{"title":"基于分区的风险规避两阶段随机规划的列约束生成方法","authors":"Jongheon Lee, Kyungsik Lee","doi":"10.1007/s10479-025-06617-5","DOIUrl":null,"url":null,"abstract":"<div><p>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 <i>partition-based risk-averse two-stage stochastic program</i>. 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.</p></div>","PeriodicalId":8215,"journal":{"name":"Annals of Operations Research","volume":"349 3","pages":"1717 - 1747"},"PeriodicalIF":4.5000,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10479-025-06617-5.pdf","citationCount":"0","resultStr":"{\"title\":\"Column-and-constraint generation approach to partition-based risk-averse two-stage stochastic programs\",\"authors\":\"Jongheon Lee, Kyungsik Lee\",\"doi\":\"10.1007/s10479-025-06617-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>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 <i>partition-based risk-averse two-stage stochastic program</i>. 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.</p></div>\",\"PeriodicalId\":8215,\"journal\":{\"name\":\"Annals of Operations Research\",\"volume\":\"349 3\",\"pages\":\"1717 - 1747\"},\"PeriodicalIF\":4.5000,\"publicationDate\":\"2025-05-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10479-025-06617-5.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Operations Research\",\"FirstCategoryId\":\"91\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10479-025-06617-5\",\"RegionNum\":3,\"RegionCategory\":\"管理学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"OPERATIONS RESEARCH & MANAGEMENT SCIENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Operations Research","FirstCategoryId":"91","ListUrlMain":"https://link.springer.com/article/10.1007/s10479-025-06617-5","RegionNum":3,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
Column-and-constraint generation approach to partition-based risk-averse two-stage stochastic programs
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 partition-based risk-averse two-stage stochastic program. 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.
期刊介绍:
The Annals of Operations Research publishes peer-reviewed original articles dealing with key aspects of operations research, including theory, practice, and computation. The journal publishes full-length research articles, short notes, expositions and surveys, reports on computational studies, and case studies that present new and innovative practical applications.
In addition to regular issues, the journal publishes periodic special volumes that focus on defined fields of operations research, ranging from the highly theoretical to the algorithmic and the applied. These volumes have one or more Guest Editors who are responsible for collecting the papers and overseeing the refereeing process.