Operational research on Assignment pptPresentation Transcript
OPERATIONAL RESEARCH (O.R)
O.R is developed “to ensure reduction in
O.R is a scientific approach to problem
For executive decision making which
requires formulation of mathematical,
economic and statistical models for decision
making and controlling.
O.R IS USED FOR
APPLICATION IN PUBLIC SECTOR
CHARACTERISTICS OF O.R
Uses mixed team approach to find optimal
Uses scientific methods to achieve at optimal
Emphasis on overall approach to the system.
Optimizes the total output by maximizing
profit and minimizing cost.
LIMITATION OF O.R
Involves the use of mathematical and
Ignores intangible factors such as better
customer satisfaction, skill attitude of
worker, initiative of management etc.
Usually associated with high cost.
Overuse of assumptions to simplify
mathematical models may not represent a
Assignment is a technique to find out lowest
possible allocable cost of the project by
assigning the best possible least costs to the
jobs and workers.
ASSIGNMENT IS USED
In assigning machines to factory orders.
In assigning sales/marketing people to sales
In assigning contracts to bidders by
In assigning teachers to classes.
In assigning accountants to accounts of the
1. Ensure that the sum is in the matrix form
2. The matrix form is used only in minimization
if it is not a minimization sum then we have to
convert it into minimization sum
3. Number of rows should be equal to number
of columns if number of row is not equal to
number of column then we have to
introduce a “Dummy” column or row to
make it balance.
CONTINUE . . .
4. Row Minima
In this step we have to choose the lowest
element in the row and deduct it from all
5. Column Minima
In this step we choose the lowest element
and deduct it from other numbers in the
CONTINUE. . .
6. Now try to cover maximum zeros using
if the lines are equal to order of matrix the
optimal solution is reached.
ASSIGNING THE JOBS
First select the row or column which has
only one zero
encircle that zero that means that the
assignment is made and all zeros, if any,
in that row or column will be cancelled.
If there are more than one zero in a row or
column then allocate zero from top-bottom
or left-right .
It is better to select the row or column with
OPTIMALITY IS NOT REACHED
If in Step 3. the number of lines is not
equal to order of matrix then the optimal
solution is not reached:
In such matrix there are three elements:
The uncovered elements which are not on
The elements covered by the lines and are
on point of intersection.
Covered elements but not on point of
CONTINUE. . .
Now find the minimum element from the
uncovered elements :
Deduct that element from all uncovered
Add that element to the elements on the
point of intersection.
The other elements should be kept as it is.
CONTINUE . . .
Now new matrix is formed.
And again we have follow the steps.
Now if the number of lines is equal to order
of matrix than optimality is reached or else
again follow the steps.
If the matrix is in the form of maximization
matrix then we have to convert it into the
To convert the maximization matrix into the
minimization we have to select the highest
element in the matrix and deduct that
element from the other elements.
Thus new matrix formed is minimization
matrix all other step remains same.
IF NQ APPEARS
NQ is means Not Assignable.
If NQ appears we have to put “M”.
“M” represents highest possible number.
If any number deducted form “M” than also it
will remain “M”.
Assignment is used to assign the jobs on
It is used to maximize the profit and minimize
If all the steps followed in the proper way the
optimality reached will be effectively useful.