Discuss below in a 350 words and use APA:
Discuss how you would use the material covered in module for a future position in management.
We examine three special types of linear programming model formulations- transportation, transshipment, and assignment problems. They are part of a larger class of linear programming problems known as network flow problems. We are considering these problems in a separate chapter because they represent a popular group of linear programming applications. These problems have special mathematical characteristics that have enabled management scientists to develop very efficient, unique mathematical solution approaches to them. These solution approaches are variations of the traditional simplex solution procedure. Like the simplex method, we have placed these detailed manual, mathematical solution procedures-called the transportation method and assignment method-on the companion Web site that accompanies this text. As in previous chapters, we will focus on model formulation and solution by using the computer, specifically by using Excel and QM for Windows.
The Transportation Model The transportation model is formulated for a class of problems with the following unique characteristics: (1) A product is transported from a number of sources to a number of destinations at the minimum possible cost; and (2) each source is able to supply a fixed number of units of the product, and each destination has a fixed demand for the product. Although the general transportation model can be applied to a wide variety of problems, it is this particular application to the transportation of goods that is most familiar and from which the problem draws its name. The following example demonstrates the formulation of the transportation model. Wheat is harvested in the Midwest and stored in grain elevators in three different cities-Kansas City, Omaha, and Des Moines. These grain elevators supply three flour mills, located in Chicago, St. Louis, and Cincinnati. Grain is shipped to the mills in railroad cars, each car capable of holding 1 ton of wheat. Each grain elevator is able to supply the following number of tons (i.e., railroad cars) of wheat to the mills on a monthly basis:
A network is an arrangement of paths connected at various points, through which one or more items move from one point to another. Everyone is familiar with such networks as highway systems, telephone networks, railroad systems, and television networks. For example, a railroad network consists of a number of fixed rail routes (paths) connected by terminals at various junctions of the rail routes. In recent years, using network models has become a very popular management science technique for a couple of very important reasons. First, a network is drawn as a diagram, which literally provides a picture of the system under analysis. This enables a manager to visually interpret the system and thus enhances the manager's understanding. Second, a large number of real-life systems can be modeled as networks, which are relatively easy to conceive and construct. In this and the next chapter, we will look at several different types of network models. In this chapter, we will present a class of network models directed at the flow of items through a system. As such, these models are referred to as network flow models. We will discuss the use of network flow models to analyze three types of problems: the shortest route problem, the minimal spanning tree problem, and the maximal flow problem. In Chapter 8, we will present the network techniques PERT and CPM, which are used extensively for project analysis.
Network Components Networks are illustrated as diagrams consisting of two main components: nodes and branches. Nodes represent junction points-for example, an intersection of several streets. Branches connect the nodes and reflect the flow from one point in the network to another. Nodes are denoted in the network diagram by circles, and branches are represented by lines connecting the nodes. Nodes typically represent localities, such as cities, intersections, or air or railroad terminals; branches are the paths connecting the nodes, such as roads connecting cities and intersections or railroad tracks or air routes connecting terminals.