{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T16:22:27Z","timestamp":1758817347710,"version":"3.40.5"},"reference-count":22,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,10,30]],"date-time":"2020-10-30T00:00:00Z","timestamp":1604016000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2020,10,30]]},"abstract":"<jats:p>The multicommodity flow problem arises when several different commodities are transshipped from specific supply nodes to the corresponding demand nodes through the arcs of an underlying capacity network. The maximum flow over time problem concerns to maximize the sum of commodity flows in a given time horizon. It becomes the earliest arrival flow problem if it maximizes the flow at each time step. The earliest arrival transshipment problem is the one that satisfies specified supplies and demands. These flow over time problems are computationally hard. By reverting the orientation of lanes towards the demand nodes, the outbound lane capacities can be increased. We introduce a partial lane reversal approach in the class of multicommodity flow problems. Moreover, a polynomial-time algorithm for the maximum static flow problem and pseudopolynomial algorithms for the earliest arrival transshipment and maximum dynamic flow problems are presented. Also, an approximation solution to the latter problem is obtained in polynomial-time.<\/jats:p>","DOI":"10.1155\/2020\/2676378","type":"journal-article","created":{"date-parts":[[2020,10,31]],"date-time":"2020-10-31T17:35:08Z","timestamp":1604165708000},"page":"1-13","source":"Crossref","is-referenced-by-count":7,"title":["Efficient Algorithms on Multicommodity Flow over Time Problems with Partial Lane Reversals"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2545-3658","authenticated-orcid":true,"given":"Urmila","family":"Pyakurel","sequence":"first","affiliation":[{"name":"Central Department of Mathematics, Tribhuvan University, P.O. Box 13143, Kathmandu, Nepal"}]},{"given":"Shiva Prakash","family":"Gupta","sequence":"additional","affiliation":[{"name":"Tribhuvan University, Tri-Chandra Multiple Campus, Kathmandu, Nepal"}]},{"given":"Durga Prasad","family":"Khanal","sequence":"additional","affiliation":[{"name":"Tribhuvan University, Saraswati Multiple Campus, Kathmandu, Nepal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3390-9707","authenticated-orcid":true,"given":"Tanka Nath","family":"Dhamala","sequence":"additional","affiliation":[{"name":"Central Department of Mathematics, Tribhuvan University, P.O. Box 13143, Kathmandu, Nepal"}]}],"member":"311","reference":[{"volume-title":"Network Flows, Theory Algorithms and Applications","year":"1993","author":"R. K. Ahuja","key":"1"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230080107"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1287\/opre.26.2.209"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1007\/s12351-020-00564-8"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1287\/opre.28.4.995"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1287\/opre.14.1.45"},{"key":"7","doi-asserted-by":"crossref","DOI":"10.1515\/9781400875184","volume-title":"Flows in Networks","author":"L. R. Ford","year":"1962"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1307\/mmj\/1028998140"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1090.0382"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2007.02.046"},{"article-title":"Generalizations of flows over time with application in evacuation optimization","year":"2015","author":"P. W. Kappmeier","key":"11"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1007\/s10878-008-9175-8"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1155\/2020\/1605806"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.21307\/IJOR-2015-005"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1155\/2016\/7902460"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-017-2427-1"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.3934\/jimo.2020102"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.3934\/jimo.2016028"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.3390\/math7100993"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.3844\/jmssp.2020.198.211"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1137\/s0097539703427215"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1137\/s0895480199355754"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2020\/2676378.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2020\/2676378.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2020\/2676378.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,31]],"date-time":"2020-10-31T17:35:11Z","timestamp":1604165711000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/ijmms\/2020\/2676378\/"}},"subtitle":[],"editor":[{"given":"Vladimir V.","family":"Mityushev","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2020,10,30]]},"references-count":22,"alternative-id":["2676378","2676378"],"URL":"https:\/\/doi.org\/10.1155\/2020\/2676378","relation":{},"ISSN":["1687-0425","0161-1712"],"issn-type":[{"type":"electronic","value":"1687-0425"},{"type":"print","value":"0161-1712"}],"subject":[],"published":{"date-parts":[[2020,10,30]]}}}