The document discusses several assignment problems involving allocating jobs or tasks to machines, employees, clerks or cities in an optimal way to minimize time, cost or maximize returns. Specific problems include assigning 5 jobs to 5 machines to minimize total time, assigning jobs to machines to maximize total returns, assigning 4 jobs to 3 staff to minimize total time, assigning clerks to tasks where some assignments are prohibited, and finding the optimal tour for a salesman to visit 5 cities while minimizing total distance traveled. Solutions to these assignment problems are to be found using techniques like the assignment algorithm, Hungarian method, column reduction, row reduction and prohibiting certain assignments.

1. Assignment
Problem
ITFT COLLEGE 1
4/26/2014

2. • Meaning
• Methods
• Steps
• Practical Problems
ITFT COLLEGE 2
4/26/2014

3. ITFT COLLEGE 3
4/26/2014
Allocating various resources
to various activities
On one to one basis
The time and cost are
minimised
Sale and profit are
maximised

4. •The Hungarian
Mathematician
D. Konig
developed
simpler & more
efficient
method.
ITFT COLLEGE 4
4/26/2014

5. Minimisation Problem
Maximisation Problem
Unbalanced Problem
Prohibitive Problem
Travelling Salesman Problem
Air-Crew Problem
ITFT COLLEGE 5
4/26/2014

6. Solution
Re-Assignment
Making an Assignment
Column Reduction
Row Reduction
ITFT COLLEGE 6
4/26/2014

7. ITFT COLLEGE 7
4/26/2014
Problem: Five jobs are to be assigned to 5 machines to
minimize the total time required to process the jobs on
machines. The time in hours for processing each job on
each machine are given in the matrix below. By using
assignment algorithm make the assignment for
minimizing the time of processing.
Machines (time in hours)
Jobs V W X Y Z
A 2 4 3 5 4
B 7 4 6 8 4
C 2 9 8 10 4
D 8 6 12 7 4
E 2 8 5 8 8

8. • Problem: A company has five jobs V, W, X, Y and Z and
five machines A, B, C, D and E. The given matrix shows
the return in Rs. of assigning a job to a machine. Assign
the jobs to machines so as to maximize the total
returns. Machines
Returns in Rs.
ITFT COLLEGE 8
4/26/2014
Jobs A B C D E
V 5 11 10 12 4
W 2 4 6 3 5
X 3 12 5 14 6
Y 6 14 4 11 7
Z 7 9 8 12 5

9. • Problem: A manager has 4 jobs on hand to be
assigned to 3 of his clerical staff. Clerical staff differs
in efficiency. The efficiency is a measure of time taken
by them to do various jobs. The manager wants to
assign the duty to his staff, so that the total time
taken by the staff should be minimum. The matrix
given below shows the time taken by each person to
do a particular job. Help the manager in assigning the
jobs to the personnel.
ITFT COLLEGE 9
4/26/2014
Jobs Men (time taken to do job in hours)
X Y Z
A 10 27 16
B 14 28 7
C 36 21 16
D 19 31 21

10. • Consider a problem of assigning four clerks to four
tasks. The time (hours) required to complete the
tasks is given below:
Clerk 2 cannot be assigned to task A and Clerk 3
cannot be assigned to task B. Find all the optimal
assignment solutionITFT COLLEGE 10
4/26/2014

11. • Problem: A salesman stationed at city A has to decide
his tour plan to visit cities B, C, D, E and back to city A I
the order of his choice so that total distance traveled is
minimum. No sub touring is permitted. He cannot
travel from city A to city A itself. The distance between
cities in Kilometers is given below:
ITFT COLLEGE 11
4/26/2014
Cities A B C D E
A ∞ 16 18 13 20
B 21 ∞ 16 27 14
C 12 14 ∞ 15 21
D 11 18 19 ∞ 21
E 16 14 17 12 ∞