Page 153 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes
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Caution Assignment Problem may not necessarily have an optimal solution. It may also
have multiple solutions to a given problem.

7.5 Summary

 An assignment problem seeks to minimize the total cost assignment of n workers to n
jobs.

 It assumes all workers are assigned and each job is performed.
 An assignment problem is a special case of a transportation problem in which all supplies
and all demands are equal to 1; hence assignment problems may be solved as linear
programs.
 Applications of assignment problems are varied in the real world.
 It can be useful for the classic task of assigning employees to tasks or machines to production
jobs, but its uses are more widespread.

7.6 Keywords

Allocate: To distribute according to a plan; allot
Assignment Problem: Assignment problem is used to assign n number of resources to n number
of activities so as to minimize the total cost or to maximize the total profit of allocation in such
a way that the measure of effectiveness is optimized.

7.7 Review Questions

1. Describe the assignment problem giving a suitable example. Give two areas of its
application.
2. Explain the difference between a transportation problem and an assignment problem.

3. Give the mathematical formulation of the assignment problem.
4. Show that the optimal solution of an assignment problem is unchanged if we add or
subtract the same constant to the entries of any row or column of the cost matrix.

5. Describe the method of drawing minimum number of lines in the context of assignment
problem. Name the method.
Problems

6. A firm plans to begin production of three new products. They own three plants and wish
to assign one new plant. The unit cost of producing i at plant j is Cij as given by the
following matrix. Find the assignment that minimizes the total unit cost.

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