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Ch7_NetworkFlowModels_Corrected

# Ch7_NetworkFlowModels_Corrected - Chapter 7 Network Flow...

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Click to edit Master subtitle style 11/5/10 BIT 2406 Chapter 7 Network Flow Models 11

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11/5/10 BIT 2406 Chapter Topics Shortest Route Problem Minimal Spanning Tree Problem Maximum Flow Problem 22
11/5/10 BIT 2406 Networks A network is an arrangement of paths connected at various points, through which one or more items move from one point to another. For example, highway systems, telephone networks, railroad systems, and television networks. Networks are popular because they provide a picture of a system. Enables a manager to visually interpret the system and thus enhances the manager’s understanding. 33

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11/5/10 BIT 2406 Networks Network flow models: class of network models directed at the flow of items through a system. We will discuss the use of network flow models to analyze three types of problems: Shortest route problem Minimal spanning tree problem Maximal flow problem 44
11/5/10 BIT 2406 Networks Networks are illustrated as diagrams consisting of two main components: nodes and branches. Nodes, denoted by circles, represent junction points connecting branches. Nodes typically represent localities, such as cities, intersections, or air or railroad terminals. Branches, represented as lines, connect nodes and show flow from one point to another. Branches are the paths connecting the nodes such as roads connecting cities and intersections or air routes connecting terminals. 55

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11/5/10 BIT 2406 The Shortest Route Problem The shortest route problem is to find the shortest distance between an origin and various destination points. Can be solved in many ways, one of the most popular method is The Shortest Route solution approach (a.k.a Shortest path node correcting algorithm OR Dijktra’s Algorithm) Main concepts: Path lengths as labels, permanently labeled nodes, temporarily labeled nodes, finding shortest path from the source to every other node. 66
11/5/10 BIT 2406 77 1 2 3 5 6 7 4 1 6 3 5 9 1 5 2 2 1 4 8 1 4 2 5 1 2 1 9 1 7 l& l & l & l & l 0 1&

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88 1 2 3 5 6 7 4 1 6 3 5 9 1 5 2 2 1 4 8 1 4 2 5 1 2 1 9 1 7 l & l & l & 1 6 1 0 1 9 Node Branch Label 2 1-2 0 + 16 = 16 3 1-3 0 + 9 = 9 4 1-4 0 + 35 = 35 Permanent Nodes: 1 Neighbor Nodes: 2, 3, 4 l 3 5 Node 3 has the minimum temporary label and therefore will be added to the permanent nodes, and branch (1-3) will be added to the shortest route tree.
99 1 2 3 5 6 7 4 1 6 3 5 9 1 5 2 2 1 4 8 1 4 2 5 1 2 1 9 1 7 l & l & 3 1 1 6 1 0 1 9 Node Branch Label 2 1-2 0 + 16 = 16 4 1-4 0 + 35 = 35 4 3-4 9 + 15 = 24 6 3-6 9 + 22 = 31 Permanent Nodes: 1, 3 Neighbor Nodes: 2, 4, 6 l 2 4 Node 2 has the minimum temporary label and therefore will be added to the permanent nodes, and branch (1-2) will be added to the shortest route tree.

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11/5/10 BIT 2406 1010 1 2 3 5 6 7 4 1 6 3 5 9 1 5 2 2 1 4 8 1 4 2 5 1 2 1 9 1 7 l & l 4 1 3 1 1 6 1 0 1 9 Node Branch
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Ch7_NetworkFlowModels_Corrected - Chapter 7 Network Flow...

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