{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,23]],"date-time":"2026-05-23T12:08:40Z","timestamp":1779538120124,"version":"3.53.1"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T00:00:00Z","timestamp":1769990400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T00:00:00Z","timestamp":1769990400000},"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":["Oper Res Int J"],"published-print":{"date-parts":[[2026,6]]},"DOI":"10.1007\/s12351-025-01015-y","type":"journal-article","created":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T14:03:28Z","timestamp":1770041008000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Supply chain coordination with buyback contract in uncertain environment: one supplier-two retailers"],"prefix":"10.1007","volume":"26","author":[{"given":"Nassim","family":"Mongeri","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4537-2767","authenticated-orcid":false,"given":"Alireza","family":"Ghaffari-Hadigheh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,2,2]]},"reference":[{"issue":"8","key":"1015_CR1","doi-asserted-by":"publisher","first-page":"1022","DOI":"10.1016\/j.indmarman.2006.02.010","volume":"36","author":"S Auh","year":"2007","unstructured":"Auh S, Menguc B (2007) Performance implications of the direct and moderating effects of centralization and formalization on customer orientation. Ind Mark Manage 36(8):1022\u20131034","journal-title":"Ind Mark Manage"},{"issue":"3","key":"1015_CR2","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1016\/j.ejor.2009.11.023","volume":"204","author":"MA Darwish","year":"2010","unstructured":"Darwish MA, Odah OM (2010) Vendor managed inventory model for single-vendor multi-retailer supply chains. Eur J Oper Res 204(3):473\u2013484","journal-title":"Eur J Oper Res"},{"issue":"3","key":"1015_CR3","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1287\/opre.1090.0741","volume":"58","author":"E Delage","year":"2010","unstructured":"Delage E, Ye Y (2010) Distributionally robust optimization under moment uncertainty with application to data-driven problems. Oper Res 58(3):595\u2013612","journal-title":"Oper Res"},{"key":"1015_CR4","doi-asserted-by":"publisher","first-page":"101835","DOI":"10.1016\/j.seps.2024.101835","volume":"92","author":"TIbn Faiz","year":"2024","unstructured":"Faiz TIbn, Harrison Kenneth W (2024) A risk-averse stochastic optimization model for community resilience planning. Socioecon Plann Sci 92:101835","journal-title":"Socioecon Plann Sci"},{"issue":"8","key":"1015_CR5","doi-asserted-by":"publisher","first-page":"825","DOI":"10.1057\/jors.1993.141","volume":"44","author":"G Gallego","year":"1993","unstructured":"Gallego G, Moon I (1993) The distribution free newsboy problem: review and extensions. J Oper Res Soc 44(8):825\u2013834","journal-title":"J Oper Res Soc"},{"issue":"4","key":"1015_CR6","doi-asserted-by":"publisher","first-page":"2283","DOI":"10.1007\/s12351-019-00527-8","volume":"21","author":"MR Gholamian","year":"2021","unstructured":"Gholamian MR, Ebrahimzadeh-Afruzi M (2021) Credit and discount incentive options for two-level supply chain coordination, under uncertain price-dependent demand. Oper Res Int J 21(4):2283\u20132307","journal-title":"Oper Res Int J"},{"issue":"1","key":"1015_CR7","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1016\/j.ijpe.2010.11.001","volume":"131","author":"I Giannoccaro","year":"2011","unstructured":"Giannoccaro I (2011) Assessing the influence of the organization in the supply chain management using nk simulation. Int J Prod Econ 131(1):263\u2013272","journal-title":"Int J Prod Econ"},{"issue":"2","key":"1015_CR8","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1016\/S0925-5273(03)00047-1","volume":"89","author":"I Giannoccaro","year":"2004","unstructured":"Giannoccaro I, Pontrandolfo P (2004) Supply chain coordination by revenue sharing contracts. Int J Prod Econ 89(2):131\u2013139","journal-title":"Int J Prod Econ"},{"issue":"1","key":"1015_CR9","first-page":"1","volume":"1","author":"DK Jana","year":"2013","unstructured":"Jana DK, Maity K, Roy TK (2013) A three-layer supply chain integrated production-inventory model under permissible delay in payments in uncertain environments. J Uncertainty Anal Appl 1(1):1\u201317","journal-title":"J Uncertainty Anal Appl"},{"issue":"6","key":"1015_CR10","doi-asserted-by":"publisher","first-page":"841","DOI":"10.1016\/S0898-1221(01)00325-X","volume":"43","author":"C Kao","year":"2002","unstructured":"Kao C, Hsu W-K (2002) A single-period inventory model with fuzzy demand. Comput Math Appl 43(6):841\u2013848","journal-title":"Comput Math Appl"},{"issue":"4","key":"1015_CR11","doi-asserted-by":"publisher","first-page":"2279","DOI":"10.3390\/su14042279","volume":"14","author":"P-H Koo","year":"2022","unstructured":"Koo P-H (2022) A capacity cost-sharing contract for a two-stage supply chain with a risk-averse supplier under a bargaining power. Sustainability 14(4):2279","journal-title":"Sustainability"},{"key":"1015_CR12","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2021.108089","volume":"235","author":"CH Lee","year":"2021","unstructured":"Lee CH, Rhee BD (2021) Retailer-run resale market and supply chain coordination. Int J Prod Econ 235:108089","journal-title":"Int J Prod Econ"},{"key":"1015_CR13","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-73165-8_5","volume-title":"Uncertainty theory","author":"B Liu","year":"2007","unstructured":"Liu B (2007) Uncertainty theory. Springer, Berlin"},{"issue":"1","key":"1015_CR14","first-page":"3","volume":"3","author":"B Liu","year":"2009","unstructured":"Liu B (2009) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3\u201310","journal-title":"J Uncertain Syst"},{"key":"1015_CR15","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-13959-8","volume-title":"Uncertainty theory: a branch of mathematics for modeling human uncertainty","author":"Baoding Liu","year":"2010","unstructured":"Liu Baoding (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer Verlag, Berlin"},{"key":"1015_CR16","unstructured":"Liu B (2025) Uncertainty theory. Uncertainty Theory Laboratory. Tsinghua University, Beijing"},{"issue":"10","key":"1015_CR17","doi-asserted-by":"publisher","first-page":"3523","DOI":"10.1111\/poms.13447","volume":"30","author":"B Liu","year":"2021","unstructured":"Liu B, Guan X, Wang Y (2021) Supplier encroachment with multiple retailers. Prod Oper Manag 30(10):3523\u20133539","journal-title":"Prod Oper Manag"},{"issue":"21","key":"1015_CR18","doi-asserted-by":"publisher","first-page":"7624","DOI":"10.1080\/03610926.2023.2269451","volume":"53","author":"Y Liu","year":"2024","unstructured":"Liu Y, Liu B (2024) Estimation of uncertainty distribution function by the principle of least squares. Commun Stat-Theor Meth 53(21):7624\u20137641","journal-title":"Commun Stat-Theor Meth"},{"issue":"3","key":"1015_CR19","doi-asserted-by":"publisher","first-page":"1482","DOI":"10.3390\/vehicles6030070","volume":"6","author":"H Mawengkang","year":"2024","unstructured":"Mawengkang H, Syahputra MR, Sutarman S, Salhi A (2024) A non-linear optimization model for the multi-depot multi-supplier vehicle routing problem with relaxed time windows. Vehicles 6(3):1482\u20131495","journal-title":"Vehicles"},{"key":"1015_CR20","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-024-05918-5","author":"Y Merzifonluoglu","year":"2024","unstructured":"Merzifonluoglu Y (2024) Procurement portfolio management for resilient supply chains: value of information for risk averse decision making. Ann Oper Res. https:\/\/doi.org\/10.1007\/s10479-024-05918-5","journal-title":"Ann Oper Res"},{"issue":"4","key":"1015_CR21","first-page":"2307","volume":"20","author":"I Moon","year":"2020","unstructured":"Moon I, Jeong YJ, Saha S (2020) Investment and coordination decisions in a supply chain of fresh agricultural products. Oper Res 20(4):2307\u20132331","journal-title":"Oper Res"},{"issue":"1","key":"1015_CR22","first-page":"349","volume":"20","author":"A Muzaffar","year":"2020","unstructured":"Muzaffar A, Deng S, Malik MN (2020) Contracting mechanism with imperfect information in a two-level supply chain. Oper Res 20(1):349\u2013368","journal-title":"Oper Res"},{"issue":"1","key":"1015_CR23","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1007\/s12351-018-0434-x","volume":"21","author":"M Nouri","year":"2021","unstructured":"Nouri M, Hosseini-Motlagh S-M, Nematollahi M (2021) Proposing a discount policy for two-level supply chain coordination with periodic review replenishment and promotional efforts decisions. Oper Res Int J 21(1):365\u2013398","journal-title":"Oper Res Int J"},{"key":"1015_CR24","doi-asserted-by":"publisher","first-page":"108204","DOI":"10.1016\/j.ijpe.2021.108204","volume":"239","author":"Y Peng","year":"2021","unstructured":"Peng Y, Yan X, Jiang Y, Ji M, Cheng TCE (2021) Competition and coordination for supply chain networks with random yields. Intl J Prod Eco 239:108204","journal-title":"Intl J Prod Eco"},{"issue":"1","key":"1015_CR25","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1016\/0925-5273(96)00014-X","volume":"45","author":"D Petrovi\u0107","year":"1996","unstructured":"Petrovi\u0107 D, Petrovi\u0107 R, Vujo\u0161evi\u0107 M (1996) Fuzzy models for the newsboy problem. Int J Prod Econ 45(1):435\u2013441","journal-title":"Int J Prod Econ"},{"issue":"1","key":"1015_CR26","first-page":"269","volume":"19","author":"X Qin","year":"2019","unstructured":"Qin X, Su Q, Huang SH, Wiersma UJ, Liu M (2019) Service quality coordination contracts for online shopping service supply chain with competing service providers: integrating fairness and individual rationality. Oper Res 19(1):269\u2013296","journal-title":"Oper Res"},{"issue":"18","key":"1015_CR27","first-page":"9630","volume":"219","author":"Z Qin","year":"2013","unstructured":"Qin Z, Kar S (2013) Single-period inventory problem under uncertain environment. Appl Math Comput 219(18):9630\u20139638","journal-title":"Appl Math Comput"},{"issue":"2","key":"1015_CR28","first-page":"280","volume":"8","author":"L Rong","year":"2011","unstructured":"Rong L (2011) Two new uncertainty programming models of inventory with uncertain costs. J Inform Comput Sci 8(2):280\u2013288","journal-title":"J Inform Comput Sci"},{"key":"1015_CR29","volume-title":"Operations management","author":"W Stevenson","year":"2011","unstructured":"Stevenson W (2011) Operations management. McGraw-Hill\/Irwin, Columbus"},{"issue":"3","key":"1015_CR30","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1016\/S0925-5273(99)00129-2","volume":"66","author":"GL Vairaktarakis","year":"2000","unstructured":"Vairaktarakis GL (2000) Robust multi-item newsboy models with a budget constraint. Intl J Prod Econ 66(3):213\u2013226","journal-title":"Intl J Prod Econ"},{"issue":"1","key":"1015_CR31","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1007\/s12351-017-0328-3","volume":"20","author":"F Ye","year":"2020","unstructured":"Ye F, Lin Q, Li Y (2020) Coordination for contract farming supply chain with stochastic yield and demand under CVaR criterion. Oper Res Int J 20(1):369\u2013397","journal-title":"Oper Res Int J"},{"key":"1015_CR32","doi-asserted-by":"publisher","first-page":"1727","DOI":"10.1016\/j.proeng.2011.08.322","volume":"15","author":"D Yu-Zhen","year":"2011","unstructured":"Yu-Zhen D, Chen H, He-Qin W (2011) What is wrong with fuzzy logic. Procedia Eng 15:1727\u20131731","journal-title":"Procedia Eng"},{"key":"1015_CR33","doi-asserted-by":"publisher","first-page":"1722","DOI":"10.1016\/j.proeng.2011.08.321","volume":"15","author":"D Yu-Zhen","year":"2011","unstructured":"Yu-Zhen D, Huan C (2011) Credibility measure theory analysis. Procedia Eng 15:1722\u20131726","journal-title":"Procedia Eng"},{"key":"1015_CR34","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1016\/j.tre.2019.08.013","volume":"130","author":"Q Zheng","year":"2019","unstructured":"Zheng Q, Zhou L, Fan T, Ieromonachou P (2019) Joint procurement and pricing of fresh produce for multiple retailers with a quantity discount contract. Transp Res E Logist Transp Rev 130:16\u201336","journal-title":"Transp Res E Logist Transp Rev"}],"container-title":["Operational Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12351-025-01015-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12351-025-01015-y","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12351-025-01015-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,23]],"date-time":"2026-05-23T11:50:22Z","timestamp":1779537022000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12351-025-01015-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,2]]},"references-count":34,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,6]]}},"alternative-id":["1015"],"URL":"https:\/\/doi.org\/10.1007\/s12351-025-01015-y","relation":{},"ISSN":["1109-2858","1866-1505"],"issn-type":[{"value":"1109-2858","type":"print"},{"value":"1866-1505","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,2]]},"assertion":[{"value":"4 May 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 November 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 December 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 February 2026","order":4,"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 no conflict of interest in any stage of this research.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"26"}}