What is a transportation problem? Briefly discuss the decision variables, the ob

Question

What is a transportation problem? Briefly discuss the decision variables, the objective function and constraint requirements in a transportation problem. Give a real world example of the transportation problem.

(b) What is a marketing problem in applications of linear programming? Briefly discuss the objective function and constraint requirements in a marketing problem. Give a real world example of a marketing problem.

(c) What are the dual prices? In what range are they valid? Why are they useful in making recommendations to the decision maker? Give a real world example.

(d) What is the required format of a linear programming problem needed if we want to solve it by using QM for Windows? What information about the solution can you collect from the results provided by QM for Windows? Discuss briefly.

Explanation / Answer

One of the most important and successful applications of quanti- tative analysis to solving business problems has been in the physical distribution of products, commonly referred to as trans- portation problems. Basically, the purpose is to minimize the cost of shipping goods from one location to another so that the needs of each arrival area are met and every shipping location operates within its capacity. However, quantitative analysis has been used for many problems other than the physical distribution of goods. For example, it has been used to efficiently place employees at certain jobs within an organization. (This application sometimes is called the assignment problem.) We could set up a transportation problem and solve it using the simplex method as with any LP problem (see Using the Simplex Method to Solve Linear Programming Maximization Problems, EM 8720, or another of the sources listed on page 35 for informa- tion about the simplex method). However, the special structure of the transportation problem allows us to solve it with a faster, more economical algorithm than simplex. Problems of this type, contain- ing thousands of variables and constraints, can be solved in only a few seconds on a computer. In fact, we can solve a relatively large transportation problem by hand. There are some requirements for placing an LP problem into the transportation problem category.

In the term linear programming, programming refers to mathematical pro- gramming. In this context, it refers to a planning process that allocates resources

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