The document describes 3 assignment optimization questions: 1) Assign 3 programmers to 3 application programs to minimize total computer time based on an expertise matrix. 2) Assign 5 employees to 5 jobs to minimize total man-hours based on an effectiveness matrix showing time for each employee on each job. 3) Assign 5 existing agencies to supply product to 5 additional cities to minimize total travel distance based on a distance matrix between agencies and cities.

1. Assignment Model

2. Question 1
A computer centre has three expert programmers. The centre wants three
application programmes to be developed. The head of the computer centre, after
studying carefully the programmes to be develop, estimates the computer time
in minutes required by the experts for the application programmes as follows.
A B C
1 120 100 80
2 80 90 110
3 110 140 120
Programmes
Programmers
Assign the programmers to the programmes in such a way that the total computer
time is minimum.

3. Question 2
A department has five employees with five jobs to be performed. The time (in
hours) each men will take to perform each job is given in the effectiveness
matrix.
I II III IV V
A 10 5 13 15 16
B 3 9 18 13 6
C 10 7 2 2 2
D 7 11 9 7 12
E 7 9 10 4 12
How should the jobs be allocated, one per employee, so as to minimize the total
man-hours

4. Question 3
A pharmaceutical company is producing a single product and is selling it through
five agencies situated in different cities. All of a sudden, there is a demand for
the product in another five cities not having any agency of the company. The
company is faced with the problem of deciding on how to assign the existing
agencies to despatch the product to needy cities in such a way that the travelling
distance is minimised. The distance between the surplus and deficit cities (in km)
is given in the following table.
a b c d e
A 160 130 115 190 200
B 135 120 130 160 175
C 140 110 125 170 185
D 50 50 80 80 110
E 55 35 70 80 105
Determine the optimum assignment schedule.