1. Chapter 12 Network Models 12-1
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
12-1

2. Learning Objectives Students will be able to
Connect all points of a network while minimizing total distance using the minimal-spanning tree technique.
Determine the maximum flow through a network using the maximal-flow technique.
Find the shortest path through a network using the shortest-route technique.
Understand the important role of software in solving network problems.
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
12-2

3. Chapter Outline 12.1 Introduction 12.2 Minimal-Spanning Tree Technique
12.3 Maximal-Flow Technique
12.4 Shortest-Route technique
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
12-3

4. Minimal-Spanning Tree Technique
Determines the path through the network that connects all the points while minimizing total distance.
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
12-4

5. Minimal-Spanning Tree Steps
1. Select any node in the network.
2. Connect this node to the nearest node that minimizes the total distance.
3. Considering all of the nodes that are now connected, find and connect the nearest node that is not connected. If there is a tie for the nearest node, select one arbitrarily. A tie suggests that there may be more than one optimal solution.
4. Repeat the third step until all nodes are connected.
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
12-5

6. Minimal-Spanning Tree Lauderdale Construction1 2 3 4 5 7 8 6
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
12-6

7. Minimal-Spanning Tree Iterations 1&23 4 5 7 8 6
First Iteration
Second Iteration
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
12-7

8. Minimal-Spanning Tree Iterations 3&41 2 3 4 5 7 8 6
Third Iteration
Fourth Iteration
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
12-8

9. Minimal-Spanning Tree Iterations 5 & 63 5 4 2 1 6 7 8
Fifth Iteration
Sixth iteration
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
12-9

10. 7th Iteration 2 5 Seventh & final iteration 7 1 3 8 64 5 7 8 6
Seventh & final iteration
Minimum Distance: 16
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
12-10

11. The Maximal-Flow Technique
1. Pick any path from start (source) to finish (sink) with some flow. If no path with flow exists, then the optimal solution has been found.
2. Find the arc on this path with the smallest capacity available. Call this capacity C. This represents the maximum additional capacity that can be allocated to this route.
3.For each node on this path decrease the flow capacity in the direction of flow by the amount C. For each node on this path, increase the flow capacity in the reverse direction by C
4. Repeat these steps until an increase in flow is no longer possible.
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
12-11

12. Maximal-Flow Road Network for Waukesha1 2 4 3 5 6 10
East
Point
West
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
12-12

13. Capacity Adjustment Iteration 1 East Point West Add 2 2 Subtract 2 6 13
East
Point
West
Add 2
Subtract 2
Iteration 1 4
New path
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
12-13

14. Maximal-Flow Road Network for Waukesha1 2 4 3 5 6 10
East
Point
West
Add 2
Subtract 2
Path = 1, 2, 6
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
12-14

15. Second Iteration East Point West Add 1 Subtract 1 5 3 4 1 10 6 2 12-154 6 2 10
East
Point 5
West
Add 1
Subtract 1
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
12-15

16. Second Iteration New Path East Point West 5 Path = 1, 2, 4, 6 4 2 10 62 6 1 3 10
East
Point 5
West
Path = 1, 2, 4, 6
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
12-16

17. Third Iteration East Point West 2 6 1 4 Subtract 2 5 3 Add 2 10 12-1710
East
Point
West
Add 2
Subtract 2
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
12-17

18. Third Iteration New Path East Point West 2 6 1 4 5 3 Path = 1, 3, 5, 610
East
Point
West
Path = 1, 3, 5, 6
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
12-18

19. Road Network for Waukesha Third Iteration
Path
Flow
(Cars Per
Hour)
1-2-6
200
100
Total
500 1 2 4 3 5 6 8
East
Point
West
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
12-19

20. The Shortest-Route Technique
1. Find the nearest node to the origin. Put the distance in a box by the node.
2.Find the next nearest node to the origin, and put the distance in a box by the node. In some cases, several paths will have to be checked to find the nearest node.
3. Repeat this process until you have gone through the entire network. The last distance at the ending node will be the distance of the shortest route. You should note that the distances placed in the boxes by each node are the shortest route to this node. These distances are used as intermediate results in finding the next nearest node.
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
12-20

21. Shortest-Route Problem Ray Design, Inc.
Roads from Ray’s Plant to the Warehouse
200 1 6 5 3 4 2
Plant
Warehouse
100
150 40 50
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
12-21

22. Ray Design, Inc. First Iteration
200 1 6 5 3 4 2
Plant
Warehouse
100
150 40 50
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
12-22

23. Ray Design, Inc. Second Iteration
200 1 6 5 3 4 2
Plant
Warehouse
100
150 40 50
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
12-23

24. Ray Design, Inc. Third Iteration
200 1 6 5 3 4 2
Plant
Warehouse
100
150 40 50
190
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
12-24

25. Ray Design, Inc. Fourth Iteration
200 1 6 5 3 4 2
Plant
Warehouse
100
150 40 50
190
290
To accompany Quantitative Analysis for Management, 8e
by Render/Stair/Hanna
12-25