The network shown gives the major roads that would be part of the hurricane evac

Question

The network shown gives the major roads that would be part of the hurricane evacuation routes for Hilton Head, South Carolina with the indicated flow capacities along each branch. Determine the maximal flow from source node 1 to destination node 9.

Information

Hurricane Evacuation

1. What is the reverse capacity of branch 6 to 8?

3

2

0

4

2. In order to solve the above problem, which would be the best quantitative method to use?

Shortest Route Problem-Single Solution

Maximal Flow Problem

Minimal Spanning Tree Problem

Shortest Route Problem-All Destinations Solution

3. What is the model's solution?

11

10

Unsolvable

13

12

Maximal Flow Problem

Minimal Spanning Tree Problem

Shortest Route Problem-All Destinations Solution

3. What is the model's solution?

11

10

Unsolvable

13

12

7)8 0( 2 2 28 0( 6 09 28 2 0-0 16 5 2 0 62 23 7 3)2 24 22 0 ,O 4-7

Explanation / Answer

given

1- 2,3,4{5,4,7}

2-5,7    {6,2}

3-5,6,4 {2,3,2}

4-6,3 {7,2}

5-7,6,2 { 3,1,2}

6-8,5,3 {4,1,3}

7-9,8 { 8,2}

8-6,9,7 {2,7,9}

9-{}

1 ) reverse capacity of branch 6-8 {2}= 2

2 } by shortest path :

step 1 > 1-3 =4, 1-2= 5,1-4= 7

step 2 > 1-3-4= 4+2=6, 1-3-5= 4+2=6,1-3-6=4+3 =7, 1-2-5= 5+2=7 ,1-2-7= 5+6=11, 1-4-6=7+7=14,

optimize > 1-3-4 =6, 1-3-5=5,1-3-6=7,1-2-7=11,

step 3> 1-3-4-6=6+7=13,1-3-5-6=6+1=7, 1-3-5-7=6+3=9,1-3-6-8=7+4=11

1-3-5-7=9,1-3-6-8=14

step 4> 1-3-5-7-9=9+8=17, 1-3-5-7-8= 9+2=11, 1-3-6-8-9=14+7=21

optimization

1-3-5-7-9=17, 1-3-5-7-8=11

step 5

1-3-5-7-9=17,1-3-5-7-8-9=11+7=18

shortest path will be 1-3-5-7-9=17

minimum spanning tree:

step one: 5-6

step 2: 5-2

step 3: 5-7

step 4:7-8

step 5: 5-3 ,6-3

step 6: 3-4

step 7: 1-3

minimum spanning tree will be

1-3, 3-4,3-5,5-2,5-6,5-7,7-8,7-9

4+2+2+2+1+2+2+8=23

the shortest parth will we the best quantative method for this problem

3: model's solution will be

1-3, 3-6, 6-8,8-9= 4 +(3/3)+(4/2)+7

=4+1+2+7=14

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