The simplex algorithm for multicommodity networks
We consider multicommodity network flow problems, where external flow is allowed to vary and where flows of individual commodities may be constrained. For this problem, we describe the simplex algorithm. The simplex algorithm is based upon the inverse of the basis matrix. We discuss an approach wher...
Gespeichert in:
| Veröffentlicht in: | Networks 2002-01, Vol.39 (1), p.15-28 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 28 |
|---|---|
| container_issue | 1 |
| container_start_page | 15 |
| container_title | Networks |
| container_volume | 39 |
| creator | Detlefsen, Nina K. Wallace, Stein W. |
| description | We consider multicommodity network flow problems, where external flow is allowed to vary and where flows of individual commodities may be constrained. For this problem, we describe the simplex algorithm. The simplex algorithm is based upon the inverse of the basis matrix. We discuss an approach where we only have to invert a working matrix with dimension at most equal to the number of arcs in the network. The dimension is independent of the number of commodities. The reduced cost of a nonbasic variable is found only using the working matrix that is explicitly inverted and some simple network operations. We also discuss how to pivot in the working matrix. The focus is on the detailed interpretation of the network structures arising in terms of cycles for the individual commodities. © 2002 John Wiley & Sons, Inc. |
| doi_str_mv | 10.1002/net.10006 |
| format | Article |
| fullrecord | <record><control><sourceid>wiley_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1002_net_10006</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>NET10006</sourcerecordid><originalsourceid>FETCH-LOGICAL-c3356-48bdeadb7e0b86fa2aa2c1b7df93815ed88a928e5825b97b1fa3571cb0a7e00b3</originalsourceid><addsrcrecordid>eNp1jz1PwzAQhi0EEqUw8A-yMDCEnuM6dkZU9QNRlaWI0TonNjVNmsoOavvvmxI-JqY76Z7n1b2E3FJ4oADJYGOa0wLpGelRyEQMwMQ56bU3GTMY8ktyFcIHAKWcyh6hy5WJgqu2pdlHWL7X3jWrKrK1j6rPsnF5XVV14ZpD1Cbvar8O1-TCYhnMzffsk9fJeDmaxfOX6dPocR7njPE0HkpdGCy0MKBlajFBTHKqRWEzJik3hZSYJdJwmXCdCU0tMi5orgFbBTTrk_suN_d1CN5YtfWuQn9QFNSpq2o_Ul9dW_auY7cYciytx03uwp_AhiAzSVtu0HE7V5rD_4FqMV7-JMed4UJj9r8G-rVKBRNcvS2majZNnlO5mKgZOwKSp3JJ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>The simplex algorithm for multicommodity networks</title><source>Wiley Online Library Journals Frontfile Complete</source><creator>Detlefsen, Nina K. ; Wallace, Stein W.</creator><creatorcontrib>Detlefsen, Nina K. ; Wallace, Stein W.</creatorcontrib><description>We consider multicommodity network flow problems, where external flow is allowed to vary and where flows of individual commodities may be constrained. For this problem, we describe the simplex algorithm. The simplex algorithm is based upon the inverse of the basis matrix. We discuss an approach where we only have to invert a working matrix with dimension at most equal to the number of arcs in the network. The dimension is independent of the number of commodities. The reduced cost of a nonbasic variable is found only using the working matrix that is explicitly inverted and some simple network operations. We also discuss how to pivot in the working matrix. The focus is on the detailed interpretation of the network structures arising in terms of cycles for the individual commodities. © 2002 John Wiley & Sons, Inc.</description><identifier>ISSN: 0028-3045</identifier><identifier>EISSN: 1097-0037</identifier><identifier>DOI: 10.1002/net.10006</identifier><identifier>CODEN: NTWKAA</identifier><language>eng</language><publisher>New York: John Wiley & Sons, Inc</publisher><subject>Algebra ; Applied sciences ; basis characterization ; basis interpretation ; Exact sciences and technology ; Flows in networks. Combinatorial problems ; Linear and multilinear algebra, matrix theory ; Mathematics ; multicommodity ; Operational research and scientific management ; Operational research. Management science ; Sciences and techniques of general use ; simplex algorithm ; Telecommunications ; Telecommunications and information theory ; Teleprocessing networks. Isdn</subject><ispartof>Networks, 2002-01, Vol.39 (1), p.15-28</ispartof><rights>Copyright © 2002 John Wiley & Sons, Inc.</rights><rights>2002 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c3356-48bdeadb7e0b86fa2aa2c1b7df93815ed88a928e5825b97b1fa3571cb0a7e00b3</citedby><cites>FETCH-LOGICAL-c3356-48bdeadb7e0b86fa2aa2c1b7df93815ed88a928e5825b97b1fa3571cb0a7e00b3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fnet.10006$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fnet.10006$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,778,782,1414,4012,27906,27907,27908,45557,45558</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=13408981$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Detlefsen, Nina K.</creatorcontrib><creatorcontrib>Wallace, Stein W.</creatorcontrib><title>The simplex algorithm for multicommodity networks</title><title>Networks</title><addtitle>Networks</addtitle><description>We consider multicommodity network flow problems, where external flow is allowed to vary and where flows of individual commodities may be constrained. For this problem, we describe the simplex algorithm. The simplex algorithm is based upon the inverse of the basis matrix. We discuss an approach where we only have to invert a working matrix with dimension at most equal to the number of arcs in the network. The dimension is independent of the number of commodities. The reduced cost of a nonbasic variable is found only using the working matrix that is explicitly inverted and some simple network operations. We also discuss how to pivot in the working matrix. The focus is on the detailed interpretation of the network structures arising in terms of cycles for the individual commodities. © 2002 John Wiley & Sons, Inc.</description><subject>Algebra</subject><subject>Applied sciences</subject><subject>basis characterization</subject><subject>basis interpretation</subject><subject>Exact sciences and technology</subject><subject>Flows in networks. Combinatorial problems</subject><subject>Linear and multilinear algebra, matrix theory</subject><subject>Mathematics</subject><subject>multicommodity</subject><subject>Operational research and scientific management</subject><subject>Operational research. Management science</subject><subject>Sciences and techniques of general use</subject><subject>simplex algorithm</subject><subject>Telecommunications</subject><subject>Telecommunications and information theory</subject><subject>Teleprocessing networks. Isdn</subject><issn>0028-3045</issn><issn>1097-0037</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2002</creationdate><recordtype>article</recordtype><recordid>eNp1jz1PwzAQhi0EEqUw8A-yMDCEnuM6dkZU9QNRlaWI0TonNjVNmsoOavvvmxI-JqY76Z7n1b2E3FJ4oADJYGOa0wLpGelRyEQMwMQ56bU3GTMY8ktyFcIHAKWcyh6hy5WJgqu2pdlHWL7X3jWrKrK1j6rPsnF5XVV14ZpD1Cbvar8O1-TCYhnMzffsk9fJeDmaxfOX6dPocR7njPE0HkpdGCy0MKBlajFBTHKqRWEzJik3hZSYJdJwmXCdCU0tMi5orgFbBTTrk_suN_d1CN5YtfWuQn9QFNSpq2o_Ul9dW_auY7cYciytx03uwp_AhiAzSVtu0HE7V5rD_4FqMV7-JMed4UJj9r8G-rVKBRNcvS2majZNnlO5mKgZOwKSp3JJ</recordid><startdate>200201</startdate><enddate>200201</enddate><creator>Detlefsen, Nina K.</creator><creator>Wallace, Stein W.</creator><general>John Wiley & Sons, Inc</general><general>John Wiley & Sons</general><scope>BSCLL</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>200201</creationdate><title>The simplex algorithm for multicommodity networks</title><author>Detlefsen, Nina K. ; Wallace, Stein W.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3356-48bdeadb7e0b86fa2aa2c1b7df93815ed88a928e5825b97b1fa3571cb0a7e00b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2002</creationdate><topic>Algebra</topic><topic>Applied sciences</topic><topic>basis characterization</topic><topic>basis interpretation</topic><topic>Exact sciences and technology</topic><topic>Flows in networks. Combinatorial problems</topic><topic>Linear and multilinear algebra, matrix theory</topic><topic>Mathematics</topic><topic>multicommodity</topic><topic>Operational research and scientific management</topic><topic>Operational research. Management science</topic><topic>Sciences and techniques of general use</topic><topic>simplex algorithm</topic><topic>Telecommunications</topic><topic>Telecommunications and information theory</topic><topic>Teleprocessing networks. Isdn</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Detlefsen, Nina K.</creatorcontrib><creatorcontrib>Wallace, Stein W.</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><jtitle>Networks</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Detlefsen, Nina K.</au><au>Wallace, Stein W.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The simplex algorithm for multicommodity networks</atitle><jtitle>Networks</jtitle><addtitle>Networks</addtitle><date>2002-01</date><risdate>2002</risdate><volume>39</volume><issue>1</issue><spage>15</spage><epage>28</epage><pages>15-28</pages><issn>0028-3045</issn><eissn>1097-0037</eissn><coden>NTWKAA</coden><abstract>We consider multicommodity network flow problems, where external flow is allowed to vary and where flows of individual commodities may be constrained. For this problem, we describe the simplex algorithm. The simplex algorithm is based upon the inverse of the basis matrix. We discuss an approach where we only have to invert a working matrix with dimension at most equal to the number of arcs in the network. The dimension is independent of the number of commodities. The reduced cost of a nonbasic variable is found only using the working matrix that is explicitly inverted and some simple network operations. We also discuss how to pivot in the working matrix. The focus is on the detailed interpretation of the network structures arising in terms of cycles for the individual commodities. © 2002 John Wiley & Sons, Inc.</abstract><cop>New York</cop><pub>John Wiley & Sons, Inc</pub><doi>10.1002/net.10006</doi><tpages>14</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0028-3045 |
| ispartof | Networks, 2002-01, Vol.39 (1), p.15-28 |
| issn | 0028-3045 1097-0037 |
| language | eng |
| recordid | cdi_crossref_primary_10_1002_net_10006 |
| source | Wiley Online Library Journals Frontfile Complete |
| subjects | Algebra Applied sciences basis characterization basis interpretation Exact sciences and technology Flows in networks. Combinatorial problems Linear and multilinear algebra, matrix theory Mathematics multicommodity Operational research and scientific management Operational research. Management science Sciences and techniques of general use simplex algorithm Telecommunications Telecommunications and information theory Teleprocessing networks. Isdn |
| title | The simplex algorithm for multicommodity networks |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-16T17%3A32%3A27IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-wiley_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=The%20simplex%20algorithm%20for%20multicommodity%20networks&rft.jtitle=Networks&rft.au=Detlefsen,%20Nina%20K.&rft.date=2002-01&rft.volume=39&rft.issue=1&rft.spage=15&rft.epage=28&rft.pages=15-28&rft.issn=0028-3045&rft.eissn=1097-0037&rft.coden=NTWKAA&rft_id=info:doi/10.1002/net.10006&rft_dat=%3Cwiley_cross%3ENET10006%3C/wiley_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |