{"title":"部分自适应多阶段随机程序设计","authors":"","doi":"10.1016/j.ejor.2024.09.034","DOIUrl":null,"url":null,"abstract":"<div><div>Multistage stochastic programming is a powerful tool allowing decision-makers to revise their decisions at each stage based on the realized uncertainty. However, organizations are not able to be fully flexible, as decisions cannot be revised too frequently in practice. Consequently, decision commitment becomes crucial to ensure that initially made decisions remain unchanged for a certain period of time. This paper introduces partially adaptive multistage stochastic programming, a new optimization paradigm that strikes an optimal balance between decision flexibility and commitment by determining the best stages to revise decisions depending on the allowed level of flexibility. We introduce a novel mathematical formulation and theoretical properties eliminating certain constraint sets. Furthermore, we develop a decomposition method that effectively handles mixed-integer partially adaptive multistage programs by adapting the integer L-shaped method and Benders decomposition. Computational experiments on stochastic lot-sizing and generation expansion planning problems show substantial advantages attained through optimal selections of revision times when flexibility is limited, while demonstrating computational efficiency attained by employing the proposed properties and solution methodology. By adhering to these optimal revision times, organizations can achieve performance levels comparable to fully flexible settings.</div></div>","PeriodicalId":55161,"journal":{"name":"European Journal of Operational Research","volume":null,"pages":null},"PeriodicalIF":6.0000,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Partially adaptive multistage stochastic programming\",\"authors\":\"\",\"doi\":\"10.1016/j.ejor.2024.09.034\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Multistage stochastic programming is a powerful tool allowing decision-makers to revise their decisions at each stage based on the realized uncertainty. However, organizations are not able to be fully flexible, as decisions cannot be revised too frequently in practice. Consequently, decision commitment becomes crucial to ensure that initially made decisions remain unchanged for a certain period of time. This paper introduces partially adaptive multistage stochastic programming, a new optimization paradigm that strikes an optimal balance between decision flexibility and commitment by determining the best stages to revise decisions depending on the allowed level of flexibility. We introduce a novel mathematical formulation and theoretical properties eliminating certain constraint sets. Furthermore, we develop a decomposition method that effectively handles mixed-integer partially adaptive multistage programs by adapting the integer L-shaped method and Benders decomposition. Computational experiments on stochastic lot-sizing and generation expansion planning problems show substantial advantages attained through optimal selections of revision times when flexibility is limited, while demonstrating computational efficiency attained by employing the proposed properties and solution methodology. By adhering to these optimal revision times, organizations can achieve performance levels comparable to fully flexible settings.</div></div>\",\"PeriodicalId\":55161,\"journal\":{\"name\":\"European Journal of Operational Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":6.0000,\"publicationDate\":\"2024-09-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"European Journal of Operational Research\",\"FirstCategoryId\":\"91\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0377221724007379\",\"RegionNum\":2,\"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":"European Journal of Operational Research","FirstCategoryId":"91","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0377221724007379","RegionNum":2,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 0
摘要
多阶段随机程序设计是一种强大的工具,允许决策者在每个阶段根据已实现的不确定性修改其决策。然而,组织无法做到完全灵活,因为在实践中不可能频繁修改决策。因此,决策承诺对于确保最初做出的决策在一定时期内保持不变至关重要。本文介绍了部分自适应多阶段随机程序设计,这是一种新的优化范例,它能根据允许的灵活性水平确定修改决策的最佳阶段,从而在决策灵活性和承诺之间取得最佳平衡。我们介绍了一种新的数学公式和理论特性,消除了某些约束集。此外,我们还开发了一种分解方法,通过调整整数 L 型方法和本德斯分解法,有效处理混合整数部分自适应多阶段程序。在随机批量规模和发电量扩展规划问题上的计算实验表明,当灵活性受到限制时,通过优化选择修正时间可以获得巨大优势,同时也证明了采用所提出的特性和求解方法所能达到的计算效率。通过遵守这些最佳修订时间,企业可以达到与完全灵活设置相当的性能水平。
Multistage stochastic programming is a powerful tool allowing decision-makers to revise their decisions at each stage based on the realized uncertainty. However, organizations are not able to be fully flexible, as decisions cannot be revised too frequently in practice. Consequently, decision commitment becomes crucial to ensure that initially made decisions remain unchanged for a certain period of time. This paper introduces partially adaptive multistage stochastic programming, a new optimization paradigm that strikes an optimal balance between decision flexibility and commitment by determining the best stages to revise decisions depending on the allowed level of flexibility. We introduce a novel mathematical formulation and theoretical properties eliminating certain constraint sets. Furthermore, we develop a decomposition method that effectively handles mixed-integer partially adaptive multistage programs by adapting the integer L-shaped method and Benders decomposition. Computational experiments on stochastic lot-sizing and generation expansion planning problems show substantial advantages attained through optimal selections of revision times when flexibility is limited, while demonstrating computational efficiency attained by employing the proposed properties and solution methodology. By adhering to these optimal revision times, organizations can achieve performance levels comparable to fully flexible settings.
期刊介绍:
The European Journal of Operational Research (EJOR) publishes high quality, original papers that contribute to the methodology of operational research (OR) and to the practice of decision making.