Lecture14 - IE 505 MATHEMATICAL PROGRAMMING Bahar Yetis...

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IE 505 MATHEMATICAL PROGRAMMING Bahar Yetis Kara Lecture # 14 Date: 18 November 2008 MIT notes (adapted) 1
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Network Flows Network Flow problems are the most frequently solved linear programming problems. They include as special cases, the assignment, transportation, max flow, and shortest path problems. 2
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3 Where Network Flows Arise Transportation Transportation of goods over transportation networks Scheduling of fleets of airplanes: time/space networks Manufacturing Scheduling of goods for manufacturing Flow of manufactured items within inventory systems Communications Design and expansion of communication systems Flow of information across networks Personnel Assignment Assignment of crews to airline schedules Assignment of drivers to vehicles
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4 Network Flows and Routing Models Phone network: route calls, messages, data Power network: transmit power from power plants to consumers Highway, street, rail, airline, shipping networks: transport people, vehicles, goods Computer networks: transmit info, data, messages Pipeline networks: transport crude oil, gasoline Satellite networks: worldwide communication system
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5 History 1736: Euler’s work on the Koenisgsberg Bridges 1800s: Kirchoff constructed network flow models to analyze current flows 1940s: Kantorovich, Hitchhock & Koopmans considered transportation problems 1947: Dantzig pioneered Linear Programming 1956: Ford & Fulkerson proved max flow min cut theorem and developed a labelling algorithm for max flow. (Start of algorithmic developments)
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6 The Bridges of Koenigsberg: Euler 1736 “Graph Theory” began in 1736 Leonard E ü ler Visited Koenigsberg People wondered whether it is possible to take a walk, end up where you started from, and cross each bridge in Koenigsberg exactly once Generally it was believed to be impossible
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This note was uploaded on 04/15/2010 for the course INDUSTRIAL ie513 taught by Professor Zeynephuygur during the Spring '10 term at Bilkent University.

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Lecture14 - IE 505 MATHEMATICAL PROGRAMMING Bahar Yetis...

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