{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T04:50:19Z","timestamp":1777870219485,"version":"3.51.4"},"reference-count":46,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR-21-CE05-0039"],"award-info":[{"award-number":["ANR-21-CE05-0039"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Computers & Industrial Engineering"],"published-print":{"date-parts":[[2026,4]]},"DOI":"10.1016\/j.cie.2026.111909","type":"journal-article","created":{"date-parts":[[2026,2,17]],"date-time":"2026-02-17T20:01:57Z","timestamp":1771358517000},"page":"111909","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Bi-level optimization of hydrogen supply chains with Cournot-competing producers under capacity constraints"],"prefix":"10.1016","volume":"214","author":[{"given":"Jose-Manuel","family":"Flores-Perez","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5571-9352","authenticated-orcid":false,"given":"Sylvain","family":"Bourjade","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-7675-8509","authenticated-orcid":false,"given":"Christophe","family":"Bernard","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9813-9657","authenticated-orcid":false,"given":"Alberto A.","family":"Aguilar-Lasserre","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5832-5199","authenticated-orcid":false,"given":"Catherine","family":"Azzaro-Pantel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.cie.2026.111909_b1","doi-asserted-by":"crossref","first-page":"3965","DOI":"10.1016\/j.ijhydene.2011.11.091","article-title":"Design and operation of a stochastic hydrogen supply chain network under demand uncertainty","volume":"37","author":"Almansoori","year":"2012","journal-title":"International Journal of Hydrogen Energy","ISSN":"https:\/\/id.crossref.org\/issn\/0360-3199","issn-type":"print"},{"key":"10.1016\/j.cie.2026.111909_b2","series-title":"2013 IEEE Congress on Evolutionary Computation","isbn-type":"print","doi-asserted-by":"crossref","first-page":"470","DOI":"10.1109\/CEC.2013.6557606","article-title":"Differential evolution for bilevel programming","volume":"vol. 1","author":"Angelo","year":"2013","ISBN":"https:\/\/id.crossref.org\/isbn\/9781479904549"},{"key":"10.1016\/j.cie.2026.111909_b3","first-page":"1","article-title":"Mixed integer bilevel optimization through multi-parametric programming","author":"Avraamidou","year":"2011","journal-title":"Computers & Chemical Engineering"},{"key":"10.1016\/j.cie.2026.111909_b4","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/j.compchemeng.2018.07.007","article-title":"B-POP: Bi-level parametric optimization toolbox","volume":"122","author":"Avraamidou","year":"2019","journal-title":"Computers and Chemical Engineering","ISSN":"https:\/\/id.crossref.org\/issn\/0098-1354","issn-type":"print"},{"key":"10.1016\/j.cie.2026.111909_b5","series-title":"Practical Bilevel Optimization","isbn-type":"print","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2836-1","author":"Bard","year":"1998","ISBN":"https:\/\/id.crossref.org\/isbn\/9781441948076"},{"key":"10.1016\/j.cie.2026.111909_b6","series-title":"Practical bilevel optimization","isbn-type":"print","doi-asserted-by":"crossref","first-page":"1689","DOI":"10.1007\/978-1-4757-2836-1","author":"Bard","year":"1998","ISBN":"https:\/\/id.crossref.org\/isbn\/9781441948076"},{"issue":"1","key":"10.1016\/j.cie.2026.111909_b7","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1287\/moor.2015.0719","article-title":"Optimal transport and cournot-Nash equilibria","volume":"41","author":"Blanchet","year":"2015","journal-title":"Mathematics of Operations Research"},{"issue":"5","key":"10.1016\/j.cie.2026.111909_b8","doi-asserted-by":"crossref","first-page":"1086","DOI":"10.1287\/opre.22.5.1086","article-title":"Defense applications of mathematical programs with optimization problems in the constraints","volume":"22","author":"Bracken","year":"1974","journal-title":"Operations Research","ISSN":"https:\/\/id.crossref.org\/issn\/0030-364X","issn-type":"print"},{"key":"10.1016\/j.cie.2026.111909_b9","first-page":"200","article-title":"Game theory in supply chain analysis","author":"Cachon","year":"2006","journal-title":"Models, Methods, and Applications for Innovative Decision Making"},{"key":"10.1016\/j.cie.2026.111909_b10","doi-asserted-by":"crossref","DOI":"10.1016\/j.asoc.2021.107442","article-title":"Constraint-handling techniques within differential evolution for solving process engineering problems","volume":"108","author":"Cant\u00fa","year":"2021","journal-title":"Applied Soft Computing","ISSN":"https:\/\/id.crossref.org\/issn\/1568-4946","issn-type":"print"},{"key":"10.1016\/j.cie.2026.111909_b11","article-title":"Beyond the \u201cbottom-up\u201d and \u201ctop-down\u201d controversy: A methodological inquiry into hybrid modeling methods for hydrogen supply chains","volume":"268","author":"Cayet","year":"2024","journal-title":"International Journal of Production Economics","ISSN":"https:\/\/id.crossref.org\/issn\/0925-5273","issn-type":"print"},{"key":"10.1016\/j.cie.2026.111909_b12","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1109\/TEM.2013.2246569","article-title":"An investigation on centralized and decentralized supply chain scenarios at the product design stage to increase performance","volume":"61","author":"Chiu","year":"2014","journal-title":"IEEE Transactions on Engineering Management","ISSN":"https:\/\/id.crossref.org\/issn\/0018-9391","issn-type":"print"},{"key":"10.1016\/j.cie.2026.111909_b13","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1007\/s10479-007-0176-2","article-title":"An overview of bilevel optimization","volume":"153","author":"Colson","year":"2007","journal-title":"Annals of Operations Research","ISSN":"https:\/\/id.crossref.org\/issn\/1572-9338","issn-type":"print"},{"key":"10.1016\/j.cie.2026.111909_b14","doi-asserted-by":"crossref","first-page":"1935","DOI":"10.3390\/su12051935","article-title":"Insights on multi-agent systems applications for supply chain management","volume":"12","author":"Dominguez","year":"2020","journal-title":"Sustainability","ISSN":"https:\/\/id.crossref.org\/issn\/2071-1050","issn-type":"print"},{"issue":"4","key":"10.1016\/j.cie.2026.111909_b15","doi-asserted-by":"crossref","DOI":"10.3390\/fractalfract5040233","article-title":"Stability of parametric intuitionistic fuzzy multi-objective fractional transportation problem","volume":"5","author":"El Sayed","year":"2021","journal-title":"Fractal and Fractional","ISSN":"https:\/\/id.crossref.org\/issn\/2504-3110","issn-type":"print"},{"issue":"8","key":"10.1016\/j.cie.2026.111909_b16","doi-asserted-by":"crossref","DOI":"10.3390\/math13081242","article-title":"Two TOPSIS-based approaches for multi-choice rough bi-level multi-objective nonlinear programming problems","volume":"13","author":"El Sayed","year":"2025","journal-title":"Mathematics","ISSN":"https:\/\/id.crossref.org\/issn\/2227-7390","issn-type":"print"},{"key":"10.1016\/j.cie.2026.111909_b17","series-title":"A hydrogen strategy for a climate-neutral europe","author":"European Commission","year":"2020"},{"key":"10.1016\/j.cie.2026.111909_b18","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1007\/s10898-006-9100-6","article-title":"Parametric global optimisation for bilevel programming","volume":"38","author":"Faisca","year":"2007","journal-title":"Journal of Global Optimization","ISSN":"https:\/\/id.crossref.org\/issn\/0925-5001","issn-type":"print"},{"key":"10.1016\/j.cie.2026.111909_b19","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1007\/s10287-007-0062-z","article-title":"A multi-parametric programming approach for multilevel hierarchical and decentralised optimisation problems","volume":"6","author":"Faisca","year":"2009","journal-title":"Computational Management Science","ISSN":"https:\/\/id.crossref.org\/issn\/1619-697X","issn-type":"print"},{"key":"10.1016\/j.cie.2026.111909_b20","series-title":"Integrating engineering and economic methods for non-cooperative supply chains: a multi-follower bilevel problem in cournot competition applied to the hydrogen supply chain","author":"Flores-Perez","year":"2023"},{"key":"10.1016\/j.cie.2026.111909_b21","series-title":"Modelling and Simulation 2020 - the European Simulation and Modelling Conference, ESM 2020","first-page":"277","article-title":"A hybrid strategy for mixed integer bi-level optimization applied to hydrogen energy supply chain management","author":"Flores-Perez","year":"2020"},{"key":"10.1016\/j.cie.2026.111909_b22","doi-asserted-by":"crossref","DOI":"10.1016\/j.ijhydene.2025.152501","article-title":"Bridging strategic design and bi-level operational management for hydrogen supply chains under cournot game-based producer competition","volume":"197","author":"Flores-Perez","year":"2026","journal-title":"International Journal of Hydrogen Energy","ISSN":"https:\/\/id.crossref.org\/issn\/0360-3199","issn-type":"print"},{"key":"10.1016\/j.cie.2026.111909_b23","article-title":"Models for supply chain management: A taxonomy global supply chain management","author":"Giannoccaro","year":"2001","journal-title":"Proceedings of the Twelfth Annual Conference of the Production and Operations Management Society"},{"key":"10.1016\/j.cie.2026.111909_b24","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/j.indmarman.2018.01.034","article-title":"Centralized vs. decentralized supply chains: The importance of decision maker\u2019s cognitive ability and resistance to change","volume":"73","author":"Giannoccaro","year":"2018","journal-title":"Industrial Marketing Management","ISSN":"https:\/\/id.crossref.org\/issn\/0019-8501","issn-type":"print"},{"key":"10.1016\/j.cie.2026.111909_b25","doi-asserted-by":"crossref","first-page":"1084","DOI":"10.1016\/j.ijhydene.2024.10.054","article-title":"A joint cournot equilibrium model for the hydrogen and electricity markets","volume":"90","author":"Herrero Rozas","year":"2024","journal-title":"International Journal of Hydrogen Energy","ISSN":"https:\/\/id.crossref.org\/issn\/0360-3199","issn-type":"print"},{"key":"10.1016\/j.cie.2026.111909_b26","unstructured":"Hydrogen Council and McKinsey & Company (2021). Hydrogen Insights. A perspective on hydrogen investment, market development and cost competitiveness: Tech. rep.."},{"key":"10.1016\/j.cie.2026.111909_b27","doi-asserted-by":"crossref","first-page":"1921","DOI":"10.1257\/aer.20141529","article-title":"Sequential markets, market power, and arbitrage","volume":"106","author":"Ito","year":"2016","journal-title":"American Economic Review","ISSN":"https:\/\/id.crossref.org\/issn\/0002-8282","issn-type":"print"},{"key":"10.1016\/j.cie.2026.111909_b28","series-title":"34th European symposium on computer aided process engineering \/ 15th international symposium on process systems engineering","first-page":"907","article-title":"A bilevel framework for environmental and economic optimisation of hydrogen supply chains","volume":"vol. 53","author":"Jacquot","year":"2024"},{"key":"10.1016\/j.cie.2026.111909_b29","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1016\/j.enpol.2011.10.047","article-title":"A modified cournot model of the natural gas market in the European union: Mixed-motives delegation in a politicized environment","volume":"41","author":"Jansen","year":"2012","journal-title":"Energy Policy","ISSN":"https:\/\/id.crossref.org\/issn\/0301-4215","issn-type":"print"},{"key":"10.1016\/j.cie.2026.111909_b30","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1007\/BF01586088","article-title":"The polynomial hierarchy and a simple model for competitive analysis","volume":"32","author":"Jeroslow","year":"1985","journal-title":"Mathematical Programming","ISSN":"https:\/\/id.crossref.org\/issn\/1436-4646","issn-type":"print"},{"key":"10.1016\/j.cie.2026.111909_b31","series-title":"2007 IEEE Congress on Evolutionary Computation, CEC 2007","isbn-type":"print","first-page":"2243","article-title":"Solving transportation bi-level programs with differential evolution","author":"Koh","year":"2007","ISBN":"https:\/\/id.crossref.org\/isbn\/1424413400"},{"key":"10.1016\/j.cie.2026.111909_b32","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1007\/s11579-012-0076-3","article-title":"Oligopoly games under asymmetric costs and an application to energy production","volume":"6","author":"Ledvina","year":"2012","journal-title":"Mathematics and Financial Economics","ISSN":"https:\/\/id.crossref.org\/issn\/1862-9660","issn-type":"print"},{"key":"10.1016\/j.cie.2026.111909_b33","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1080\/10556780903448052","article-title":"Solving multi-leader\u2013common-follower games","volume":"25","author":"Leyffer","year":"2010","journal-title":"Optimization Methods & Software","ISSN":"https:\/\/id.crossref.org\/issn\/1055-6788","issn-type":"print"},{"key":"10.1016\/j.cie.2026.111909_b34","article-title":"Hydrogen supply chain modelling at energy system scale: A review","volume":"210","author":"Lueckel","year":"2025","journal-title":"Renewable and Sustainable Energy Reviews","ISSN":"https:\/\/id.crossref.org\/issn\/1364-0321","issn-type":"print"},{"key":"10.1016\/j.cie.2026.111909_b35","doi-asserted-by":"crossref","DOI":"10.1016\/j.ijindorg.2019.102536","article-title":"Cournot competition in wholesale electricity markets: The nordic power exchange, nord pool","volume":"68","author":"Lundin","year":"2020","journal-title":"International Journal of Industrial Organization","ISSN":"https:\/\/id.crossref.org\/issn\/0167-7187","issn-type":"print"},{"key":"10.1016\/j.cie.2026.111909_b36","doi-asserted-by":"crossref","DOI":"10.1016\/j.apenergy.2020.115089","article-title":"Optimization of renewable energy subsidy and carbon tax for multi energy systems using bilevel programming","volume":"267","author":"Martelli","year":"2020","journal-title":"Applied Energy","ISSN":"https:\/\/id.crossref.org\/issn\/0306-2619","issn-type":"print"},{"key":"10.1016\/j.cie.2026.111909_b37","doi-asserted-by":"crossref","DOI":"10.1016\/j.apenergy.2025.126827","article-title":"Hydrogen supply chains: Modeling challenges and sustainability gaps","volume":"401","author":"Oliveira","year":"2025","journal-title":"Applied Energy","ISSN":"https:\/\/id.crossref.org\/issn\/0306-2619","issn-type":"print"},{"key":"10.1016\/j.cie.2026.111909_b38","series-title":"Revue \u00e9conomique","first-page":"1487","article-title":"The theory of the market economy","author":"Richardson","year":"1995"},{"issue":"37","key":"10.1016\/j.cie.2026.111909_b39","doi-asserted-by":"crossref","first-page":"13731","DOI":"10.1016\/j.ijhydene.2022.12.242","article-title":"A review of hydrogen production and supply chain modeling and optimization","volume":"48","author":"Riera","year":"2023","journal-title":"International Journal of Hydrogen Energy","ISSN":"https:\/\/id.crossref.org\/issn\/0360-3199","issn-type":"print"},{"key":"10.1016\/j.cie.2026.111909_b40","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1051\/ro:2006017","article-title":"Centralized versus decentralized production planning","volume":"40","author":"Saharidis","year":"2006","journal-title":"RAIRO - Operations Research","ISSN":"https:\/\/id.crossref.org\/issn\/2804-7303","issn-type":"print"},{"key":"10.1016\/j.cie.2026.111909_b41","doi-asserted-by":"crossref","first-page":"1699","DOI":"10.1016\/j.jclepro.2008.04.020","article-title":"From a literature review to a conceptual framework for sustainable supply chain management","volume":"16","author":"Seuring","year":"2008","journal-title":"Journal of Cleaner Production","ISSN":"https:\/\/id.crossref.org\/issn\/0959-6526","issn-type":"print"},{"key":"10.1016\/j.cie.2026.111909_b42","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/978-3-030-85476-8_12","article-title":"Design and planning of green supply chains with risk concerns","volume":"374","author":"da Silva","year":"2021","journal-title":"Springer Proceedings in Mathematics and Statistics","ISSN":"https:\/\/id.crossref.org\/issn\/2194-1017","issn-type":"print"},{"key":"10.1016\/j.cie.2026.111909_b43","series-title":"Rational decision making in business organizations","first-page":"493","author":"Simon","year":"1979"},{"key":"10.1016\/j.cie.2026.111909_b44","series-title":"A review on bilevel optimization: From classical to evolutionary approaches and applications","author":"Sinha","year":"2018"},{"key":"10.1016\/j.cie.2026.111909_b45","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/j.cie.2017.01.008","article-title":"A bi-level programming approach to the decision problems in a vendor-buyer eco-friendly supply chain","volume":"105","author":"Wang","year":"2017","journal-title":"Computers & Industrial Engineering","ISSN":"https:\/\/id.crossref.org\/issn\/0360-8352","issn-type":"print"},{"key":"10.1016\/j.cie.2026.111909_b46","series-title":"Proceedings of the 5th IEEE International Conference on Cognitive Informatics, ICCI 2006","first-page":"126","article-title":"A hybrid differential evolution algorithm for solving nonlinear bilevel programming with linear constraints","volume":"vol. 1","author":"Zhu","year":"2006"}],"container-title":["Computers & Industrial Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0360835226001105?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0360835226001105?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T15:38:24Z","timestamp":1777563504000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0360835226001105"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4]]},"references-count":46,"alternative-id":["S0360835226001105"],"URL":"https:\/\/doi.org\/10.1016\/j.cie.2026.111909","relation":{},"ISSN":["0360-8352"],"issn-type":[{"value":"0360-8352","type":"print"}],"subject":[],"published":{"date-parts":[[2026,4]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Bi-level optimization of hydrogen supply chains with Cournot-competing producers under capacity constraints","name":"articletitle","label":"Article Title"},{"value":"Computers & Industrial Engineering","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cie.2026.111909","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Published by Elsevier Ltd.","name":"copyright","label":"Copyright"}],"article-number":"111909"}}