{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T13:13:56Z","timestamp":1723036436248},"reference-count":6,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":4788,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1993,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper, we are concerned with the problem of optimally covering a large region with rectilinear distances by many service facilities. We assume that the number of customers is proportional to the area that they occupy and that each customer patronizes the nearest facility. Our objective is to locate the facilities in such a manner that the maximal area any future competitor facility can capture will be minimized. For Euclidean distances, it has been conjectured that the best arrangement is a triangular grid, yielding hexagonal service areas (honeycomb). In this paper, we show that an analogous arrangement is optimal for rectilinear distances. Furthermore, as in the Euclidean case, it minimizes both the average and the maximal distance for all customers to their nearest facilities. The service areas under the optimal solution are rectilinear circles\u2014which are shaped as Euclidean squares tilted at 45\u00b0 to the <jats:italic>X<\/jats:italic>\u2010 and <jats:italic>Y<\/jats:italic>\u2010axes. \u00a9 <jats:italic>1993 by John Wiley &amp; Sons, Inc.<\/jats:italic><\/jats:p>","DOI":"10.1002\/net.3230230602","type":"journal-article","created":{"date-parts":[[2007,5,12]],"date-time":"2007-05-12T16:18:08Z","timestamp":1178986688000},"page":"517-523","source":"Crossref","is-referenced-by-count":1,"title":["Optimal multifacility defensive location on planes with rectilinear distances"],"prefix":"10.1002","volume":"23","author":[{"given":"Dan","family":"Trietsch","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0166-0462(82)90003-5"},{"key":"e_1_2_1_3_2","unstructured":"Z.DreznerandE.Zemel Competitive location in the plane Discussion Paper No. 720R Center for Mathematical Studies in Economics and Management Science Northwestern University (September 1986; revised February (1987))."},{"key":"e_1_2_1_4_2","first-page":"1","article-title":"Spatial competition and the location of firms","volume":"2","author":"Gabszewich J. J.","year":"1986","journal-title":"Funda. Pure Appl. Econ."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0377-2217(83)90180-7"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.2307\/2224214"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01874390"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230230602","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230230602","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T13:44:31Z","timestamp":1698241471000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230230602"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,9]]},"references-count":6,"journal-issue":{"issue":"6","published-print":{"date-parts":[[1993,9]]}},"alternative-id":["10.1002\/net.3230230602"],"URL":"https:\/\/doi.org\/10.1002\/net.3230230602","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,9]]}}}