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Lesson 9. solution of assignment problem.
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Transportation and Assignment Problems
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- James K. Strayer 2
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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. In the case of transportation problems, the algorithm is essentially a disguised form of the dual simplex algorithm of 4§2. 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.
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Department of Mathematics, Lock Haven University, Lock Haven, PA, 17745, USA
James K. Strayer
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© 1989 Springer Science+Business Media New York
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Strayer, J.K. (1989). Transportation and Assignment Problems. In: Linear Programming and Its Applications. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1009-2_7
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IMAGES
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COMMENTS
Transportation problem is a special kind of Linear Programming Problem (LPP) in which goods are transported from a set of sources to a set of destinations subject to the supply and demand of the sources and destination respectively such that the total cost of transportation is minimized. It is also sometimes called as Hitchcock problem.
formulate special linear programming problems using the transportation model. solve assignment problems with the Hungarian method. In this unit we extend the theory of linear programming to two special linear programming problems, the Transportation and Assignment Problems.
The assignment problem is a special case of transportation problem in which the objective is to assign ‘m’ jobs or workers to ‘n’ machines such that the cost incurred is minimized. The element Cij represents the cost of assigning worker I to job (I,j= 1,2,---n).
Transportation, Assignment, and Transshipment Problems 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. 7.1 Formulating Transportation ...
we defined the decision variables for the transportation problem. Thus, in this examplewedenoteby a 11 , a 12 , a 13 , a 21 , a 22 , a 23 thesixcolumnvectorsofthe
Identify the relationship between assignment problems and transportation problems. Formulate a spreadsheet model for an assignment problem from a description of the problem. Do the same for some variants of assignment problems. Give the name of an algorithm that can solve huge assignment problems that are well beyond the scope of Solver.
Although assignment problem can be solved either by using the techniques of Linear Programming or by the transportation method yet the assignment method developed by D. Konig, a Hungarian mathematician known as the Hungarian method of assignment problem is much faster and efficient.
Formulate a transportation problem as a linear programming model. Use the transportation method to solve problems with Excel. Solve maximization transportation problems, unbalanced problems, and problems with prohibited routes. Solve aggregate planning problems using the transportation model.
The assignment problem is a special case of the transportation problem where the supply from every source and the demand at every sink are equal to 1. Such a situation arises naturally in the setting of assigning workers to jobs, or of assigning workers to a time schedule.
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.