{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T15:24:27Z","timestamp":1772119467080,"version":"3.50.1"},"reference-count":13,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,5,10]],"date-time":"2024-05-10T00:00:00Z","timestamp":1715299200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,5,10]],"date-time":"2024-05-10T00:00:00Z","timestamp":1715299200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100005416","name":"Norges Forskningsr\u00e5d","doi-asserted-by":"publisher","award":["296207"],"award-info":[{"award-number":["296207"]}],"id":[{"id":"10.13039\/501100005416","id-type":"DOI","asserted-by":"publisher"}]},{"name":"NTNU Norwegian University of Science and Technology"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Manag Sci"],"published-print":{"date-parts":[[2024,6]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Multi-horizon stochastic programming includes short-term and long-term uncertainty in investment planning problems more efficiently than traditional multi-stage stochastic programming. In this paper, we exploit the block separable structure of multi-horizon stochastic linear programming, and establish that it can be decomposed by Benders decomposition and Lagrangean decomposition. In addition, we propose parallel Lagrangean decomposition with primal reduction that, (1) solves the scenario subproblems in parallel, (2) reduces the primal problem by keeping one copy for each scenario group at each stage, and (3) solves the reduced primal problem in parallel. We apply the parallel Lagrangean decomposition with primal reduction, Lagrangean decomposition and Benders decomposition to solve a stochastic energy system investment planning problem. The computational results show that: (a) the Lagrangean type decomposition algorithms have better convergence at the first iterations to Benders decomposition, and (b) parallel Lagrangean decomposition with primal reduction is very efficient for solving multi-horizon stochastic programming problems. Based on the computational results, the choice of algorithms for multi-horizon stochastic programming is discussed.<\/jats:p>","DOI":"10.1007\/s10287-024-00509-y","type":"journal-article","created":{"date-parts":[[2024,5,10]],"date-time":"2024-05-10T10:01:57Z","timestamp":1715335317000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Decomposition methods for multi-horizon stochastic programming"],"prefix":"10.1007","volume":"21","author":[{"given":"Hongyu","family":"Zhang","sequence":"first","affiliation":[]},{"given":"Ignacio E.","family":"Grossmann","sequence":"additional","affiliation":[]},{"given":"Asgeir","family":"Tomasgard","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,5,10]]},"reference":[{"key":"509_CR1","doi-asserted-by":"publisher","first-page":"100877","DOI":"10.1016\/j.softx.2021.100877","volume":"17","author":"S Backe","year":"2022","unstructured":"Backe S, Skar C, del Granado PC, Turgut O, Tomasgard A (2022) EMPIRE: An open-source model based on multi-horizon programming for energy transition analyses. SoftwareX 17:100877. https:\/\/doi.org\/10.1016\/j.softx.2021.100877","journal-title":"SoftwareX"},{"key":"509_CR2","doi-asserted-by":"publisher","first-page":"238","DOI":"10.1007\/BF01386316","volume":"4","author":"JF Benders","year":"1962","unstructured":"Benders JF (1962) Partitioning procedures for solving mixed-variables programming problems. Numer Math 4:238\u2013252. https:\/\/doi.org\/10.1007\/BF01386316","journal-title":"Numer Math"},{"key":"509_CR3","doi-asserted-by":"publisher","first-page":"989","DOI":"10.1287\/OPRE.33.5.989","volume":"33","author":"JR Birge","year":"1985","unstructured":"Birge JR (1985) Decomposition and partitioning methods for multistage stochastic linear programs. Oper Res 33:989\u20131007. https:\/\/doi.org\/10.1287\/OPRE.33.5.989","journal-title":"Oper Res"},{"key":"509_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-0237-4","volume-title":"Introduction to stochastic programming","author":"JR Birge","year":"2011","unstructured":"Birge JR, Louveaux F (2011) Introduction to stochastic programming. Springer Science & Business Media, Heidelberg. https:\/\/doi.org\/10.1007\/978-1-4614-0237-4"},{"key":"509_CR5","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1137\/15M1020575","volume":"59","author":"I Dunning","year":"2017","unstructured":"Dunning I, Huchette J, Lubin M (2017) JuMP: A modeling language for mathematical optimization. SIAM Rev 59:295\u2013320. https:\/\/doi.org\/10.1137\/15M1020575","journal-title":"SIAM Rev"},{"key":"509_CR6","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1007\/S10287-018-0318-9\/FIGURES\/4","volume":"15","author":"LF Escudero","year":"2018","unstructured":"Escudero LF, Monge JF (2018) On capacity expansion planning under strategic and operational uncertainties based on stochastic dominance risk averse management. CMS 15:479\u2013500. https:\/\/doi.org\/10.1007\/S10287-018-0318-9\/FIGURES\/4","journal-title":"CMS"},{"key":"509_CR7","unstructured":"Gurobi Optimization LLC (2022) Gurobi optimizer reference manual. https:\/\/www.gurobi.com"},{"key":"509_CR8","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1007\/s10287-013-0182-6","volume":"11","author":"M Kaut","year":"2014","unstructured":"Kaut M, Midthun KT, Werner AS, Tomasgard A, Hellemo L, Fodstad M (2014) Multi-horizon stochastic programming. CMS 11:179\u2013193. https:\/\/doi.org\/10.1007\/s10287-013-0182-6","journal-title":"CMS"},{"key":"509_CR9","doi-asserted-by":"publisher","first-page":"48","DOI":"10.1007\/BFB0121125\/COVER","volume":"28","author":"FV Louveaux","year":"1986","unstructured":"Louveaux FV (1986) Multistage stochastic programs with block-separable recourse. Math Program Study 28:48\u201362. https:\/\/doi.org\/10.1007\/BFB0121125\/COVER","journal-title":"Math Program Study"},{"key":"509_CR10","doi-asserted-by":"publisher","first-page":"605","DOI":"10.1007\/S10479-019-03244-9\/TABLES\/5","volume":"292","author":"F Maggioni","year":"2020","unstructured":"Maggioni F, Allevi E, Tomasgard A (2020) Bounds in multi-horizon stochastic programs. Ann Oper Res 292:605\u2013625. https:\/\/doi.org\/10.1007\/S10479-019-03244-9\/TABLES\/5","journal-title":"Ann Oper Res"},{"key":"509_CR11","doi-asserted-by":"publisher","first-page":"683","DOI":"10.1007\/s12532-020-00197-0","volume":"13","author":"N Mazzi","year":"2021","unstructured":"Mazzi N, Grothey A, McKinnon K, Sugishita N (2021) Benders decomposition with adaptive oracles for large scale optimization. Math Program Comput 13:683\u2013703. https:\/\/doi.org\/10.1007\/s12532-020-00197-0","journal-title":"Math Program Comput"},{"key":"509_CR12","unstructured":"Zhang H, Grossmann IE, Knudsen BR, McKinnon K, Nava RG, Tomasgard A (2023) Integrated investment, retrofit and abandonment planning of energy systems with short-term and long-term uncertainty using enhanced Benders decomposition. arXiv:2303.09927"},{"key":"509_CR13","unstructured":"Zhang H, Mazzi N, McKinnon K, Nava RG, Tomasgard A (2022) A stabilised Benders decomposition with adaptive oracles applied to investment planning of multi-region power systems with short-term and long-term uncertainty. arXiv:2209.03471"}],"container-title":["Computational Management Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10287-024-00509-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10287-024-00509-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10287-024-00509-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,22]],"date-time":"2024-06-22T08:15:11Z","timestamp":1719044111000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10287-024-00509-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,10]]},"references-count":13,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["509"],"URL":"https:\/\/doi.org\/10.1007\/s10287-024-00509-y","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-3258743\/v1","asserted-by":"object"},{"id-type":"doi","id":"10.21203\/rs.3.rs-3258743\/v2","asserted-by":"object"}]},"ISSN":["1619-697X","1619-6988"],"issn-type":[{"value":"1619-697X","type":"print"},{"value":"1619-6988","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,5,10]]},"assertion":[{"value":"12 August 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 March 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 May 2024","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 that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"32"}}