# American Institute of Mathematical Sciences

July  2022, 18(4): 2959-2975. doi: 10.3934/jimo.2021098

## 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 Published  July 2022 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 and Management Optimization, 2022, 18 (4) : 2959-2975. 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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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). [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. [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. [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. [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. [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. [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. [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. [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. [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.

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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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). [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. [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. [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. [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. [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. [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. [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. [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. [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.
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
 [1] Yaling Cui, Srdjan D. Stojanovic. Equity valuation under stock dilution and buy-back. Discrete and Continuous Dynamical Systems - B, 2012, 17 (6) : 1809-1829. doi: 10.3934/dcdsb.2012.17.1809 [2] Yafei Zu. Inter-organizational contract control of advertising strategies in the supply chain. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021126 [3] Yongjian Wang, Fei Wang. Effects of the carbon credits buy-back policy on manufacturing/remanufacturing decisions of the capital-constrained manufacturer. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021198 [4] R.H. Fabiano, Scott W. Hansen. Modeling and analysis of a three-layer damped sandwich beam. Conference Publications, 2001, 2001 (Special) : 143-155. doi: 10.3934/proc.2001.2001.143 [5] Katherinne Salas Navarro, Jaime Acevedo Chedid, Whady F. Florez, Holman Ospina Mateus, Leopoldo Eduardo Cárdenas-Barrón, Shib Sankar 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 and Management Optimization, 2020, 16 (4) : 1613-1633. doi: 10.3934/jimo.2019020 [6] Bibhas C. Giri, Bhaba R. Sarker. Coordinating a multi-echelon supply chain under production disruption and price-sensitive stochastic demand. Journal of Industrial and Management Optimization, 2019, 15 (4) : 1631-1651. doi: 10.3934/jimo.2018115 [7] Honglin Yang, Jiawu Peng. Coordinating a supply chain with demand information updating. Journal of Industrial and Management Optimization, 2022, 18 (2) : 843-872. doi: 10.3934/jimo.2020181 [8] Sushil Kumar Dey, Bibhas C. Giri. Coordination of a sustainable reverse supply chain with revenue sharing contract. Journal of Industrial and Management Optimization, 2022, 18 (1) : 487-510. doi: 10.3934/jimo.2020165 [9] Min Li, Jiahua Zhang, Yifan Xu, Wei Wang. Effect of disruption risk on a supply chain with price-dependent demand. Journal of Industrial and Management Optimization, 2020, 16 (6) : 3083-3103. doi: 10.3934/jimo.2019095 [10] Benrong Zheng, Xianpei Hong. Effects of take-back legislation on pricing and coordination in a closed-loop supply chain. Journal of Industrial and Management Optimization, 2022, 18 (3) : 1603-1627. doi: 10.3934/jimo.2021035 [11] Jingming Pan, Wenqing Shi, Xiaowo Tang. Pricing and ordering strategies of supply chain with selling gift cards. Journal of Industrial and Management Optimization, 2018, 14 (1) : 349-369. doi: 10.3934/jimo.2017050 [12] Nina Yan, Baowen Sun. Comparative analysis of supply chain financing strategies between different financing modes. Journal of Industrial and Management Optimization, 2015, 11 (4) : 1073-1087. doi: 10.3934/jimo.2015.11.1073 [13] Qiang Yan, Mingqiao Luan, Yu Lin, Fangyu Ye. Equilibrium strategies in a supply chain with capital constrained suppliers: The impact of external financing. Journal of Industrial and Management Optimization, 2021, 17 (6) : 3027-3047. doi: 10.3934/jimo.2020106 [14] Han Zhao, Bangdong Sun, Hui Wang, Shiji Song, Yuli Zhang, Liejun Wang. Optimization and coordination in a service-constrained supply chain with the bidirectional option contract under conditional value-at-risk. Discrete and Continuous Dynamical Systems - S, 2022  doi: 10.3934/dcdss.2022021 [15] Feimin Zhong, Jinxing Xie, Yuwei Shen. Bargaining in a multi-echelon supply chain with power structure: KS solution vs. Nash solution. Journal of Industrial and Management Optimization, 2022, 18 (1) : 635-654. doi: 10.3934/jimo.2020172 [16] Jianxin Chen, Lin Sun, Tonghua Zhang, Rui Hou. Low carbon joint strategy and coordination for a dyadic supply chain with Nash bargaining fairness. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2021229 [17] Ashkan Mohsenzadeh Ledari, Alireza Arshadi Khamseh, Mohammad Mohammadi. A three echelon revenue oriented green supply chain network design. Numerical Algebra, Control and Optimization, 2018, 8 (2) : 157-168. doi: 10.3934/naco.2018009 [18] Jonas C. P. Yu, H. M. Wee, K. J. Wang. Supply chain partnership for Three-Echelon deteriorating inventory model. Journal of Industrial and Management Optimization, 2008, 4 (4) : 827-842. doi: 10.3934/jimo.2008.4.827 [19] Kun Fan, Wenjin Mao, Hua Qu, Xinning Li, Meng Wang. Study on government subsidy in a two-level supply chain of direct-fired biomass power generation based on contract coordination. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022049 [20] Arman Hamedirostami, Alireza Goli, Yousef Gholipour-Kanani. Green cross-dock based supply chain network design under demand uncertainty using new metaheuristic algorithms. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021105

2021 Impact Factor: 1.411