Chapter+7+-+Network+Flow+Models

# Chapter+7+-+Network+Flow+Models - Reading Questions •...

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Unformatted text preview: Reading Questions • What is a network? Be able to give some examples of networks. • Why are networks popular? • What are nodes and branches? • What is the shortest route problem? What are the steps of the shortest route solution method? Be able to explain each step. • What is the minimal spanning tree problem? Be able to compare and contrast minimal spanning tree and shortest route. • What are the steps of the minimal spanning tree solution method? Be able to explain each step. • What did E.W. Dijkstra do? • What is the maximal flow problem? How is the maximal flow problem different from the shortest route problem and the minimal spanning tree problem? • What is the difference between directed branches and undirected branches? • What are the steps of the maximal flow solution method? Be able to explain each step. Introduction • This chapter focuses on several types of network flow problems: – Transshipment Problems (discussed in Ch. 6) – Shortest Path Problems – Maximal Flow Problems – Transportation/Assignment Problems (also Ch. 6) – Generalized Network Flow Problems • We also consider a different type of network problem called the Minimum Spanning Tree Problem Characteristics of Network Flow Problems • Network flow problems can be represented as a collection of nodes connected by arcs. • There are three types of nodes: • We’ll use negative numbers to represent supplies and positive numbers to represent demand. 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. • Networks are also popular because a large number of systems can be easily modeled as networks. 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. BIT 2406 Networks • Four nodes, four branches in figure. • “Atlanta”, node 1, termed origin, any of others could be destination. • Branches identified by beginning and ending node numbers....
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