{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T21:54:06Z","timestamp":1769810046837,"version":"3.49.0"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1972,12,1]],"date-time":"1972-12-01T00:00:00Z","timestamp":92016000000},"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":[[1972,12]]},"DOI":"10.1007\/bf01584987","type":"journal-article","created":{"date-parts":[[2005,4,28]],"date-time":"2005-04-28T09:06:55Z","timestamp":1114679215000},"page":"157-177","source":"Crossref","is-referenced-by-count":28,"title":["A partitioning algorithm for the multicommodity network flow problem"],"prefix":"10.1007","volume":"3-3","author":[{"given":"M. D.","family":"Grigoriadis","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"W. W.","family":"White","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"CR1","volume-title":"\u201cFurther extension of the tanker scheduling problem\u201d, MTP-339","author":"M. Bellmore","year":"1969","unstructured":"M.Bellmore, G.Bennington and S.Lubore, \u201cFurther extension of the tanker scheduling problem\u201d, MTP-339. The Mitre Corporation, Washington, D.C., 1969."},{"key":"CR2","doi-asserted-by":"crossref","DOI":"10.21236\/AD0649828","volume-title":"\u201cSolution techniques for the traffic assignment problem\u201d, ORC 65-35","author":"S.P. Bradley","year":"1965","unstructured":"S.P.Bradley, \u201cSolution techniques for the traffic assignment problem\u201d, ORC 65-35. Operations Research Center, University of California, Berkeley, 1965."},{"key":"CR3","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/0038-0121(68)90014-1","volume":"1","author":"S. Clarke","year":"1968","unstructured":"S.Clarke and J.Surkis, \u201cAn operations research approach to racial desegregation of school systems\u201d,Socio-Econ. Plan. Sci. 1 (1968) 259\u2013272.","journal-title":"Socio-Econ. Plan. Sci."},{"key":"CR4","volume-title":"RS MSUB-linear programming subroutine","author":"R.J. Clasen","year":"1961","unstructured":"R.J.Clasen, \u201cRS MSUB-linear programming subroutine\u201d. The RAND Corporation, Santa Monica, California, 1961."},{"key":"CR5","doi-asserted-by":"crossref","first-page":"174","DOI":"10.2307\/1907876","volume":"23","author":"G.B. Dantzig","year":"1955","unstructured":"G.B.Dantzig, \u201cUpper bounds, secondary constraints, and block triangularity in linear programming\u201d,Econometrica 23 (1955) 174\u2013183.","journal-title":"Econometrica"},{"key":"CR6","doi-asserted-by":"crossref","first-page":"767","DOI":"10.2307\/1911818","volume":"29","author":"G.B. Dantzig","year":"1961","unstructured":"G.B.Dantzig and P.Wolfe, \u201cThe decomposition algorithm for linear programs\u201d,Econometrica 29 (1961) 767\u2013778.","journal-title":"Econometrica"},{"key":"CR7","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1287\/mnsc.5.1.97","volume":"5","author":"L.R. Ford","year":"1958","unstructured":"L.R.Ford and D.R.Fulkerson, \u201cA suggested computation for maximal multi-commodity network flows\u201d,Management Science 5 (1958) 97\u2013101.","journal-title":"Management Science"},{"key":"CR8","doi-asserted-by":"crossref","DOI":"10.1515\/9781400875184","volume-title":"Flows in networks","author":"L.R. Ford","year":"1963","unstructured":"L.R.Ford and D.R.Fulkerson,Flows in networks (Princeton University Press, Princeton, 1963)."},{"key":"CR9","doi-asserted-by":"crossref","first-page":"652","DOI":"10.1287\/mnsc.16.11.652","volume":"16","author":"A.M. Geoffrion","year":"1970","unstructured":"A.M.Geoffrion, \u201cElements of large-scale mathematical programming\u201d,Management Science 16 (1970) 652\u2013675.","journal-title":"Management Science"},{"key":"CR10","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1287\/mnsc.17.5.269","volume":"17","author":"M.D. Grigoriadis","year":"1971","unstructured":"M.D.Grigoriadis, \u201cA dual generalized upper bounding technique\u201d,Management Science 17 (1971) 269\u2013284.","journal-title":"Management Science"},{"key":"CR11","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1016\/S0022-0000(69)80026-7","volume":"3","author":"M.D. Grigoriadis","year":"1969","unstructured":"M.D.Grigoriadis and K.Ritter, \u201cA decomposition method for structured linear and nonlinear programs\u201d,Journal of Computer and System Sciences 3 (1969) 335\u2013360.","journal-title":"Journal of Computer and System Sciences"},{"key":"CR12","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1287\/mnsc.14.9.565","volume":"14","author":"M.D. Grigoriadis","year":"1968","unstructured":"M.D.Grigoriadis and W.F.Walker, \u201cA treatment of transportation problems by primal partition programming\u201d,Management Science 14 (1968) 565\u2013599.","journal-title":"Management Science"},{"key":"CR13","unstructured":"M.D. Grigoriadis and W.W. White, \u201cComputational experience with a multicommodity network flow algorithm\u201d, NATO Conference on Applications of Optimization Methods for Large-Scale Resource-Allocation Problems\u201d, Elsinore, Denmark, 1971. To appear inOptimization methods for resource allocation, R. Cottle and J. Krarup, eds. (English Universities Press, 1972). Also, Scientific Center Report No. 320-3011, IBM Corporation, Philadelphia, Pa., 1972."},{"key":"CR14","volume-title":"Linear programming","author":"G. Hadley","year":"1962","unstructured":"G.Hadley,Linear programming (Addison-Wesley, Reading, Mass., 1962)."},{"key":"CR15","series-title":"Technical Memorandum","volume-title":"A generalized upper bounding algorithm for multicommodity flow networks","author":"J.K. Hartman","year":"1970","unstructured":"J.K.Hartman and L.S.Lasdon, \u201cA generalized upper bounding algorithm for multicommodity flow networks\u201d, Technical Memorandum No. 193. Operations Research Department, Case Western Reserve University, Cleveland, Ohio, 1970."},{"key":"CR16","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1287\/opre.11.3.344","volume":"11","author":"T.C. Hu","year":"1963","unstructured":"T.C.Hu, \u201cMulticommodity network flows\u201d,Operations Research 11 (1963) 344\u2013360.","journal-title":"Operations Research"},{"key":"CR17","volume-title":"Mathematical programming system\/360","author":"IBM","year":"1969","unstructured":"IBM, \u201cMathematical programming system\/360\u201d (IBM Corporation, White Plains, New York, 1969)."},{"key":"CR18","volume-title":"\u201cA primal-dual multi-commodity flow algorithm\u201d, ORC 66-24","author":"W.S. Jewell","year":"1966","unstructured":"W.S.Jewell, \u201cA primal-dual multi-commodity flow algorithm\u201d, ORC 66-24. Operations Research Center, University of California, Berkeley, 1966."},{"key":"CR19","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1287\/opre.14.4.619","volume":"14","author":"E.L. Johnson","year":"1966","unstructured":"E.L.Johnson, \u201cNetworks and basic solutions\u201d,Operations Research 14 (1966) 619\u2013623.","journal-title":"Operations Research"},{"key":"CR20","volume-title":"Optimization theory for large systems","author":"L.S. Lasdon","year":"1970","unstructured":"L.S.Lasdon,Optimization theory for large systems (McMillan, New York, 1970)."},{"key":"CR21","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1002\/nav.3800010107","volume":"1","author":"C.E. Lemke","year":"1954","unstructured":"C.E.Lemke, \u201cThe dual method of solving the linear programming problem\u201d,Naval Research Logistics Quarterly 1 (1954) 36\u201347.","journal-title":"Naval Research Logistics Quarterly"},{"key":"CR22","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1007\/BF01386073","volume":"6","author":"J.B. Rosen","year":"1964","unstructured":"J.B.Rosen, \u201cPrimal partition programming for block diagonal matrices\u201d,Numerische Mathematik 6 (1964) 250\u2013260.","journal-title":"Numerische Mathematik"},{"key":"CR23","volume-title":"\u201cMulticommodity flowsin directed networks\u201d, ORC 67-38","author":"R. Saigal","year":"1967","unstructured":"R.Saigal, \u201cMulticommodity flowsin directed networks\u201d, ORC 67-38. Operations Research Center, University of California, Berkeley, 1967."},{"key":"CR24","volume-title":"\u201cThe multi-commodity maximum flow problem\u201d, ORC 66-25","author":"M. Sakarovitch","year":"1966","unstructured":"M.Sakarovitch, \u201cThe multi-commodity maximum flow problem\u201d, ORC 66-25. Operations Research Center, University of California, Berkeley, 1966."},{"key":"CR25","volume-title":"Programmation lineaire","author":"M. Simonnard","year":"1962","unstructured":"M.Simonnard,Programmation lineaire (Dunod, Paris, 1962)."},{"key":"CR26","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1287\/opre.14.1.45","volume":"14","author":"J.A. Tomlin","year":"1966","unstructured":"J.A.Tomlin, \u201cMinimum-cost multicommodity network flows\u201d,Operations Research 14 (1966) 45\u201351.","journal-title":"Operations Research"},{"key":"CR27","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1147\/sj.82.0147","volume":"8","author":"W.W. White","year":"1969","unstructured":"W.W.White and A.M.Bomberault, \u201cA network algorithm for empty freight car allocation\u201dIBM Systems Journal 8 (1969) 147\u2013169.","journal-title":"IBM Systems Journal"},{"key":"CR28","unstructured":"W.W.White and E.Wrathall, \u201cA system for railroad traffic scheduling\u201d, IBM Scientific Center Technical Report 320-2993. Philadelphia, Pennsylvania, 1970."},{"key":"CR29","volume-title":"\u201cThe Dantzig-Wolfe decomposition principle and minimum cost multicommodity network flows\u201d, P-4191","author":"R.D. Wollmer","year":"1969","unstructured":"R.D.Wollmer, \u201cThe Dantzig-Wolfe decomposition principle and minimum cost multicommodity network flows\u201d, P-4191. The Rand Corp., Santa Monica, California, 1969."},{"key":"CR30","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1287\/mnsc.14.7.429","volume":"14","author":"W.I. Zangwill","year":"1968","unstructured":"W.I.Zangwill, \u201cConcave cost flows in certain networks\u201d,Management Science 14 (1968) 429\u2013450.","journal-title":"Management Science"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01584987.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01584987\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01584987","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,7]],"date-time":"2020-04-07T03:51:42Z","timestamp":1586231502000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01584987"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1972,12]]},"references-count":30,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1972,12]]}},"alternative-id":["BF01584987"],"URL":"https:\/\/doi.org\/10.1007\/bf01584987","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[1972,12]]}}}