What is Prohibited or Restricted Assignment problem?

Prohibited or Restricted problem: A Prohibited problem is the one in which there are one or more restrictions. E. g. say there are 4 contractors – C1, C2, C3 & C4. And there are 4 roads to be repaired – R1, R2, R3 & R4. But contractor C2 cannot or is not allowed to work on R3. This is a prohibited problem

Then we assign a very high or infinite value (represented by M) to C2-R3 and proceed with solution. Throughout the solution steps, M does not change. Since M is infinity, no assignment is possible in M.

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Steps –

1. Take Dummy (if required) & then convert in Regret matrix (if required)
2. Do Row minimization and Column minimization.
3. Cover all Zeroes in the Table with Minimum possible lines. (Start from maximum zeroes, either row-wise or column-wise).
4. If optimal, find assignment.
5. If not optimal, write next table, change values & check again with Minimum possible lines.
6. Continue the iterations till optimal solution is reached.