{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T00:19:15Z","timestamp":1761005955332,"version":"build-2065373602"},"reference-count":71,"publisher":"EDP Sciences","issue":"5","license":[{"start":{"date-parts":[[2025,10,20]],"date-time":"2025-10-20T00:00:00Z","timestamp":1760918400000},"content-version":"vor","delay-in-days":49,"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":["72371180"],"award-info":[{"award-number":["72371180"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["72071137"],"award-info":[{"award-number":["72071137"]}],"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":[[2025,7,20]]},"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:p>The activity that upstream suppliers introduce online channel to sell products and compete with downstream offline retailers is referred to as \u201csupplier encroachment\u201d. Previous studies on this problem mainly focus on centralized and decentralized supply chain structures, while this paper considers partial vertical integrated supply chain. We establish a three-stage Stackelberg game model to analyze the impact of partial forward integration (PFI) and partial backward integration (PBI) on supplier encroachment, and find that in PFI, supplier encroachment always harms the retailer and results in two outcomes: win\u2013lose or lose\u2013lose. Specifically, when the equity and the direct-selling cost are large, the supplier\u2019s optimal choice is to not encroach. In PBI, supplier encroachment may benefit the retailer and lead to four outcomes: win\u2013lose, win\u2013win, lose\u2013lose, or lose\u2013win. Here, when the equity is moderate and the direct-selling cost is low, encroachment will benefit both the supplier and the retailer. Furthermore, two extensions have been made to verify the robustness of our findings. We contend that the key results remain valid when considering channel substitution, while a new outcome of win\u2013win in PFI arises when considering sequential quantity decisions.<\/jats:p>","DOI":"10.1051\/ro\/2025105","type":"journal-article","created":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T07:50:53Z","timestamp":1753257053000},"page":"3015-3040","source":"Crossref","is-referenced-by-count":0,"title":["The impact of partial vertical integration on supplier encroachment"],"prefix":"10.1051","volume":"59","author":[{"given":"Jinxi","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yaoyu","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2025,10,20]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1016\/j.ejor.2024.07.003","volume":"319","author":"Amirnequiee","year":"2024","journal-title":"Eur. J. Oper. Res."},{"key":"R2","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1287\/mksc.1070.0280","volume":"26","author":"Arya","year":"2007","journal-title":"Marketing Sci."},{"key":"R3","doi-asserted-by":"crossref","first-page":"6038","DOI":"10.1287\/mnsc.2023.4673","volume":"69","author":"Avinadav","year":"2023","journal-title":"Manage. Sci."},{"key":"R4","doi-asserted-by":"crossref","first-page":"108208","DOI":"10.1016\/j.ijpe.2021.108208","volume":"239","author":"Balasubramanian","year":"2021","journal-title":"Int. J. Prod. Econ."},{"key":"R5","unstructured":"Business Wire, Jordan Brand Launches the Highly Anticipated Air Jordan 2011. Business Wire (2011)."},{"key":"R6","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1287\/msom.2020.0882","volume":"25","author":"Calvo","year":"2023","journal-title":"Manuf. Serv. Oper. Manage."},{"key":"R7","doi-asserted-by":"crossref","first-page":"109884","DOI":"10.1016\/j.cie.2024.109884","volume":"188","author":"Cao","year":"2024","journal-title":"Comput. Ind. Eng."},{"key":"R8","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1111\/j.1937-5956.2006.tb00002.x","volume":"15","author":"Cattani","year":"2006","journal-title":"Prod. Oper. Manage."},{"key":"R9","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1016\/j.ejor.2016.08.046","volume":"258","author":"Chen","year":"2017","journal-title":"Eur. J. Oper. Res."},{"key":"R10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1287\/mnsc.49.1.1.12749","volume":"49","author":"Chiang","year":"2003","journal-title":"Manage. Sci."},{"key":"R11","doi-asserted-by":"crossref","first-page":"554","DOI":"10.1016\/j.ejor.2016.11.025","volume":"259","author":"Dennis","year":"2017","journal-title":"Eur. J. Oper. Res."},{"key":"R12","doi-asserted-by":"crossref","first-page":"102903","DOI":"10.1016\/j.ijindorg.2022.102903","volume":"89","author":"Etro","year":"2023","journal-title":"Int. J. Ind. Organ."},{"key":"R13","doi-asserted-by":"crossref","first-page":"1692","DOI":"10.1111\/poms.13933","volume":"32","author":"Fang","year":"2023","journal-title":"Prod. Oper. Manage."},{"key":"R14","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1016\/j.euroecorev.2016.07.006","volume":"89","author":"Fiocco","year":"2016","journal-title":"Eur. Econ. Rev."},{"key":"R15","doi-asserted-by":"crossref","first-page":"1017","DOI":"10.1016\/j.euroecorev.2005.01.004","volume":"50","author":"Greenlee","year":"2006","journal-title":"Eur. Econ. Rev."},{"key":"R16","doi-asserted-by":"crossref","first-page":"536","DOI":"10.1287\/msom.2018.0705","volume":"21","author":"Guan","year":"2019","journal-title":"Manuf. Serv. Oper. Manage."},{"key":"R17","doi-asserted-by":"crossref","first-page":"102564","DOI":"10.1016\/j.omega.2021.102564","volume":"108","author":"Guan","year":"2022","journal-title":"Omega"},{"key":"R18","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1287\/msom.2015.0562","volume":"18","author":"Ha","year":"2016","journal-title":"Manuf. Serv. Oper. Manage."},{"key":"R19","doi-asserted-by":"crossref","first-page":"1235","DOI":"10.1111\/poms.13607","volume":"31","author":"Ha","year":"2022","journal-title":"Prod. Oper. Manage."},{"key":"R20","doi-asserted-by":"crossref","first-page":"1547","DOI":"10.1287\/msom.2021.1011","volume":"24","author":"Ha","year":"2022","journal-title":"Manuf. Serv. Oper. Manage."},{"key":"R21","doi-asserted-by":"crossref","first-page":"107688","DOI":"10.1016\/j.cie.2021.107688","volume":"162","author":"Hasiloglu","year":"2021","journal-title":"Comput. Ind. Eng."},{"key":"R22","doi-asserted-by":"crossref","first-page":"3606","DOI":"10.1080\/00207543.2021.1926571","volume":"60","author":"He","year":"2022","journal-title":"Int. J. Prod. Res."},{"key":"R23","first-page":"5301","volume":"67","author":"Hotkar","year":"2021","journal-title":"Manage. Sci."},{"key":"R24","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1111\/poms.12051","volume":"23","author":"Hsiao","year":"2014","journal-title":"Prod. Oper. Manage."},{"key":"R25","doi-asserted-by":"crossref","first-page":"1133","DOI":"10.1111\/poms.12860","volume":"27","author":"Huang","year":"2018","journal-title":"Prod. Oper. Manage."},{"key":"R26","doi-asserted-by":"crossref","first-page":"102615","DOI":"10.1016\/j.ijindorg.2020.102615","volume":"70","author":"Hunold","year":"2020","journal-title":"Int. J. Ind. Organ."},{"key":"R27","doi-asserted-by":"crossref","first-page":"891","DOI":"10.1111\/1756-2171.12158","volume":"47","author":"Hunold","year":"2016","journal-title":"RAND J. Econ."},{"key":"R28","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1111\/jems.12559","volume":"33","author":"Levy","year":"2024","journal-title":"J. Econ. Manage. Strat."},{"key":"R29","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1257\/mic.20160058","volume":"10","author":"Levy","year":"2018","journal-title":"Am. Econ. J. Microecon."},{"key":"R30","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1287\/mnsc.2013.1780","volume":"60","author":"Li","year":"2014","journal-title":"Manage. Sci."},{"key":"R31","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1111\/poms.12210","volume":"24","author":"Li","year":"2015","journal-title":"Prod. Oper. Manage."},{"key":"R32","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1016\/j.tre.2018.08.004","volume":"118","author":"Li","year":"2018","journal-title":"Transp. Res. Part E: Logistics Transp. Rev."},{"key":"R33","doi-asserted-by":"crossref","first-page":"107565","DOI":"10.1016\/j.ijpe.2019.107565","volume":"224","author":"Li","year":"2020","journal-title":"Int. J. Prod. Econ."},{"key":"R34","doi-asserted-by":"crossref","first-page":"102213","DOI":"10.1016\/j.omega.2020.102213","volume":"98","author":"Li","year":"2021","journal-title":"Omega"},{"key":"R35","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1111\/poms.13549","volume":"31","author":"Li","year":"2022","journal-title":"Prod. Oper. Manage."},{"key":"R36","doi-asserted-by":"crossref","first-page":"2775","DOI":"10.1111\/poms.14006","volume":"32","author":"Li","year":"2023","journal-title":"Prod. Oper. Manage."},{"key":"R37","doi-asserted-by":"crossref","first-page":"2788","DOI":"10.1111\/poms.14009","volume":"32","author":"Liang","year":"2023","journal-title":"Prod. Oper. Manage."},{"key":"R38","doi-asserted-by":"crossref","first-page":"3523","DOI":"10.1111\/poms.13447","volume":"30","author":"Liu","year":"2021","journal-title":"Prod. Oper. Manage."},{"key":"R39","doi-asserted-by":"crossref","first-page":"1149","DOI":"10.1007\/s10479-021-04494-2","volume":"329","author":"Lu","year":"2023","journal-title":"Ann. Oper. Res."},{"key":"R40","doi-asserted-by":"crossref","first-page":"886","DOI":"10.1016\/j.ejor.2020.11.018","volume":"292","author":"Mandal","year":"2021","journal-title":"Eur. J. Oper. Res."},{"key":"R41","doi-asserted-by":"crossref","first-page":"811","DOI":"10.1080\/01605682.2021.1880293","volume":"73","author":"Nie","year":"2022","journal-title":"J. Oper. Res. Soc."},{"key":"R42","doi-asserted-by":"crossref","first-page":"1315","DOI":"10.1007\/s10479-022-04705-4","volume":"329","author":"Pishchulov","year":"2023","journal-title":"Ann. Oper. Res."},{"key":"R43","doi-asserted-by":"crossref","first-page":"102261","DOI":"10.1016\/j.tre.2021.102261","volume":"149","author":"Ren","year":"2021","journal-title":"Transp. Res. Part E: Logistics Transp. Rev."},{"key":"R44","doi-asserted-by":"crossref","first-page":"100958","DOI":"10.1016\/j.rie.2024.100958","volume":"78","author":"Sanchez","year":"2024","journal-title":"Res. Econ."},{"key":"R45","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1080\/13504851003761772","volume":"18","author":"Serbera","year":"2011","journal-title":"Appl. Econ. Lett."},{"key":"R46","doi-asserted-by":"crossref","first-page":"2002","DOI":"10.1111\/poms.13955","volume":"32","author":"Shi","year":"2023","journal-title":"Prod. Oper. Manage."},{"key":"R47","doi-asserted-by":"crossref","first-page":"110148","DOI":"10.1016\/j.cie.2024.110148","volume":"191","author":"Shokouhifar","year":"2024","journal-title":"Comput. Ind. Eng."},{"key":"R48","doi-asserted-by":"crossref","first-page":"102245","DOI":"10.1016\/j.tre.2021.102245","volume":"147","author":"Sun","year":"2021","journal-title":"Transp. Res. Part E: Logistics Transp. Rev."},{"key":"R49","doi-asserted-by":"crossref","first-page":"103016","DOI":"10.1016\/j.omega.2023.103016","volume":"124","author":"Tong","year":"2024","journal-title":"Omega"},{"key":"R50","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1111\/j.1937-5956.2004.tb00147.x","volume":"13","author":"Tsay","year":"2004","journal-title":"Prod. Oper. Manage."},{"key":"R51","doi-asserted-by":"crossref","first-page":"7263","DOI":"10.1080\/00207543.2022.2147238","volume":"21","author":"Wan","year":"2023","journal-title":"Int. J. Prod. Res."},{"key":"R52","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/j.ejor.2023.03.005","volume":"310","author":"Wan","year":"2023","journal-title":"Eur. J. Oper. Res."},{"key":"R53","doi-asserted-by":"crossref","first-page":"106880","DOI":"10.1016\/j.cie.2020.106880","volume":"150","author":"Wang","year":"2020","journal-title":"Comput. Ind. Eng."},{"key":"R54","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/s00712-024-00871-0","volume":"143","author":"Wang","year":"2024","journal-title":"J. Econ."},{"key":"R55","doi-asserted-by":"crossref","first-page":"100876","DOI":"10.1016\/j.elerap.2019.100876","volume":"37","author":"Xia","year":"2019","journal-title":"Electron. Commer. Res. App."},{"key":"R56","doi-asserted-by":"crossref","first-page":"108037","DOI":"10.1016\/j.ijpe.2021.108037","volume":"234","author":"Xia","year":"2021","journal-title":"Int. J. Prod. Econ."},{"key":"R57","doi-asserted-by":"crossref","first-page":"108291","DOI":"10.1016\/j.ijpe.2021.108291","volume":"242","author":"Xiao","year":"2021","journal-title":"Int. J. Prod. Econ."},{"key":"R58","doi-asserted-by":"crossref","first-page":"1089","DOI":"10.1016\/j.ejor.2017.12.027","volume":"267","author":"Yang","year":"2018","journal-title":"Eur. J. Oper. Res."},{"key":"R59","doi-asserted-by":"crossref","first-page":"103582","DOI":"10.1016\/j.tre.2024.103582","volume":"187","author":"Yang","year":"2024","journal-title":"Transp. Res. Part E: Logistics Transp. Rev."},{"key":"R60","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1016\/j.ejor.2021.12.005","volume":"302","author":"Yao","year":"2022","journal-title":"Eur. J. Oper. Res."},{"key":"R61","doi-asserted-by":"crossref","first-page":"1839","DOI":"10.1111\/poms.12580","volume":"25","author":"Yoon","year":"2016","journal-title":"Prod. Oper. Manage."},{"key":"R62","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.1016\/j.ejor.2021.05.027","volume":"296","author":"Zhang","year":"2022","journal-title":"Eur. J. Oper. Res."},{"key":"R63","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/j.ejor.2018.08.002","volume":"273","author":"Zhang","year":"2019","journal-title":"Eur. J. Oper. Res."},{"key":"R64","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1016\/j.omega.2018.05.005","volume":"84","author":"Zhang","year":"2019","journal-title":"Omega"},{"key":"R65","doi-asserted-by":"crossref","first-page":"102013","DOI":"10.1016\/j.omega.2018.12.002","volume":"91","author":"Zhang","year":"2020","journal-title":"Omega"},{"key":"R66","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/j.ejor.2020.11.044","volume":"293","author":"Zhang","year":"2021","journal-title":"Eur. J. Oper. Res."},{"key":"R67","doi-asserted-by":"crossref","first-page":"108079","DOI":"10.1016\/j.ijpe.2021.108079","volume":"235","author":"Zhang","year":"2021","journal-title":"Int. J. Prod. Econ."},{"key":"R68","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.ejor.2021.09.024","volume":"301","author":"Zhang","year":"2022","journal-title":"Eur. J. Oper. Res."},{"key":"R69","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1111\/deci.12539","volume":"54","author":"Zhang","year":"2023","journal-title":"Decis. Sci."},{"key":"R70","doi-asserted-by":"crossref","first-page":"1835","DOI":"10.1007\/s10479-022-05032-4","volume":"336","author":"Zhao","year":"2024","journal-title":"Ann. Oper. Res."},{"key":"R71","doi-asserted-by":"crossref","first-page":"102346","DOI":"10.1016\/j.tre.2021.102346","volume":"152","author":"Zheng","year":"2021","journal-title":"Transp. Res. Part E: Logistics Transp. Rev."}],"container-title":["RAIRO - Operations Research"],"original-title":[],"link":[{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2025105\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,20]],"date-time":"2025-10-20T07:46:20Z","timestamp":1760946380000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2025105"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9]]},"references-count":71,"journal-issue":{"issue":"5"},"alternative-id":["ro240334"],"URL":"https:\/\/doi.org\/10.1051\/ro\/2025105","relation":{},"ISSN":["0399-0559","2804-7303"],"issn-type":[{"type":"print","value":"0399-0559"},{"type":"electronic","value":"2804-7303"}],"subject":[],"published":{"date-parts":[[2025,9]]}}}