{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T03:35:25Z","timestamp":1771558525333,"version":"3.50.1"},"reference-count":11,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":7223,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1987,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A new and much faster algorithm is presented for the problem of assigning buses to a large number of short trips in an urban area. The trips are grouped into chains, beginning and ending at the same bus depot, and a vehicle is assigned to each one of them. Fleet size costs and dead heading time are to be minimized. This problem has been already formulated as a transportation problem and more recently, as an assignment model. However, some difficulties, such as the zero pivot phenomenon, rising in many practical cases drastically affected computing times required to obtain the optimal solution. This is overcome by an algorithm based on the hungarian method and making full use of the sparsity of the assignment matrix for the bus scheduling problem. Computational results comparing the different methods are given in the last section of the paper. Significant reductions in computing time are obtained for either real case applications or random generated test problems.<\/jats:p>","DOI":"10.1002\/net.3230170302","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T22:18:18Z","timestamp":1178921898000},"page":"249-269","source":"Crossref","is-referenced-by-count":38,"title":["A quasi\u2010assignment algorithm for bus scheduling"],"prefix":"10.1002","volume":"17","author":[{"given":"J. Pinto","family":"Paix\u00e3o","sequence":"first","affiliation":[]},{"given":"I. M.","family":"Branco","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"415","article-title":"Algorithm 415\u2013Algorithm for the assignment problem","author":"Bourgeios F.","year":"1978","journal-title":"Collected Algorithms from CACM"},{"key":"e_1_2_1_3_2","unstructured":"I. M.Branco Implementa\u010d\u00e3o dum algoritmo eficiente de transportes: Parte I caso do bus scheduling problem. Internal Report Centro de Estatistica e Aplica\u010d\u00f5es da Universidade de Lisboa nota no 11\/85 (1985)."},{"key":"e_1_2_1_4_2","unstructured":"R.Eus\u00e9bioandL.Amado Modelos de planeamento\/gest\u00e3o para optimiza\u010d\u00e3o de viaturas e tripula\u010d\u00f5es numa rede de transportes. Presented to Investiga\u010d\u00e3o Operacional 84\u2013II Congresso da APDIO Porto Portugal (1984)."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1287\/trsc.8.1.13"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01593789"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0305-0548(78)90006-0"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0377-2217(79)90098-5"},{"key":"e_1_2_1_9_2","first-page":"293","article-title":"Augmented threaded index method for network optimization","volume":"12","author":"Glover F.","year":"1974","journal-title":"Information"},{"key":"e_1_2_1_10_2","first-page":"35","volume-title":"Computer Scheduling of Public Transport","author":"Hoffstadt J.","year":"1981"},{"key":"e_1_2_1_11_2","unstructured":"J.Paix\u00e3oandI. M.Branco A new assignment algorithm for bus scheduling in an urban area. Internal Report Centro de Estatistica e Aplica\u010d\u00f5es da Universidade de Lisboa nota no 9\/85 (1985). Presented to EURO VII\u2014Seventh European Congress on Operational Research Bologne Italy June1985."},{"key":"e_1_2_1_12_2","first-page":"79","volume-title":"Bus and crew scheduling on a microcomputer","author":"Paix\u00e3o J.","year":"1986"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230170302","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230170302","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T16:29:35Z","timestamp":1697905775000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230170302"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1987,1]]},"references-count":11,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1987,1]]}},"alternative-id":["10.1002\/net.3230170302"],"URL":"https:\/\/doi.org\/10.1002\/net.3230170302","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1987,1]]}}}