Page 141 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes Since only one job can be allotted to a person.

 = Sum of all persons with first job = 1, since a job can be assigned to only one person.

th
In general, sum of all jobs assigned to j person = 1
 
i.e., 
And sum of all persons with ith job = 1

 
i.e., 
And initial basic feasible solution can be found out by following:
1. Reduction Theorem

2. Hungarian Approach
Similarly, many real life problems can be solved such as assigning number of classes, for
number of rooms, number of drivers to number of trucks or vice versa, number of teachers to
number of classes, etc.
Reduction Theorem can be used for solving assignment problems with an objective of
minimization of costs. For such maximization assignment problems, commonly used rules are:

1. Blind fold assignment/assignment by intuition.
2. Converting the maximization problem into minimization by considering the largest
element in the whole matrix.

3. Converting the maximization problem into minimization by using negative signs for all
the elements in the profit matrix.

Notes Assignment Problem is a variation of the transportation problem with two
characteristics:
1. Cost matrix is a square matrix
2. The optimal solution for the problem would always be such that there would be
only one assignment in a given row or column of the cost matrix

7.1 Application of Assignment Problem

Few applications of assignment problem are as follows:
1. Assignment of employees to machines.

2. Assignment of operators to jobs.
3. Effectiveness of teachers and subjects.
4. Allocation of machines for optimum utilization of space.

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