Assignment problem
- 2. ASSIGNMENT MODEL • Assigning of jobs to factors (men or machine) to get most optimum output or get least cost. • Hungarian method is the mostly used method of solving assignment problems. • Types of Assignment problems: (i) Balanced (ii) Unbalanced
- 3. OBJECTIVES •No workers is more than one job. •No job is assigned to more than one worker. •Total time taken to complete a job is minimum. •The work done is cost effective and
- 4. BALANCED ASSIGNMENT•An assignment is called balanced assignment problem if the number of persons (factors) is same as the number of jobs. (number row = number column)
- 5. EXAMPLE : Assign the four tasks to four operators. The assigning costs are given in table.(Minimum Problem)
- 6. Step 1: Reduce the matrix by selecting the smallest value in each row and subtracting from other values in that corresponding row. the smallest value: row A, is 13,row B is 15,row C is 17 and row D is 12. HUNGARIAN METHOD
- 7. HUNGARIAN METHOD Step 2: Reduce the new matrix given in the following table by selecting the smallest value in each column and subtract from other values in that corresponding column. In column 1, the smallest value is 0, column 2 is 4, column 3 is 3 and column 4 is 0.
- 8. HUNGARIAN METHODStep 3: Draw minimum number of lines possible to cover all the zeros in the matrix given in Table Check whether number of lines drawn is equal to the order of the matrix, i.e., 3 ≠ 4. Therefore optimally is not reached.
- 9. HUNGARIAN METHODStep 4: Take the smallest element of the matrix that is not covered by single line, which is 3. Subtract 3 from all other values that are not covered and add 3 at the intersection of lines. Leave the values which are covered by single line. 3 Choose Smallest value not covered line add 3 at the intersection of lines
- 10. HUNGARIAN METHODStep 5: Do for row reduction and column reduction again
- 11. HUNGARIAN METHODStep 6: Assign the tasks to the operators. Select a row that has a single zero and assign by squaring it. Strike off remaining zeros if any in that row or column.
- 12. HUNGARIAN METHODStep 7: Assign the tasks to the operators.
- 13. UNBALANCED ASSIGNMENT•An assignment is called unbalanced assignment problem if the number of persons (factors) is not same as the number of jobs. (number row ≠ number column) (4 rows≠5 columnso unbalanced)
- 14. Example : A company has five machines that are used for four jobs. Each job can be assigned to one and only one machine. The cost of each job on each machine is given in the following table. Dumm y Row 5 Dummy Row D5 Added
- 15. Step 1: Reduce the matrix by selecting the smallest value in each row and subtracting from other values in that corresponding row. HUNGARIAN METHOD
- 16. HUNGARIAN METHOD Step 2: Reduce the new matrix given in the following table by selecting the smallest value in each column and subtract from other values in that corresponding column. Colu mn Number of lines drawn ≠ Order of matrix. Hence not optimal.
- 17. Select the least uncovered element, i.e., 1, subtract it from other uncovered elements, add to the elements at intersection of lines and leave the elements that are covered with single line unchanged as shown in Table. Number of lines drawn ≠ Order of matrix. Hence not optimal.
- 18. Number of lines drawn = Order of matrix. Hence optimality is reached.
- 19. Now assign the jobs to machines, as shown in Table. Now assign the jobs to machines, Job Machine 1 A, D 2 B, C 3 E 4 B,D,E 5 B,C,D
- 20. THANK YOU