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331-10 - Chapter 5 Transportation Assignment and Network...

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Chapter 5: Transportation, Assignment and Network Models (Maximum Flow, Shortest Route)
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The Maximal-Flow Model Networks have arcs with limited capacity, such as roads or pipelines Business applications: Traffic and transportation control Airline scheduling Image segmentation Project selection Census tabulation Hurricane evacuation
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Max Flow Problem Formulation Decisions: How much flow on each arc? Objective: Maximize flow through the network from an origin to a destination
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Max Flow Problem Formulation There is a “wrinkle” in the set-up of these applications: Since the notion of “flow” is continuous, there is really no meaning to a destination node . So, we create “flow” by adding an hypothetical arc or path that connects the ending (destination) node BACK to the start (origin). This dummy arc has unlimited capacity so as not to constrain the solution.
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Road Network Example
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Modified Road Network Arc Split dummy arc to  measure the  total flow
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Decision Variables X ij = number of cars per hour flowing from node i to node j Dummy Arc The X 61 arc was created as a “dummy” arc to measure the total flow from node 6 to node 1.
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