quantitative analysis

Under supervision of Prof. Dr. Ehab Yaseen : 

1 Under supervision of Prof. Dr. Ehab Yaseen Presented By Amr Ezz El Din Hamdy Group 16A Quantitative analysis Shortest route & Minimal spanning MIBA ESLSCA XXGroup A

Slide 2: 

2 Shortest route

Chapter 7, problem 3, page 279.Find the shortest route from origin 1 to other 6 cities. : 

3 Chapter 7, problem 3, page 279.Find the shortest route from origin 1 to other 6 cities. 1 4 3 2 5 7 6 85 31 72 24 137 88 53 61 117 65

We will use the quick way of Dr. Ehab Yaseen.First we start from the origin, and see the connected node. We choose the shortest route among and mark it up. : 

4 We will use the quick way of Dr. Ehab Yaseen.First we start from the origin, and see the connected node. We choose the shortest route among and mark it up. 1 4 3 2 85 88 53 3 1 [53,1] 53

Node 1 & 3 become permanent nodes, we look for next nodes connected to them and find shortest route among and mark it up. : 

5 Node 1 & 3 become permanent nodes, we look for next nodes connected to them and find shortest route among and mark it up. 1 4 3 2 5 7 6 85 31 72 24 137 88 53 61 117 65 [53,1] 1-2=85 1-3-5=114 1-3-7=170 1-4=88 1-3-4=118 2 85 [85,1]

Node 1,2 & 3 become permanent nodes, we look for next nodes connected to them and find shortest route among and mark it up. We remove non selected route between permanent nodes, route 3-4. : 

6 Node 1,2 & 3 become permanent nodes, we look for next nodes connected to them and find shortest route among and mark it up. We remove non selected route between permanent nodes, route 3-4. 1 4 3 5 7 6 31 72 24 137 88 53 61 117 65 [53,1] [85,1] 1-2-5=116 1-3-5 = 114 1-3-7=170 1-4=88 1-3-4=118 2 85 4 88 [88,1]

Node 1, 2, 3 & 4 become permanent nodes, we look for next nodes connected to them and find shortest route among and mark it up. We remove non selected route between permanent nodes, route 2-5. : 

7 Node 1, 2, 3 & 4 become permanent nodes, we look for next nodes connected to them and find shortest route among and mark it up. We remove non selected route between permanent nodes, route 2-5. 1 4 3 5 7 6 31 72 24 137 53 61 117 [53,1] [85,1] 1-2-5=116 1-3-5 = 114 1-3-7=170 2 85 4 88 [88,1] 1-4-6=225 5 61 [114,3]

Node 1, 2, 3, 4 & 5 become permanent nodes, we look for next nodes connected to them and find shortest route among and mark it up. We also remove non selected route between permanent nodes, route 5-7. : 

8 Node 1, 2, 3, 4 & 5 become permanent nodes, we look for next nodes connected to them and find shortest route among and mark it up. We also remove non selected route between permanent nodes, route 5-7. 1 4 3 5 7 6 72 24 137 53 61 117 [53,1] [85,1] 2 85 4 88 [88,1] 1-4-6=225 [114,3] 72 1-3-7=170 1-3-5-7=186 7 117 [170,3]

Node 1, 2, 3, 4, 5 & 7 become permanent nodes, we look for next nodes connected to them and find shortest route among and mark it up. We also remove non selected route between permanent nodes, route 4-6. : 

9 Node 1, 2, 3, 4, 5 & 7 become permanent nodes, we look for next nodes connected to them and find shortest route among and mark it up. We also remove non selected route between permanent nodes, route 4-6. 1 4 3 5 7 6 24 137 53 61 117 [53,1] [85,1] 2 85 4 88 [88,1] 1-4-6=225 1-3-7-6=194 [114,3] [170,3] 24 6 24 [194,7]

We summarize our solution in the following table : 

10 We summarize our solution in the following table

Shortest Route to 2 is 1 – 2 and equals 85 miles : 

11 Shortest Route to 2 is 1 – 2 and equals 85 miles 1 4 3 2 5 7 6 85 31 72 24 137 88 53 61 117 65

Shortest Route to 3 is 1 – 3 and equals 53 miles : 

12 Shortest Route to 3 is 1 – 3 and equals 53 miles 1 4 3 2 5 7 6 85 31 72 24 137 88 53 61 117 65

Shortest Route to 4 is 1 – 4 and equals 88 miles : 

13 Shortest Route to 4 is 1 – 4 and equals 88 miles 1 4 3 2 5 7 6 85 31 72 24 137 88 53 61 117 65

Shortest Route to 5 is 1 - 3 - 5 and equals 114 miles : 

14 Shortest Route to 5 is 1 - 3 - 5 and equals 114 miles 1 4 3 2 5 7 6 85 31 72 24 137 88 53 61 117 65

Shortest Route to 6 is 1 – 3 – 7 – 6 and equals 194 miles : 

15 Shortest Route to 6 is 1 – 3 – 7 – 6 and equals 194 miles 1 4 3 2 5 7 6 85 31 72 24 137 88 53 61 117 65

Shortest Route to 7 is 1 – 3 – 7 and equals 170 miles : 

16 Shortest Route to 7 is 1 – 3 – 7 and equals 170 miles 1 4 3 2 5 7 6 85 31 72 24 137 88 53 61 117 65

Slide 17: 

17 Minimal spanning

Let us solve the same problem for minimal spanning. Assume that, we want to supply those cities with electricity, and we want to Connect all nodes in a network so that the total branch lengths are minimized. : 

18 Let us solve the same problem for minimal spanning. Assume that, we want to supply those cities with electricity, and we want to Connect all nodes in a network so that the total branch lengths are minimized. 1 4 3 2 5 7 6 85 31 72 24 137 88 53 61 117 65

We start from any node; see the nearest node; and mark it up. We will start from node 1. : 

19 We start from any node; see the nearest node; and mark it up. We will start from node 1. 1 4 3 2 85 88 53 3 1 53

Select the closest node not presently in the spanning area and mark it up. : 

20 Select the closest node not presently in the spanning area and mark it up. 1 4 3 2 5 7 6 85 31 72 24 137 88 61 117 65 5 61 53

Select the closest node not presently in the spanning area and mark it up We remove unused branches between connected nodes (1-2). : 

21 Select the closest node not presently in the spanning area and mark it up We remove unused branches between connected nodes (1-2). 1 4 3 2 7 6 85 31 72 24 137 88 117 65 5 61 53 31 2

Select the closest node not presently in the spanning area and mark it up. We remove unused branches between connected nodes (1-4). : 

22 Select the closest node not presently in the spanning area and mark it up. We remove unused branches between connected nodes (1-4). 1 4 3 7 6 72 24 137 88 117 65 5 61 53 31 2 65 4

Select the closest node not presently in the spanning area and mark it up. We remove unused branches between connected nodes (3-7). : 

23 Select the closest node not presently in the spanning area and mark it up. We remove unused branches between connected nodes (3-7). 1 3 7 6 72 24 137 117 5 61 53 31 2 65 4 7 72

Select the closest node not presently in the spanning area and mark it up. We remove unused branches between connected nodes (4-6). : 

24 Select the closest node not presently in the spanning area and mark it up. We remove unused branches between connected nodes (4-6). 1 3 6 24 137 5 61 53 31 2 65 4 7 72 6 24

The total length distance is the sum of all branches. : 

25 The total length distance is the sum of all branches. 1 3 5 61 53 31 2 65 4 7 72 6 24 = 306 Miles of electric cables Total length distance = 53 + 65 + 61 + 31+ 72 + 24

Slide 26: 

26 Thank You for your Attention

Under supervision of Prof. Dr. Ehab Yaseen : 

27 Under supervision of Prof. Dr. Ehab Yaseen Presented By Amr Ezz El Din Hamdy Group 16A Quantitative analysis Shortest route & Minimal spanning MIBA ESLSCA XXGroup A