{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T03:13:36Z","timestamp":1761016416601},"reference-count":15,"publisher":"Springer Science and Business Media LLC","issue":"1-3","license":[{"start":{"date-parts":[[1991,5,1]],"date-time":"1991-05-01T00:00:00Z","timestamp":673056000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Programming"],"published-print":{"date-parts":[[1991,5]]},"DOI":"10.1007\/bf01582882","type":"journal-article","created":{"date-parts":[[2005,4,28]],"date-time":"2005-04-28T08:35:11Z","timestamp":1114677311000},"page":"99-123","source":"Crossref","is-referenced-by-count":32,"title":["Approximate formulas of average distances associated with regions and their applications to location problems"],"prefix":"10.1007","volume":"52","author":[{"given":"Takeshi","family":"Koshizuka","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Osamu","family":"Kurita","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"CR1","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1111\/j.1467-9787.1974.tb00435.x","volume":"14","author":"D. Bennett","year":"1974","unstructured":"D. Bennett and A. Mirakhor, \u201cOptimal facility location with respect to several regions,\u201dJournal of Regional Science 14 (1974) 131\u2013136.","journal-title":"Journal of Regional Science"},{"key":"CR2","first-page":"183","volume":"2","author":"C.J. Bouwkamp","year":"1977","unstructured":"C.J. Bouwkamp, \u201cOn the average distance between points in two coplanar non-overlapping circular disks,\u201dJournal of Applied Science and Engineering, A 2 (1977) 183\u2013186.","journal-title":"Journal of Applied Science and Engineering, A"},{"key":"CR3","first-page":"327","volume-title":"Spatial Analysis and Location\u2014Allocation Models","author":"P.A. Casillas","year":"1987","unstructured":"P.A. Casillas, \u201cData aggregation and the p-median problem in continuous space,\u201d in: A. Ghosh and G. Rushton, eds.,Spatial Analysis and Location\u2014Allocation Models (Van Nostrand Reinhold, New York, 1987) 327\u2013344."},{"key":"CR4","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1287\/opre.11.3.331","volume":"11","author":"L. Cooper","year":"1963","unstructured":"L. Cooper, \u201cLocation\u2014allocation problems,\u201dOperations Research 11 (1963) 331\u2013343.","journal-title":"Operations Research"},{"key":"CR5","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1111\/j.1467-9787.1974.tb00428.x","volume":"14","author":"L. Cooper","year":"1974","unstructured":"L. Cooper, \u201cA random locational equilibrium problem,\u201dJournal of Regional Science 14 (1974) 47\u201354.","journal-title":"Journal of Regional Science"},{"key":"CR6","first-page":"17","volume":"43","author":"B. Ghosh","year":"1951","unstructured":"B. Ghosh, \u201cRandom distances within a rectangle and between two rectangles,\u201dBulletin of Calcutta Mathematical Society 43 (1951) 17\u201324.","journal-title":"Bulletin of Calcutta Mathematical Society"},{"key":"CR7","volume-title":"Contributions to the theoretical study of urban spatial structure","author":"T. Koshizuka","year":"1977","unstructured":"T. Koshizuka, \u201cContributions to the theoretical study of urban spatial structure,\u201d Doctoral Dissertation, University of Tokyo (Tokyo, 1977). [In Japanese.]"},{"key":"CR8","first-page":"319","volume":"19","author":"T. Koshizuka","year":"1983","unstructured":"T. Koshizuka and O. Kurita, \u201cPopulation estimation and calculation of the average distance to a facility using the grid system data,\u201dPapers of the Annual Conference of the City Planning Institute of Japan 19 (1983) 319\u2013324. [In Japanese.]","journal-title":"Papers of the Annual Conference of the City Planning Institute of Japan"},{"key":"CR9","volume-title":"Approximated formulas of average distances associated with regions and their applications to urban analyses","author":"O. Kurita","year":"1989","unstructured":"O. Kurita, \u201cApproximated formulas of average distances associated with regions and their applications to urban analyses,\u201d Doctoral Dissertation, University of Tsukuba (Tsukuba, 1989a). [In Japanese.]"},{"key":"CR10","doi-asserted-by":"crossref","first-page":"331","DOI":"10.11361\/journalcpij.24.331","volume":"24","author":"O. Kurita","year":"1989","unstructured":"O. Kurita, \u201cAverage distances associated with radially symmetrically populated regions,\u201dPapers on City Planning (City Planning Institute of Japan) 24 (1989b) 331\u2013336. [In Japanese.]","journal-title":"Papers on City Planning (City Planning Institute of Japan)"},{"key":"CR11","doi-asserted-by":"crossref","first-page":"43","DOI":"10.11361\/journalcpij.23.43","volume":"23","author":"O. Kurita","year":"1988","unstructured":"O. Kurita and T. Koshizuka, \u201cApproximated formulas of average distances and their applications,\u201dPapers on City Planning (City Planning Institute of Japan) 23 (1988) 43\u201348. [In Japanese.]","journal-title":"Papers on City Planning (City Planning Institute of Japan)"},{"key":"CR12","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1111\/j.1467-9787.1972.tb00345.x","volume":"12","author":"R.F. Love","year":"1972","unstructured":"R.F. Love, \u201cA computational procedure for optimally locating a facility with respect to several rectangular regions,\u201dJournal of Regional Science 12 (1972) 233\u2013242.","journal-title":"Journal of Regional Science"},{"key":"CR13","doi-asserted-by":"crossref","first-page":"802","DOI":"10.2307\/2315242","volume":"75","author":"P.A. Schweitzer","year":"1968","unstructured":"P.A. Schweitzer, \u201cMoments of distances of uniformly distributed points,\u201dAmerican Mathematical Monthly 75 (1968) 802\u2013804.","journal-title":"American Mathematical Monthly"},{"key":"CR14","volume-title":"Introduction to applied mathematics","author":"G. Strang","year":"1986","unstructured":"G. Strang, \u201cIntroduction to applied mathematics (Wellesley-Cambridge Press, Cambridge, MA, 1986)."},{"key":"CR15","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1287\/trsc.18.3.231","volume":"18","author":"R. Vaughan","year":"1984","unstructured":"R. Vaughan, \u201cApproximate formulas for average distances associated with zones,\u201dTransportation Science 18 (1984) 231\u2013244.","journal-title":"Transportation Science"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01582882.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01582882\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01582882","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,3]],"date-time":"2023-05-03T02:32:29Z","timestamp":1683081149000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01582882"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,5]]},"references-count":15,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[1991,5]]}},"alternative-id":["BF01582882"],"URL":"https:\/\/doi.org\/10.1007\/bf01582882","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,5]]}}}