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On a “Complementary Problem” of Courant and Robbins 关于Courant和Robbins的一个“互补问题”
Location Science Pub Date : 1998-05-01 DOI: 10.1016/S0966-8349(98)00043-6
Jakob Krarup
{"title":"On a “Complementary Problem” of Courant and Robbins","authors":"Jakob Krarup","doi":"10.1016/S0966-8349(98)00043-6","DOIUrl":"https://doi.org/10.1016/S0966-8349(98)00043-6","url":null,"abstract":"<div><p>For a given triangle <em>ABC</em> with ∠<em>A</em>&gt;120°, the Simpson variant of Torricelli’s geometrical construction for solving a problem, allegedly first formulated by Fermat in the early 1600s, will identify a point which incorrectly was claimed by Courant and Robbins (Courant, R., Robbins, H., 1941. <em>What is Mathematics?</em> Oxford University Press, Oxford.) to solve the so-called <em>Complementary problem</em>: <span><math><mtext>min</mtext><mtext>{BX+CX−AX:X∈</mtext><mtext>R</mtext><msup><mi></mi><mn>2</mn></msup><mtext>}</mtext></math></span>. The correct solution for <em>any</em> triangle is provided here.</p></div>","PeriodicalId":100880,"journal":{"name":"Location Science","volume":"6 1","pages":"Pages 337-354"},"PeriodicalIF":0.0,"publicationDate":"1998-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0966-8349(98)00043-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72110428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
The 2-facility centdian network problem 二设施集中网络问题
Location Science Pub Date : 1998-05-01 DOI: 10.1016/S0966-8349(98)00057-6
Dionisio Pérez-Brito, José A. Moreno-Pérez, Inmaculada Rodrı́guez-Martı́n
{"title":"The 2-facility centdian network problem","authors":"Dionisio Pérez-Brito,&nbsp;José A. Moreno-Pérez,&nbsp;Inmaculada Rodrı́guez-Martı́n","doi":"10.1016/S0966-8349(98)00057-6","DOIUrl":"https://doi.org/10.1016/S0966-8349(98)00057-6","url":null,"abstract":"<div><p>The <em>p</em>-facility centdian network problem consists of finding the <em>p</em> points that minimize a convex combination of the <em>p</em>-center and <em>p</em>-median objective functions. The vertices and local centers constitute a dominating set for the 1-facility centdian; i.e., it contains an optimal solution for all instances of the problem. Hooker et al. (1991) give a theoretical result to extend the dominating sets for the 1-facility problems to the corresponding <em>p</em>-facility problems. They claim that the set of vertices and local centers is also a dominating set for the <em>p</em>-facility centdian problem. We give a counterexample and an alternative finite dominating set for <em>p</em>=2. We propose a solution procedure for a network that improves the complexity of the exhaustive search in the dominating set. We also provide a very efficient algorithm that solves the 2-centdian on a tree network with complexity O(<em>n</em><sup>2</sup>).</p></div>","PeriodicalId":100880,"journal":{"name":"Location Science","volume":"6 1","pages":"Pages 369-381"},"PeriodicalIF":0.0,"publicationDate":"1998-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0966-8349(98)00057-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72110429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 13
A bi-objective plant location problem: cost vs. demand served 双目标工厂选址问题：成本与服务需求
Location Science Pub Date : 1998-05-01 DOI: 10.1016/S0966-8349(98)00055-2
Jack Brimberg , Charles ReVelle
{"title":"A bi-objective plant location problem: cost vs. demand served","authors":"Jack Brimberg ,&nbsp;Charles ReVelle","doi":"10.1016/S0966-8349(98)00055-2","DOIUrl":"https://doi.org/10.1016/S0966-8349(98)00055-2","url":null,"abstract":"<div><p>The standard plant location problem requires choosing from a set of potential sites the locations of new facilities in order to serve all the demands specified on a network at a minimum total cost. In this paper, the standard model is replaced by a new model in which the acceptance of demands onto the location balance sheet becomes part of the decision process. The motivation for such an approach and its applicability in the decision process are elaborated. The mathematical formulation results in a bi-criterion model which can be used to study the trade-off between total cost and the proportion of the market to be served. Computational and theoretical results are reported which demonstrate the integer friendliness of the new model.</p></div>","PeriodicalId":100880,"journal":{"name":"Location Science","volume":"6 1","pages":"Pages 121-135"},"PeriodicalIF":0.0,"publicationDate":"1998-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0966-8349(98)00055-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72111602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 16
The P-median problem in a changing network: The case of Barcelona 变化网络中的p中值问题:以巴塞罗那为例
Location Science Pub Date : 1998-05-01 DOI: 10.1016/S0966-8349(98)00049-7
D. Serra, V. Marianov
{"title":"The P-median problem in a changing network: The case of Barcelona","authors":"D. Serra, V. Marianov","doi":"10.1016/S0966-8349(98)00049-7","DOIUrl":"https://doi.org/10.1016/S0966-8349(98)00049-7","url":null,"abstract":"","PeriodicalId":100880,"journal":{"name":"Location Science","volume":"17 1","pages":"383-394"},"PeriodicalIF":0.0,"publicationDate":"1998-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73853337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 152
α-reliable p-minimax regret: a new model for strategic facility location modeling α-可靠p-极大极小后悔:战略设施选址建模的新模型
Location Science Pub Date : 1997-12-01 DOI: 10.1016/S0966-8349(98)00036-9
Mark S. Daskin, Susan M. Hesse, C. Revelle
{"title":"α-reliable p-minimax regret: a new model for strategic facility location modeling","authors":"Mark S. Daskin, Susan M. Hesse, C. Revelle","doi":"10.1016/S0966-8349(98)00036-9","DOIUrl":"https://doi.org/10.1016/S0966-8349(98)00036-9","url":null,"abstract":"","PeriodicalId":100880,"journal":{"name":"Location Science","volume":"1 1","pages":"227-246"},"PeriodicalIF":0.0,"publicationDate":"1997-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90230628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 137
A computational method for optimizing the hierarchy and spatial configuration of successively inclusive facilities on a continuous plane 一种连续平面上连续包容性设施层次结构和空间构型优化的计算方法
Location Science Pub Date : 1997-12-01 DOI: 10.1016/S0966-8349(98)00035-7
A. Okabe, Kei-ichi Okunuki, Tsutomu Suzuki
{"title":"A computational method for optimizing the hierarchy and spatial configuration of successively inclusive facilities on a continuous plane","authors":"A. Okabe, Kei-ichi Okunuki, Tsutomu Suzuki","doi":"10.1016/S0966-8349(98)00035-7","DOIUrl":"https://doi.org/10.1016/S0966-8349(98)00035-7","url":null,"abstract":"","PeriodicalId":100880,"journal":{"name":"Location Science","volume":"1 1","pages":"255-268"},"PeriodicalIF":0.0,"publicationDate":"1997-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89753514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 17
Variable neighborhood search for the p-median p-中值的变邻域搜索
Location Science Pub Date : 1997-12-01 DOI: 10.1016/S0966-8349(98)00030-8
P. Hansen, N. Mladenović
{"title":"Variable neighborhood search for the p-median","authors":"P. Hansen,&nbsp;N. Mladenović","doi":"10.1016/S0966-8349(98)00030-8","DOIUrl":"https://doi.org/10.1016/S0966-8349(98)00030-8","url":null,"abstract":"<div><p>Consider a set <em>L</em> of potential locations for <em>p</em> facilities and a set <em>U</em> of locations of given users. The <em>p</em>-median problem is to locate simultaneously the <em>p</em> facilities at locations of <em>L</em> in order to minimize the total transportation cost for satisfying the demand of the users, each supplied from its closest facility. This model is a basic one in location theory and can also be interpreted in terms of cluster analysis where locations of users are then replaced by points in a given space. We propose several new Variable Neighborhood Search heuristics for the <em>p</em>-median problem and compare them with Greedy plus Interchange, and two Tabu Search heuristics.</p></div>","PeriodicalId":100880,"journal":{"name":"Location Science","volume":"5 4","pages":"Pages 207-226"},"PeriodicalIF":0.0,"publicationDate":"1997-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0966-8349(98)00030-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72080121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 423
Location science volume 5 contents 位置科学第5卷内容
Location Science Pub Date : 1997-12-01 DOI: 10.1016/S0966-8349(98)80128-9
{"title":"Location science volume 5 contents","authors":"","doi":"10.1016/S0966-8349(98)80128-9","DOIUrl":"https://doi.org/10.1016/S0966-8349(98)80128-9","url":null,"abstract":"","PeriodicalId":100880,"journal":{"name":"Location Science","volume":"5 4","pages":"Pages III-IV"},"PeriodicalIF":0.0,"publicationDate":"1997-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0966-8349(98)80128-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72080123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A computational method for optimizing the hierarchy and spatial configuration of successively inclusive facilities on a continuous plane 一种优化连续平面上连续包容设施层次结构和空间配置的计算方法
Location Science Pub Date : 1997-12-01 DOI: 10.1016/S0966-8349(98)00035-7
Atsuyuki Okabe, Kei-Ichi Okunuki, Tsutomu Suzuki
{"title":"A computational method for optimizing the hierarchy and spatial configuration of successively inclusive facilities on a continuous plane","authors":"Atsuyuki Okabe,&nbsp;Kei-Ichi Okunuki,&nbsp;Tsutomu Suzuki","doi":"10.1016/S0966-8349(98)00035-7","DOIUrl":"https://doi.org/10.1016/S0966-8349(98)00035-7","url":null,"abstract":"<div><p>This paper shows a computational method for optimizing a system of successively inclusive hierarchical facilities (a system in which the services provided by a certain rank of facilities include all services provided by lower rank facilities) on a continuous plane. The system is optimized with respect to not only the configuration of ranked facilities, but also its hierarchical structure (i.e. the composition of the number of ranks and the numbers of ranked facilities). The optimization procedure has two steps. The first step optimizes a system of exclusive hierarchical facilities by an analytical method. Using this optimal solution, the second step optimizes a system of successively inclusive hierarchical facilities by a computational search method. Numerical experiments show that the proposed method tends to reach a near optimal solution within a few iterations.</p></div>","PeriodicalId":100880,"journal":{"name":"Location Science","volume":"5 4","pages":"Pages 255-268"},"PeriodicalIF":0.0,"publicationDate":"1997-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0966-8349(98)00035-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72080127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 17
Multiple anticipatory moves of a server on a line 服务器在一条线上的多次预期移动
Location Science Pub Date : 1997-12-01 DOI: 10.1016/S0966-8349(98)00037-0
Xinjian Lu, Y. Gerchak
{"title":"Multiple anticipatory moves of a server on a line","authors":"Xinjian Lu, Y. Gerchak","doi":"10.1016/S0966-8349(98)00037-0","DOIUrl":"https://doi.org/10.1016/S0966-8349(98)00037-0","url":null,"abstract":"","PeriodicalId":100880,"journal":{"name":"Location Science","volume":"2 1","pages":"269-287"},"PeriodicalIF":0.0,"publicationDate":"1997-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86028016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
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