{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T09:02:29Z","timestamp":1762246949785,"version":"build-2065373602"},"reference-count":68,"publisher":"EDP Sciences","issue":"5","license":[{"start":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T00:00:00Z","timestamp":1762214400000},"content-version":"vor","delay-in-days":64,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["72202137"],"award-info":[{"award-number":["72202137"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Shanghai Pujiang Programme","award":["23PJC074"],"award-info":[{"award-number":["23PJC074"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["72271164"],"award-info":[{"award-number":["72271164"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2025,9,28]]},"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:p>Products sold to the market typically traverse the introductory and maturity stages. During maturity, retailers often raise prices to capitalize on expanding market demand. However, consumers commonly regard the first-stage price as a psychologically acceptable reference point. When the second-stage price exceeds this threshold, they tend to perceive it as unfair, leading to a decrease in demand. Conversely, a price decrease strategy can leverage the reference price effect to stimulate purchases. This study investigates optimal two-stage supply chain pricing under dynamic market expansion with the reference price effect. We develop a Stackelberg game model involving a manufacturer and a retailer, analyzing both centralized and decentralized decision-making to explore how the reference price effect affects pricing, profit allocation, and supply chain coordination. The main findings are as follows: (1) Under centralized decision-making, moderate market expansion prompts second-stage price decreases to mitigate reference price effect\u2019s negative impacts and stimulate demand; substantial expansion enables a price increase strategy to exploit reference price effect for higher unit profitability; (2) Decentralized decision-making with reference price effect exacerbates double marginalization. Moreover, manufacturers\u2019 first-stage wholesale prices are independent of reference price effect, while second-stage wholesale prices decrease as it strengthens; (3) To achieve supply chain coordination, a two-part tariff contract with fixed fees across two stages is proposed, effectively aligning incentives and enhancing profits across varying market expansion scenarios. Numerical analyses further identify parameter regions for optimal price strategies, quantify the reference price effect\u2019s profit-impact thresholds, and sensitivity analysis of key parameters.<\/jats:p>","DOI":"10.1051\/ro\/2025133","type":"journal-article","created":{"date-parts":[[2025,9,30]],"date-time":"2025-09-30T18:44:52Z","timestamp":1759257892000},"page":"3347-3373","source":"Crossref","is-referenced-by-count":0,"title":["Two-stage supply chain pricing strategies with reference price effect"],"prefix":"10.1051","volume":"59","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6871-4902","authenticated-orcid":false,"given":"Fei","family":"Pan","sequence":"first","affiliation":[{"name":"School of Business, University of Shanghai for Science and Technology","place":["P.R. China"]},{"name":"School of Intelligent Emergency Management, University of Shanghai for Science and Technology","place":["P.R. China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dengjie","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Business, University of Shanghai for Science and Technology","place":["P.R. China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiuli","family":"Geng","sequence":"additional","affiliation":[{"name":"School of Business, University of Shanghai for Science and Technology","place":["P.R. China"]},{"name":"School of Intelligent Emergency Management, University of Shanghai for Science and Technology","place":["P.R. China"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2025,11,4]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/j.ijpe.2018.03.021","volume":"201","author":"Adeinat","year":"2018","journal-title":"Int. J. Prod. Econ."},{"key":"R2","first-page":"417","volume":"33","author":"Alc\u00edvar Esp\u00edn","year":"2022","journal-title":"IMA J. Manage. Math."},{"key":"R3","doi-asserted-by":"crossref","first-page":"104586","DOI":"10.1016\/j.jedc.2022.104586","volume":"146","author":"Anton","year":"2023","journal-title":"J. Econ. Dyn. Control"},{"key":"R4","doi-asserted-by":"crossref","first-page":"2982","DOI":"10.1287\/mnsc.2018.3114","volume":"65","author":"Aviv","year":"2019","journal-title":"Manage. Sci."},{"key":"R5","doi-asserted-by":"crossref","first-page":"6633","DOI":"10.1080\/00207543.2020.1821929","volume":"59","author":"Bart","year":"2021","journal-title":"Int. J. Prod. Res."},{"key":"R6","doi-asserted-by":"crossref","first-page":"1761","DOI":"10.1287\/isre.2023.1206","volume":"34","author":"Bassellier","year":"2023","journal-title":"Inf. Syst. Res."},{"key":"R7","doi-asserted-by":"crossref","first-page":"1454","DOI":"10.1002\/mde.4071","volume":"45","author":"Can-Zhong","year":"2024","journal-title":"Manage. Decis. Econ."},{"key":"R8","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/s00500-020-05142-w","volume":"25","author":"Canbulut","year":"2021","journal-title":"Soft Comput."},{"key":"R9","doi-asserted-by":"crossref","first-page":"102963","DOI":"10.1016\/j.omega.2023.102963","volume":"122","author":"Chaab","year":"2024","journal-title":"Omega"},{"key":"R10","doi-asserted-by":"crossref","first-page":"6633893","DOI":"10.1155\/2021\/6633893","volume":"2021","author":"Che","year":"2021","journal-title":"Complexity"},{"key":"R11","doi-asserted-by":"crossref","first-page":"546","DOI":"10.1080\/00207543.2019.1598592","volume":"58","author":"Chen","year":"2020","journal-title":"Int. J. Prod. Res."},{"key":"R12","doi-asserted-by":"crossref","first-page":"1529","DOI":"10.1287\/opre.2016.1524","volume":"64","author":"Chen","year":"2016","journal-title":"Oper. Res."},{"key":"R13","doi-asserted-by":"crossref","first-page":"20180064","DOI":"10.5018\/economics-ejournal.ja.2018-64","volume":"12","author":"Chenavaz","year":"2018","journal-title":"Economics"},{"key":"R14","doi-asserted-by":"crossref","first-page":"5854","DOI":"10.1080\/00207543.2021.1973136","volume":"60","author":"Chenavaz","year":"2022","journal-title":"Int. J. Prod. Res."},{"key":"R15","first-page":"156","volume":"37","author":"Cheng","year":"2023","journal-title":"J. Manage. Eng."},{"key":"R16","doi-asserted-by":"crossref","first-page":"37","DOI":"10.3390\/computation9030037","volume":"9","author":"Chueanun","year":"2021","journal-title":"Computation"},{"key":"R17","doi-asserted-by":"crossref","first-page":"1006","DOI":"10.1016\/j.ejor.2020.06.025","volume":"288","author":"Colombo","year":"2021","journal-title":"Eur. J. Oper. Res."},{"key":"R18","first-page":"152","volume":"30","author":"Dao-Ping","year":"2021","journal-title":"Oper. Res. Manage. Sci."},{"key":"R19","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1287\/mksc.2022.1395","volume":"42","author":"Diao","year":"2023","journal-title":"Marketing Sci."},{"key":"R20","doi-asserted-by":"crossref","first-page":"750","DOI":"10.1509\/jmr.11.0068","volume":"49","author":"Ellickson","year":"2012","journal-title":"J. Marketing Res."},{"key":"R21","first-page":"24","volume":"37","author":"Farrell","year":"2016","journal-title":"Multichannel News"},{"key":"R22","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1007\/s10479-017-2632-y","volume":"287","author":"Giri","year":"2020","journal-title":"Ann. Oper. Res."},{"key":"R23","first-page":"505","volume":"83","author":"G\u00f6nsch","year":"2013","journal-title":"J. Bus. Econ."},{"key":"R24","doi-asserted-by":"crossref","first-page":"1049758","DOI":"10.1155\/2023\/1049758","volume":"2023","author":"Gu","year":"2023","journal-title":"Math. Prob. Eng."},{"key":"R25","doi-asserted-by":"crossref","first-page":"106160","DOI":"10.1016\/j.cie.2019.106160","volume":"139","author":"He","year":"2020","journal-title":"Comput. Ind. Eng."},{"key":"R26","doi-asserted-by":"crossref","first-page":"127165","DOI":"10.1016\/j.jclepro.2021.127165","volume":"309","author":"Khorshidvand","year":"2021","journal-title":"J. Clean. Prod."},{"key":"R27","doi-asserted-by":"crossref","first-page":"2980","DOI":"10.1002\/bse.2783","volume":"30","author":"Kumar","year":"2021","journal-title":"Bus. Strategy Environ."},{"key":"R28","doi-asserted-by":"crossref","first-page":"27","DOI":"10.5267\/j.dsl.2014.9.003","volume":"4","author":"Li","year":"2015","journal-title":"Decis. Sci. Lett."},{"key":"R29","first-page":"149","volume":"31","author":"Li","year":"2017","journal-title":"J. Ind. Eng. Eng. Manage."},{"key":"R30","doi-asserted-by":"crossref","first-page":"6567952","DOI":"10.1155\/2019\/6567952","volume":"2019","author":"Li","year":"2019","journal-title":"Math. Prob. Eng."},{"key":"R31","unstructured":"Li Y., Wei L. and Jiang W., A two-stage pricing strategy considering learning effects and word-of-mouth. Preprint arXiv:2110.11581 (2021)."},{"key":"R32","first-page":"1","volume":"61","author":"Li","year":"2023","journal-title":"INFOR: Inf. Syst. Oper. Res."},{"key":"R33","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.tre.2015.11.002","volume":"85","author":"Lin","year":"2016","journal-title":"Transp. Res. Part E: Logistics Transp. Rev."},{"key":"R34","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1504\/IJLSM.2022.125658","volume":"43","author":"Luong","year":"2022","journal-title":"Int. J. Logistics Syst. Manage."},{"key":"R35","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1016\/j.ijpe.2013.09.004","volume":"146","author":"Ma","year":"2013","journal-title":"Int. J. Prod. Econ."},{"key":"R36","doi-asserted-by":"crossref","first-page":"3817","DOI":"10.1051\/ro\/2022190","volume":"56","author":"Maiti","year":"2022","journal-title":"RAIRO-Oper. Res."},{"key":"R37","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1016\/j.apm.2016.10.051","volume":"42","author":"Maiti","year":"2017","journal-title":"Appl. Math. Modell."},{"key":"R38","doi-asserted-by":"crossref","first-page":"3693","DOI":"10.1016\/j.jbusres.2016.03.031","volume":"69","author":"Malc","year":"2016","journal-title":"J. Bus. Res."},{"key":"R39","doi-asserted-by":"crossref","first-page":"103166","DOI":"10.1016\/j.jretconser.2022.103166","volume":"70","author":"Mart\u00edn-Herr\u00e1n","year":"2023","journal-title":"J. Retail. Consum. Serv."},{"key":"R40","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1509\/jmkg.2005.69.4.84","volume":"69","author":"Mazumdar","year":"2005","journal-title":"J. Marketing"},{"key":"R41","doi-asserted-by":"crossref","first-page":"882","DOI":"10.1111\/poms.13144","volume":"29","author":"Mehra","year":"2020","journal-title":"Prod. Oper. Manage."},{"key":"R42","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1287\/mksc.7.4.335","volume":"7","author":"Moorthy","year":"1988","journal-title":"Marketing Sci."},{"key":"R43","doi-asserted-by":"crossref","first-page":"108386","DOI":"10.1016\/j.ijpe.2021.108386","volume":"244","author":"Pan","year":"2022","journal-title":"Int. J. Prod. Econ."},{"key":"R44","doi-asserted-by":"crossref","first-page":"1528","DOI":"10.1002\/mde.3200","volume":"41","author":"Park","year":"2020","journal-title":"Manage. Decis. Econ."},{"key":"R45","doi-asserted-by":"crossref","first-page":"102094","DOI":"10.1016\/j.tre.2020.102094","volume":"143","author":"Ponte","year":"2020","journal-title":"Transp. Res. Part E: Logistics Transp. Rev."},{"key":"R46","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1016\/j.jbusres.2022.07.037","volume":"152","author":"Prakash","year":"2022","journal-title":"J. Bus. Res."},{"key":"R47","doi-asserted-by":"crossref","first-page":"1641","DOI":"10.1111\/itor.13520","volume":"32","author":"Qi","year":"2025","journal-title":"Int. Trans. Oper. Res."},{"key":"R48","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.jbusres.2022.06.043","volume":"152","author":"Qin","year":"2022","journal-title":"J. Bus. Res."},{"key":"R49","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1016\/j.ejor.2019.07.020","volume":"280","author":"Shams-Shoaaee","year":"2020","journal-title":"Eur. J. Oper. Res."},{"key":"R50","doi-asserted-by":"crossref","first-page":"604","DOI":"10.1108\/MIP-02-2022-0049","volume":"40","author":"Srivastava","year":"2022","journal-title":"Marketing Intell. Planning"},{"key":"R51","first-page":"517","volume":"20","author":"Taleizadeh","year":"2020","journal-title":"Oper. Res."},{"key":"R52","doi-asserted-by":"crossref","first-page":"2387","DOI":"10.3390\/math11102387","volume":"11","author":"Wang","year":"2023","journal-title":"Mathematics"},{"key":"R53","doi-asserted-by":"crossref","unstructured":"Wang C., Liu T., Zhu Y., Wang H., Wang X. and Zhao S., The influence of consumer perception on purchase intention: evidence from cross-border e-commerce platforms. Heliyon 9 (2023). DOI: 10.1016\/j.heliyon.2023.e21617.","DOI":"10.1016\/j.heliyon.2023.e21617"},{"key":"R54","doi-asserted-by":"crossref","first-page":"1150","DOI":"10.1108\/APJML-07-2023-0685","volume":"36","author":"Wang","year":"2024","journal-title":"Asia Pac. J. Marketing Logistics"},{"key":"R55","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1108\/CMS-10-2021-0454","volume":"18","author":"Wang","year":"2024","journal-title":"Chin. Manage. Stud."},{"key":"R56","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1016\/j.ejor.2024.10.037","volume":"322","author":"Wang","year":"2025","journal-title":"Eur. J. Oper. Res."},{"key":"R57","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/j.jretconser.2011.04.001","volume":"18","author":"Yan","year":"2011","journal-title":"J. Retail. Consum. Serv."},{"key":"R58","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1051\/ro\/2022004","volume":"56","author":"Yan","year":"2022","journal-title":"RAIRO-Oper. Res."},{"key":"R59","doi-asserted-by":"crossref","first-page":"1045","DOI":"10.1016\/j.ejor.2022.01.032","volume":"302","author":"Yan","year":"2022","journal-title":"Eur. J. Oper. Res."},{"key":"R60","doi-asserted-by":"crossref","first-page":"1429","DOI":"10.1007\/s10479-021-04124-x","volume":"324","author":"Yun","year":"2023","journal-title":"Ann. Oper. Res."},{"key":"R61","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/j.omega.2013.07.002","volume":"44","author":"Zhang","year":"2014","journal-title":"Omega"},{"key":"R62","doi-asserted-by":"crossref","first-page":"106988","DOI":"10.1016\/j.cie.2020.106988","volume":"151","author":"Zhang","year":"2021","journal-title":"Comput. Ind. Eng."},{"key":"R63","doi-asserted-by":"crossref","first-page":"1273","DOI":"10.1111\/poms.13321","volume":"30","author":"Zhang","year":"2021","journal-title":"Prod. Oper. Manage."},{"key":"R64","doi-asserted-by":"crossref","first-page":"1879","DOI":"10.1108\/K-11-2021-1096","volume":"52","author":"Zhang","year":"2023","journal-title":"Kybernetes"},{"key":"R65","doi-asserted-by":"crossref","first-page":"2045","DOI":"10.1051\/ro\/2023102","volume":"57","author":"Zhang","year":"2023","journal-title":"RAIRO-Oper. Res."},{"key":"R66","doi-asserted-by":"crossref","first-page":"101222","DOI":"10.1016\/j.elerap.2022.101222","volume":"57","author":"Zhao","year":"2023","journal-title":"Electron. Commer. Res. App."},{"key":"R67","doi-asserted-by":"crossref","first-page":"817","DOI":"10.20965\/jaciii.2018.p0817","volume":"22","author":"Zhou","year":"2018","journal-title":"J. Adv. Comput. Intell. Intell. Inf."},{"key":"R68","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.ejor.2024.07.025","volume":"320","author":"Zhou","year":"2025","journal-title":"Eur. J. Oper. Res."}],"container-title":["RAIRO - Operations Research"],"original-title":[],"link":[{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2025133\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T08:51:27Z","timestamp":1762246287000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2025133"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9]]},"references-count":68,"journal-issue":{"issue":"5"},"alternative-id":["ro240488"],"URL":"https:\/\/doi.org\/10.1051\/ro\/2025133","relation":{},"ISSN":["0399-0559","2804-7303"],"issn-type":[{"type":"print","value":"0399-0559"},{"type":"electronic","value":"2804-7303"}],"subject":[],"published":{"date-parts":[[2025,9]]}}}