{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T15:23:40Z","timestamp":1772119420030,"version":"3.50.1"},"reference-count":60,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,2,1]],"date-time":"2025-02-01T00:00:00Z","timestamp":1738368000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,2,1]],"date-time":"2025-02-01T00:00:00Z","timestamp":1738368000000},"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":["Soft Comput"],"published-print":{"date-parts":[[2025,2]]},"DOI":"10.1007\/s00500-025-10453-x","type":"journal-article","created":{"date-parts":[[2025,2,11]],"date-time":"2025-02-11T22:09:41Z","timestamp":1739311781000},"page":"1811-1827","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A game-theoretic exploration with surplus profit-sharing in a three-channel supply chain, featuring e-commerce dynamics"],"prefix":"10.1007","volume":"29","author":[{"given":"Maryam","family":"Vatanara","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8756-4922","authenticated-orcid":false,"given":"Masoud","family":"Rabbani","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jafar","family":"Heydari","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,2,12]]},"reference":[{"key":"10453_CR1","doi-asserted-by":"publisher","DOI":"10.1504\/IJAOM.2016.076206","author":"SM Ali","year":"2016","unstructured":"Ali SM, Nakade K (2016) Coordinating a supply chain system for production, pricing and service strategies with disruptions. Int J Adv Oper Manag. https:\/\/doi.org\/10.1504\/IJAOM.2016.076206","journal-title":"Int J Adv Oper Manag"},{"key":"10453_CR2","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1016\/j.jretconser.2017.08.025","volume":"40","author":"SM Ali","year":"2018","unstructured":"Ali SM, Rahman MH, Tumpa TJ, Moghul Rifat AA, Paul SK (2018) Examining price and service competition among retailers in a supply chain under potential demand disruption. J Retail Consum Serv 40:40\u201347. https:\/\/doi.org\/10.1016\/j.jretconser.2017.08.025","journal-title":"J Retail Consum Serv"},{"key":"10453_CR3","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2022.108439","volume":"171","author":"M Asghari","year":"2022","unstructured":"Asghari M, Afshari H, Mirzapour Al-e-hashem SMJ, Fathollahi-Fard AM, Dulebenets MA (2022) Pricing and advertising decisions in a direct-sales closed-loop supply chain. Comput Ind Eng 171:108439. https:\/\/doi.org\/10.1016\/j.cie.2022.108439","journal-title":"Comput Ind Eng"},{"key":"10453_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/s11846-023-00645-w","author":"J Ballerini","year":"2023","unstructured":"Ballerini J, Yahiaoui D, Giovando G, Ferraris A (2023) E-commerce channel management on the manufacturers\u2019 side: ongoing debates and future research pathways. RMS. https:\/\/doi.org\/10.1007\/s11846-023-00645-w","journal-title":"RMS"},{"key":"10453_CR5","doi-asserted-by":"publisher","first-page":"232","DOI":"10.1016\/j.jclepro.2017.01.060","volume":"145","author":"Z Basiri","year":"2017","unstructured":"Basiri Z, Heydari J (2017) A mathematical model for green supply chain coordination with substitutable products. J Clean Prod 145:232\u2013249. https:\/\/doi.org\/10.1016\/j.jclepro.2017.01.060","journal-title":"J Clean Prod"},{"key":"10453_CR6","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2023.108992","volume":"177","author":"J Cai","year":"2023","unstructured":"Cai J, Sun H, Hu X, Zhang W (2023) How reverse information sharing supports pricing and sales effort decisions: Signaling game-based incentive mechanism design. Comput Ind Eng 177:108992. https:\/\/doi.org\/10.1016\/j.cie.2023.108992","journal-title":"Comput Ind Eng"},{"key":"10453_CR7","doi-asserted-by":"publisher","first-page":"290","DOI":"10.1016\/j.jbusres.2022.03.044","volume":"147","author":"C Chauhan","year":"2022","unstructured":"Chauhan C, Kaur P, Arrawatia R, Ractham P, Dhir A (2022) Supply chain collaboration and sustainable development goals (SDGs). Teamwork makes achieving SDGs dream work. J Bus Res 147:290\u2013307. https:\/\/doi.org\/10.1016\/j.jbusres.2022.03.044","journal-title":"J Bus Res"},{"issue":"3","key":"10453_CR8","doi-asserted-by":"publisher","first-page":"996","DOI":"10.1016\/j.ejor.2019.03.013","volume":"277","author":"J Chen","year":"2019","unstructured":"Chen J, Chen B (2019) When should the offline retailer implement price matching? Eur J Oper Res 277(3):996\u20131009. https:\/\/doi.org\/10.1016\/j.ejor.2019.03.013","journal-title":"Eur J Oper Res"},{"issue":"4","key":"10453_CR9","doi-asserted-by":"publisher","first-page":"2693","DOI":"10.1007\/s00500-019-03894-8","volume":"24","author":"Y-Z Chen","year":"2020","unstructured":"Chen Y-Z, Chen W (2020) Incentive contracts of knowledge investment for cooperative innovation in project-based supply chain with double moral hazard. Soft Comput 24(4):2693\u20132702. https:\/\/doi.org\/10.1007\/s00500-019-03894-8","journal-title":"Soft Comput"},{"key":"10453_CR10","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2022.108617","volume":"250","author":"T-M Choi","year":"2022","unstructured":"Choi T-M, Wang Y, Shen B (2022) Selling to Profit-Target-Oriented retailers: optimal supply chain contracting with bargaining. Int J Prod Econ 250:108617. https:\/\/doi.org\/10.1016\/j.ijpe.2022.108617","journal-title":"Int J Prod Econ"},{"key":"10453_CR11","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1016\/j.neucom.2017.04.027","volume":"260","author":"Y Dai","year":"2017","unstructured":"Dai Y, Gao Y, Gao H, Zhu H (2017) Real-time pricing scheme based on Stackelberg game in smart grid with multiple power retailers. Neurocomputing 260:149\u2013156. https:\/\/doi.org\/10.1016\/j.neucom.2017.04.027","journal-title":"Neurocomputing"},{"key":"10453_CR12","doi-asserted-by":"publisher","first-page":"103561","DOI":"10.1016\/j.jretconser.2023.103561","volume":"76","author":"A Datta","year":"2024","unstructured":"Datta A, Sarkar B, Dey BK, Sangal I, Yang L, Fan S-KS, Thangavelu L (2024) The impact of sales effort on a dual-channel dynamical system under a price-sensitive stochastic demand. J Retail Consum Serv 76:103561. https:\/\/doi.org\/10.1016\/j.jretconser.2023.103561","journal-title":"J Retail Consum Serv"},{"issue":"2","key":"10453_CR13","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1016\/j.ejor.2010.08.003","volume":"208","author":"P De Giovanni","year":"2011","unstructured":"De Giovanni P (2011) Quality improvement vs. advertising support: Which strategy works better for a manufacturer? Eur J Oper Res 208(2):119\u2013130. https:\/\/doi.org\/10.1016\/j.ejor.2010.08.003","journal-title":"Eur J Oper Res"},{"key":"10453_CR14","doi-asserted-by":"publisher","first-page":"2043","DOI":"10.1016\/j.jclepro.2015.01.066","volume":"112","author":"J Gao","year":"2016","unstructured":"Gao J, Han H, Hou L, Wang H (2016) Pricing and effort decisions in a closed-loop supply chain under different channel power structures. J Clean Prod 112:2043\u20132057. https:\/\/doi.org\/10.1016\/j.jclepro.2015.01.066","journal-title":"J Clean Prod"},{"key":"10453_CR15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jclepro.2023.138621","volume":"422","author":"M Gharegozlu","year":"2023","unstructured":"Gharegozlu M, Seddighi AH, Ghaderi A (2023) Location-pricing decisions with carbon emission considerations: A behavioral game-theoretic approach. J Clean Prod 422:138621. https:\/\/doi.org\/10.1016\/j.jclepro.2023.138621","journal-title":"J Clean Prod"},{"key":"10453_CR16","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2023.109285","volume":"181","author":"D Gong","year":"2023","unstructured":"Gong D, Gao H, Ren L, Yan X (2023) Consumers\u2019 free riding: pricing and retailer service decisions in a closed-loop supply chain. Comput Ind Eng 181:109285. https:\/\/doi.org\/10.1016\/j.cie.2023.109285","journal-title":"Comput Ind Eng"},{"key":"10453_CR17","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1016\/j.ijpe.2018.08.004","volume":"215","author":"K Govindan","year":"2019","unstructured":"Govindan K, Malomfalean A (2019) A framework for evaluation of supply chain coordination by contracts under O2O environment. Int J Prod Econ 215:11\u201323. https:\/\/doi.org\/10.1016\/j.ijpe.2018.08.004","journal-title":"Int J Prod Econ"},{"key":"10453_CR18","doi-asserted-by":"publisher","DOI":"10.1016\/j.jretconser.2023.103483","volume":"75","author":"S-Q Gu","year":"2023","unstructured":"Gu S-Q, Liu Y, Zhao G (2023) Pricing coordination of a dual-channel supply chain considering offline in-sale service. J Retail Consum Serv 75:103483. https:\/\/doi.org\/10.1016\/j.jretconser.2023.103483","journal-title":"J Retail Consum Serv"},{"key":"10453_CR19","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2023.109607","volume":"185","author":"P Haghi Motlagh","year":"2023","unstructured":"Haghi Motlagh P, Reza Nasiri G (2023) Developing a pricing strategy and coordination in a dual-channel supply chain incorporating inventory policy and marketing considerations. Comput Ind Eng 185:109607. https:\/\/doi.org\/10.1016\/j.cie.2023.109607","journal-title":"Comput Ind Eng"},{"key":"10453_CR20","doi-asserted-by":"publisher","first-page":"366","DOI":"10.1016\/j.jebo.2021.07.038","volume":"190","author":"N Hanaki","year":"2021","unstructured":"Hanaki N, Hayashi T, Lombardi M, Ogawa K (2021) Partial equilibrium mechanism and inter-sectoral coordination: an experiment. J Econ Behav Organ 190:366\u2013389. https:\/\/doi.org\/10.1016\/j.jebo.2021.07.038","journal-title":"J Econ Behav Organ"},{"key":"10453_CR21","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1016\/j.iref.2023.07.007","volume":"89","author":"M Hayashibara","year":"2024","unstructured":"Hayashibara M, Ohkawa T, Nomura R, Okamura M (2024) Optimal degree of interagency coordination of subsidy and tariff policies. Int Rev Econ Financ 89:327\u2013336. https:\/\/doi.org\/10.1016\/j.iref.2023.07.007","journal-title":"Int Rev Econ Financ"},{"issue":"6","key":"10453_CR22","doi-asserted-by":"publisher","first-page":"2777","DOI":"10.1016\/j.apm.2008.08.016","volume":"33","author":"Y He","year":"2009","unstructured":"He Y, Zhao X, Zhao L, He J (2009) Coordinating a supply chain with effort and price dependent stochastic demand. Appl Math Model 33(6):2777\u20132790. https:\/\/doi.org\/10.1016\/j.apm.2008.08.016","journal-title":"Appl Math Model"},{"issue":"2","key":"10453_CR23","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1016\/j.ejor.2021.10.059","volume":"301","author":"S-M Hosseini-Motlagh","year":"2022","unstructured":"Hosseini-Motlagh S-M, Choi T-M, Johari M, Nouri-Harzvili M (2022) A profit surplus distribution mechanism for supply chain coordination: an evolutionary game-theoretic analysis. Eur J Oper Res 301(2):561\u2013575. https:\/\/doi.org\/10.1016\/j.ejor.2021.10.059","journal-title":"Eur J Oper Res"},{"issue":"1","key":"10453_CR24","doi-asserted-by":"publisher","first-page":"258","DOI":"10.1016\/j.ejor.2007.11.041","volume":"194","author":"W Huang","year":"2009","unstructured":"Huang W, Swaminathan JM (2009) Introduction of a second channel: Implications for pricing and profits. Eur J Oper Res 194(1):258\u2013279. https:\/\/doi.org\/10.1016\/j.ejor.2007.11.041","journal-title":"Eur J Oper Res"},{"key":"10453_CR25","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2023.121302","volume":"237","author":"N Khanlarzade","year":"2024","unstructured":"Khanlarzade N, Farughi H (2024) Modeling the Stackelberg game with a boundedly rational follower in deterioration supply chain-based interaction with the leader\u2019s hybrid pricing strategy. Expert Syst Appl 237:121302. https:\/\/doi.org\/10.1016\/j.eswa.2023.121302","journal-title":"Expert Syst Appl"},{"key":"10453_CR26","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijepes.2023.109237","volume":"152","author":"Z Lei","year":"2023","unstructured":"Lei Z, Liu M, Shen Z (2023a) Analysis of strategic bidding of a DER aggregator in energy markets through the Stackelberg game model with the mixed-integer lower-level problem. Int J Electr Power Energy Syst 152:109237. https:\/\/doi.org\/10.1016\/j.ijepes.2023.109237","journal-title":"Int J Electr Power Energy Syst"},{"key":"10453_CR27","doi-asserted-by":"publisher","DOI":"10.1016\/j.segan.2023.101111","volume":"35","author":"Z Lei","year":"2023","unstructured":"Lei Z, Liu M, Shen Z, Lu J, Lu Z (2023b) A Nash-Stackelberg game approach to analyze strategic bidding for multiple DER aggregators in electricity markets. Sustain Energy Grids Netw 35:101111. https:\/\/doi.org\/10.1016\/j.segan.2023.101111","journal-title":"Sustain Energy Grids Netw"},{"issue":"15","key":"10453_CR28","doi-asserted-by":"publisher","first-page":"7349","DOI":"10.1016\/j.apm.2016.03.010","volume":"40","author":"Q-H Li","year":"2016","unstructured":"Li Q-H, Li B (2016) Dual-channel supply chain equilibrium problems regarding retail services and fairness concerns. Appl Math Model 40(15):7349\u20137367. https:\/\/doi.org\/10.1016\/j.apm.2016.03.010","journal-title":"Appl Math Model"},{"key":"10453_CR29","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1016\/j.tre.2019.03.019","volume":"126","author":"G Li","year":"2019","unstructured":"Li G, Li L, Sun J (2019) Pricing and service effort strategy in a dual-channel supply chain with showrooming effect. Transport Res Part E Log Transport Rev 126:32\u201348. https:\/\/doi.org\/10.1016\/j.tre.2019.03.019","journal-title":"Transport Res Part E Log Transport Rev"},{"key":"10453_CR30","doi-asserted-by":"publisher","DOI":"10.1007\/s10668-022-02845-y","author":"M Li","year":"2022","unstructured":"Li M, Shan M, Meng Q (2022) Pricing and promotion efforts strategies of dual-channel green supply chain considering service cooperation and free-riding between online and offline retailers. Environ Dev Sustain. https:\/\/doi.org\/10.1007\/s10668-022-02845-y","journal-title":"Environ Dev Sustain"},{"issue":"3","key":"10453_CR31","doi-asserted-by":"publisher","first-page":"633","DOI":"10.1080\/02331934.2020.1812064","volume":"71","author":"Y Liang","year":"2022","unstructured":"Liang Y, Sun X (2022) Product green degree, service free-riding, strategic price difference in a dual-channel supply chain based on dynamic game. Optimization 71(3):633\u2013674. https:\/\/doi.org\/10.1080\/02331934.2020.1812064","journal-title":"Optimization"},{"issue":"2","key":"10453_CR32","doi-asserted-by":"publisher","first-page":"320","DOI":"10.1108\/IMDS-03-2016-0088","volume":"117","author":"L Liang","year":"2017","unstructured":"Liang L, Xie J, Liu L, Xia Y (2017) Revenue sharing contract coordination of wind turbine order policy and aftermarket service based on joint effort. Ind Manag Data Syst 117(2):320\u2013345. https:\/\/doi.org\/10.1108\/IMDS-03-2016-0088","journal-title":"Ind Manag Data Syst"},{"key":"10453_CR33","doi-asserted-by":"publisher","DOI":"10.1016\/j.elerap.2020.101001","volume":"43","author":"C Liu","year":"2020","unstructured":"Liu C, Dan Y, Dan B, Xu G (2020a) Cooperative strategy for a dual-channel supply chain with the influence of free-riding customers. Electron Commer Res Appl 43:101001. https:\/\/doi.org\/10.1016\/j.elerap.2020.101001","journal-title":"Electron Commer Res Appl"},{"key":"10453_CR34","doi-asserted-by":"publisher","DOI":"10.1016\/j.jretconser.2019.101950","volume":"53","author":"Y Liu","year":"2020","unstructured":"Liu Y, Wang D-D, Xu Q (2020b) A supply chain coordination mechanism with suppliers\u2019 effort performance level and fairness concern. J Retail Consum Serv 53:101950. https:\/\/doi.org\/10.1016\/j.jretconser.2019.101950","journal-title":"J Retail Consum Serv"},{"issue":"2","key":"10453_CR35","doi-asserted-by":"publisher","first-page":"572","DOI":"10.1016\/j.ijpe.2013.04.020","volume":"144","author":"P Ma","year":"2013","unstructured":"Ma P, Wang H, Shang J (2013) Supply chain channel strategies with quality and marketing effort-dependent demand. Int J Prod Econ 144(2):572\u2013581. https:\/\/doi.org\/10.1016\/j.ijpe.2013.04.020","journal-title":"Int J Prod Econ"},{"issue":"4","key":"10453_CR36","doi-asserted-by":"publisher","first-page":"2769","DOI":"10.1007\/s00500-019-04435-z","volume":"24","author":"H Ma","year":"2020","unstructured":"Ma H, Li X, Liu Y (2020) Multi-period multi-scenario optimal design for closed-loop supply chain network of hazardous products with consideration of facility expansion. Soft Comput 24(4):2769\u20132780. https:\/\/doi.org\/10.1007\/s00500-019-04435-z","journal-title":"Soft Comput"},{"key":"10453_CR37","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2023.122085","volume":"238","author":"S Ma","year":"2024","unstructured":"Ma S, Zhang LL, Cai X (2024) Optimizing joint technology selection, production planning and pricing decisions under emission tax: a Stackelberg game model and nested genetic algorithm. Expert Syst Appl 238:122085. https:\/\/doi.org\/10.1016\/j.eswa.2023.122085","journal-title":"Expert Syst Appl"},{"key":"10453_CR38","doi-asserted-by":"crossref","unstructured":"McGuire K, Staelin R (2008) An industry equilibrium analysis of downstream vertical integration. Published By: INFORMS Published on: January\u2013February 2008. Retrieved from https:\/\/www.researchgate.net\/publication\/220659115_An_Industry_Equilibrium_Analysis_of_Downstream_Vertical_Integration","DOI":"10.1287\/mksc.1070.0335"},{"key":"10453_CR39","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2023.121960","volume":"238","author":"C Mondal","year":"2024","unstructured":"Mondal C, Giri BC (2024) Pricing and bundling strategies for complementary products in a closed-loop green supply chain under manufacturers\u2019 different behaviors. Expert Syst Appl 238:121960. https:\/\/doi.org\/10.1016\/j.eswa.2023.121960","journal-title":"Expert Syst Appl"},{"issue":"1","key":"10453_CR40","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1016\/j.ejor.2004.04.048","volume":"169","author":"J Mostard","year":"2006","unstructured":"Mostard J, Teunter R (2006) The newsboy problem with resalable returns: a single period model and case study. Eur J Oper Res 169(1):81\u201396. https:\/\/doi.org\/10.1016\/j.ejor.2004.04.048","journal-title":"Eur J Oper Res"},{"issue":"3","key":"10453_CR41","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1080\/17509653.2022.2043196","volume":"18","author":"A Namazi","year":"2023","unstructured":"Namazi A, Khodabakhshi M (2023) A novel game theoretic method on fair economic resource allocation with multiple Criteria. Int J Manag Sci Eng Manag 18(3):170\u2013176. https:\/\/doi.org\/10.1080\/17509653.2022.2043196","journal-title":"Int J Manag Sci Eng Manag"},{"key":"10453_CR42","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2023.109242","volume":"180","author":"S Patare","year":"2023","unstructured":"Patare S, Venkataraman SV (2023) Strategies in supply chain competition: a game theoretic approach. Comput Ind Eng 180:109242. https:\/\/doi.org\/10.1016\/j.cie.2023.109242","journal-title":"Comput Ind Eng"},{"key":"10453_CR43","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1016\/j.ijpe.2018.11.025","volume":"208","author":"P Patra","year":"2019","unstructured":"Patra P, Kumar UD, Nowicki DR, Randall WS (2019) Effective management of performance-based contracts for sustainment dominant systems. Int J Prod Econ 208:369\u2013382. https:\/\/doi.org\/10.1016\/j.ijpe.2018.11.025","journal-title":"Int J Prod Econ"},{"key":"10453_CR44","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1016\/j.cie.2018.03.020","volume":"119","author":"M Radhi","year":"2018","unstructured":"Radhi M, Zhang G (2018) Pricing policies for a dual-channel retailer with cross-channel returns. Comput Ind Eng 119:63\u201375. https:\/\/doi.org\/10.1016\/j.cie.2018.03.020","journal-title":"Comput Ind Eng"},{"key":"10453_CR45","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1016\/j.jclepro.2019.01.297","volume":"218","author":"A Ranjan","year":"2019","unstructured":"Ranjan A, Jha JK (2019) Pricing and coordination strategies of a dual-channel supply chain considering green quality and sales effort. J Clean Prod 218:409\u2013424. https:\/\/doi.org\/10.1016\/j.jclepro.2019.01.297","journal-title":"J Clean Prod"},{"key":"10453_CR46","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-023-09469-y","author":"P Sahw","year":"2024","unstructured":"Sahw P, Maity T, Yadav RK (2024) Cooperative approach for electric vehicle charging: a multi-polynomial regression-based model predictive controller with advanced techniques. Soft Comput. https:\/\/doi.org\/10.1007\/s00500-023-09469-y","journal-title":"Soft Comput"},{"key":"10453_CR47","doi-asserted-by":"publisher","first-page":"512","DOI":"10.1016\/j.ijpe.2018.12.006","volume":"208","author":"M Shafiq","year":"2019","unstructured":"Shafiq M, Savino MM (2019) Supply chain coordination to optimize manufacturer\u2019s capacity procurement decisions through a new commitment-based model with penalty and revenue-sharing. Int J Prod Econ 208:512\u2013528. https:\/\/doi.org\/10.1016\/j.ijpe.2018.12.006","journal-title":"Int J Prod Econ"},{"key":"10453_CR48","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijepes.2022.108376","volume":"142","author":"Z Shen","year":"2022","unstructured":"Shen Z, Liu M, Xu L, Lu W (2022) An accelerated Stackelberg game approach for distributed energy resource aggregator participating in energy and reserve markets considering security check. Int J Electr Power Energy Syst 142:108376. https:\/\/doi.org\/10.1016\/j.ijepes.2022.108376","journal-title":"Int J Electr Power Energy Syst"},{"key":"10453_CR49","doi-asserted-by":"publisher","DOI":"10.1016\/j.tre.2023.103285","volume":"179","author":"S Sun","year":"2023","unstructured":"Sun S, Liu T (2023) Pricing and sales-effort coordination facing free riding behaviors between a brick-and-mortar retailer and a platform store owned by the manufacturer. Transport Res Part e Log Transport Rev 179:103285. https:\/\/doi.org\/10.1016\/j.tre.2023.103285","journal-title":"Transport Res Part e Log Transport Rev"},{"issue":"2","key":"10453_CR50","doi-asserted-by":"publisher","first-page":"174","DOI":"10.1016\/j.jretai.2015.02.005","volume":"91","author":"PC Verhoef","year":"2015","unstructured":"Verhoef PC, Kannan PK, Inman JJ (2015) From multi-channel retailing to omni-channel retailing: introduction to the special issue on multi-channel retailing. J Retail 91(2):174\u2013181. https:\/\/doi.org\/10.1016\/j.jretai.2015.02.005","journal-title":"J Retail"},{"key":"10453_CR51","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2020.107834","volume":"231","author":"N Yan","year":"2021","unstructured":"Yan N, Zhang Y, Xu X, Gao Y (2021) Online finance with dual channels and bidirectional free-riding effect. Int J Prod Econ 231:107834. https:\/\/doi.org\/10.1016\/j.ijpe.2020.107834","journal-title":"Int J Prod Econ"},{"key":"10453_CR52","doi-asserted-by":"publisher","first-page":"1174","DOI":"10.1016\/j.jclepro.2017.02.138","volume":"149","author":"D Yang","year":"2017","unstructured":"Yang D, Xiao T (2017) Pricing and green level decisions of a green supply chain with governmental interventions under fuzzy uncertainties. J Clean Prod 149:1174\u20131187. https:\/\/doi.org\/10.1016\/j.jclepro.2017.02.138","journal-title":"J Clean Prod"},{"issue":"9","key":"10453_CR53","doi-asserted-by":"publisher","first-page":"6483","DOI":"10.1007\/s00500-019-04633-9","volume":"24","author":"X Yang","year":"2020","unstructured":"Yang X, Jing F, Ma N, Nie F (2020) Supply chain pricing and effort decisions with the participants\u2019 belief under the uncertain demand. Soft Comput 24(9):6483\u20136497. https:\/\/doi.org\/10.1007\/s00500-019-04633-9","journal-title":"Soft Comput"},{"issue":"2","key":"10453_CR54","doi-asserted-by":"publisher","first-page":"661","DOI":"10.1016\/j.ejor.2021.08.026","volume":"300","author":"N Yu","year":"2022","unstructured":"Yu N, Wang S, Liu Z (2022) Managing brand competition with consumer fairness concern via manufacturer incentive. Eur J Oper Res 300(2):661\u2013675. https:\/\/doi.org\/10.1016\/j.ejor.2021.08.026","journal-title":"Eur J Oper Res"},{"key":"10453_CR55","doi-asserted-by":"crossref","unstructured":"Yuan-ga, C (2010) internet acceptance, service competition and channel profit in dual-channel supply chain. In: Paper presented at the 2010 International Conference on E-Business and E-Government","DOI":"10.1109\/ICEE.2010.814"},{"issue":"1","key":"10453_CR56","doi-asserted-by":"publisher","first-page":"646","DOI":"10.1016\/j.ejor.2004.12.020","volume":"174","author":"X Yue","year":"2006","unstructured":"Yue X, Liu J (2006) Demand forecast sharing in a dual-channel supply chain. Eur J Oper Res 174(1):646\u2013667. https:\/\/doi.org\/10.1016\/j.ejor.2004.12.020","journal-title":"Eur J Oper Res"},{"key":"10453_CR57","doi-asserted-by":"publisher","first-page":"352","DOI":"10.1016\/j.ijpe.2014.03.019","volume":"153","author":"Q Zhang","year":"2014","unstructured":"Zhang Q, Dong M, Luo J, Segerstedt A (2014) Supply chain coordination with trade credit and quantity discount incorporating default risk. Int J Prod Econ 153:352\u2013360. https:\/\/doi.org\/10.1016\/j.ijpe.2014.03.019","journal-title":"Int J Prod Econ"},{"issue":"9","key":"10453_CR58","doi-asserted-by":"publisher","first-page":"2476","DOI":"10.1016\/j.apm.2013.10.063","volume":"38","author":"J Zhao","year":"2014","unstructured":"Zhao J, Wei J (2014) The coordinating contracts for a fuzzy supply chain with effort and price dependent demand. Appl Math Model 38(9):2476\u20132489. https:\/\/doi.org\/10.1016\/j.apm.2013.10.063","journal-title":"Appl Math Model"},{"issue":"4","key":"10453_CR59","doi-asserted-by":"publisher","DOI":"10.1016\/j.lrp.2019.101892","volume":"53","author":"Y Zhao","year":"2020","unstructured":"Zhao Y, von Delft S, Morgan-Thomas A, Buck T (2020) The evolution of platform business models: Exploring competitive battles in the world of platforms. Long Range Plan 53(4):101892. https:\/\/doi.org\/10.1016\/j.lrp.2019.101892","journal-title":"Long Range Plan"},{"key":"10453_CR60","doi-asserted-by":"publisher","first-page":"198","DOI":"10.1016\/j.ijpe.2017.11.014","volume":"196","author":"Y-W Zhou","year":"2018","unstructured":"Zhou Y-W, Guo J, Zhou W (2018) Pricing\/service strategies for a dual-channel supply chain with free riding and service-cost sharing. Int J Prod Econ 196:198\u2013210. https:\/\/doi.org\/10.1016\/j.ijpe.2017.11.014","journal-title":"Int J Prod Econ"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-025-10453-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00500-025-10453-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-025-10453-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,27]],"date-time":"2025-02-27T16:50:22Z","timestamp":1740675022000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00500-025-10453-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2]]},"references-count":60,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,2]]}},"alternative-id":["10453"],"URL":"https:\/\/doi.org\/10.1007\/s00500-025-10453-x","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-3923525\/v1","asserted-by":"object"}]},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,2]]},"assertion":[{"value":"6 November 2024","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 February 2025","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest. In addition, this article does not contain any studies with human participants or animals performed by the author. The undersigned authors declare that this manuscript is original, has not been published before, and is not currently being considered for publication elsewhere.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Informed consent"}}]}}