ITFT - Assignment problem
- 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 ∞