Chapter 7: Network Flow Models

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Questions and Answers

What is the purpose of subtracting the maximum flow along a path from the branches along the path?

To update the flow values along the path (correct)

To determine the next path arbitrarily

To add the flow to the total flow through the network

To find the maximum flow along the path

What is the primary reason why network models have become a popular management science technique?

They are only used for highway systems

They provide a visual representation of the system (correct)

They are easy to conceive and construct

They are used extensively for project analysis

What is the term used to describe the class of network models that deal with the flow of items through a system?

Network design models

Network optimization models

Network analysis models

Network flow models (correct)

What is the term used to describe the points in a network where items can change direction or flow?

Nodes Signup and view all the answers

What is the purpose of the network flow models?

All of the above Signup and view all the answers

What is the primary advantage of using network diagrams?

They provide a visual representation of the system Signup and view all the answers

What is the term used to describe the lines that connect nodes in a network diagram?

Branches Signup and view all the answers

What is the term used to describe the network components that represent junction points in a network?

Nodes Signup and view all the answers

What is the primary focus of network flow models in this chapter?

Flow of items through a system Signup and view all the answers

What is the purpose of step 2 in the maximal flow solution method?

To adjust the capacities at each node by subtracting the maximal flow for the path selected. Signup and view all the answers

What is a necessary condition to stop repeating the steps in the maximal flow solution method?

When there are no more paths with available flow capacity. Signup and view all the answers

What is the advantage of using Excel to solve the maximal flow problem?

It can be formulated as an integer linear programming model and solved using Solver. Signup and view all the answers

What is the purpose of eliminating flow along a branch in the opposite direction in the Excel model?

To reduce the size and complexity of the model formulation. Signup and view all the answers

What is the decision variable in the integer linear programming model for the maximal flow problem?

Flow along each branch, as an integer. Signup and view all the answers

What is the purpose of a network flow problem?

To determine the shortest distance, shortest length of time, or lowest cost between points in the network. Signup and view all the answers

What is the goal in the Minimum Spanning Tree problem?

To connect all nodes in a network so that the total branch lengths are minimized. Signup and view all the answers

What determines the shortest distance between an originating point and several destination points?

Shortest Path Problem Signup and view all the answers

How are networks typically illustrated?

As diagrams consisting of nodes and branches. Signup and view all the answers

What type of network problem occurs when the branches of the network have limited flow capacities?

Network Flow Problem with Limited Capacities Signup and view all the answers

What is the purpose of the constraint formula in the Solver?

To ensure that the flow through each node is consistent with the capacities. Signup and view all the answers

Study Notes

Network Flow Models

Network flow models are used to analyze the flow of items through a system, and are a type of network model that can be used to solve three types of problems: the shortest route problem, the minimal spanning tree problem, and the maximal flow problem.

Components of a Network

Networks consist of two main components: nodes and branches.
Nodes represent junction points, such as intersections of streets, and are denoted in the network diagram by circles.
Branches connect the nodes and reflect the flow from one point in the network to another, and are represented by lines connecting the nodes.

Network Flow Problems

The shortest route problem involves finding the shortest path between two nodes in a network.
The minimal spanning tree problem involves finding the minimum number of branches required to connect all nodes in a network.
The maximal flow problem involves finding the maximum flow of items through a network, given the limited flow capacities of the branches.

Solving Network Flow Problems

Network flow problems can be solved using computer solutions, such as QM for Windows or Excel.
The maximal flow problem can be solved by formulating it as an integer linear programming model and solving it using Solver in Excel.
The solution involves determining the flow along each branch, and the total network flow.

Key Concepts

Permanent set: a set of nodes that have been determined to be part of the shortest route.
Branch capacities: the maximum flow of items that can pass through a branch.
Flow capacity: the amount of flow available along a branch.
Net flow: the flow of items along a branch in the correct direction.

Learning Outcomes

Students should be able to differentiate network components and apply computer solutions for the problem.
Students should be able to learn the process of building a flow of network and its components.

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Description

Explore network flow models, a popular management science technique used to optimize flow in networks, such as highway systems, telephone networks, and more.