{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,26]],"date-time":"2026-01-26T11:47:00Z","timestamp":1769428020478,"version":"3.49.0"},"reference-count":64,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2021,6,3]],"date-time":"2021-06-03T00:00:00Z","timestamp":1622678400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2021,6,3]],"date-time":"2021-06-03T00:00:00Z","timestamp":1622678400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2022,8]]},"DOI":"10.1007\/s10479-021-04121-0","type":"journal-article","created":{"date-parts":[[2021,6,3]],"date-time":"2021-06-03T19:05:23Z","timestamp":1622747123000},"page":"1665-1702","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["A combined approach for modeling multi-echelon multi-period decentralized supply chain"],"prefix":"10.1007","volume":"315","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2036-7294","authenticated-orcid":false,"given":"Marjia","family":"Haque","sequence":"first","affiliation":[]},{"given":"Sanjoy Kumar","family":"Paul","sequence":"additional","affiliation":[]},{"given":"Ruhul","family":"Sarker","sequence":"additional","affiliation":[]},{"given":"Daryl","family":"Essam","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,6,3]]},"reference":[{"issue":"4","key":"4121_CR1","doi-asserted-by":"publisher","first-page":"1297","DOI":"10.1007\/s10898-012-9894-3","volume":"56","author":"J Ang","year":"2012","unstructured":"Ang, J., Fukushima, M., Meng, F., Noda, T., & Sun, J. (2012). Establishing Nash equilibrium of the manufacturer\u2013supplier game in supply chain management. Journal of Global Optimization, 56(4), 1297\u20131312.","journal-title":"Journal of Global Optimization"},{"issue":"2","key":"4121_CR2","doi-asserted-by":"publisher","first-page":"316","DOI":"10.1016\/j.ijpe.2008.05.011","volume":"115","author":"KA Arshinder","year":"2008","unstructured":"Arshinder, K. A., & Deshmukh, S. G. (2008). Supply chain coordination: Perspectives, empirical studies and research directions. International Journal of Production Economics, 115(2), 316\u2013335.","journal-title":"International Journal of Production Economics"},{"issue":"1","key":"4121_CR3","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1007\/s10479-011-0937-9","volume":"191","author":"\u0130S Bakal","year":"2011","unstructured":"Bakal, \u0130S., Erkip, N., & G\u00fcll\u00fc, R. (2011). Value of supplier\u2019s capacity information in a two-echelon supply chain. Annals of Operations Research, 191(1), 115\u2013135.","journal-title":"Annals of Operations Research"},{"issue":"1\u20132","key":"4121_CR4","first-page":"47","volume":"267","author":"F Ben Abdelaziz","year":"2016","unstructured":"Ben Abdelaziz, F., & Mejri, S. (2016). Multiobjective bi-level programming for shared inventory with emergency and backorders. Annals of Operations Research, 267(1\u20132), 47\u201363.","journal-title":"Annals of Operations Research"},{"issue":"2\u20137","key":"4121_CR5","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1016\/S0098-1354(00)00469-5","volume":"24","author":"S Bose","year":"2000","unstructured":"Bose, S., & Pekny, J. F. (2000). A model predictive framework for planning and scheduling problems: A case study of consumer goods supply chain. Computers and Chemical Engineering, 24(2\u20137), 329\u2013335.","journal-title":"Computers and Chemical Engineering"},{"key":"4121_CR6","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1016\/j.omega.2014.05.004","volume":"49","author":"HI Calvete","year":"2014","unstructured":"Calvete, H. I., Gal\u00e9, C., & Iranzo, J. A. (2014). Planning of a decentralized distribution network using bilevel optimization. Omega, 49, 30\u201341.","journal-title":"Omega"},{"issue":"1","key":"4121_CR8","doi-asserted-by":"publisher","first-page":"320","DOI":"10.1016\/j.cor.2010.05.007","volume":"38","author":"HI Calvete","year":"2011","unstructured":"Calvete, H. I., Gal\u00e9, C., & Oliveros, M.-J. (2011). Bilevel model for production\u2013distribution planning solved by using ant colony optimization. Computers & Operations Research, 38(1), 320\u2013327.","journal-title":"Computers & Operations Research"},{"issue":"1","key":"4121_CR9","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/j.ejor.2004.05.016","volume":"169","author":"D Cao","year":"2006","unstructured":"Cao, D., & Chen, M. (2006). Capacitated plant selection in a decentralized manufacturing environment: A bilevel optimization approach. European Journal of Operational Research, 169(1), 97\u2013110.","journal-title":"European Journal of Operational Research"},{"issue":"19","key":"4121_CR10","doi-asserted-by":"publisher","first-page":"5544","DOI":"10.1080\/00207543.2011.649802","volume":"50","author":"KK Castillo-Villar","year":"2012","unstructured":"Castillo-Villar, K. K., Smith, N. R., & Simonton, J. L. (2012). The impact of the cost of quality on serial supply-chain network design. International Journal of Production Research, 50(19), 5544\u20135566.","journal-title":"International Journal of Production Research"},{"key":"4121_CR11","first-page":"341","volume-title":"Handbooks in OR and MS","author":"F Chen","year":"2003","unstructured":"Chen, F. (2003). Information sharing and supply chain coordination. In S. C. Graves & A. G. de Kok (Eds.), Handbooks in OR and MS (Vol. 11, pp. 341\u2013421). Elsevier."},{"key":"4121_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.cie.2014.02.003","volume":"71","author":"D Choudhary","year":"2014","unstructured":"Choudhary, D., & Shankar, R. (2014). A goal programming model for joint decision making of inventory lot-size, supplier selection and carrier selection. Computers & Industrial Engineering, 71, 1\u20139.","journal-title":"Computers & Industrial Engineering"},{"key":"4121_CR13","doi-asserted-by":"publisher","first-page":"102271","DOI":"10.1016\/j.tre.2021.102271","volume":"148","author":"P Chowdhury","year":"2021","unstructured":"Chowdhury, P., Paul, S. K., Kaisar, S., & Moktadir, M. A. (2021). COVID-19 pandemic related supply chain studies: A systematic review. Transportation Research Part E: Logistics and Transportation Review, 148, 102271.","journal-title":"Transportation Research Part E: Logistics and Transportation Review"},{"issue":"1","key":"4121_CR15","doi-asserted-by":"publisher","first-page":"194","DOI":"10.1016\/j.ijpe.2012.11.004","volume":"142","author":"Q Duan","year":"2013","unstructured":"Duan, Q., & Warren Liao, T. (2013). Optimization of replenishment policies for decentralized and centralized capacitated supply chains under various demands. International Journal of Production Economics, 142(1), 194\u2013204.","journal-title":"International Journal of Production Economics"},{"key":"4121_CR17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.2298\/YJOR181115001E","volume":"30","author":"P Ezimadu","year":"2020","unstructured":"Ezimadu, P. (2020). Modelling cooperative advertising decisions in a manufacturer\u2013distributor\u2013retailer supply chain using game theory. Yugoslav Journal of Operations Research, 30, 1\u201333.","journal-title":"Yugoslav Journal of Operations Research"},{"key":"4121_CR18","doi-asserted-by":"publisher","first-page":"111277","DOI":"10.1016\/j.jenvman.2020.111277","volume":"275","author":"AM Fathollahi-Fard","year":"2020","unstructured":"Fathollahi-Fard, A. M., Ahmadi, A., & Al-e-Hashem, E. H. S. (2020). Sustainable closed-loop supply chain network for an integrated water supply and wastewater collection system under uncertainty. Journal of Environmental Management, 275, 111277.","journal-title":"Journal of Environmental Management"},{"issue":"6","key":"4121_CR19","doi-asserted-by":"publisher","first-page":"896","DOI":"10.1016\/j.tre.2010.03.003","volume":"46","author":"KN Francis Leung","year":"2010","unstructured":"Francis Leung, K. N. (2010). A generalized algebraic model for optimizing inventory decisions in a centralized or decentralized multi-stage multi-firm supply chain. Transportation Research Part E: Logistics and Transportation Review, 46(6), 896\u2013912.","journal-title":"Transportation Research Part E: Logistics and Transportation Review"},{"key":"4121_CR21","unstructured":"Gallego, G., & Talebian, M. (2013, 1\u20136 December). Multi-supplier and single retailer contracts: Profit splits under equilibrium. In 22nd National conference of the australian society for operations research, Adelaide."},{"issue":"1","key":"4121_CR22","doi-asserted-by":"publisher","first-page":"434","DOI":"10.1016\/j.ijpe.2010.08.002","volume":"128","author":"W Geng","year":"2010","unstructured":"Geng, W., Qiu, M., & Zhao, X. (2010). An inventory system with single distributor and multiple retailers: Operating scenarios and performance comparison. International Journal of Production Economics, 128(1), 434\u2013444.","journal-title":"International Journal of Production Economics"},{"issue":"1","key":"4121_CR23","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1016\/j.ejor.2020.01.048","volume":"285","author":"CH Glock","year":"2020","unstructured":"Glock, C. H., Rekik, Y., & Ries, J. M. (2020). A coordination mechanism for supply chains with capacity expansions and order-dependent lead times. European Journal of Operational Research, 285(1), 247\u2013262.","journal-title":"European Journal of Operational Research"},{"issue":"9","key":"4121_CR25","doi-asserted-by":"publisher","first-page":"5343","DOI":"10.1007\/s00521-018-3369-5","volume":"31","author":"M Hajiaghaei-Keshteli","year":"2018","unstructured":"Hajiaghaei-Keshteli, M., & Fathollahi Fard, A. M. (2018). Sustainable closed-loop supply chain network design with discount supposition. Neural Computing and Applications, 31(9), 5343\u20135377.","journal-title":"Neural Computing and Applications"},{"key":"4121_CR27","doi-asserted-by":"crossref","unstructured":"Haque, M., Paul, S. K., Sarker, R., & Essam, D. (2020a). Bi-objective multistage decentralized supply chain planning. In IEEE International conference on industrial engineering and engineering management (IEEM), Singapore.","DOI":"10.1109\/IEEM45057.2020.9309991"},{"key":"4121_CR26","doi-asserted-by":"publisher","first-page":"121865","DOI":"10.1016\/j.jclepro.2020.121865","volume":"266","author":"M Haque","year":"2020","unstructured":"Haque, M., Paul, S. K., Sarker, R., & Essam, D. (2020b). Managing decentralized supply chain using bilevel with Nash game approach. Journal of Cleaner Production, 266, 121865.","journal-title":"Journal of Cleaner Production"},{"issue":"2","key":"4121_CR28","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1007\/s10726-013-9358-2","volume":"23","author":"JE Hern\u00e1ndez","year":"2013","unstructured":"Hern\u00e1ndez, J. E., Mula, J., Poler, R., & Lyons, A. C. (2013). Collaborative planning in multi-tier supply chains supported by a negotiation-based mechanism and multi-agent system. Group Decision and Negotiation, 23(2), 235\u2013269.","journal-title":"Group Decision and Negotiation"},{"key":"4121_CR29","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1016\/j.tre.2014.01.004","volume":"63","author":"J Heydari","year":"2014","unstructured":"Heydari, J. (2014). Lead time variation control using reliable shipment equipment: An incentive scheme for supply chain coordination. Transportation Research Part E: Logistics and Transportation Review, 63, 44\u201358.","journal-title":"Transportation Research Part E: Logistics and Transportation Review"},{"key":"4121_CR30","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1007\/978-0-230-36514-8_2","volume-title":"Mastering: Fashion buying and merchandising management","author":"T Jackson","year":"2001","unstructured":"Jackson, T., & Shaw, D. (2001). The roles of the fashion buyer and garment technologist. In T. Jackson & D. Shaw (Eds.), Mastering: Fashion buying and merchandising management (pp. 9\u201325). Macmillan Education."},{"issue":"5","key":"4121_CR31","doi-asserted-by":"publisher","first-page":"501","DOI":"10.1080\/07408170601180536","volume":"39","author":"Z Jema\u00cf","year":"2007","unstructured":"Jema\u00cf, Z., & Karaesmen, F. (2007). Decentralized inventory control in a two-stage capacitated supply chain. IIE Transactions, 39(5), 501\u2013512.","journal-title":"IIE Transactions"},{"issue":"1","key":"4121_CR32","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1080\/01605682.2018.1524349","volume":"71","author":"A Jokar","year":"2019","unstructured":"Jokar, A., & Hosseini-Motlagh, S.-M. (2019). Simultaneous coordination of order quantity and corporate social responsibility in a two-echelon supply chain: A combined contract approach. Journal of the Operational Research Society, 71(1), 69\u201384.","journal-title":"Journal of the Operational Research Society"},{"issue":"2","key":"4121_CR33","doi-asserted-by":"publisher","first-page":"348","DOI":"10.1016\/j.cie.2007.12.017","volume":"55","author":"H Jung","year":"2008","unstructured":"Jung, H., Frank Chen, F., & Jeong, B. (2008). Decentralized supply chain planning framework for third party logistics partnership. Computers & Industrial Engineering, 55(2), 348\u2013364.","journal-title":"Computers & Industrial Engineering"},{"issue":"8","key":"4121_CR35","doi-asserted-by":"publisher","first-page":"3905","DOI":"10.1016\/j.apm.2011.02.008","volume":"35","author":"RJ Kuo","year":"2011","unstructured":"Kuo, R. J., & Han, Y. S. (2011). A hybrid of genetic algorithm and particle swarm optimization for solving bi-level linear programming problem\u2014A case study on supply chain model. Applied Mathematical Modelling, 35(8), 3905\u20133917.","journal-title":"Applied Mathematical Modelling"},{"key":"4121_CR37","unstructured":"Larbi, E. Y. A. S., Bekrar, A., Trentesaux, D., & Beldjilali, B. (2012). Multi-stage optimization in supply chain: An industrial case study. In 9th International conference on modeling, optimization."},{"issue":"5","key":"4121_CR38","doi-asserted-by":"publisher","first-page":"633","DOI":"10.1287\/mnsc.45.5.633","volume":"45","author":"H Lee","year":"1999","unstructured":"Lee, H., & Whang, S. (1999). Decentralized multi-echelon supply chains: Incentives and information. Management Science, 45(5), 633\u2013640.","journal-title":"Management Science"},{"issue":"1","key":"4121_CR40","doi-asserted-by":"publisher","first-page":"88","DOI":"10.1016\/j.ijpe.2008.07.015","volume":"120","author":"S Li","year":"2009","unstructured":"Li, S., Zhu, Z., & Huang, L. (2009). Supply chain coordination and decision making under consignment contract with revenue sharing. International Journal of Production Economics, 120(1), 88\u201399.","journal-title":"International Journal of Production Economics"},{"issue":"1","key":"4121_CR41","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1016\/j.ijpe.2010.07.028","volume":"128","author":"X Li","year":"2010","unstructured":"Li, X. (2010). Optimal inventory policies in decentralized supply chains. International Journal of Production Economics, 128(1), 303\u2013309.","journal-title":"International Journal of Production Economics"},{"issue":"1","key":"4121_CR42","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ejor.2006.06.023","volume":"179","author":"X Li","year":"2007","unstructured":"Li, X., & Wang, Q. (2007). Coordination mechanisms of supply chain systems. European Journal of Operational Research, 179(1), 1\u201316.","journal-title":"European Journal of Operational Research"},{"issue":"1\u20132","key":"4121_CR43","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1007\/s10479-019-03259-2","volume":"285","author":"C Liu","year":"2020","unstructured":"Liu, C., Xiang, X., & Zheng, L. (2020). Value of information sharing in a multiple producers\u2013distributor supply chain. Annals of Operations Research, 285(1\u20132), 121\u2013148.","journal-title":"Annals of Operations Research"},{"issue":"4","key":"4121_CR44","doi-asserted-by":"publisher","first-page":"2703","DOI":"10.1007\/s00500-019-03930-7","volume":"24","author":"H Luo","year":"2019","unstructured":"Luo, H., Liu, L., & Yang, X. (2019). Bi-level programming problem in the supply chain and its solution algorithm. Soft Computing, 24(4), 2703\u20132714.","journal-title":"Soft Computing"},{"issue":"6","key":"4121_CR45","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1080\/08839514.2013.805596","volume":"27","author":"W Ma","year":"2013","unstructured":"Ma, W., & Wang, M. (2013). Particle swarm optimization-based algorithm for bilevel joint pricing and lot-sizing decisions in a supply chain. Applied Artificial Intelligence, 27(6), 441\u2013460.","journal-title":"Applied Artificial Intelligence"},{"issue":"1","key":"4121_CR46","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1016\/j.ejor.2013.03.033","volume":"230","author":"SMJ Mirzapour Al-e-hashem","year":"2013","unstructured":"Mirzapour Al-e-hashem, S. M. J., Baboli, A., & Sazvar, Z. (2013). A stochastic aggregate production planning model in a green supply chain: Considering flexible lead times, nonlinear purchase and shortage cost functions. European Journal of Operational Research, 230(1), 26\u201341.","journal-title":"European Journal of Operational Research"},{"issue":"9\u201312","key":"4121_CR47","doi-asserted-by":"publisher","first-page":"1975","DOI":"10.1007\/s00170-013-5601-x","volume":"71","author":"M Mokhlesian","year":"2014","unstructured":"Mokhlesian, M., & Zegordi, S. H. (2014). Application of multidivisional bi-level programming to coordinate pricing and inventory decisions in a multiproduct competitive supply chain. The International Journal of Advanced Manufacturing Technology, 71(9\u201312), 1975\u20131989.","journal-title":"The International Journal of Advanced Manufacturing Technology"},{"issue":"3\u20134","key":"4121_CR48","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1007\/s12159-012-0085-x","volume":"5","author":"D Mourtzis","year":"2012","unstructured":"Mourtzis, D., & Doukas, M. (2012). Decentralized manufacturing systems review: Challenges and outlook. Logistics Research, 5(3\u20134), 113\u2013121.","journal-title":"Logistics Research"},{"issue":"1","key":"4121_CR49","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1007\/s12351-017-0327-4","volume":"20","author":"A Muzaffar","year":"2017","unstructured":"Muzaffar, A., Deng, S., & Malik, M. N. (2017). Contracting mechanism with imperfect information in a two-level supply chain. Operational Research, 20(1), 349\u2013368.","journal-title":"Operational Research"},{"issue":"5","key":"4121_CR50","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1016\/S1366-5545(01)00020-5","volume":"38","author":"A Nagurney","year":"2002","unstructured":"Nagurney, A., Dong, J., & Zhang, D. (2002). A supply chain network equilibrium model. Transportation Research Part E: Logistics and Transportation Review, 38(5), 281\u2013303.","journal-title":"Transportation Research Part E: Logistics and Transportation Review"},{"issue":"1","key":"4121_CR51","doi-asserted-by":"publisher","first-page":"144","DOI":"10.1016\/j.advengsoft.2011.09.008","volume":"45","author":"A Naimi Sadigh","year":"2012","unstructured":"Naimi Sadigh, A., Mozafari, M., & Karimi, B. (2012). Manufacturer\u2013retailer supply chain coordination: A bi-level programming approach. Advances in Engineering Software, 45(1), 144\u2013152.","journal-title":"Advances in Engineering Software"},{"issue":"1","key":"4121_CR52","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/j.indmarman.2003.08.006","volume":"33","author":"R Narasimhan","year":"2004","unstructured":"Narasimhan, R., & Mahapatra, S. (2004). Decision models in global supply chain management. Industrial Marketing Management, 33(1), 21\u201327.","journal-title":"Industrial Marketing Management"},{"key":"4121_CR53","doi-asserted-by":"publisher","first-page":"3956","DOI":"10.1016\/j.jclepro.2016.10.062","volume":"142","author":"M Nematollahi","year":"2017","unstructured":"Nematollahi, M., Hosseini-Motlagh, S.-M., & Heydari, J. (2017). Economic and social collaborative decision-making on visit interval and service level in a two-echelon pharmaceutical supply chain. Journal of Cleaner Production, 142, 3956\u20133969.","journal-title":"Journal of Cleaner Production"},{"issue":"2","key":"4121_CR56","doi-asserted-by":"publisher","first-page":"262","DOI":"10.1016\/j.ijpe.2009.08.008","volume":"127","author":"T Qu","year":"2010","unstructured":"Qu, T., Huang, G. Q., Zhang, Y., & Dai, Q. Y. (2010). A generic analytical target cascading optimization system for decentralized supply chain configuration over supply chain grid. International Journal of Production Economics, 127(2), 262\u2013277.","journal-title":"International Journal of Production Economics"},{"issue":"1","key":"4121_CR57","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1007\/s10100-018-0594-z","volume":"28","author":"G Rius-Sorolla","year":"2020","unstructured":"Rius-Sorolla, G., Maheut, J., Estell\u00e9s-Miguel, S., & Garcia-Sabater, J. P. (2020). Coordination mechanisms with mathematical programming models for decentralized decision-making: A literature review. Central European Journal of Operations Research, 28(1), 61\u2013104.","journal-title":"Central European Journal of Operations Research"},{"issue":"12","key":"4121_CR58","doi-asserted-by":"publisher","first-page":"1244","DOI":"10.3390\/su8121244","volume":"8","author":"B Sarkar","year":"2016","unstructured":"Sarkar, B., Saren, S., Sarkar, M., & Seo, Y. (2016). A Stackelberg game approach in an integrated inventory model with carbon-emission and setup cost reduction. Sustainability, 8(12), 1244.","journal-title":"Sustainability"},{"issue":"3","key":"4121_CR59","doi-asserted-by":"publisher","first-page":"396","DOI":"10.1016\/j.tre.2006.11.001","volume":"44","author":"H Selim","year":"2008","unstructured":"Selim, H., Araz, C., & Ozkarahan, I. (2008). Collaborative production\u2013distribution planning in supply chain: A fuzzy goal programming approach. Transportation Research Part E: Logistics and Transportation Review, 44(3), 396\u2013419.","journal-title":"Transportation Research Part E: Logistics and Transportation Review"},{"issue":"2","key":"4121_CR60","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1016\/j.ejor.2010.11.014","volume":"211","author":"MM SeyedEsfahani","year":"2011","unstructured":"SeyedEsfahani, M. M., Biazaran, M., & Gharakhani, M. (2011). A game theoretic approach to coordinate pricing and vertical co-op advertising in manufacturer\u2013retailer supply chains. European Journal of Operational Research, 211(2), 263\u2013273.","journal-title":"European Journal of Operational Research"},{"issue":"3","key":"4121_CR61","doi-asserted-by":"publisher","first-page":"607","DOI":"10.1111\/j.1540-5915.1998.tb01356.x","volume":"29","author":"JM Swaminathan","year":"1998","unstructured":"Swaminathan, J. M., Smith, S. F., & Sadeh, N. M. (1998). Modeling supply chain dynamics: A multiagent approach. Decision Sciences, 29(3), 607\u2013632.","journal-title":"Decision Sciences"},{"issue":"9","key":"4121_CR62","doi-asserted-by":"publisher","first-page":"2715","DOI":"10.1080\/00207543.2012.737952","volume":"51","author":"A Taghipour","year":"2013","unstructured":"Taghipour, A., & Frayret, J.-M. (2013). Dynamic mutual adjustment search for supply chain operations planning co-ordination. International Journal of Production Research, 51(9), 2715\u20132739.","journal-title":"International Journal of Production Research"},{"issue":"4","key":"4121_CR63","doi-asserted-by":"publisher","first-page":"919","DOI":"10.1080\/00207721.2014.909544","volume":"47","author":"AA Taleizadeh","year":"2014","unstructured":"Taleizadeh, A. A., & Noori-daryan, M. (2014). Pricing, manufacturing and inventory policies for raw material in a three-level supply chain. International Journal of Systems Science, 47(4), 919\u2013931.","journal-title":"International Journal of Systems Science"},{"issue":"9","key":"4121_CR64","doi-asserted-by":"publisher","first-page":"2807","DOI":"10.1080\/00207543.2016.1154621","volume":"54","author":"AA Taleizadeh","year":"2016","unstructured":"Taleizadeh, A. A., Noori-daryan, M., & Govindan, K. (2016). Pricing and ordering decisions of two competing supply chains with different composite policies: A Stackelberg game-theoretic approach. International Journal of Production Research, 54(9), 2807\u20132836.","journal-title":"International Journal of Production Research"},{"issue":"2","key":"4121_CR65","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1080\/00207543.2015.1096977","volume":"54","author":"A Thomas","year":"2015","unstructured":"Thomas, A., Krishnamoorthy, M., Venkateswaran, J., & Singh, G. (2015). Decentralised decision-making in a multi-party supply chain. International Journal of Production Research, 54(2), 405\u2013425.","journal-title":"International Journal of Production Research"},{"issue":"2","key":"4121_CR66","doi-asserted-by":"publisher","first-page":"372","DOI":"10.1016\/S0377-2217(03)00233-9","volume":"157","author":"H Wang","year":"2004","unstructured":"Wang, H., Guo, M., & Efstathiou, J. (2004). A game-theoretical cooperative mechanism design for a two-echelon decentralized supply chain. European Journal of Operational Research, 157(2), 372\u2013388.","journal-title":"European Journal of Operational Research"},{"key":"4121_CR67","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1016\/j.cie.2017.01.008","volume":"105","author":"M Wang","year":"2017","unstructured":"Wang, M., Zhang, R., & Zhu, X. (2017). A bi-level programming approach to the decision problems in a vendor-buyer eco-friendly supply chain. Computers & Industrial Engineering, 105, 299\u2013312.","journal-title":"Computers & Industrial Engineering"},{"key":"4121_CR68","unstructured":"Yang, M.-H., & Bialas, W. (2007). Nash\u2013Stackelberg equilibrium solutions for linear multidivisional multilevel programming problems. University at Buffalo Technical Report, Buffalo."},{"key":"4121_CR69","doi-asserted-by":"publisher","first-page":"242","DOI":"10.1016\/j.compchemeng.2014.05.025","volume":"68","author":"K Yeh","year":"2014","unstructured":"Yeh, K., Realff, M. J., Lee, J. H., & Whittaker, C. (2014). Analysis and comparison of single period single level and bilevel programming representations of a pre-existing timberlands supply chain with a new biorefinery facility. Computers & Chemical Engineering, 68, 242\u2013254.","journal-title":"Computers & Chemical Engineering"},{"issue":"3","key":"4121_CR70","doi-asserted-by":"publisher","first-page":"929","DOI":"10.1016\/j.ejor.2007.10.016","volume":"192","author":"Y Yu","year":"2009","unstructured":"Yu, Y., Chu, F., & Chen, H. (2009a). A Stackelberg game and its improvement in a VMI system with a manufacturing vendor. European Journal of Operational Research, 192(3), 929\u2013948.","journal-title":"European Journal of Operational Research"},{"issue":"1","key":"4121_CR71","doi-asserted-by":"publisher","first-page":"368","DOI":"10.1016\/j.cie.2008.12.003","volume":"57","author":"Y Yu","year":"2009","unstructured":"Yu, Y., Huang, G. Q., & Liang, L. (2009b). Stackelberg game-theoretic model for optimizing advertising, pricing and inventory policies in vendor managed inventory (VMI) production supply chains. Computers & Industrial Engineering, 57(1), 368\u2013382.","journal-title":"Computers & Industrial Engineering"},{"key":"4121_CR72","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1016\/j.compchemeng.2014.08.010","volume":"71","author":"D Yue","year":"2014","unstructured":"Yue, D., & You, F. (2014). Game-theoretic modeling and optimization of multi-echelon supply chain design and operation under Stackelberg game and market equilibrium. Computers & Chemical Engineering, 71, 347\u2013361.","journal-title":"Computers & Chemical Engineering"},{"issue":"4","key":"4121_CR73","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1080\/13675560600836910","volume":"9","author":"Y Yugang","year":"2006","unstructured":"Yugang, Y., Liang, L., & Huang, G. Q. (2006). Leader\u2013follower game in vendor-managed inventory system with limited production capacity considering wholesale and retail prices. International Journal of Logistics Research and Applications, 9(4), 335\u2013350.","journal-title":"International Journal of Logistics Research and Applications"},{"key":"4121_CR74","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.asoc.2016.11.049","volume":"51","author":"F Zaman","year":"2017","unstructured":"Zaman, F., Elsayed, S. M., Ray, T., & Sarker, R. A. (2017). Co-evolutionary approach for strategic bidding in competitive electricity markets. Applied Soft Computing, 51, 1\u201322.","journal-title":"Applied Soft Computing"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-021-04121-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10479-021-04121-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-021-04121-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,9]],"date-time":"2025-04-09T09:00:19Z","timestamp":1744189219000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10479-021-04121-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,3]]},"references-count":64,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,8]]}},"alternative-id":["4121"],"URL":"https:\/\/doi.org\/10.1007\/s10479-021-04121-0","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,3]]},"assertion":[{"value":"12 May 2021","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 June 2021","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}