论多重可纳包分配问题的上界

IF 0.8 4区管理学 Q4 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Operations Research Letters Pub Date : 2024-03-06 DOI:10.1016/j.orl.2024.107104

Laura Galli , Adam N. Letchford

{"title":"论多重可纳包分配问题的上界","authors":"Laura Galli , Adam N. Letchford","doi":"10.1016/j.orl.2024.107104","DOIUrl":null,"url":null,"abstract":"<div><p>The <em>Multiple Knapsack Assignment Problem</em> is a strongly <span><math><mi>NP</mi></math></span>-hard combinatorial optimisation problem, with several applications. We show that an <em>upper bound</em> for the problem, due to Kataoka and Yamada, can be computed in linear time. We then show that some bounds due to Martello and Monaci dominate the Kataoka-Yamada bound. Finally, we define an even stronger bound, which turns out to be particularly effective when the number of knapsacks is not a multiple of the number of item classes.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167637724000403/pdfft?md5=8b202ac03ed56140ad2cbd151c395934&pid=1-s2.0-S0167637724000403-main.pdf","citationCount":"0","resultStr":"{\"title\":\"On upper bounds for the multiple knapsack assignment problem\",\"authors\":\"Laura Galli , Adam N. Letchford\",\"doi\":\"10.1016/j.orl.2024.107104\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The <em>Multiple Knapsack Assignment Problem</em> is a strongly <span><math><mi>NP</mi></math></span>-hard combinatorial optimisation problem, with several applications. We show that an <em>upper bound</em> for the problem, due to Kataoka and Yamada, can be computed in linear time. We then show that some bounds due to Martello and Monaci dominate the Kataoka-Yamada bound. Finally, we define an even stronger bound, which turns out to be particularly effective when the number of knapsacks is not a multiple of the number of item classes.</p></div>\",\"PeriodicalId\":54682,\"journal\":{\"name\":\"Operations Research Letters\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-03-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0167637724000403/pdfft?md5=8b202ac03ed56140ad2cbd151c395934&pid=1-s2.0-S0167637724000403-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Operations Research Letters\",\"FirstCategoryId\":\"91\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0167637724000403\",\"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}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Operations Research Letters","FirstCategoryId":"91","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167637724000403","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

摘要

多重背包分配问题是一个强 NP 难的组合优化问题，有多种应用。我们证明，由片冈和山田提出的问题上限可以在线性时间内计算。然后，我们证明了 Martello 和 Monaci 提出的一些约束条件支配着片冈-山田约束条件。最后，我们定义了一个更强的约束，当背包的数量不是项类数量的倍数时，这个约束特别有效。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

On upper bounds for the multiple knapsack assignment problem

The Multiple Knapsack Assignment Problem is a strongly $NP$ -hard combinatorial optimisation problem, with several applications. We show that an upper bound for the problem, due to Kataoka and Yamada, can be computed in linear time. We then show that some bounds due to Martello and Monaci dominate the Kataoka-Yamada bound. Finally, we define an even stronger bound, which turns out to be particularly effective when the number of knapsacks is not a multiple of the number of item classes.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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.