Cost allocation for set covering: The happy nucleolus

IF 0.8 4区管理学 Q4 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Letters Pub Date : 2024-08-28 DOI:10.1016/j.orl.2024.107158

Jannis Blauth, Antonia Ellerbrock, Vera Traub, Jens Vygen

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.

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成套覆盖的成本分配：快乐的核仁

我们考虑的是集合覆盖问题的成本分配。我们在不违反群体合理性条件的前提下，尽可能多地为各元素（玩家）分配成本，从而使多余向量在词典上最大化。这种快乐核有几个很好的特性。特别是，我们证明只需考虑一小部分 "简单 "联盟就能计算出它。计算集合覆盖的核子是 NP 难的，而我们的结果意味着快乐核子可以在多项式时间内计算出来。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Operations Research Letters 管理科学-运筹学与管理科学

CiteScore

2.10

自引率

9.10%

发文量

111

审稿时长

83 days

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.