect to climate change and magnitudes of extreme events. Agric Water Manag 180(A):50–60
Vicente LN, Calamai PH (2004) Bilevel and multilevel programming: a bibliography review. J Global Optim 5(3):291–306
Von Neumann J, Morgenstern O (1944) Theory of games and economic behavior. Princeton University Press, Princeton
Wang Y, Jiao YC, Li H (2005) An evolutionary algorithm for solving nonlinear bilevel programming based on a new constrainthandling scheme. IEEE Tran Syst Man Cybern C 35(2):221–232
Wang G, Wan Z, Wang X, Lv Y (2008) GA based on simplex method for solving linear-quadratic bilevel programming problem. Comput Math Appl 56(10):2550–2555
Wilkerson T (2005) Can one green deliver another? Harvard Business School Publishing Corporation. http://www.supplychainstrategy.org/. Accessed 15 Jan 2018
Wullink G, Gademann AJRM, Hans EW, Van Harten A (2004) Scenario-based approach for flexible resource loading under
uncertainty. Int J Prod Res 42(24):5079–5098
Xiao T, Yang D (2008) Price and service competition of supply chains with risk-averse retailers under demand uncertainty. Int J Prod Econ 114:187–200
Xiao-xi W, Wei-qing X (2012) Evolutionary game analysis of the reverse supply chain based on the government subsidy mechanism. In: Second international conference on business computing and global informatization (BCGIN), pp 99–102
Yali LU (2010) Research on evolutionary mechanisms of green supply chain constraints by macro-environment. In: ICLEM,
pp 1009–1016 
Zhu QH, Cote RP (2004) Integrating green supply chain management into an embryonic eco industrial development: a case study of the Guitang Group. J Clean Prod 12:1025–1035
Zhu Q, Sarkis J (2004) Relationships between operational practices and performance among early adopters of green supply chain management practices in Chinese manufacturing enterprises. J Oper Manag 22(3):265–289
Zhu QH, Dou YJ (2007) Evolutionary game model between governments and core enterprises in greening supply chains.
Syst Eng Theory Pract 27(12):85–89 
Zhu QH, Sarkis J, Lai KH (2008) Confirmation of a measurement model for green supply chain management practices implementation. Int J Prod Econ 111:261–273