# Applying Network Models: Part II

**DUE: 02.21.15 @ 11:59PM**

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**THIS is what I need you to do –> Review the post 1 below: Further the conversation by explicitly stating what the nodes and arcs would be in the examples in the context of the person’s real life situation.**

**Post 1:** Provide at least one example of when you might use (1) the minimal-tree technique, (2) the shortest path, and (3) the maximal flow through a netowrk technique. Explain why it would be the appropriate technique to apply each of the situations described. Please be thorough and provide enough details:

A minimal spanning tree could be utilized to form an electrical circuit or group electrical circuits. The reason why that spanning tree are utilized are for the purposes of effeciency. Meaning that a construction company may try and cut on cost by running the least amount of wires possible to electrify a building for example. Shortest path techniques would be utilized to find the shortest distant among a group of different paths. Or for the sake of simplicity shortest path techniques can be utilized to build roads. And last but not least the maximal flow technique is utilized by individuals in construction who wan to erect pipes to run water and with this particular technique they are enabled to know how much water that they are able to run through the pipes without damaging them. (Water pressure)

**THIS is what I need you to do –> Review the post 2 below: In the context of one of the examples, make general comments on how using a network could potentially increase production, profit, or benefit the business in some way. Compose a professionally written statement to the CEO of the business sharing your information on network models and how this might benefit their business. **

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**Post 2:** Provide at least one example of when you might use (1) the minimal-tree technique, (2) the shortest path, and (3) the maximal flow through a netowrk technique. Explain why it would be the appropriate technique to apply each of the situations described. Please be thorough and provide enough details:

A network is characterized by a collection of nodes and directed edges, called a directed graph. Graphs can be used to model many real networked systems. For example in modeling an air travel, each node might represent an airport and each edge a route taken by some flight. Here are some examples of the tree spanning trees:

The Minimum Spanning Wheel:

A minimum spanning wheel (MST), of an edge weight graph is a spanning tree whose weight (the sum of the weights of its edges) is no longer than the weight of any other spanning tree. The object is to “span” all the places with minimal distance (as well as minimize expenses)

As an example, say we want to hook up all the houses in a neighborhood with a new phone wire. We want to find the order of houses so that when we are finished connecting the houses we have used the least amount of wire.

On the next screen I have a map of the house locations and the distances between each. The houses are a geometric shape and have been labeled with a number – the locations are called nodes. The distance between each location is marked and we call each connection between nodes a branch. In the final analysis we do not have to hook-up each distance shown, for we only have to get all connected. As an example we may not have wire between 3 and 7. 7 might be hooked-up from 8.

Maximum Flow Technique:

Maximal flow is a technique used to determine the amount that can flow through a system. Each part of the system may not have the same capacity.

An example here may be that we have a system of streets in a town and we want to know the maximal flow of traffic from west to east that may occur.

Another example would be how many gallons of fluid could flow through a system of pipes. Like in the spanning problem, we have nodes (connections), but now we have capacity amounts. The amount that can flow in one direction may not have the same capacity in the reverse direction. In the traffic flow analogy, you could have one lane in the east direction, but two lanes going west. Another difference is that we have to pick a starting node and an ending node in terms of the direction of the flow.

Sometimes the solution will be such that you will ship toward the intended flow, but because of capacity constraints you will reverse course and take some on a different route. That really isn’t the case in this example, but that could happen.

The Shortest Route:

The shortest route, here we have many ways to get from A to B, but we want the shortest (could mean distance or time) route, because it will cheapest.

We want to get stuff from the plant to the warehouse. We still have nodes and branches and distance or time between nodes. Here you do not want to reverse course and back track because that is costly here. In QM for windows you will go to module-> networks, file-> new-> Shortest route. Again you have to tell it how many branches there are. On each branch you input the staring node, ending node, and the distance or time. Plus you have to say which node is the origin and which is the destination

The output section “Network Results” shows the branches used and shows the minimum distance covered.

References:

http://algs4.cs.princeton.edu/43mst/

http://web.stanford.edu/~ashishg/msande111/notes/chapter5.pdf

*Document Requirements:*

Use standard 12-point font size

MS Word Document

3/4-1 page paper PER Post – there’s two post(Nothing less then 3/4 of a page and nothing more then 1-page necessary)

1-2 sources in APA citation PER Post – there’s two post(I willn’t need anymore then 3 sources for sure)

Thorough Response is a must!!

And NO plagiarism!!

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***Homework Field of Study: Business Statistics**

**If you don’t have any expertise in this area of study please don’t waste my time sending a handshake.**

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