{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,23]],"date-time":"2025-12-23T18:58:56Z","timestamp":1766516336041,"version":"3.41.0"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,2,10]],"date-time":"2025-02-10T00:00:00Z","timestamp":1739145600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,2,10]],"date-time":"2025-02-10T00:00:00Z","timestamp":1739145600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100004225","name":"Petrobras","doi-asserted-by":"publisher","award":["4324713","4324713","4324713","4324713","4324713","4324713"],"award-info":[{"award-number":["4324713","4324713","4324713","4324713","4324713","4324713"]}],"id":[{"id":"10.13039\/501100004225","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000147","name":"Division of Civil, Mechanical and Manufacturing Innovation","doi-asserted-by":"publisher","award":["2113891"],"award-info":[{"award-number":["2113891"]}],"id":[{"id":"10.13039\/100000147","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Manag Sci"],"published-print":{"date-parts":[[2025,6]]},"DOI":"10.1007\/s10287-024-00527-w","type":"journal-article","created":{"date-parts":[[2025,2,10]],"date-time":"2025-02-10T12:37:11Z","timestamp":1739191031000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Theoretical results for gas market equilibrium modeling with application to Brazil"],"prefix":"10.1007","volume":"22","author":[{"given":"Steven A.","family":"Gabriel","sequence":"first","affiliation":[]},{"given":"Dominic C.","family":"Flocco","sequence":"additional","affiliation":[]},{"given":"Filipe Ferreira","family":"Mazzini","sequence":"additional","affiliation":[]},{"given":"David","family":"Sotelo","sequence":"additional","affiliation":[]},{"given":"Kamaiaji de Souza","family":"Castor","sequence":"additional","affiliation":[]},{"given":"Mario","family":"Levorato","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,2,10]]},"reference":[{"key":"527_CR1","unstructured":"ANP: Modelo Conceitual do Mercado de G\u00e1s na Esfera de Compet\u00eancia da Uni\u00e3o - Comercializa\u00e7\u00e3, Carregamento e Balanceamento (2020)"},{"key":"527_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11067-012-9171-5","volume":"13","author":"I Abada","year":"2013","unstructured":"Abada I, Gabriel S, Briat V, Massol O (2013) A generalized Nash-Cournot model for the northwestern European natural gas markets with a fuel substitution demand function: the gammes model. Netw Spat Econ 13:1\u201342","journal-title":"Netw Spat Econ"},{"key":"527_CR3","unstructured":"Abada I (2012) Mod\u00e9lisation des march\u00e9s du gaz naturel en europe en concurrence oligopolistique: le modele gammes et quelques applications. PhD thesis, Paris 10"},{"key":"527_CR4","volume-title":"Nonlinear programming: theory and algorithms","author":"MS Bazaraa","year":"2013","unstructured":"Bazaraa MS, Sherali HD, Shetty CM (2013) Nonlinear programming: theory and algorithms. Wiley, New Jersey"},{"key":"527_CR5","unstructured":"Boots MG, Rijkers FA, Hobbs BF (2003) GASTALE: an oligopolistic model of production and trade in the European gas market. ECN, Netherlands, Petten"},{"issue":"24","key":"527_CR6","doi-asserted-by":"publisher","first-page":"254","DOI":"10.36428\/revistadacgu.v13i24.453","volume":"13","author":"BE Carvalho","year":"2021","unstructured":"Carvalho BE, Ara\u00fajo S, Matsumoto F, Mattos C, Junior A (2021) Brazilian new gas market: challenges & opportunities. Revista da CGU 13(24):254\u2013268","journal-title":"Revista da CGU"},{"key":"527_CR7","doi-asserted-by":"publisher","first-page":"198","DOI":"10.1016\/j.eneco.2014.04.006","volume":"44","author":"CK Chyong","year":"2014","unstructured":"Chyong CK, Hobbs BF (2014) Strategic eurasian natural gas market model for energy security and policy analysis: Formulation and application to south stream. Energy Econ 44:198\u2013211","journal-title":"Energy Econ"},{"key":"527_CR8","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719000","volume-title":"The linear complementarity problem","author":"RW Cottle","year":"2009","unstructured":"Cottle RW, Pang J-S, Stone RE (2009) The linear complementarity problem. Society for Industrial and Applied Mathematics, Philadelphia"},{"key":"527_CR9","doi-asserted-by":"publisher","first-page":"994","DOI":"10.1016\/j.apenergy.2012.06.021","volume":"102","author":"C Dieckh\u00f6ner","year":"2013","unstructured":"Dieckh\u00f6ner C, Lochner S, Lindenberger D (2013) European natural gas infrastructure: the impact of market developments on gas flows and physical market integration. Appl Energy 102:994\u20131003","journal-title":"Appl Energy"},{"issue":"2","key":"527_CR10","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1080\/10556789508805606","volume":"5","author":"SP Dirkse","year":"1995","unstructured":"Dirkse SP, Ferris MC (1995) The path solver: a nommonotone stabilization scheme for mixed complementarity problems. Optim Methods Softw 5(2):123\u2013156","journal-title":"Optim Methods Softw"},{"issue":"17","key":"527_CR11","doi-asserted-by":"publisher","first-page":"2762","DOI":"10.1016\/j.enpol.2005.04.018","volume":"34","author":"RG Egging","year":"2006","unstructured":"Egging RG, Gabriel SA (2006) Examining market power in the European natural gas market. Energy Policy 34(17):2762\u20132778","journal-title":"Energy Policy"},{"issue":"7","key":"527_CR12","doi-asserted-by":"publisher","first-page":"2385","DOI":"10.1016\/j.enpol.2008.01.044","volume":"36","author":"R Egging","year":"2008","unstructured":"Egging R, Gabriel SA, Holz F, Zhuang J (2008) A complementarity model for the European natural gas market. Energy Policy 36(7):2385\u20132414","journal-title":"Energy Policy"},{"key":"527_CR13","unstructured":"Egging R, Holz F (2019) Global gas model: Model and data documentation v3. 0 (2019). Technical report, DIW Data Documentation"},{"key":"527_CR14","unstructured":"Fernandes LF (2022) O mercado brasileiro de g\u00e1s natural: an\u00e1lise das a\u00e7\u00f5es regulat\u00f3rias para abertura do mercado e aumento da concorr\u00eancia"},{"issue":"5","key":"527_CR16","doi-asserted-by":"publisher","first-page":"799","DOI":"10.1287\/opre.1040.0199","volume":"53","author":"SA Gabriel","year":"2005","unstructured":"Gabriel SA, Kiet S, Zhuang J (2005a) A mixed complementarity-based equilibrium model of natural gas markets. Oper Res 53(5):799\u2013818","journal-title":"Oper Res"},{"issue":"4","key":"527_CR19","doi-asserted-by":"publisher","first-page":"639","DOI":"10.1016\/j.eneco.2005.03.007","volume":"27","author":"SA Gabriel","year":"2005","unstructured":"Gabriel SA, Zhuang J, Kiet S (2005b) A large-scale linear complementarity model of the north American natural gas market. Energy economics 27(4):639\u2013665","journal-title":"Energy economics"},{"key":"527_CR15","volume-title":"Complementarity modeling in energy markets","author":"SA Gabriel","year":"2012","unstructured":"Gabriel SA, Conejo AJ, Fuller JD, Hobbs BF, Ruiz C (2012a) Complementarity modeling in energy markets, vol 180. Springer, New York"},{"key":"527_CR20","doi-asserted-by":"crossref","unstructured":"Gabriel SA, Rosendahl KE, Egging R, Avetisyan HG, Siddiqui S (2012b) Cartelization in gas markets: Studying the potential for a \u201cgas opec.\u201d Energy Econ 34(1):137\u2013152","DOI":"10.1016\/j.eneco.2011.05.014"},{"issue":"12","key":"527_CR17","doi-asserted-by":"publisher","first-page":"2706","DOI":"10.1080\/01605682.2021.2015254","volume":"73","author":"SA Gabriel","year":"2022","unstructured":"Gabriel SA, Leal M, Schmidt M (2022) On linear bilevel optimization problems with complementarity-constrained lower levels. J Oper Res Soc 73(12):2706\u20132716","journal-title":"J Oper Res Soc"},{"key":"527_CR21","unstructured":"Gutierrez MBGPS (2022) O setor de g\u00e1s natural no brasil: Uma compara\u00e7\u00e3o com os pa\u00edses da ocde. Technical report, Texto para Discuss\u00e3o"},{"key":"527_CR22","doi-asserted-by":"crossref","unstructured":"Heather P (2016) The evolution of european traded gas hubs (2016)","DOI":"10.26889\/9781784670467"},{"issue":"2","key":"527_CR23","doi-asserted-by":"publisher","first-page":"638","DOI":"10.1109\/59.867153","volume":"15","author":"BF Hobbs","year":"2000","unstructured":"Hobbs BF, Metzler CB, Pang J-S (2000) Strategic gaming analysis for electric power systems: an mpec approach. IEEE Trans Power Syst 15(2):638\u2013645","journal-title":"IEEE Trans Power Syst"},{"issue":"3","key":"527_CR24","doi-asserted-by":"publisher","first-page":"766","DOI":"10.1016\/j.eneco.2007.01.018","volume":"30","author":"F Holz","year":"2008","unstructured":"Holz F, Von Hirschhausen C, Kemfert C (2008) A strategic model of european gas supply (gasmod). Energy Econ 30(3):766\u2013788","journal-title":"Energy Econ"},{"key":"527_CR25","doi-asserted-by":"publisher","DOI":"10.1016\/j.jngse.2021.104198","volume":"97","author":"J Huemme","year":"2022","unstructured":"Huemme J, Gabriel S, Chanpiwat P, Shu T (2022) An analysis of the us-china trade war\u2019s impact on global natural gas markets and the us coast guard\u2019s lng inspection workforce. J Nat Gas Sci Eng 97:104-198","journal-title":"J Nat Gas Sci Eng"},{"key":"527_CR26","unstructured":"IEA: Implementing Gas Market Reforms in Brazil (2021). https:\/\/www.iea.org\/reports\/implementing-gas-market-reforms-in-brazil"},{"issue":"6","key":"527_CR27","doi-asserted-by":"publisher","first-page":"1890","DOI":"10.1016\/j.enpol.2008.01.042","volume":"36","author":"W Lise","year":"2008","unstructured":"Lise W, Hobbs BF, Van Oostvoorn F (2008) Natural gas corridors between the eu and its main suppliers: Simulation results with the dynamic gastale model. Energy Policy 36(6):1890\u20131906","journal-title":"Energy Policy"},{"key":"527_CR28","unstructured":"Lochner S, Bothe D (2007) From russia with gas: an analysis of the nord stream pipeline\u2019s impact on the european gas transmission system with the tiger-model. Technical report, EWI Working Paper"},{"key":"527_CR31","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1023\/A:1023907818360","volume":"3","author":"C Metzler","year":"2003","unstructured":"Metzler C, Hobbs BF, Pang J-S (2003) Nash-cournot equilibria in power markets on a linearized dc network with arbitrage: formulations and properties. Netw Spat Econ 3:123\u2013150","journal-title":"Netw Spat Econ"},{"key":"527_CR32","unstructured":"Metzler CB (2000) Complementarity models of competitive oligopolistic electric power generation markets. PhD thesis, The Johns Hopkins University (2000)"},{"issue":"4","key":"527_CR33","doi-asserted-by":"publisher","first-page":"155","DOI":"10.5547\/ISSN0195-6574-EJ-Vol30-No4-6","volume":"30","author":"KT Midthun","year":"2009","unstructured":"Midthun KT, Bj\u00f8rndal M, Tomasgard A (2009) Modeling optimal economic dispatch and system effects in natural gas networks. Energy J 30(4):155\u2013180","journal-title":"Energy J"},{"key":"527_CR34","unstructured":"Midthun KT (2007) Optimization models for liberalized natural gas markets. PhD thesis, Norwegian University of Science and Technology"},{"key":"527_CR29","unstructured":"MME: Monthly National Gas Industry Bulletin (2023)"},{"key":"527_CR30","unstructured":"MME: Monthly Energy Billetin (2023)"},{"key":"527_CR36","unstructured":"Moryadee S (2015) One-and-two-level natural gas equilibrium models and algorithms. PhD thesis, University of Maryland, College Park"},{"issue":"1","key":"527_CR18","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1016\/j.jngse.2014.06.015","volume":"20","author":"S Moryadee","year":"2014","unstructured":"Moryadee S, Gabriel SA, Rehulka F (2010) The influence of the Panama Canal on global gas trade. J Nat Gas Sci Eng 20(1):161\u2013174","journal-title":"Journal of Natural Gas Science and Engineering"},{"issue":"3\u20134","key":"527_CR35","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1016\/j.esr.2013.12.004","volume":"2","author":"S Moryadee","year":"2014","unstructured":"Moryadee S, Gabriel SA, Avetisyan HG (2014) Investigating the potential effects of us lng exports on global natural gas markets. Energ Strat Rev 2(3\u20134):273\u2013288","journal-title":"Energ Strat Rev"},{"key":"527_CR37","unstructured":"Mulder M, Zwart G (2006) Natgas. a model of the european natural gas market (2006)"},{"key":"527_CR38","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1007\/s40070-013-0019-0","volume":"2","author":"C Ruiz","year":"2014","unstructured":"Ruiz C, Conejo AJ, Fuller JD, Gabriel SA, Hobbs BF (2014) A tutorial review of complementarity models for decision-making in energy markets. EURO J Decis Process 2:91\u2013120","journal-title":"EURO J Decis Process"},{"key":"527_CR39","doi-asserted-by":"publisher","DOI":"10.1016\/j.resourpol.2023.103305","volume":"81","author":"VO Silva","year":"2023","unstructured":"Silva VO, Relva SG, Mondragon M, Mendes AB, Nishimoto K, Peyerl D (2023) Building options for the brazilian pre-salt: a technical-economic and infrastructure analysis of offshore integration between energy generation and natural gas exploration. Resour Policy 81:103-305","journal-title":"Resour Policy"},{"issue":"3","key":"527_CR40","doi-asserted-by":"publisher","first-page":"1622","DOI":"10.1109\/JSYST.2014.2370372","volume":"11","author":"A Soroudi","year":"2017","unstructured":"Soroudi A, Rabiee A, Keane A (2017) Stochastic real-time scheduling of wind-thermal generation units in an electric utility. IEEE Syst J 11(3):1622\u20131631","journal-title":"IEEE Syst J"},{"key":"527_CR41","doi-asserted-by":"publisher","first-page":"226","DOI":"10.1016\/j.jngse.2015.11.039","volume":"28","author":"C U-tapao","year":"2016","unstructured":"U-tapao C, Moryadee S, Gabriel SA, Peot C, Ramirez M et al (2016) A stochastic, two-level optimization model for compressed natural gas infrastructure investments in wastewater management. J Nat Gas Sci Eng 28:226\u2013240","journal-title":"J Nat Gas Sci Eng"}],"container-title":["Computational Management Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10287-024-00527-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10287-024-00527-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10287-024-00527-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T12:29:41Z","timestamp":1750249781000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10287-024-00527-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,10]]},"references-count":41,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["527"],"URL":"https:\/\/doi.org\/10.1007\/s10287-024-00527-w","relation":{},"ISSN":["1619-697X","1619-6988"],"issn-type":[{"type":"print","value":"1619-697X"},{"type":"electronic","value":"1619-6988"}],"subject":[],"published":{"date-parts":[[2025,2,10]]},"assertion":[{"value":"26 March 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 November 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 February 2025","order":3,"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 competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"The opinions expressed in this article are solely those of the author and do not reflect the views or positions of Petrobras.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Disclaimer"}}],"article-number":"2"}}