{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,21]],"date-time":"2025-11-21T05:21:00Z","timestamp":1763702460895,"version":"3.45.0"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T00:00:00Z","timestamp":1760745600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T00:00:00Z","timestamp":1760745600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100012456","name":"National Social Science Fund of China","doi-asserted-by":"publisher","award":["21BGL238"],"award-info":[{"award-number":["21BGL238"]}],"id":[{"id":"10.13039\/501100012456","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Fuzzy Optim Decis Making"],"published-print":{"date-parts":[[2025,12]]},"DOI":"10.1007\/s10700-025-09458-w","type":"journal-article","created":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T04:28:46Z","timestamp":1760761726000},"page":"669-693","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Optimizing supply chain cooperation with rebate mechanisms under demand and price uncertainty"],"prefix":"10.1007","volume":"24","author":[{"given":"Sibo","family":"Ding","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-9428-9418","authenticated-orcid":false,"given":"Linshuang","family":"Yuan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiao-Jun","family":"Zeng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,10,18]]},"reference":[{"issue":"1","key":"9458_CR1","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1016\/j.ijpe.2012.06.031","volume":"140","author":"FJ Arcelus","year":"2012","unstructured":"Arcelus, F. J., Gor, R., & Srinivasan, G. (2012). Price, rebate and order quantity decisions in a newsvendor framework with rebate-dependent recapture of lost sales. International Journal of Production Economics, 140(1), 473\u2013482.","journal-title":"International Journal of Production Economics"},{"issue":"2","key":"9458_CR2","doi-asserted-by":"publisher","first-page":"466","DOI":"10.1109\/TEM.2018.2882843","volume":"67","author":"C-H Chiu","year":"2019","unstructured":"Chiu, C.-H., Chan, H.-L., & Choi, T.-M. (2019). Risk minimizing price-rebate-return contracts in supply chains with ordering and pricing decisions: A multimethodological analysis. IEEE Transactions on Engineering Management, 67(2), 466\u2013482.","journal-title":"IEEE Transactions on Engineering Management"},{"issue":"2","key":"9458_CR3","doi-asserted-by":"publisher","first-page":"736","DOI":"10.1016\/j.ijpe.2011.06.002","volume":"133","author":"O Caliskan-Demirag","year":"2011","unstructured":"Caliskan-Demirag, O., Chen, Y. F., & Li, J. (2011). Customer and retailer rebates under risk aversion. International Journal of Production Economics, 133(2), 736\u2013750.","journal-title":"International Journal of Production Economics"},{"issue":"6","key":"9458_CR4","doi-asserted-by":"publisher","first-page":"667","DOI":"10.1002\/nav.20239","volume":"54","author":"X Chen","year":"2007","unstructured":"Chen, X., Li, C.-L., Rhee, B.-D., & Simchi-Levi, D. (2007). The impact of manufacturer rebates on supply chain profits. Naval Research Logistics (NRL), 54(6), 667\u2013680.","journal-title":"Naval Research Logistics (NRL)"},{"issue":"4","key":"9458_CR5","doi-asserted-by":"publisher","first-page":"426","DOI":"10.1111\/j.1937-5956.2009.01035.x","volume":"18","author":"S-H Cho","year":"2009","unstructured":"Cho, S.-H., McCardle, K. F., & Tang, C. S. (2009). Optimal pricing and rebate strategies in a two-level supply chain. Production and Operations Management, 18(4), 426\u2013446.","journal-title":"Production and Operations Management"},{"issue":"1","key":"9458_CR6","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1080\/00207543.2016.1204475","volume":"55","author":"L Chen","year":"2017","unstructured":"Chen, L., Peng, J., Liu, Z., & Zhao, R. (2017). Pricing and effort decisions for a supply chain with uncertain information. International Journal of Production Research, 55(1), 264\u2013284.","journal-title":"International Journal of Production Research"},{"issue":"2","key":"9458_CR7","doi-asserted-by":"publisher","first-page":"661","DOI":"10.1016\/j.ejor.2018.01.057","volume":"269","author":"TS Genc","year":"2018","unstructured":"Genc, T. S., & De Giovanni, P. (2018). Optimal return and rebate mechanism in a closed-loop supply chain game. European Journal of Operational Research, 269(2), 661\u2013681.","journal-title":"European Journal of Operational Research"},{"key":"9458_CR8","doi-asserted-by":"publisher","first-page":"781","DOI":"10.1007\/s12652-017-0502-8","volume":"8","author":"H Ke","year":"2017","unstructured":"Ke, H., & Liu, J. (2017). Dual-channel supply chain competition with channel preference and sales effort under uncertain environment. Journal of Ambient Intelligence and Humanized Computing, 8, 781\u2013795.","journal-title":"Journal of Ambient Intelligence and Humanized Computing"},{"key":"9458_CR9","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2021.108290","volume":"242","author":"G Liang","year":"2021","unstructured":"Liang, G., & Gu, C. (2021). The value of target sales rebate contracts in a supply chain with downstream competition. International Journal of Production Economics, 242, Article 108290.","journal-title":"International Journal of Production Economics"},{"issue":"1","key":"9458_CR10","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1080\/09720510.2009.10701381","volume":"12","author":"C-N Liao","year":"2009","unstructured":"Liao, C.-N. (2009). A joint demand uncertainty, sales effort, and rebate form in marketing channel. Journal of Statistics and Management Systems, 12(1), 155\u2013172.","journal-title":"Journal of Statistics and Management Systems"},{"key":"9458_CR11","unstructured":"Liu, B. (2007). Uncertainty Theory(2nd ed.). Springer."},{"issue":"1","key":"9458_CR12","first-page":"3","volume":"3","author":"B Liu","year":"2009","unstructured":"Liu, B. (2009). Some research problems in uncertainty theory. Journal of Uncertain systems, 3(1), 3\u201310.","journal-title":"Journal of Uncertain systems"},{"key":"9458_CR13","unstructured":"Liu, B. (2010). Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty. Springer."},{"key":"9458_CR14","doi-asserted-by":"crossref","unstructured":"Liu, B. (2015). Uncertainty Theory(4th ed.). Springer.","DOI":"10.1007\/978-3-662-44354-5"},{"key":"9458_CR15","unstructured":"Liu, B. (2024). Uncertainty Theory(5th ed.). (https:\/\/cloud.tsinghua.edu.cn\/d\/df71e9ec330e49e59c9c\/.)"},{"issue":"2","key":"9458_CR16","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1080\/07408170600710408","volume":"39","author":"X Lu","year":"2007","unstructured":"Lu, X., Song, J.-S., & Regan, A. (2007). Rebate, returns and price protection policies in channel coordination. IIE Transactions, 39(2), 111\u2013124.","journal-title":"IIE Transactions"},{"key":"9458_CR17","doi-asserted-by":"publisher","first-page":"781","DOI":"10.1016\/j.ins.2022.07.112","volume":"609","author":"J Peng","year":"2022","unstructured":"Peng, J., Chen, L., & Zhang, B. (2022). Transportation planning for sustainable supply chain network using big data technology. Information Sciences, 609, 781\u2013798.","journal-title":"Information Sciences"},{"key":"9458_CR18","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1016\/j.tre.2012.11.002","volume":"50","author":"S Saha","year":"2013","unstructured":"Saha, S. (2013). Supply chain coordination through rebate induced contracts. Transportation Research Part E: Logistics and Transportation Review, 50, 120\u2013137.","journal-title":"Transportation Research Part E: Logistics and Transportation Review"},{"key":"9458_CR19","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2024.109260","volume":"272","author":"P Sarkar","year":"2024","unstructured":"Sarkar, P., Wahab, M., & Fang, L. (2024). Weather rebate sharing contract for enhancing supply chain performance. International Journal of Production Economics, 272, Article 109260.","journal-title":"International Journal of Production Economics"},{"issue":"8","key":"9458_CR20","doi-asserted-by":"publisher","first-page":"992","DOI":"10.1287\/mnsc.48.8.992.168","volume":"48","author":"TA Taylor","year":"2002","unstructured":"Taylor, T. A. (2002). Supply chain coordination under channel rebates with sales effort effects. Management science, 48(8), 992\u20131007.","journal-title":"Management science"},{"key":"9458_CR21","doi-asserted-by":"crossref","unstructured":"Taylor, T.A., Xiao, W. (2009). Incentives for retailer forecasting: Rebates vs. returns. Management Science 55(10), 1654\u20131669.","DOI":"10.1287\/mnsc.1090.1045"},{"issue":"4","key":"9458_CR22","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1111\/deci.12586","volume":"55","author":"P Xu","year":"2024","unstructured":"Xu, P., & Xiao, T. (2024). Analysis of online rebates and commission formats in a retailer-stackelberg supply chain with cashback website. Decision Sciences, 55(4), 363\u2013380.","journal-title":"Decision Sciences"},{"issue":"2","key":"9458_CR23","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1080\/00207543.2018.1442946","volume":"57","author":"J Zhan","year":"2019","unstructured":"Zhan, J., Chen, X., & Hu, Q. (2019). The value of trade credit with rebate contract in a capital-constrained supply chain. International Journal of Production Research, 57(2), 379\u2013396.","journal-title":"International Journal of Production Research"},{"issue":"1","key":"9458_CR24","doi-asserted-by":"publisher","first-page":"108","DOI":"10.1016\/j.ejor.2017.03.037","volume":"262","author":"Y-W Zhou","year":"2017","unstructured":"Zhou, Y.-W., Cao, B., Tang, Q., & Zhou, W. (2017). Pricing and rebate strategies for an e-shop with a cashback website. European Journal of Operational Research, 262(1), 108\u2013122.","journal-title":"European Journal of Operational Research"},{"key":"9458_CR25","doi-asserted-by":"crossref","unstructured":"Zheng, Y., Xiao, T. (2024). Interaction between rebate strategy and wholesale-ordering contracts under retailer optimism and information asymmetry. Annals of Operations Research, 1\u201329.","DOI":"10.1007\/s10479-024-06269-x"}],"container-title":["Fuzzy Optimization and Decision Making"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10700-025-09458-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10700-025-09458-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10700-025-09458-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,21]],"date-time":"2025-11-21T05:16:33Z","timestamp":1763702193000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10700-025-09458-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,18]]},"references-count":25,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["9458"],"URL":"https:\/\/doi.org\/10.1007\/s10700-025-09458-w","relation":{},"ISSN":["1568-4539","1573-2908"],"issn-type":[{"type":"print","value":"1568-4539"},{"type":"electronic","value":"1573-2908"}],"subject":[],"published":{"date-parts":[[2025,10,18]]},"assertion":[{"value":"4 July 2025","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 October 2025","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}