{"title":"On the combined inverse-square effect of multiple points in multidimensional space","authors":"Keaton Coletti , Pawel Kalczynski , Zvi Drezner","doi":"10.1016/j.orl.2024.107139","DOIUrl":null,"url":null,"abstract":"<div><p>The inverse-square law states that a source's effect is inversely proportional to the distance from that source squared. In continuous location problems, objective functions often obey the inverse-square law. This work shows that for any region in D dimensions, the maximum inverse-square effect is on the region's boundary if <span><math><mi>D</mi><mo><</mo><mn>4</mn></math></span>, the minimum is on the boundary if <span><math><mi>D</mi><mo>></mo><mn>4</mn></math></span>, and both the maximum and minimum are on the boundary if <span><math><mi>D</mi><mo>=</mo><mn>4</mn></math></span>.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"55 ","pages":"Article 107139"},"PeriodicalIF":0.8000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Operations Research Letters","FirstCategoryId":"91","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167637724000750","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 inverse-square law states that a source's effect is inversely proportional to the distance from that source squared. In continuous location problems, objective functions often obey the inverse-square law. This work shows that for any region in D dimensions, the maximum inverse-square effect is on the region's boundary if , the minimum is on the boundary if , and both the maximum and minimum are on the boundary if .
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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