Prepared by Lee Revere and John Large Chapter 12 Network Models Prepared by Lee Revere and John Large To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 12-1

Learning Objectives Students will be able to: Connect all points of a network while minimizing total distance using the minimal-spanning tree 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, 9e by Render/Stair/Hanna 12-2

Chapter Outline 12.1 Introduction 12.2 Minimal-Spanning Tree Technique 12.4 Shortest-Route Technique To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 12-3

Introduction The presentation will cover two network models that can be used to solve a variety of problems: the minimal-spanning tree technique, and the shortest-route technique. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 12-4

Minimal-Spanning Tree Technique Definition: The minimal-spanning tree technique determines the path through the network that connects all the points while minimizing total distance. For example: If the points represent houses in a subdivision, the minimal spanning tree technique can be used to determine the best way to connect all of the houses to electrical power, water systems, etc. in a way that minimizes the total distance or length of power lines or water pipes. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 12-5

Shortest Route Technique Definition: Shortest route technique can find the shortest path through a network. For example: This technique can find the shortest route from one city to another through a network of roads. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 12-6

Minimal-Spanning Tree Steps Select any node in the network. Connect this node to the nearest node minimizing the total distance. Find and connect the nearest unconnected node to one of the connected nodes. If there is a tie for the nearest node, one can be selected arbitrarily. A tie suggests that there may be more than one optimal solution. Repeating the third step until all nodes are connected. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 12-7

Figure 12.1: Network for Lauderdale Construction To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 12-8

Minimal-Spanning Tree Technique Solving the network for Melvin Lauderdale construction Start by arbitrarily selecting node 1. Since the nearest node is the third node at a distance of 2 (200 feet), connect node 1 to node 3. Shown in Figure 12.2 (2 slides hence) Considering nodes 1 and 3, look for the next-nearest node. This is node 4, which is the closest to node 3 with a distance of 2 (200 feet). Once again, connect these nodes (Figure 12.3a (3 slides hence). To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 12-9

Figure 12.1: Network for Lauderdale Construction To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 12-10

Figure 12.2: First Iteration Lauderdale Construction To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 12-11

Fig 12.3a: Second Iteration To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 12-12

Fig 12.3b: Third Iteration 12-13 To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 12-13

Summarize: Minimal-Spanning Tree Technique Step 1: Select node 1 Step 2: Connect node 1 to node 3 Step 3: Connect the next nearest node Step 4: Repeat the process The total number of iterations to solve this example is 7. This final solution is shown in the following slide. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 12-14

Fig 12.5b: Third Iteration 12-15 To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 12-15

The Shortest-Route Technique The shortest-route technique minimizes the distance through a network. The shortest-route technique finds how a person or item can travel from one location to another while minimizing the total distance traveled. The shortest-route technique finds the shortest route to a series of destinations. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 12-16

Example: From Ray’s Plant to Warehouse For example, Every day, Ray Design, Inc., must transport beds, chairs, and other furniture items from the factory to the warehouse. This involves going through several cities. Ray would like to find the route with the shortest distance. The road network is shown on the next slide. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 12-17

Shortest-Route Technique (continued) Roads from Ray’s Plant to Warehouse: 1 2 3 4 5 6 100 150 200 50 40 Warehouse Plant To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 12-18

Steps of the Shortest-Route Technique Find the nearest node to the origin (plant). Put the distance in a box by the node. Find the next-nearest node to the origin (plant), 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. 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. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 12-19

Shortest-Route Technique (continued) Ray Design: 1st Iteration 100 1 2 3 4 5 6 100 150 200 50 40 Warehouse Plant The nearest node to the plant is node 2, with a distance of 100 miles. Thus, connect these two nodes. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 12-20

Shortest Route Technique (continued) Ray Design: 2nd Iteration 1 2 3 4 5 6 100 150 200 50 40 The nearest node to the plant is node 3, with a distance of 50 miles. Thus, connect these two nodes. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 12-21

Shortest-Route Technique (continued) Ray Design: 3rd Iteration 1 2 3 4 5 6 100 150 200 50 40 190 The nearest node to the plant is node 5, with a distance of 40 miles. Thus, connect these two nodes. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 12-22

Shortest Route Technique (continued) 4th and Final Iteration 1 2 3 4 5 6 100 150 200 50 40 190 290 Total Shortest Route = 100 + 50 + 40 + 100 = 290 miles. To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 12-23