Page 167 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes Step 5: Trial assignment.
Job A B C D E
Machinist 1 3.20 2.30 5.10 0 1.20
2 0.60 0 2.30 1.10 1.80
3 1.70 1.90 0 4.00 2.30
4 3.20 2.30 0 1.00 0
5 0 0.70 0.70 0.70 0.70

Step 6: Calculation of maximum profit for the assignment.
From To Total Sales (`)
A 5 0
B 2 8.40
C 3 11.10
D 1 10.10
E 4 8.00
Total profit 37.60

Inference
The maximum total profit for the assignment is ` 37.60. And the job to be declined is A as the
machinist available 5th is supposed to be fictitious.

Self Assessment

Fill in the blanks:

4. If the given matrix is not a ………….matrix, the assignment problem is called an unbalanced
problem
5. A dummy row(s) or column(s) with the cost elements as ………….. is added to convert the
matrix of an unbalanced assignment problem as a square matrix.
6. A given assignment problem can be classified into balanced or unbalanced on the basis of
……………………

8.5 Routing Problems/Travelling Salesman Problems

A salesman, who wishes to travel through his territory visiting various cities, wishes to visit
one city only once and wants to come back to the city from where be started and then go to other
cities one after other. As he is a single person who has to visit various cities, mere Reduction
Theorem Rules or Hungarian approach would not help in arriving at optimum solution always.
Hence, a modified solution would be found out to arrive at an optimal solution.

162 LOVELY PROFESSIONAL UNIVERSITY