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Network Flow for Different Models

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Problem 4
The plant engineer for the Bitco manufacturing plant is designing an overhead conveyor system that will connect the distribution/inventory center to all areas of the plant. The network of possible conveyor routes through the plant, with the length (in feet) along each branch follows. Determine the shortest conveyor route from the distribution/inventory center at node 1 to each of the other six areas of the plant.
See attachment for diagram as problem 4

Problem 20
One of the opposing forces in a simulated army battle wishes to set up a communication system that will connect the eight camps in its command. The following network indicate the distances (in hundreds of yards) between the camps and the different paths over which a communication line can be constructed. Using the minimal spanning tree approach, determine the minimum distance communication system that will connect all eight camps.
See attachment for diagram from problem 20

Problem 32
A new stadium is being planned for Denver, and the Denver traffic engineer is attempting to determine whether the city streets between the stadium complex and the interstate highway can accommodate the expected flow of 21,000 cars after each game. The various traffic arteries between the stadium (node 1) and the interstate (node 8) are shown in the diagram found in the attachment as problem 23. The flow capacities on each street are determined by the number of available lanes, the use of traffic police and lights, and whether any lanes can be opened or closed i either direction. The flow capacities are given in thousands of cars. Determine the maximum traffic flows the streets can accommodate and the amount of traffic along each street. Will the streets be able to handle the expected flow after a game?

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Solution Summary

The network flows for different models are examined.

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Problem 4
1. Determine the initial shortest route from the origin (node 1) to the closest node
Permanent node Branch Distance
1 1-2 80
1-3 130
1-4 140

The node 2 is at a minimum distance from node 1. Therefore, now add 2 also to permanent node set.

2. Determine all nodes directly connected to the permanent set.
Permanent node Branch Distance
1,2 1-3 130
1-4 140
2-5 =80+120=200
The path with shortest length is path 1-2 at 130 feet

3. Redefine the permanent set. Continue with step 2 and 3.
New permanent set is {1,3}
4. We repeat step 2 for the new permanent set.
Permanent node Branch Distance
1,2, 3 1-4 140
2-5 80+120=200
3-4 130+40=170
3-6 130+50=180
3-7 130+210=340
Branch 1-4 has the shortest route. Therefore, the permanent node set is modified to {1,2,3,4}
Permanent node Branch Distance
1,2, 3,4 2-5 80+120=200
3-6 130+50=180
3-7 130+210=340
4-5 140+50=190
Branch 3-6 has the shortest route of 180 feet. Therefore, the permanent node set is modified to {1,2,3,4,6}

Permanent node Branch Distance
1,2, 3,4 ,6 2-5 80+120=200
3-7 130+210=340
4-5 140+50=190
6-7 130+50+190=370

Branch 2-6 has the shortest route of 190 feet. Therefore, the permanent node set is modified to {1,2,3,4,5,6}
Permanent node Branch Distance
1,2, 3,4 ,5, 6 ...

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