OMIS 327 Lecture 9. Network Models

OMIS 327 Lecture 9. Network Models - OMIS 327 Lecture 9...

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1 OMIS 327 Lecture 9: Network Models Instructor: Dr. Lee, Jung Young
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2 Announcement Homework #2 is due March 30 th .
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3 Today’s Learning Goals 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.
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This chapter covers three network models that can be used to solve a variety of problems. The minimal-spanning tree technique minimal-spanning tree technique determines a path through a network that connects all the points while minimizing the total distance. The maximal-flow technique maximal-flow technique finds the maximum flow of any quantity or substance through a network. The shortest-route technique shortest-route technique can find the shortest path through a network. Introduction 4
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Large scale problems may require hundreds or thousands of iterations making efficient computer programs a necessity. All types of networks use a common terminology. The points on a network are called nodes nodes and may be represented as circles of squares. The lines connecting the nodes are called arcs. arcs. A spanning tree for an N-node network is a set of N-1 arcs that connects every node to every other node. Introduction 5
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Minimal-Spanning Tree Technique The minimal-spanning tree technique involves connecting all the points of a network together while minimizing the distance between them. The Lauderdale Construction Company is developing a housing project. It wants to determine the least expensive way to provide water and power to each house. There are eight houses in the project and the distance between them is shown in Figure 11.1. 6
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Network for Lauderdale Construction 3 3 2 3 2 4 2 5 6 7 1 5 1 2 3 4 5 6 7 8 3 Gulf Figure 11.1 7
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Steps for the Minimal- Spanning Tree Technique 1. Select any node in the network. 2. Connect this node to the nearest node that minimizes the total distance. 3. Considering all the nodes that are now connected, find and connect the nearest node that is not connected. If there is a tie, select one arbitrarily. A tie suggests there may be more than one optimal solution.
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  • Spring '14
  • JungYoungLee
  • Graph Theory, Shortest path problem, Flow network, road network, maximal-flow technique, Lauderdale

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