This document discusses operations research and the assignment problem. It defines operations research as applying scientific methods to optimize systems. The assignment problem aims to minimize the cost or time of assigning jobs to people. For maximization problems, the Hungarian method cannot be directly applied, so values are subtracted from the maximum to convert it to a minimization problem. An example shows assigning classes to professors, with the optimal solution being C1 to P2, C2 to P1, etc. for a total efficiency of 330.

1. OPERATIONS RESEARCH
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2. OPERATION RESEARCH
“Operations Research as the application of a
scientific methods, techniques and tools to
operation of a system with optimum solutions
to the problems”.
“Operation Research is the use of scientific
methods to provide criteria for decisions
regarding man, machine, systems involving
repetitive operations”.

3. ASSIGNMENT PROBLEM
“The assignment problem is a special case of
the transport problem, where the objective is
to minimize the cost or time of completing a
number of jobs by a number of persons and
Maximize efficiently Revenue, sales etc.

4. MAXIMIZATION IN
ASSIGNMENT PROBLEM
Hungarian Method cannot be applied to
maximization problems. Therefore we reduce
it to maximization problem by subtracting
every value form the highest value of the
Matrix and then proceed as usual.

5. EXAMPLE
Classes
Professors
P1 P2 P3 P4
C1 70 75 80 65
C2 80 70 65 75
C3 75 76 85 80
C4 60 65 70 90

6. Since it is a Maximization problem we
subtract every value from the maximum
value of 90.
Classes
Professors
P1 P2 P3 P4
C1 20 15 10 25
C2 10 20 25 15
C3 15 20 5 10
C4 30 25 20 0

7. Classes
Row Reduced Matrix
Professors
P1 P2 P3 P4
C1 10 5 0 15
C2 0 10 15 5
C3 10 15 0 5
C4 30 25 20 0

9. Optimum solution
C1 – P2 75
C2 – P1 80
C3 – P3 85
C4 – P4 90
330 Max Efficiency

10. THANK YOU