{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T08:33:10Z","timestamp":1769761990530,"version":"3.49.0"},"reference-count":15,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2017,8,9]],"date-time":"2017-08-09T00:00:00Z","timestamp":1502236800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/http\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia, under projects","award":["UID\/MAT\/04561\/2013"],"award-info":[{"award-number":["UID\/MAT\/04561\/2013"]}]},{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia, under projects","award":["PTDC\/MAT NAN\/2196\/2014"],"award-info":[{"award-number":["PTDC\/MAT NAN\/2196\/2014"]}]},{"name":"Programa de Bolsas de Doutoramento da Universidade de Lisboa"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[2017,10]]},"abstract":"<jats:p>Multi\u2010depot routing problems arise in distribution logistics where a set of vehicles based at several depots are used to serve a number of clients. Most variants of this problem have the basic requirement that the route of each vehicle starts and ends at the same depot. This article describes new inequalities, namely multi\u2010cut constraints (MCC), which enforce this requirement in mathematical programming formulations of multi\u2010depot routing problems. The MCCs are exponential in size, and are equivalent to a compact three\u2010index formulation for the problem in terms of the associated linear programming relaxations. The article describes how a generalization of the MCCs can be obtained, in a similar manner, by using a stronger version of the three\u2010index formulation. The connection between the compact and the exponential formulations implies a separation procedure based on max\u2010flow\/min\u2010cut computations, which has reduced complexity in comparison with a previously known set of constraints described for the same purpose. The new inequalities are used in a branch\u2010and\u2010cut algorithm. Computational results are presented for instances with up to 300 clients and 60 depots. \u00a9 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(3), 246\u2013261 2017<\/jats:p>","DOI":"10.1002\/net.21760","type":"journal-article","created":{"date-parts":[[2017,8,9]],"date-time":"2017-08-09T05:52:39Z","timestamp":1502257959000},"page":"246-261","source":"Crossref","is-referenced-by-count":12,"title":["New path elimination constraints for multi\u2010depot routing problems"],"prefix":"10.1002","volume":"70","author":[{"given":"Tolga","family":"Bekta\u015f","sequence":"first","affiliation":[{"name":"Centre for Operational Research, Management Science and Information Systems (CORMSIS), Southampton Business School, University of Southampton Highfield Southampton SO17 1BJ United Kingdom"}]},{"given":"Lu\u00eds","family":"Gouveia","sequence":"additional","affiliation":[{"name":"Centro de Matem\u00e1tica, Aplica\u00e7\u00f5es Fundamentais e Investiga\u00e7\u00e3o Operacional (CMAF\u2010CIO), DEIO, Faculdade de Ci\u00eancias, Universidade de Lisboa C6 \u2010 Piso 4 Lisbon 1749\u2010016 Portugal"}]},{"given":"Daniel","family":"Santos","sequence":"additional","affiliation":[{"name":"Centro de Matem\u00e1tica, Aplica\u00e7\u00f5es Fundamentais e Investiga\u00e7\u00e3o Operacional (CMAF\u2010CIO), DEIO, Faculdade de Ci\u00eancias, Universidade de Lisboa C6 \u2010 Piso 4 Lisbon 1749\u2010016 Portugal"}]}],"member":"311","published-online":{"date-parts":[[2017,8,9]]},"reference":[{"key":"e_1_2_6_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2007.11.008"},{"key":"e_1_2_6_3_1","first-page":"223","volume-title":"Progress in combinatorial optimization","author":"Godinho M. 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