{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,9]],"date-time":"2024-04-09T00:06:31Z","timestamp":1712621191861},"reference-count":24,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2011,1,1]],"date-time":"2011-01-01T00:00:00Z","timestamp":1293840000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Operations Research"],"published-print":{"date-parts":[[2011]]},"abstract":"<jats:p>The Fermat-Weber problem of optimally locating a service facility in the Euclidean continuous two-dimensional space is usually solved by the iterative process first suggested by Weiszfeld or by later versions thereof. The methods are usually rather efficient, but exceptional problems are described in the literature in which the iterative solution is exceedingly long. These problems are such that the solution either coincides with one of the demand points or nearly coincides with it. We describe a noniterative direct alternative, based on the insight that the gradient components of the individual demand points can be considered as pooling forces with respect to the solution point. It is demonstrated that symmetrical problems can thus be optimally solved with no iterations, in analogy to finding the equilibrium point in statics. These include a well-known ill-conditioned problem and its variants, which can now be easily solved to optimality using geometrical considerations.<\/jats:p>","DOI":"10.1155\/2011\/379505","type":"journal-article","created":{"date-parts":[[2011,7,18]],"date-time":"2011-07-18T21:40:39Z","timestamp":1311025239000},"page":"1-10","source":"Crossref","is-referenced-by-count":3,"title":["Noniterative Solution of Some Fermat-Weber Location Problems"],"prefix":"10.1155","volume":"2011","author":[{"given":"Reuven","family":"Chen","sequence":"first","affiliation":[{"name":"The Raymond & Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"98","reference":[{"key":"15","volume-title":"On a pair of dual nonlinear programs","year":"1967"},{"issue":"3","key":"14","first-page":"215","volume":"8","year":"1997","journal-title":"IMA Journal of Mathematics Applied in Business and Industry"},{"key":"26","year":"1909"},{"issue":"1","key":"28","first-page":"5","volume":"1","year":"1993","journal-title":"Location Science"},{"issue":"10","key":"19","first-page":"53","year":"1996","journal-title":"Studies in Locational Analysis"},{"key":"9","year":"1971"},{"issue":"1","key":"24","first-page":"335","volume":"43","year":"1937","journal-title":"T\u00f4hoku Mathematical Journal"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-008-0352-z"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1287\/opre.26.4.597"},{"issue":"2","key":"27","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1111\/j.1538-4632.1973.tb01000.x","volume":"5","year":"1973","journal-title":"Geographical Analysis"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1007\/s11750-008-0056-1"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1137\/0117113"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1007\/BF01580224"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1007\/BF02060474"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-008-0336-z"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1007\/s101070200297"},{"issue":"4","key":"7","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1016\/0966-8349(96)00004-6","volume":"3","year":"1995","journal-title":"Location Science"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1007\/PL00011435"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1007\/BF01587094"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01592245"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.2298\/YJOR0302199B"},{"issue":"1","key":"5","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1119\/1.13952","volume":"53","year":"1985","journal-title":"American Journal of Physics"},{"issue":"10","key":"10","doi-asserted-by":"crossref","first-page":"891","DOI":"10.1057\/jors.1981.183","volume":"32","year":"1981","journal-title":"Journal of the Operational Research Society"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2009.07.007"}],"container-title":["Advances in Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/aor\/2011\/379505.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/aor\/2011\/379505.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/aor\/2011\/379505.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,8]],"date-time":"2024-04-08T21:11:37Z","timestamp":1712610697000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/aor\/2011\/379505\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"references-count":24,"alternative-id":["379505","379505"],"URL":"https:\/\/doi.org\/10.1155\/2011\/379505","relation":{},"ISSN":["1687-9147","1687-9155"],"issn-type":[{"value":"1687-9147","type":"print"},{"value":"1687-9155","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011]]}}}