# Linear Programming Transportation And Assignment Problems Pdf

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## Transportation and Assignment Problem

The Transportation and Assignment problems deal with assigning sources and jobs to destinations and machines. We will discuss the transportation problem first. Suppose a company has m factories where it manufactures its product and n outlets from where the product is sold. Transporting the product from a factory to an outlet costs some money which depends on several factors and varies for each choice of factory and outlet. The total amount of the product a particular factory makes is fixed and so is the total amount a particular outlet can store. The problem is to decide how much of the product should be supplied from each factory to each outlet so that the total cost is minimum. Suppose an auto company has three plants in cities A, B and C and two major distribution centers in D and E.

In this chapter, we discuss three special types of linear programming problems: transporta-tion, assignment, and transshipment. Each of these can be solved by the simplex algorithm, but specialized algorithms for each type of problem are much more efficient. We begin our discussion of transportation problems by formulating a linear programming model of the following situation. Powerco has three electric power plants that supply the needs of four cities. The peak power de-mands in these cities, which occur at the same time 2 P. The costs of sending 1 million kwh of electricity from plant to city depend on the distance the elec-tricity must travel. Because Powerco must determine how much power is sent from each plant to each city, we define for i 1, 2, 3 and j 1, 2, 3, 4.

## Operations Research/Transportation and Assignment Problem

Daniel J. Nicolau D. Gualda 1. Traditionally, the initial steps on airline planning — Schedule Generation and Fleet Assignment problems — are solved separately. This traditional approach usually leads to suboptimal solutions, since flight profitability — the decision criteria to schedule a flight — depends on what aircraft type will be used on that flight. On the other hand, the type of aircraft assigned to a flight will be different accordingly to the available scheduled flights. Because of this interdependence, airlines avoid complete redesign of their flight network, adopting a conservative approach and slightly improving existing suboptimal schedules over time.

Linear Programming and Its Applications pp Cite as. Transportation and assignment problems are traditional examples of linear programming problems. Although these problems are solvable by using the techniques of Chapters 2—4 directly, the solution procedure is cumbersome; hence, we develop much more efficient algorithms for handling these problems. Assignment problems, which are special cases of transportation problems, pose difficulties for the transportation algorithm and require the development of an algorithm which takes advantage of the simpler nature of these problems. Unable to display preview. Download preview PDF.

Both of these problems can be solved by the simplex algorithm, but the process would result in very large simplex tableaux and numerous simplex iterations. Because of the special characteristics of each problem, however, alternative solution methods requiring significantly less mathematical manipulation have been developed. Each source is able to supply a fixed number of units of the product, usually called the capacity or availability, and each destination has a fixed demand, often called the requirement. Good financial decisions concerning facility location also attempt to minimize total transportation and production costs for the entire system Setting up a Transportation problem To illustrate how to set up a transportation problem we consider the following example; Example 4. The plants are able to supply the following numbers of tons per week: Plant Supply capacity The requirements of the sites, in number of tons per week, are: Construction site Demand requirement A B C The cost of transporting 1 ton of concrete from each plant to each site is shown in the figure 8 in Emalangeni per ton. For computational purposes it is convenient to put all the above information into a table, as in the simplex method. In this table each row represents a source and each column represents a destination.

## Assignment Problem in Linear Programming : Introduction and Assignment Model

Assignment problem is a special type of linear programming problem which deals with the allocation of the various resources to the various activities on one to one basis. It does it in such a way that the cost or time involved in the process is minimum and profit or sale is maximum. Though there problems can be solved by simplex method or by transportation method but assignment model gives a simpler approach for these problems. In a factory, a supervisor may have six workers available and six jobs to fire.

### Transportation and Assignment Problems

In this work, the problem of job-machine assignment was formulated as a linear programming LP models and then solved by the simplex method. Three case studies were involved in this study to cover all kinds of problems may be faced. To verify the results of the LP models, these problems also solved using transportation algorithm and has been found that the LP model is more efficient for solving the assignment problems. The article was added to IASJ on Total full text downloads since the date of addition Year Total Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 48 42 96 83 65 45 74 93 95 64 87 2 15 19 9 24 48 81 58 87 5 12 13 20 9 7 8 2 6 11 26 9 12 1 2 5 4 Usage is updated on a monthly basis. Journals Subjects Institutions.

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