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doi: 10.3934/jimo.2021098
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A three echelon supply chain model with stochastic demand dependent on price, quality and energy reduction

1. 

Department of Mathematics, Kazi Nazrul University, Asansol, West Bengal-713340, India

2. 

Department of Mathematics, Tamralipta Mahavidyalaya, Tamluk, West Bengal-721636, India

* Corresponding author: Santanu Kumar Ghosh

Received  December 2020 Revised  March 2021 Early access May 2021

While developing supply chain models, many researchers have shown great interest on how to reduce the consumption of non-renewable sources of energy, as non-renewable sources of energy is limited. The purpose of this paper is to formulate a three echelon supply chain model when the demand of items is assumed to be stochastically dependent on price, quality and reduction of energy. In the centralized model, suppler, manufacturer and retailer are the three members of the supply chain. The model is solved analytically to obtain optimal values of order quantity, unit price, promotional effort and amount of energy consumption which maximizes the profit function of the supply chain. Two decentralized models namely MR-Nash and MS-Nash have also been considered in a separate section. These two models have also been solved analytically to obtain the optimal solution of the decision variables. Three proposed models have been illustrated with a numerical example by considering exponential distribution of customer's demand. The sensitivity of the optimal solution revealed the appropriate channel strategy in case of decentralized scenario. It is speculated that when the manufacturer and the supplier collaborates, the profit difference is reduced by $ 39 \% $ than that of the MR-Nash.

Citation: Chandan Pathak, Saswati Mukherjee, Santanu Kumar Ghosh, Sudhansu Khanra. A three echelon supply chain model with stochastic demand dependent on price, quality and energy reduction. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021098
References:
[1]

H. M. Abdelsalam and M. M. Elassal, Joint economic lot sizing problem for a threelayer supply chain with stochastic demand, International Journal of Production Economics, 155 (2014), 272-283. doi: 10.1016/j.ijpe.2014.01.015.  Google Scholar

[2]

A. M. Abu, D. Svetinovic and A. Diabat, A carbon-sensitive two-echelon-inventory supply chain model with stochastic demand, Transportation Research Part E: Logistics and Transportation Review, 142 (2016), 102038. Google Scholar

[3]

M. AlDurgam, K. Adegbola and C. H. Glock, A single-vendor single-manufacturer integrated inventory model with stochastic demand and variable production rate, International Journal of Production Economics, 191 (2017), 335-350. doi: 10.1016/j.ijpe.2017.05.017.  Google Scholar

[4]

C. K. Chan, F. Fang and A. Langevin, Single-vendor multi-buyer supply chain coordination with stochastic demand, International Journal of Production Economics, 206 (2018), 110-133. doi: 10.1016/j.ijpe.2018.09.024.  Google Scholar

[5]

Y. Daryanto, H. M. Wee and R. D. Astanti, Three-echelon supply chain model considering carbon emission and item deterioration, Transportation Research Part E: Logistics and Transportation Review, 122 (2019), 368-383. doi: 10.1016/j.tre.2018.12.014.  Google Scholar

[6]

M. M. de Souza Grilo, M. Mayara, A. F. C. Fortes, R. P. G. de Souza, J. A. M. Silva and M. Carvalho, Carbon footprints for the supply of electricity to a heat pump: Solar energy vs. electric grid, Journal of Renewable and Sustainable Energy, 10 (2018), 023701. doi: 10.1063/1.4997306.  Google Scholar

[7]

D. Gao, X. Zhao and W. Geng, A delay-in-payment contract for Pareto improvement of a supply chain with stochastic demand, Omega, 49 (2014), 60-68. doi: 10.1016/j.omega.2014.05.008.  Google Scholar

[8]

S. K. Ghosh, M. R. Seikh and M. Chakrabortty, Analyzing a stochastic dual-channel supply chain under consumers' low carbon preferences and cap-and-trade regulation, Computers & Industrial Engineering, 149 (2020) 106765. doi: 10.1016/j.cie.2020.106765.  Google Scholar

[9]

B. C. Giri, B. Roy and T. Maiti, Coordinating a three-echelon supply chain under price and quality dependent demand with sub-supply chain and RFM strategies, Applied Mathematical Modelling, 52 (2017), 747-769. doi: 10.1016/j.apm.2017.05.039.  Google Scholar

[10]

J. L. Glover, D. Champion, K. J. Daniels and A. J. D. Dainty, An Institutional Theory perspective on sustainable practices across the dairy supply chain, International Journal of Production Economics, 152 (2014), 102-111. doi: 10.1016/j.ijpe.2013.12.027.  Google Scholar

[11]

K. Govindan, The optimal replenishment policy for time-varying stochastic demand under vendor managed inventory, European Journal of Operational Research, 242 (2015), 402-423. doi: 10.1016/j.ejor.2014.09.045.  Google Scholar

[12]

A. Haddadsisakht and S. M. Ryan, Closed-loop supply chain network design with multiple transportation modes under stochastic demand and uncertain carbon tax, International Journal of Production Economics, 195 (2018), 118-131. doi: 10.1016/j.ijpe.2017.09.009.  Google Scholar

[13]

H. Hishamuddin, R. Sarker and D. Essam, A simulation model of a three echelon supply chain system with multiple suppliers subject to supply and transportation disruptions, IFAC-PapersOnLine, 48 (2015), 2036-2040. doi: 10.1016/j.ifacol.2015.06.388.  Google Scholar

[14]

K. M. R. Hoen, T. Tan, J. C. Fransoo and G. H Van Houtum, Effect of carbon emission regulations on transport mode selection under stochastic demand, Flexible Services and Manufacturing Journal, 26 (2014), 170-195. doi: 10.1007/s10696-012-9151-6.  Google Scholar

[15]

Y. Hou, F. Wei, S. X. Li, Z. Huang and A. Ashley, Coordination and performance analysis for a three-echelon supply chain with a revenue sharing contract, International Journal of Production Research, 55 (2017), 202-227. doi: 10.1080/00207543.2016.1201601.  Google Scholar

[16]

B. Hu, C. Meng, D. Xu ang Y.-J. Son, Three-echelon supply chain coordination with a loss-averse retailer and revenue sharing contracts, International Journal of Production Economics, 179 (2016), 192-202. doi: 10.1016/j.ijpe.2016.06.001.  Google Scholar

[17]

M. W. Iqbal, Y. Kang and H. W. Jeon, Zero waste strategy for green supply chain management with minimization of energy consumption, Journal of Cleaner Production, 245 (2020), 118827. doi: 10.1016/j.jclepro.2019.118827.  Google Scholar

[18]

H. Jafari, S. R. Hejazi and M. Rasti-Barzoki, Sustainable development by waste recycling under a three-echelon supply chain: A game-theoretic approach, Journal of cleaner production, 142 (2017), 2252-2261. Google Scholar

[19]

D. K. Kadambala, N. Subramanian, M. K. Tiwari, M. Abdulrahman and C. Liu, Closed loop supply chain networks: Designs for energy and time value efficiency, International Journal of Production Economics, 183 (2017), 382-393. doi: 10.1016/j.ijpe.2016.02.004.  Google Scholar

[20]

B. K. Kumar, D. Nagaraju and S. Narayanan, Three-echelon supply chain with centralised and decentralised inventory decisions under linear price dependent demand, International Journal of Logistics Systems and Management, 23 (2016), 231-254. doi: 10.1504/IJLSM.2016.073970.  Google Scholar

[21]

P. Li, Y. Ji, Z. Wu and S.-J. Qu, A new multi-attribute emergency decision-making algorithm based on intuitionistic fuzzy cross-entropy and comprehensive grey correlation analysis, Entropy (Basel), 22 (2020), 768. doi: 10.3390/e22070768.  Google Scholar

[22]

C.-C. Lin and Y.-C. Wu, Combined pricing and supply chain operations under price-dependent stochastic demand, Applied Mathematical Modelling, 38 (2014), 1823-1837. doi: 10.1016/j.apm.2013.09.017.  Google Scholar

[23]

X. Ma, J. Wang, Q. Bai and S. Wang, Optimization of a three-echelon cold chain considering freshness-keeping efforts under cap-and-trade regulation in Industry 4.0, International Journal of Production Economics, 220 (2020), 107457. doi: 10.1016/j.ijpe.2019.07.030.  Google Scholar

[24]

A. Mahmoodi and K. Eshghi, Price competition in duopoly supply chains with stochastic demand, Journal of Manufacturing Systems, 33 (2014), 604-612. doi: 10.1016/j.jmsy.2014.05.008.  Google Scholar

[25]

J. Meng, X. Hu, P. Chen, D. M. Coffman and M. Han, The unequal contribution to global energy consumption along the supply chain, Journal of Environmental Management, 268 (2020), 110701. doi: 10.1016/j.jenvman.2020.110701.  Google Scholar

[26]

N. M. Modak, S. Panda and S. S. Sana, Three-echelon supply chain coordination considering duopolistic retailers with perfect quality products, International Journal of Production Economics, 182 (2016), 564-578. doi: 10.1016/j.ijpe.2015.05.021.  Google Scholar

[27]

Z. Mohtashami, A. Aghsami and F. Jolai, A green closed loop supply chain design using queuing system for reducing environmental impact and energy consumption, Journal of Cleaner Production, 242 (2020), 118452. doi: 10.1016/j.jclepro.2019.118452.  Google Scholar

[28]

K. S. Navarro, J. A. Chedid, W. F. Florez, H. O. Mateus, L. E. Cárdenas-Barrón and S. S. Sana, A collaborative EPQ inventory model for a three-echelon supply chain with multiple products considering the effect of marketing effort on demand, Journal of Industrial & Management Optimization, 16 (2020), 1613-1633. doi: 10.3934/jimo.2019020.  Google Scholar

[29]

T. Paksoy, E. Özceylan and G.-W. Weber, A multi objective model for optimization of a green supply chain network, AIP Conference Proceedings, 1239 (2010), 311-320. doi: 10.1063/1.3459765.  Google Scholar

[30]

S. Pal and G. S. Mahapatra, A manufacturing-oriented supply chain model for imperfect quality with inspection errors, stochastic demand under rework and shortages, Computers & Industrial Engineering, 106 (2017), 299-314. doi: 10.1016/j.cie.2017.02.003.  Google Scholar

[31]

S. Panda, N. M. Modak and M. Basu, Disposal cost sharing and bargaining for coordination and profit division in a three-echelon supply chain, International Journal of Management Science and Engineering Management, 9 (2014), 276-285. doi: 10.1080/17509653.2014.903810.  Google Scholar

[32]

A. Rezaee, F. Dehghanian, B. Fahimnia and B. Behnam, Green supply chain network design with stochastic demand and carbon price, Annals of Operations Research, 250 (2017), 463-485. doi: 10.1007/s10479-015-1936-z.  Google Scholar

[33]

B. Sarkar, B. Ganguly, M. Sarkar and S. Pareek, Effect of variable transportation and carbon emission in a three-echelon supply chain model, Transportation Research Part E: Logistics and Transportation Review, 91 (2016), 112-128. doi: 10.1016/j.tre.2016.03.018.  Google Scholar

[34]

B. Sarkar, M. Omair and S.-B. Choi, A multi-objective optimization of energy, economic, and carbon emission in a production model under sustainable supply chain management, Applied Sciences, 8 (2018), 1744. doi: 10.3390/app8101744.  Google Scholar

[35]

N. H. Shah, U. Chaudhari and L. E. Cárdenas-Barrón, Integrating credit and replenishment policies for deteriorating items under quadratic demand in a three echelon supply chain, International Journal of Systems Science: Operations & Logistics, 7 (2020), 34-45. doi: 10.1080/23302674.2018.1487606.  Google Scholar

[36]

Q. Shaojian, X. Yuan, W. Zhong, X. Zeshui, J. Ying, Q. Deqiang and H. Yefan, An Interval-Valued Best - Worst Method with Normal Distribution for Multi-criteria Decision-Making, Arabian Journal for Science and Engineering, 46 (2020). Google Scholar

[37]

S. Qu, H. Cai, D. Xu and N. Mohamed, Correction to: Uncertainty in the prediction and management of CO2 emissions: A robust minimum entropy approach, Natural Hazards, (2020). doi: 10.1007/s11069-020-04434-6.  Google Scholar

[38]

N. Singh, Narayan, B. Vaish and S. R. Singh, Three level supply chain model with variable demand rate under partial trade credit policy, International Journal of Services and Operations Management, 21 (2015), 479-503. doi: 10.1504/IJSOM.2015.070254.  Google Scholar

[39]

E. B. Tirkolaee, A. Mardani, Z. Dashtian, M. Soltani and G.-W. Weber, A novel hybrid method using fuzzy decision making and multi-objective programming for sustainable-reliable supplier selection in two-echelon supply chain design, Journal of Cleaner Production, 250 (2020), 119517. doi: 10.1016/j.jclepro.2019.119517.  Google Scholar

[40]

Y. Yi and J. Li, Cost-sharing contracts for energy saving and emissions reduction of a supply chain under the conditions of government subsidies and a carbon tax, Sustainability, 10 (2018), 895. Google Scholar

[41]

Y. He, X. Zhao, L. Zhao and J. He, Coordinating a supply chain with effort and price dependent stochastic demand, Applied Mathematical Modelling, 33 (2009), 2777-2790. doi: 10.1016/j.apm.2008.08.016.  Google Scholar

[42]

Y. Yi and J. Li, The effect of governmental policies of carbon taxes and energy-saving subsidies on enterprise decisions in a two-echelon supply chain, Journal of Cleaner Production, 181 (2018), 675-691. doi: 10.1016/j.jclepro.2018.01.188.  Google Scholar

[43]

R. Zhang and K. Wang, A multi-echelon global supply chain network design based on transfer-pricing strategy, Journal of Industrial Integration & Management, 4 (2019), 1850020. doi: 10.1142/S2424862218500203.  Google Scholar

[44]

K. Zhu, J. Shen and X. Yao, A three-echelon supply chain with asymmetric information under uncertainty, Journal of Ambient Intelligence and Humanized Computing, 10 (2019), 579-591. doi: 10.1007/s12652-018-0705-7.  Google Scholar

[45]

Q. Zhu and Y. Geng, Drivers and barriers of extended supply chain practices for energy saving and emission reduction among Chinese manufacturers, Journal of Cleaner Production, 40 (2013), 6-12. doi: 10.1016/j.jclepro.2010.09.017.  Google Scholar

show all references

References:
[1]

H. M. Abdelsalam and M. M. Elassal, Joint economic lot sizing problem for a threelayer supply chain with stochastic demand, International Journal of Production Economics, 155 (2014), 272-283. doi: 10.1016/j.ijpe.2014.01.015.  Google Scholar

[2]

A. M. Abu, D. Svetinovic and A. Diabat, A carbon-sensitive two-echelon-inventory supply chain model with stochastic demand, Transportation Research Part E: Logistics and Transportation Review, 142 (2016), 102038. Google Scholar

[3]

M. AlDurgam, K. Adegbola and C. H. Glock, A single-vendor single-manufacturer integrated inventory model with stochastic demand and variable production rate, International Journal of Production Economics, 191 (2017), 335-350. doi: 10.1016/j.ijpe.2017.05.017.  Google Scholar

[4]

C. K. Chan, F. Fang and A. Langevin, Single-vendor multi-buyer supply chain coordination with stochastic demand, International Journal of Production Economics, 206 (2018), 110-133. doi: 10.1016/j.ijpe.2018.09.024.  Google Scholar

[5]

Y. Daryanto, H. M. Wee and R. D. Astanti, Three-echelon supply chain model considering carbon emission and item deterioration, Transportation Research Part E: Logistics and Transportation Review, 122 (2019), 368-383. doi: 10.1016/j.tre.2018.12.014.  Google Scholar

[6]

M. M. de Souza Grilo, M. Mayara, A. F. C. Fortes, R. P. G. de Souza, J. A. M. Silva and M. Carvalho, Carbon footprints for the supply of electricity to a heat pump: Solar energy vs. electric grid, Journal of Renewable and Sustainable Energy, 10 (2018), 023701. doi: 10.1063/1.4997306.  Google Scholar

[7]

D. Gao, X. Zhao and W. Geng, A delay-in-payment contract for Pareto improvement of a supply chain with stochastic demand, Omega, 49 (2014), 60-68. doi: 10.1016/j.omega.2014.05.008.  Google Scholar

[8]

S. K. Ghosh, M. R. Seikh and M. Chakrabortty, Analyzing a stochastic dual-channel supply chain under consumers' low carbon preferences and cap-and-trade regulation, Computers & Industrial Engineering, 149 (2020) 106765. doi: 10.1016/j.cie.2020.106765.  Google Scholar

[9]

B. C. Giri, B. Roy and T. Maiti, Coordinating a three-echelon supply chain under price and quality dependent demand with sub-supply chain and RFM strategies, Applied Mathematical Modelling, 52 (2017), 747-769. doi: 10.1016/j.apm.2017.05.039.  Google Scholar

[10]

J. L. Glover, D. Champion, K. J. Daniels and A. J. D. Dainty, An Institutional Theory perspective on sustainable practices across the dairy supply chain, International Journal of Production Economics, 152 (2014), 102-111. doi: 10.1016/j.ijpe.2013.12.027.  Google Scholar

[11]

K. Govindan, The optimal replenishment policy for time-varying stochastic demand under vendor managed inventory, European Journal of Operational Research, 242 (2015), 402-423. doi: 10.1016/j.ejor.2014.09.045.  Google Scholar

[12]

A. Haddadsisakht and S. M. Ryan, Closed-loop supply chain network design with multiple transportation modes under stochastic demand and uncertain carbon tax, International Journal of Production Economics, 195 (2018), 118-131. doi: 10.1016/j.ijpe.2017.09.009.  Google Scholar

[13]

H. Hishamuddin, R. Sarker and D. Essam, A simulation model of a three echelon supply chain system with multiple suppliers subject to supply and transportation disruptions, IFAC-PapersOnLine, 48 (2015), 2036-2040. doi: 10.1016/j.ifacol.2015.06.388.  Google Scholar

[14]

K. M. R. Hoen, T. Tan, J. C. Fransoo and G. H Van Houtum, Effect of carbon emission regulations on transport mode selection under stochastic demand, Flexible Services and Manufacturing Journal, 26 (2014), 170-195. doi: 10.1007/s10696-012-9151-6.  Google Scholar

[15]

Y. Hou, F. Wei, S. X. Li, Z. Huang and A. Ashley, Coordination and performance analysis for a three-echelon supply chain with a revenue sharing contract, International Journal of Production Research, 55 (2017), 202-227. doi: 10.1080/00207543.2016.1201601.  Google Scholar

[16]

B. Hu, C. Meng, D. Xu ang Y.-J. Son, Three-echelon supply chain coordination with a loss-averse retailer and revenue sharing contracts, International Journal of Production Economics, 179 (2016), 192-202. doi: 10.1016/j.ijpe.2016.06.001.  Google Scholar

[17]

M. W. Iqbal, Y. Kang and H. W. Jeon, Zero waste strategy for green supply chain management with minimization of energy consumption, Journal of Cleaner Production, 245 (2020), 118827. doi: 10.1016/j.jclepro.2019.118827.  Google Scholar

[18]

H. Jafari, S. R. Hejazi and M. Rasti-Barzoki, Sustainable development by waste recycling under a three-echelon supply chain: A game-theoretic approach, Journal of cleaner production, 142 (2017), 2252-2261. Google Scholar

[19]

D. K. Kadambala, N. Subramanian, M. K. Tiwari, M. Abdulrahman and C. Liu, Closed loop supply chain networks: Designs for energy and time value efficiency, International Journal of Production Economics, 183 (2017), 382-393. doi: 10.1016/j.ijpe.2016.02.004.  Google Scholar

[20]

B. K. Kumar, D. Nagaraju and S. Narayanan, Three-echelon supply chain with centralised and decentralised inventory decisions under linear price dependent demand, International Journal of Logistics Systems and Management, 23 (2016), 231-254. doi: 10.1504/IJLSM.2016.073970.  Google Scholar

[21]

P. Li, Y. Ji, Z. Wu and S.-J. Qu, A new multi-attribute emergency decision-making algorithm based on intuitionistic fuzzy cross-entropy and comprehensive grey correlation analysis, Entropy (Basel), 22 (2020), 768. doi: 10.3390/e22070768.  Google Scholar

[22]

C.-C. Lin and Y.-C. Wu, Combined pricing and supply chain operations under price-dependent stochastic demand, Applied Mathematical Modelling, 38 (2014), 1823-1837. doi: 10.1016/j.apm.2013.09.017.  Google Scholar

[23]

X. Ma, J. Wang, Q. Bai and S. Wang, Optimization of a three-echelon cold chain considering freshness-keeping efforts under cap-and-trade regulation in Industry 4.0, International Journal of Production Economics, 220 (2020), 107457. doi: 10.1016/j.ijpe.2019.07.030.  Google Scholar

[24]

A. Mahmoodi and K. Eshghi, Price competition in duopoly supply chains with stochastic demand, Journal of Manufacturing Systems, 33 (2014), 604-612. doi: 10.1016/j.jmsy.2014.05.008.  Google Scholar

[25]

J. Meng, X. Hu, P. Chen, D. M. Coffman and M. Han, The unequal contribution to global energy consumption along the supply chain, Journal of Environmental Management, 268 (2020), 110701. doi: 10.1016/j.jenvman.2020.110701.  Google Scholar

[26]

N. M. Modak, S. Panda and S. S. Sana, Three-echelon supply chain coordination considering duopolistic retailers with perfect quality products, International Journal of Production Economics, 182 (2016), 564-578. doi: 10.1016/j.ijpe.2015.05.021.  Google Scholar

[27]

Z. Mohtashami, A. Aghsami and F. Jolai, A green closed loop supply chain design using queuing system for reducing environmental impact and energy consumption, Journal of Cleaner Production, 242 (2020), 118452. doi: 10.1016/j.jclepro.2019.118452.  Google Scholar

[28]

K. S. Navarro, J. A. Chedid, W. F. Florez, H. O. Mateus, L. E. Cárdenas-Barrón and S. S. Sana, A collaborative EPQ inventory model for a three-echelon supply chain with multiple products considering the effect of marketing effort on demand, Journal of Industrial & Management Optimization, 16 (2020), 1613-1633. doi: 10.3934/jimo.2019020.  Google Scholar

[29]

T. Paksoy, E. Özceylan and G.-W. Weber, A multi objective model for optimization of a green supply chain network, AIP Conference Proceedings, 1239 (2010), 311-320. doi: 10.1063/1.3459765.  Google Scholar

[30]

S. Pal and G. S. Mahapatra, A manufacturing-oriented supply chain model for imperfect quality with inspection errors, stochastic demand under rework and shortages, Computers & Industrial Engineering, 106 (2017), 299-314. doi: 10.1016/j.cie.2017.02.003.  Google Scholar

[31]

S. Panda, N. M. Modak and M. Basu, Disposal cost sharing and bargaining for coordination and profit division in a three-echelon supply chain, International Journal of Management Science and Engineering Management, 9 (2014), 276-285. doi: 10.1080/17509653.2014.903810.  Google Scholar

[32]

A. Rezaee, F. Dehghanian, B. Fahimnia and B. Behnam, Green supply chain network design with stochastic demand and carbon price, Annals of Operations Research, 250 (2017), 463-485. doi: 10.1007/s10479-015-1936-z.  Google Scholar

[33]

B. Sarkar, B. Ganguly, M. Sarkar and S. Pareek, Effect of variable transportation and carbon emission in a three-echelon supply chain model, Transportation Research Part E: Logistics and Transportation Review, 91 (2016), 112-128. doi: 10.1016/j.tre.2016.03.018.  Google Scholar

[34]

B. Sarkar, M. Omair and S.-B. Choi, A multi-objective optimization of energy, economic, and carbon emission in a production model under sustainable supply chain management, Applied Sciences, 8 (2018), 1744. doi: 10.3390/app8101744.  Google Scholar

[35]

N. H. Shah, U. Chaudhari and L. E. Cárdenas-Barrón, Integrating credit and replenishment policies for deteriorating items under quadratic demand in a three echelon supply chain, International Journal of Systems Science: Operations & Logistics, 7 (2020), 34-45. doi: 10.1080/23302674.2018.1487606.  Google Scholar

[36]

Q. Shaojian, X. Yuan, W. Zhong, X. Zeshui, J. Ying, Q. Deqiang and H. Yefan, An Interval-Valued Best - Worst Method with Normal Distribution for Multi-criteria Decision-Making, Arabian Journal for Science and Engineering, 46 (2020). Google Scholar

[37]

S. Qu, H. Cai, D. Xu and N. Mohamed, Correction to: Uncertainty in the prediction and management of CO2 emissions: A robust minimum entropy approach, Natural Hazards, (2020). doi: 10.1007/s11069-020-04434-6.  Google Scholar

[38]

N. Singh, Narayan, B. Vaish and S. R. Singh, Three level supply chain model with variable demand rate under partial trade credit policy, International Journal of Services and Operations Management, 21 (2015), 479-503. doi: 10.1504/IJSOM.2015.070254.  Google Scholar

[39]

E. B. Tirkolaee, A. Mardani, Z. Dashtian, M. Soltani and G.-W. Weber, A novel hybrid method using fuzzy decision making and multi-objective programming for sustainable-reliable supplier selection in two-echelon supply chain design, Journal of Cleaner Production, 250 (2020), 119517. doi: 10.1016/j.jclepro.2019.119517.  Google Scholar

[40]

Y. Yi and J. Li, Cost-sharing contracts for energy saving and emissions reduction of a supply chain under the conditions of government subsidies and a carbon tax, Sustainability, 10 (2018), 895. Google Scholar

[41]

Y. He, X. Zhao, L. Zhao and J. He, Coordinating a supply chain with effort and price dependent stochastic demand, Applied Mathematical Modelling, 33 (2009), 2777-2790. doi: 10.1016/j.apm.2008.08.016.  Google Scholar

[42]

Y. Yi and J. Li, The effect of governmental policies of carbon taxes and energy-saving subsidies on enterprise decisions in a two-echelon supply chain, Journal of Cleaner Production, 181 (2018), 675-691. doi: 10.1016/j.jclepro.2018.01.188.  Google Scholar

[43]

R. Zhang and K. Wang, A multi-echelon global supply chain network design based on transfer-pricing strategy, Journal of Industrial Integration & Management, 4 (2019), 1850020. doi: 10.1142/S2424862218500203.  Google Scholar

[44]

K. Zhu, J. Shen and X. Yao, A three-echelon supply chain with asymmetric information under uncertainty, Journal of Ambient Intelligence and Humanized Computing, 10 (2019), 579-591. doi: 10.1007/s12652-018-0705-7.  Google Scholar

[45]

Q. Zhu and Y. Geng, Drivers and barriers of extended supply chain practices for energy saving and emission reduction among Chinese manufacturers, Journal of Cleaner Production, 40 (2013), 6-12. doi: 10.1016/j.jclepro.2010.09.017.  Google Scholar

Table 1.  Optimal solutions for different scenarios with energy reduction
Parameters Centralized Decentralized
MR- Nash MS- Nash
$ p^* $ 1767.57 965.4 920.63
$ u^* $ 516.89 480.87 450.23
$ T^* $ 339.19 330.5 310.46
$ Q^* $ 640.10 540.25 500.3
$ \Pi_c $ 429211.0 - -
$ \Pi_{mr} $ - 256874.56 -
$ \Pi_{ms} $ - - 210456.7
$ \Pi_s $ - 5214.5 -
$ \Pi_r $ - - 8795.34
$ \Pi_T $ - 262089.06 219251.34
Parameters Centralized Decentralized
MR- Nash MS- Nash
$ p^* $ 1767.57 965.4 920.63
$ u^* $ 516.89 480.87 450.23
$ T^* $ 339.19 330.5 310.46
$ Q^* $ 640.10 540.25 500.3
$ \Pi_c $ 429211.0 - -
$ \Pi_{mr} $ - 256874.56 -
$ \Pi_{ms} $ - - 210456.7
$ \Pi_s $ - 5214.5 -
$ \Pi_r $ - - 8795.34
$ \Pi_T $ - 262089.06 219251.34
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