Page 142 - DCOM303_DMGT504_OPERATION_RESEARCH

Unit 7: Assignment Problem – Balanced

5. Allocation of salesmen to different sales areas. Notes
6. Allocation of clerks to various counters.
In all the cases, the objective is to minimize the total time and cost or otherwise maximize the
sales and returns.
Self Assessment

Multiple Choice Questions:
1. An assignment problem will have the following solution
(a) optimal (b) unique
(c) multiple (d) all of the above

2. Maximization assignment problem is transformed into minimization problem by
(a) Adding each entry in a column from the maximum value in that column
(b) Subtracting each entry in a column from maximum value in that column

(c) Subtracting each entry in the table from the maximum value in that table
(d) Any one of the above
3. The main objective of an assignment problem is to
(a) Minimize the total cost (b) Maximize the sales and returns.
(c) Both (a) and (b) (d) None

7.2 Types of Assignment Problem

The assignment problems are of two types. It can be either
(i) Balanced or
(ii) Unbalanced.

If the number of rows is equal to the number of columns or if the given problem is a square
matrix, the problem is termed as a balanced assignment problem. If the given problem is not a
square matrix, the problem is termed as an unbalanced assignment problem.
If the problem is an unbalanced one, add dummy rows /dummy columns as required so that the
matrix becomes a square matrix or a balanced one. The cost or time values for the dummy cells
are assumed as zero.

Self Assessment

Fill in the blanks:
4. An assignment problem is said to be unbalanced when ...................................
5. When the number of rows is equal to the number of columns then the problem is said to
be .................................... assignment problem.
6. For solving an assignment problem the matrix should be a ................................ matrix.

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