lines. Leave the remaining elements of the matrix unchanged. Proceeding in this manner we get a new matrix. v)
Again check, if optimal assignment can be made in the above current feasible solution or not. For this repeat all the sub-steps of step (iii). After repeating the sub-steps, if the number of lines is equal to number of assignments, optimal solution has been obtained. Optimal assignments will always be at the zero locations of the table.
vi)
In case in the above step, optimal solution is not obtained because number of lines is different from number of assignments to be made, again steps (iv) and (v) have to be repeated.
Let us explain the above steps with the help of following example: Example: Four different jobs (J1, J2, J3, and J4) are to be allocated to four different machines (M1, M2, M3, and M4). The set-up costs are assumed to be prohibitively high for changeovers. The cost (in rupees) of producing i th job on jth machine is given in the following matrix):
How should the jobs be assigned to various machines to minimize the total cost? Solution:
222