# Some problems on network models

I have attached some quantitative Analysis Questions that I need help solving so I can add to my study guide. The book used was Quantitative analysis for Management by Barry Render but as you already know these concepts are found in any Quantitative Analysis book.

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Please see the attached files.

Chapter 12 - Additional Problems

Network Models

1. The west-to-east air traffic system passing through the United States can handle aircraft flows with capacities in hundreds of planes per hour as shown. What is the peak air traffic load (From city 1 to city 5) in aircraft per hour that this system can handle?

To

From 1 2 3 4 5

1 - 2 - 4 -

2 1 - 2 3 3

3 2 2 - 5 2

4 - - - - 3

5 - 2 2 1 -

1. Pick any path from start (source) to finish (sink) with some flow. If no path with flow exists, then the optimal solution has been found.

We pick path 1-2-3-5.

2. Find the arc on this path with the smallest capacity available. Call this capacity C. This represents the maximum additional capacity that can be allocated to this route.

Smallest capacity available on this path is 2. Thus, maximum additional capacity on this path =2.

3. For each node on this path decrease the flow capacity in the direction of flow by the amount C. For each node on this path, increase the flow capacity in the reverse direction by C

4. Repeat these steps until an increase in flow is no longer possible.

It can be seen that on the given path, no increase in flow is possible.

Next path that we chose is 1-4-5. Here the minimum flow is = 3.

Repeating step 3, we get following path.

As there is no more ...

#### Solution Summary

This posting contains solutions to following problems on network models.