Problem 2 Maximum Flow Problem Consider the north south interstate highway system passing through Cincinnati, Ohio The north south vehicle flow reaches a level of 15,000 vehicles per hour at peak times Due to a summer highway maintenance program, which calls a for the temporary closing of lanes and lower speed limits, a network alternative routes through Cincinnati has been proposed by a transportation planner committee The alternative routes include other highways as well as city streets 2 4 Solve the problem using MS Excel ( sheet Maxflow Problem) X Flows (x1000 veh hr) X12 X13 X14 X23 X25 X32 X34 X35 X46 X56 X57 X65 X67 X71 Because of differences in speed limits and traffic patterns, flow capacities vary, depending on the particular streets and roads used The proposed network with arc flow capacities is shown in Figure 2 The direction of flow for each arc is indicated, and the arc capacity is shown next to each arc Note that most of the streets are one way However, a two way street can be found between nodes 2 and 3 and between node 5 and 6 In both cases, the capacity is the same in each direction

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Question: Problem 2 Maximum Flow Problem Consider the north-south interstate highway system passing through Cincinnati, Ohio. The north-south vehicle flow reaches a level of 15,000 vehicles

Problem 2 Maximum Flow Problem

Consider the north-south interstate highway system passing through Cincinnati, Ohio. The north-south vehicle flow reaches a level of 15,000 vehicles per hour at peak times. Due to a summer highway maintenance program, which calls a for the temporary closing of lanes and lower speed limits, a network alternative routes through Cincinnati has been proposed by a transportation planner committee. The alternative routes include other highways as well as city streets.

2.4 Solve the problem using MS Excel ( sheet Maxflow Problem) X	Flows (x1000 veh/hr)
X12
X13
X14
X23
X25
X32
X34
X35
X46
X56
X57
X65
X67
X71

Because of differences in speed limits and traffic patterns, flow capacities vary, depending on the particular streets and roads used. The proposed network with arc flow capacities is shown in Figure 2.

The direction of flow for each arc is indicated, and the arc capacity is shown next to each arc. Note that most of the streets are one-way. However, a two-way street can be found between nodes 2 and 3 and between node 5 and 6. In both cases, the capacity is the same in each direction.

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