Jannis Blauth, Antonia Ellerbrock, Vera Traub, Jens Vygen
{"title":"Cost allocation for set covering: The happy nucleolus","authors":"Jannis Blauth, Antonia Ellerbrock, Vera Traub, Jens Vygen","doi":"10.1016/j.orl.2024.107158","DOIUrl":null,"url":null,"abstract":"<div><p>We consider cost allocation for set covering problems. We allocate as much cost to the elements (players) as possible without violating the group rationality condition, and so that the excess vector is lexicographically maximized. This <em>happy nucleolus</em> has several nice properties. In particular, we show that it can be computed considering a small subset of “simple” coalitions only. While computing the nucleolus for set covering is NP-hard, our results imply that the happy nucleolus can be computed in polynomial time.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107158"},"PeriodicalIF":0.8000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167637724000944/pdfft?md5=454040e1a23cb747f7de28cf7ad50ee4&pid=1-s2.0-S0167637724000944-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Operations Research Letters","FirstCategoryId":"91","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167637724000944","RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 0
Abstract
We consider cost allocation for set covering problems. We allocate as much cost to the elements (players) as possible without violating the group rationality condition, and so that the excess vector is lexicographically maximized. This happy nucleolus has several nice properties. In particular, we show that it can be computed considering a small subset of “simple” coalitions only. While computing the nucleolus for set covering is NP-hard, our results imply that the happy nucleolus can be computed in polynomial time.
期刊介绍：
Operations Research Letters is committed to the rapid review and fast publication of short articles on all aspects of operations research and analytics. Apart from a limitation to eight journal pages, quality, originality, relevance and clarity are the only criteria for selecting the papers to be published. ORL covers the broad field of optimization, stochastic models and game theory. Specific areas of interest include networks, routing, location, queueing, scheduling, inventory, reliability, and financial engineering. We wish to explore interfaces with other fields such as life sciences and health care, artificial intelligence and machine learning, energy distribution, and computational social sciences and humanities. Our traditional strength is in methodology, including theory, modelling, algorithms and computational studies. We also welcome novel applications and concise literature reviews.
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