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Operations Research - Assignment Problems
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ITFT COLLEGE 1
Assignment Problem
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ITFT COLLEGE 2
TABLE OF CONTENT
•Meaning•Methods• Steps•Practical Problems
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ITFT COLLEGE 3
MEANING04/10/2023
Allocating various resources to various activities
On one to one basis
The time and cost are minimised
Sale and profit are maximised
ITFT COLLEGE 4
Assignment Problem
• The Hungarian Mathematician D. Konig developed simpler & more efficient method.
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ITFT COLLEGE 5
Methods of Assignment Problem
Minimisation ProblemMaximisation ProblemUnbalanced ProblemProhibitive Problem
Travelling Salesman ProblemAir-Crew Problem
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ITFT COLLEGE 6
Steps to follow
Solution
Re-Assignment
Making an Assignment
Column Reduction
Row Reduction
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ITFT COLLEGE 7
Minimization Problem04/10/2023
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 4B 7 4 6 8 4C 2 9 8 10 4D 8 6 12 7 4E 2 8 5 8 8
ITFT COLLEGE 8
Maximization problem• 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.
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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
ITFT COLLEGE 9
Unbalanced problem• 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.
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Jobs Men (time taken to do job in hours)X Y Z
A 10 27 16B 14 28 7C 36 21 16D 19 31 21
ITFT COLLEGE
Prohibitive problem• 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 solution
10
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ITFT COLLEGE 11
Travelling Salesman Problem• 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:
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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 ∞
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