{"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}
引用次数: 0
Abstract
The Multiple Knapsack Assignment Problem is a strongly -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.
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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