{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T00:28:20Z","timestamp":1767140900535,"version":"build-2238731810"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,5,6]],"date-time":"2025-05-06T00:00:00Z","timestamp":1746489600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,5,6]],"date-time":"2025-05-06T00:00:00Z","timestamp":1746489600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"crossref","award":["2021R1A2C2005531"],"award-info":[{"award-number":["2021R1A2C2005531"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100007053","name":"Korea Institute of Energy Technology Evaluation and Planning","doi-asserted-by":"publisher","award":["2019371010006B"],"award-info":[{"award-number":["2019371010006B"]}],"id":[{"id":"10.13039\/501100007053","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2025,6]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Typically, two-stage stochastic programs have been modeled and solved based on the finite support assumption, but the large number of scenarios makes it hard to solve, and there also are potential risks of inaccurate estimation of underlying distribution. In this paper, to mitigate the drawbacks, we present a novel risk-averse two-stage stochastic program with finite support, which we call\n                    <jats:italic>partition-based risk-averse two-stage stochastic program<\/jats:italic>\n                    . In the program, a set of scenarios is partitioned into several groups, and the second-stage cost is defined as the expectation of risk levels for all of the groups. In particular, the conditional value-at-risk is considered as a risk measure for each group, and so the risk level of the model is affected by a quantile parameter or a partition of a given set of scenarios. In order to solve the model exactly for a given partition, a column-and-constraint generation algorithm is proposed. In addition, a scenario partitioning algorithm to enable the risk level of the model to be close to a given target is devised, and partitioning schemes for combining it with the proposed column-and-constraint generation algorithm are proposed. Extensive numerical experiments were performed that demonstrated the effectiveness of the proposed partitioning schemes and the efficiency of the proposed solution approach.\n                  <\/jats:p>","DOI":"10.1007\/s10479-025-06617-5","type":"journal-article","created":{"date-parts":[[2025,5,6]],"date-time":"2025-05-06T07:48:32Z","timestamp":1746517712000},"page":"1717-1747","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Column-and-constraint generation approach to partition-based risk-averse two-stage stochastic programs"],"prefix":"10.1007","volume":"349","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6438-9260","authenticated-orcid":false,"given":"Jongheon","family":"Lee","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4543-2312","authenticated-orcid":false,"given":"Kyungsik","family":"Lee","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,5,6]]},"reference":[{"issue":"1","key":"6617_CR1","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1287\/ijoc.2017.0765","volume":"30","author":"W van Ackooij","year":"2018","unstructured":"van Ackooij, W., de Oliveira, W., & Song, Y. (2018). Adaptive partition-based level decomposition methods for solving two-stage stochastic programs with fixed recourse. INFORMS Journal on Computing, 30(1), 57\u201370.","journal-title":"INFORMS Journal on Computing"},{"issue":"1","key":"6617_CR2","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1109\/TPWRS.2014.2320880","volume":"30","author":"Y An","year":"2015","unstructured":"An, Y., & Zeng, B. (2015). Exploring the modeling capacity of two-stage robust optimization: Variants of robust unit commitment model. IEEE Transactions on Power Systems, 30(1), 109\u2013122.","journal-title":"IEEE Transactions on Power Systems"},{"issue":"3","key":"6617_CR3","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1111\/1467-9965.00068","volume":"9","author":"P Artzner","year":"1999","unstructured":"Artzner, P., Delbaen, F., Eber, J. M., et al. (1999). Coherent measures of risk. Mathematical Finance, 9(3), 203\u2013228.","journal-title":"Mathematical Finance"},{"issue":"3","key":"6617_CR4","doi-asserted-by":"publisher","first-page":"2360","DOI":"10.1137\/17M1115046","volume":"28","author":"M Bansal","year":"2018","unstructured":"Bansal, M., Huang, K. L., & Mehrotra, S. (2018). Decomposition algorithms for two-stage distributionally robust mixed binary programs. SIAM Journal on Optimization, 28(3), 2360\u20132383.","journal-title":"SIAM Journal on Optimization"},{"issue":"2","key":"6617_CR5","doi-asserted-by":"publisher","first-page":"548","DOI":"10.1016\/j.ejor.2020.11.002","volume":"292","author":"B Basciftci","year":"2021","unstructured":"Basciftci, B., Ahmed, S., & Shen, S. (2021). Distributionally robust facility location problem under decision-dependent stochastic demand. European Journal of Operational Research, 292(2), 548\u2013561.","journal-title":"European Journal of Operational Research"},{"issue":"1","key":"6617_CR6","doi-asserted-by":"publisher","first-page":"314","DOI":"10.1007\/BF01585113","volume":"24","author":"JR Birge","year":"1982","unstructured":"Birge, J. R. (1982). The value of the stochastic solution in stochastic linear programs with fixed recourse. Mathematical Programming, 24(1), 314\u2013325.","journal-title":"Mathematical Programming"},{"key":"6617_CR7","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. (2011). Introduction to stochastic programming. Springer Science & Business Media."},{"issue":"6","key":"6617_CR8","doi-asserted-by":"publisher","first-page":"4477","DOI":"10.1109\/TPWRS.2017.2683263","volume":"32","author":"I Blanco","year":"2017","unstructured":"Blanco, I., & Morales, J. M. (2017). An efficient robust solution to the two-stage stochastic unit commitment problem. IEEE Transactions on Power Systems, 32(6), 4477\u20134488.","journal-title":"IEEE Transactions on Power Systems"},{"issue":"1\u20132","key":"6617_CR9","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/S0167-6377(98)00050-9","volume":"24","author":"CC Car\u00f8e","year":"1999","unstructured":"Car\u00f8e, C. C., & Schultz, R. (1999). Dual decomposition in stochastic integer programming. Operations Research Letters, 24(1\u20132), 37\u201345.","journal-title":"Operations Research Letters"},{"issue":"2","key":"6617_CR10","doi-asserted-by":"publisher","first-page":"1067","DOI":"10.1109\/59.496196","volume":"11","author":"P Carpentier","year":"1996","unstructured":"Carpentier, P., Gohen, G., Culioli, J. C., et al. (1996). Stochastic optimization of unit commitment: A new decomposition framework. IEEE Transactions on Power Systems, 11(2), 1067\u20131073.","journal-title":"IEEE Transactions on Power Systems"},{"key":"6617_CR11","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1016\/j.cor.2013.08.020","volume":"43","author":"TG Crainic","year":"2014","unstructured":"Crainic, T. G., Hewitt, M., & Rei, W. (2014). Scenario grouping in a progressive hedging-based meta-heuristic for stochastic network design. Computers & Operations Research, 43, 90\u201399.","journal-title":"Computers & Operations Research"},{"issue":"2","key":"6617_CR12","first-page":"757","volume":"33","author":"Y Deng","year":"2021","unstructured":"Deng, Y., Jia, H., Ahmed, S., et al. (2021). Scenario grouping and decomposition algorithms for chance-constrained programs. INFORMS Journal on Computing, 33(2), 757\u2013773.","journal-title":"INFORMS Journal on Computing"},{"issue":"1","key":"6617_CR13","doi-asserted-by":"publisher","first-page":"362","DOI":"10.1016\/j.cor.2012.07.009","volume":"40","author":"LF Escudero","year":"2013","unstructured":"Escudero, L. F., Gar\u00edn, M. A., P\u00e9rez, G., et al. (2013). Scenario cluster decomposition of the Lagrangian dual in two-stage stochastic mixed 0\u20131 optimization. Computers & Operations Research, 40(1), 362\u2013377.","journal-title":"Computers & Operations Research"},{"issue":"5","key":"6617_CR14","doi-asserted-by":"publisher","first-page":"1390","DOI":"10.1287\/opre.2018.1729","volume":"66","author":"R Jiang","year":"2018","unstructured":"Jiang, R., & Guan, Y. (2018). Risk-averse two-stage stochastic program with distributional ambiguity. Operations Research, 66(5), 1390\u20131405.","journal-title":"Operations Research"},{"key":"6617_CR15","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1002\/9780470316801.ch2","volume":"344","author":"L Kaufman","year":"1990","unstructured":"Kaufman, L., & Rousseeuw, P. J. (1990). Partitioning around medoids (program pam). Finding groups in data: An introduction to cluster analysis, 344, 68\u2013125.","journal-title":"Finding groups in data: An introduction to cluster analysis"},{"issue":"1","key":"6617_CR16","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1109\/59.485989","volume":"11","author":"SA Kazarlis","year":"1996","unstructured":"Kazarlis, S. A., Bakirtzis, A., & Petridis, V. (1996). A genetic algorithm solution to the unit commitment problem. IEEE Transactions on Power Systems, 11(1), 83\u201392.","journal-title":"IEEE Transactions on Power Systems"},{"issue":"6","key":"6617_CR17","doi-asserted-by":"publisher","first-page":"1431","DOI":"10.1287\/opre.2015.1421","volume":"63","author":"K Kim","year":"2015","unstructured":"Kim, K., & Mehrotra, S. (2015). A two-stage stochastic integer programming approach to integrated staffing and scheduling with application to nurse management. Operations Research, 63(6), 1431\u20131451.","journal-title":"Operations Research"},{"issue":"2","key":"6617_CR18","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1137\/S1052623499363220","volume":"12","author":"AJ Kleywegt","year":"2002","unstructured":"Kleywegt, A. J., Shapiro, A., & Homem-de Mello, T. (2002). The sample average approximation method for stochastic discrete optimization. SIAM Journal on Optimization, 12(2), 479\u2013502.","journal-title":"SIAM Journal on Optimization"},{"issue":"1","key":"6617_CR19","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s10287-005-0042-0","volume":"3","author":"A K\u00fcnzi-Bay","year":"2006","unstructured":"K\u00fcnzi-Bay, A., & Mayer, J. (2006). Computational aspects of minimizing conditional value-at-risk. Computational Management Science, 3(1), 3\u201327.","journal-title":"Computational Management Science"},{"issue":"1","key":"6617_CR20","doi-asserted-by":"publisher","first-page":"194","DOI":"10.1016\/j.ejor.2020.05.064","volume":"288","author":"R M\u00ednguez","year":"2021","unstructured":"M\u00ednguez, R., van Ackooij, W., & Garc\u00eda-Bertrand, R. (2021). Constraint generation for risk averse two-stage stochastic programs. European Journal of Operational Research, 288(1), 194\u2013206.","journal-title":"European Journal of Operational Research"},{"issue":"3","key":"6617_CR21","doi-asserted-by":"publisher","first-page":"578","DOI":"10.1287\/opre.2013.1174","volume":"61","author":"A Papavasiliou","year":"2013","unstructured":"Papavasiliou, A., & Oren, S. S. (2013). Multiarea stochastic unit commitment for high wind penetration in a transmission constrained network. Operations Research, 61(3), 578\u2013592.","journal-title":"Operations Research"},{"key":"6617_CR22","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1007\/s11590-016-1002-z","volume":"11","author":"K Park","year":"2017","unstructured":"Park, K., & Lee, K. (2017). Distribution-robust loss-averse optimization. Optimization Letters, 11, 153\u2013163.","journal-title":"Optimization Letters"},{"key":"6617_CR23","doi-asserted-by":"publisher","first-page":"1","DOI":"10.5802\/ojmo.15","volume":"3","author":"H Rahimian","year":"2022","unstructured":"Rahimian, H., & Mehrotra, S. (2022). Frameworks and results in distributionally robust optimization. Open Journal of Mathematical Optimization, 3, 1\u201385.","journal-title":"Open Journal of Mathematical Optimization"},{"key":"6617_CR24","doi-asserted-by":"publisher","first-page":"21","DOI":"10.21314\/JOR.2000.038","volume":"2","author":"RT Rockafellar","year":"2000","unstructured":"Rockafellar, R. T., & Uryasev, S. (2000). Optimization of conditional value-at-risk. Journal of Risk, 2, 21\u201342.","journal-title":"Journal of Risk"},{"issue":"1","key":"6617_CR25","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1287\/moor.16.1.119","volume":"16","author":"RT Rockafellar","year":"1991","unstructured":"Rockafellar, R. T., & Wets, R. J. B. (1991). Scenarios and policy aggregation in optimization under uncertainty. Mathematics of Operations Research, 16(1), 119\u2013147.","journal-title":"Mathematics of Operations Research"},{"issue":"3","key":"6617_CR26","doi-asserted-by":"publisher","first-page":"805","DOI":"10.1287\/ijoc.2019.0924","volume":"32","author":"K Ryan","year":"2020","unstructured":"Ryan, K., Ahmed, S., Dey, S. S., et al. (2020). Optimization-driven scenario grouping. INFORMS Journal on Computing, 32(3), 805\u2013821.","journal-title":"INFORMS Journal on Computing"},{"issue":"3","key":"6617_CR27","doi-asserted-by":"publisher","first-page":"1772","DOI":"10.1137\/16M1075594","volume":"27","author":"B Sandik\u00e7i","year":"2017","unstructured":"Sandik\u00e7i, B., & \u00d6zaltin, O. Y. (2017). A scalable bounding method for multistage stochastic programs. SIAM Journal on Optimization, 27(3), 1772\u20131800.","journal-title":"SIAM Journal on Optimization"},{"issue":"1","key":"6617_CR28","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1007\/s10107-012-0526-y","volume":"138","author":"B Sand\u0131k\u00e7\u0131","year":"2013","unstructured":"Sand\u0131k\u00e7\u0131, B., Kong, N., & Schaefer, A. J. (2013). A hierarchy of bounds for stochastic mixed-integer programs. Mathematical Programming, 138(1), 253\u2013272.","journal-title":"Mathematical Programming"},{"issue":"1","key":"6617_CR29","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1016\/j.ejor.2004.01.046","volume":"167","author":"T Santoso","year":"2005","unstructured":"Santoso, T., Ahmed, S., Goetschalckx, M., et al. (2005). A stochastic programming approach for supply chain network design under uncertainty. European Journal of Operational Research, 167(1), 96\u2013115.","journal-title":"European Journal of Operational Research"},{"issue":"3","key":"6617_CR30","doi-asserted-by":"publisher","first-page":"1344","DOI":"10.1137\/140967337","volume":"25","author":"Y Song","year":"2015","unstructured":"Song, Y., & Luedtke, J. (2015). An adaptive partition-based approach for solving two-stage stochastic programs with fixed recourse. SIAM Journal on Optimization, 25(3), 1344\u20131367.","journal-title":"SIAM Journal on Optimization"},{"issue":"3","key":"6617_CR31","doi-asserted-by":"publisher","first-page":"1497","DOI":"10.1109\/59.535691","volume":"11","author":"S Takriti","year":"1996","unstructured":"Takriti, S., Birge, J. R., & Long, E. (1996). A stochastic model for the unit commitment problem. IEEE Transactions on Power Systems, 11(3), 1497\u20131508.","journal-title":"IEEE Transactions on Power Systems"},{"issue":"1","key":"6617_CR32","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1002\/wics.56","volume":"2","author":"ST Tokdar","year":"2010","unstructured":"Tokdar, S. T., & Kass, R. E. (2010). Importance sampling: A review. Wiley Interdisciplinary Reviews: Computational Statistics, 2(1), 54\u201360.","journal-title":"Wiley Interdisciplinary Reviews: Computational Statistics"},{"issue":"1","key":"6617_CR33","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1007\/s10479-018-3003-z","volume":"271","author":"W Van Ackooij","year":"2018","unstructured":"Van Ackooij, W., Danti Lopez, I., Frangioni, A., et al. (2018). Large-scale unit commitment under uncertainty: An updated literature survey. Annals of Operations Research, 271(1), 11\u201385.","journal-title":"Annals of Operations Research"},{"issue":"5","key":"6617_CR34","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1016\/j.orl.2013.05.003","volume":"41","author":"B Zeng","year":"2013","unstructured":"Zeng, B., & Zhao, L. (2013). Solving two-stage robust optimization problems using a column-and-constraint generation method. Operations Research Letters, 41(5), 457\u2013461.","journal-title":"Operations Research Letters"},{"key":"6617_CR35","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1007\/s10479-012-1092-7","volume":"210","author":"QP Zheng","year":"2013","unstructured":"Zheng, Q. P., Wang, J., Pardalos, P. M., et al. (2013). A decomposition approach to the two-stage stochastic unit commitment problem. Annals of Operations Research, 210, 387\u2013410.","journal-title":"Annals of Operations Research"}],"updated-by":[{"DOI":"10.1007\/s10479-025-06680-y","type":"correction","label":"Correction","source":"publisher","updated":{"date-parts":[[2025,6,10]],"date-time":"2025-06-10T00:00:00Z","timestamp":1749513600000}}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-025-06617-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10479-025-06617-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-025-06617-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,16]],"date-time":"2025-06-16T13:09:21Z","timestamp":1750079361000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10479-025-06617-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,6]]},"references-count":35,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["6617"],"URL":"https:\/\/doi.org\/10.1007\/s10479-025-06617-5","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,5,6]]},"assertion":[{"value":"12 February 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 April 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 May 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 June 2025","order":4,"name":"change_date","label":"Change Date","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Correction","order":5,"name":"change_type","label":"Change Type","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"A Correction to this paper has been published:","order":6,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"https:\/\/doi.org\/10.1007\/s10479-025-06680-y","URL":"https:\/\/doi.org\/10.1007\/s10479-025-06680-y","order":7,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of Interest"}}]}}