{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T10:22:43Z","timestamp":1779272563914,"version":"3.51.4"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,11,3]],"date-time":"2021-11-03T00:00:00Z","timestamp":1635897600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,11,3]],"date-time":"2021-11-03T00:00:00Z","timestamp":1635897600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"name":"National Science Foundation","award":["1854960"],"award-info":[{"award-number":["1854960"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2022,1]]},"DOI":"10.1007\/s10589-021-00323-1","type":"journal-article","created":{"date-parts":[[2021,11,3]],"date-time":"2021-11-03T10:02:53Z","timestamp":1635933773000},"page":"201-250","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Adaptive partition-based SDDP algorithms for multistage stochastic linear programming with fixed recourse"],"prefix":"10.1007","volume":"81","author":[{"given":"Murwan","family":"Siddig","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6839-522X","authenticated-orcid":false,"given":"Yongjia","family":"Song","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,11,3]]},"reference":[{"key":"323_CR1","unstructured":"Abrahamson, P.G.: Nested-decomposition approach for solving staircase linear programs. Tech. rep., Stanford Univ., CA (USA). Dept. of Operations Research (1983)"},{"issue":"1","key":"323_CR2","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1287\/ijoc.2017.0765","volume":"30","author":"W van Ackooij","year":"2017","unstructured":"van Ackooij, W., de Oliveira, W., Song, Y.: Adaptive partition-based level decomposition methods for solving two-stage stochastic programs with fixed recourse. INFORMS J. Comput. 30(1), 57\u201370 (2017)","journal-title":"INFORMS J. Comput."},{"issue":"1","key":"323_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10589-019-00104-x","volume":"74","author":"W van Ackooij","year":"2019","unstructured":"van Ackooij, W., de Oliveira, W., Song, Y.: On level regularization with normal solutions in decomposition methods for multistage stochastic programming problems. Comput. Optim. Appl. 74(1), 1\u201342 (2019)","journal-title":"Comput. Optim. Appl."},{"issue":"1","key":"323_CR4","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1023\/A:1023062915106","volume":"26","author":"S Ahmed","year":"2003","unstructured":"Ahmed, S., King, A.J., Parija, G.: A multi-stage stochastic integer programming approach for capacity expansion under uncertainty. J. Global Optim. 26(1), 3\u201324 (2003)","journal-title":"J. Global Optim."},{"issue":"1","key":"323_CR5","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/S0377-2217(98)00381-6","volume":"120","author":"A Alonso","year":"2000","unstructured":"Alonso, A., Escudero, L.F., Ortuno, M.T.: A stochastic 0\u20131 program based approach for the air traffic flow management problem. Eur. J. Oper. Res. 120(1), 47\u201362 (2000)","journal-title":"Eur. J. Oper. Res."},{"issue":"2","key":"323_CR6","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1287\/opre.35.2.215","volume":"35","author":"JC Bean","year":"1987","unstructured":"Bean, J.C., Birge, J.R., Smith, R.L.: Aggregation in dynamic programming. Oper. Res. 35(2), 215\u2013220 (1987)","journal-title":"Oper. Res."},{"key":"323_CR7","volume-title":"Dynamic Programming","author":"R Bellman","year":"1957","unstructured":"Bellman, R.: Dynamic Programming. Princeton University Press, Princeton (1957)"},{"issue":"1","key":"323_CR8","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/BF02591859","volume":"31","author":"JR Birge","year":"1985","unstructured":"Birge, J.R.: Aggregation bounds in stochastic linear programming. Math. Program. 31(1), 25\u201341 (1985)","journal-title":"Math. Program."},{"key":"323_CR9","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, J.R., Louveaux, F.: Introduction to Stochastic Programming. Springer Science & Business Media, Berlin (2011)"},{"key":"323_CR10","doi-asserted-by":"crossref","unstructured":"Bomze, I.M., Budinich, M., Pardalos, P.M., Pelillo, M.: The maximum clique problem. In: Du, D.-Z., Pardalos, P.M. (eds.) Handbook of combinatorial optimization, pp. 1\u201374. Springer, Boston, MA (1999)","DOI":"10.1007\/978-1-4757-3023-4_1"},{"key":"323_CR11","volume-title":"Modeling, Measuring and Managing Risk","author":"PG Ch","year":"2007","unstructured":"Ch, P.G., Werner, R.: Modeling, Measuring and Managing Risk. World Scientific, Singapore (2007)"},{"issue":"3","key":"323_CR12","doi-asserted-by":"publisher","first-page":"497","DOI":"10.1023\/A:1022641805263","volume":"102","author":"ZL Chen","year":"1999","unstructured":"Chen, Z.L., Powell, W.B.: Convergent cutting-plane and partial-sampling algorithm for multistage stochastic linear programs with recourse. J. Optim. Theory Appl. 102(3), 497\u2013524 (1999)","journal-title":"J. Optim. Theory Appl."},{"issue":"2","key":"323_CR13","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.: Jump: a modeling language for mathematical optimization. SIAM Rev. 59(2), 295\u2013320 (2017)","journal-title":"SIAM Rev."},{"key":"323_CR14","volume-title":"Portfolio Optimization and Risk Management via Stochastic Programming","author":"J Dupa\u010dov\u00e1","year":"2009","unstructured":"Dupa\u010dov\u00e1, J.: Portfolio Optimization and Risk Management via Stochastic Programming. Osaka University Press, Osaka (2009)"},{"issue":"1","key":"323_CR15","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1007\/s10479-008-0358-6","volume":"165","author":"J Dupa\u010dov\u00e1","year":"2009","unstructured":"Dupa\u010dov\u00e1, J., Pol\u00edvka, J.: Asset-liability management for czech pension funds using stochastic programming. Ann. Oper. Res. 165(1), 5\u201328 (2009)","journal-title":"Ann. Oper. Res."},{"key":"323_CR16","doi-asserted-by":"crossref","unstructured":"Fhoula, B., Hajji, A., Rekik, M.: Stochastic dual dynamic programming for transportation planning under demand uncertainty. In: 2013 International Conference on Advanced Logistics and Transport, pp. 550\u2013555. IEEE (2013)","DOI":"10.1109\/ICAdLT.2013.6568518"},{"issue":"8","key":"323_CR17","doi-asserted-by":"publisher","first-page":"1409","DOI":"10.1016\/j.compchemeng.2003.10.005","volume":"28","author":"V Goel","year":"2004","unstructured":"Goel, V., Grossmann, I.E.: A stochastic programming approach to planning of offshore gas field developments under uncertainty in reserves. Comput. Chem. Eng. 28(8), 1409\u20131429 (2004)","journal-title":"Comput. Chem. Eng."},{"key":"323_CR18","unstructured":"Gurobi\u00a0Optimization, L.: Gurobi optimizer reference manual (2019). http:\/\/www.gurobi.com"},{"issue":"4","key":"323_CR19","doi-asserted-by":"publisher","first-page":"619","DOI":"10.1287\/opre.38.4.619","volume":"38","author":"\u00c5 Hallefjord","year":"1990","unstructured":"Hallefjord, \u00c5., Stor\u00f8y, S.: Aggregation and disaggregation in integer programming problems. Oper. Res. 38(4), 619\u2013623 (1990)","journal-title":"Oper. Res."},{"issue":"3","key":"323_CR20","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1080\/07408170500434539","volume":"38","author":"YT Herer","year":"2006","unstructured":"Herer, Y.T., Tzur, M., Y\u00fccesan, E.: The multilocation transshipment problem. IIE Trans. 38(3), 185\u2013200 (2006)","journal-title":"IIE Trans."},{"key":"323_CR21","doi-asserted-by":"crossref","unstructured":"Jardim, D., Maceira, M., Falcao, D.: Stochastic streamflow model for hydroelectric systems using clustering techniques. In: 2001 IEEE Porto Power Tech Proceedings (Cat. No. 01EX502), vol.\u00a03, pp. 6\u2013pp. IEEE (2001)","DOI":"10.1109\/PTC.2001.964916"},{"key":"323_CR22","volume-title":"Stochastic Programming","author":"P Kall","year":"1994","unstructured":"Kall, P., Wallace, S.W., Kall, P.: Stochastic Programming. Springer, New York (1994)"},{"issue":"4","key":"323_CR23","doi-asserted-by":"publisher","first-page":"703","DOI":"10.1137\/0108053","volume":"8","author":"JE Kelley Jr","year":"1960","unstructured":"Kelley, J.E., Jr.: The cutting-plane method for solving convex programs. J. Soc. Industrial Appl. Math. 8(4), 703\u2013712 (1960)","journal-title":"J. Soc. Industrial Appl. Math."},{"issue":"2","key":"323_CR24","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1007\/s10957-004-1842-z","volume":"125","author":"K Linowsky","year":"2005","unstructured":"Linowsky, K., Philpott, A.B.: On the convergence of sampling-based decomposition algorithms for multistage stochastic programs. J. Optim. Theory Appl. 125(2), 349\u2013366 (2005)","journal-title":"J. Optim. Theory Appl."},{"issue":"2","key":"323_CR25","doi-asserted-by":"publisher","first-page":"713","DOI":"10.1007\/s10479-016-2107-6","volume":"253","author":"VL de Matos","year":"2017","unstructured":"de Matos, V.L., Morton, D.P., Finardi, E.C.: Assessing policy quality in a multistage stochastic program for long-term hydrothermal scheduling. Ann. Oper. Res. 253(2), 713\u2013731 (2017)","journal-title":"Ann. Oper. Res."},{"issue":"1","key":"323_CR26","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s12667-011-0024-y","volume":"2","author":"T Homem-de Mello","year":"2011","unstructured":"Homem-de Mello, T., De Matos, V.L., Finardi, E.C.: Sampling strategies and stopping criteria for stochastic dual dynamic programming: a case study in long-term hydrothermal scheduling. Energy Syst. 2(1), 1\u201331 (2011)","journal-title":"Energy Syst."},{"issue":"1","key":"323_CR27","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1007\/BF02187647","volume":"64","author":"DP Morton","year":"1996","unstructured":"Morton, D.P.: An enhanced decomposition algorithm for multistage stochastic hydroelectric scheduling. Ann. Oper. Res. 64(1), 211\u2013235 (1996)","journal-title":"Ann. Oper. Res."},{"issue":"6","key":"323_CR28","doi-asserted-by":"publisher","first-page":"1180","DOI":"10.1080\/10556788.2013.871282","volume":"29","author":"W de Oliveira","year":"2014","unstructured":"de Oliveira, W., Sagastiz\u00e1bal, C.: Level bundle methods for oracles with on-demand accuracy. Optim. Methods Softw. 29(6), 1180\u20131209 (2014)","journal-title":"Optim. Methods Softw."},{"issue":"3","key":"323_CR29","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1515\/jqas-2017-0030","volume":"13","author":"G Pantuso","year":"2017","unstructured":"Pantuso, G.: The football team composition problem: a stochastic programming approach. J. Quant. Anal. Sports 13(3), 113\u2013129 (2017)","journal-title":"J. Quant. Anal. Sports"},{"issue":"1","key":"323_CR30","doi-asserted-by":"publisher","first-page":"180","DOI":"10.1109\/TPWRS.2004.840397","volume":"20","author":"MV Pereira","year":"2005","unstructured":"Pereira, M.V., Granville, S., Fampa, M.H., Dix, R., Barroso, L.A.: Strategic bidding under uncertainty: a binary expansion approach. IEEE Trans. Power Syst. 20(1), 180\u2013188 (2005)","journal-title":"IEEE Trans. Power Syst."},{"issue":"1\u20133","key":"323_CR31","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1007\/BF01582895","volume":"52","author":"MV Pereira","year":"1991","unstructured":"Pereira, M.V., Pinto, L.M.: Multi-stage stochastic optimization applied to energy planning. Math. Program. 52(1\u20133), 359\u2013375 (1991)","journal-title":"Math. Program."},{"issue":"4","key":"323_CR32","doi-asserted-by":"publisher","first-page":"450","DOI":"10.1016\/j.orl.2008.01.013","volume":"36","author":"AB Philpott","year":"2008","unstructured":"Philpott, A.B., Guan, Z.: On the convergence of stochastic dual dynamic programming and related methods. Oper. Res. Lett. 36(4), 450\u2013455 (2008)","journal-title":"Oper. Res. Lett."},{"issue":"1\u20132","key":"323_CR33","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1007\/s10107-015-0884-3","volume":"156","author":"S Rebennack","year":"2016","unstructured":"Rebennack, S.: Combining sampling-based and scenario-based nested benders decomposition methods: application to stochastic dual dynamic programming. Math. Program. 156(1\u20132), 343\u2013389 (2016)","journal-title":"Math. Program."},{"issue":"4","key":"323_CR34","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1287\/opre.39.4.553","volume":"39","author":"DF Rogers","year":"1991","unstructured":"Rogers, D.F., Plante, R.D., Wong, R.T., Evans, J.R.: Aggregation and disaggregation techniques and methodology in optimization. Oper. Res. 39(4), 553\u2013582 (1991)","journal-title":"Oper. Res."},{"issue":"3","key":"323_CR35","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1016\/S0167-6377(99)00019-X","volume":"24","author":"CH Rosa","year":"1999","unstructured":"Rosa, C.H., Takriti, S.: Improving aggregation bounds for two-stage stochastic programs. Oper. Res Lett. 24(3), 127\u2013137 (1999)","journal-title":"Oper. Res Lett."},{"issue":"1","key":"323_CR36","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1016\/j.ejor.2010.08.007","volume":"209","author":"A Shapiro","year":"2011","unstructured":"Shapiro, A.: Analysis of stochastic dual dynamic programming method. Eur. J. Oper. Res. 209(1), 63\u201372 (2011)","journal-title":"Eur. J. Oper. Res."},{"key":"323_CR37","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611973433","volume-title":"Lectures on Stochastic Programming: Modeling and Theory","author":"A Shapiro","year":"2014","unstructured":"Shapiro, A., Dentcheva, D., Ruszczy\u0144ski, A.: Lectures on Stochastic Programming: Modeling and Theory, 2nd edn. Society for Industrial and Applied Mathematics, Philadelphia, PA (2014)","edition":"2"},{"issue":"2","key":"323_CR38","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1016\/j.ejor.2012.08.022","volume":"224","author":"A Shapiro","year":"2013","unstructured":"Shapiro, A., Tekaya, W., da Costa, J.P., Soares, M.P.: Risk neutral and risk averse stochastic dual dynamic programming method. Eur. J. Oper. Res. 224(2), 375\u2013391 (2013)","journal-title":"Eur. J. Oper. Res."},{"issue":"4","key":"323_CR39","doi-asserted-by":"publisher","first-page":"638","DOI":"10.1137\/0117061","volume":"17","author":"RM van Slyke","year":"1969","unstructured":"van Slyke, R.M., Wets, R.: L-shaped linear programs with applications to optimal control and stochastic programming. SIAM J. Appl. Math. 17(4), 638\u2013663 (1969)","journal-title":"SIAM J. Appl. Math."},{"issue":"3","key":"323_CR40","doi-asserted-by":"publisher","first-page":"1344","DOI":"10.1137\/140967337","volume":"25","author":"Y Song","year":"2015","unstructured":"Song, Y., Luedtke, J.: An adaptive partition-based approach for solving two-stage stochastic programs with fixed recourse. SIAM J. Optim. 25(3), 1344\u20131367 (2015)","journal-title":"SIAM J. Optim."},{"issue":"2","key":"323_CR41","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1016\/j.ejor.2010.02.025","volume":"206","author":"S Trukhanov","year":"2010","unstructured":"Trukhanov, S., Ntaimo, L., Schaefer, A.: Adaptive multicut aggregation for two-stage stochastic linear programs with recourse. Eur. J. Oper. Res. 206(2), 395\u2013406 (2010)","journal-title":"Eur. J. Oper. Res."},{"key":"323_CR42","unstructured":"Wittrock, R.J.: Advances in a nested decomposition algorithm for solving staircase linear programs. Tech. rep., Stanford Univ., CA (USA). Dept. of Operations Research (1984)"},{"issue":"4","key":"323_CR43","doi-asserted-by":"publisher","first-page":"893","DOI":"10.1287\/moor.19.4.893","volume":"19","author":"S Wright","year":"1994","unstructured":"Wright, S.: Primal-dual aggregation and disaggregation for stochastic linear programs. Math. Oper. Res. 19(4), 893\u2013908 (1994)","journal-title":"Math. Oper. Res."},{"issue":"4","key":"323_CR44","doi-asserted-by":"publisher","first-page":"903","DOI":"10.1287\/opre.28.4.903","volume":"28","author":"PH Zipkin","year":"1980","unstructured":"Zipkin, P.H.: Bounds for row-aggregation in linear programming. Oper. Res. 28(4), 903\u2013916 (1980)","journal-title":"Oper. Res."},{"issue":"2","key":"323_CR45","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1287\/opre.28.2.403","volume":"28","author":"PH Zipkin","year":"1980","unstructured":"Zipkin, P.H.: Bounds on the effect of aggregating variables in linear programs. Oper. Res. 28(2), 403\u2013418 (1980)","journal-title":"Oper. Res."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-021-00323-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10589-021-00323-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-021-00323-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T10:54:03Z","timestamp":1726052043000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10589-021-00323-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,3]]},"references-count":45,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,1]]}},"alternative-id":["323"],"URL":"https:\/\/doi.org\/10.1007\/s10589-021-00323-1","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,3]]},"assertion":[{"value":"26 August 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 October 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 November 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}