Question

If the opportunity cost for an assignment that is not part of the optimal solution equals zero, then there must be multiple optimal solutions.

Answer 1

The steps of the assignment solution method are:

1. Perform row reductions by subtracting the minimum value in each row from all row values.

2. Perform column reductions by subtracting the minimum value in each column from all column values.

3. In the completed opportunity cost table, cross out all zeros, using the minimum number of horizontal or vertical lines.

4. If fewer than m lines are required (where mthe number of rows or columns), sub-tract the minimum uncrossed value from all other uncrossed values, and add this same minimum value to all cells where two lines intersect. Leave all other values unchanged, and repeat step 3.

5. If m lines are required, the tableau contains the optimal solution and m unique assignments can be made. If fewer than m lines are required, repeat step 4

Yes,if the opportunity cost of an assignment that is not part of the optimal solution equals zero,then there must be multiple optimal solutions.

An Assignment problem can have more than one optimal solution, which is called multiple optimal solutions. The meaning of multiple optimal solutions is – The total cost or total profit will remain same for different sets or combinations of allocations. It means we have the flexibility of assigning different allocations while still maintaining Minimum (Optimal) cost or Maximum (Optimal) profit.We can detect multiple optimal solutions when there are multiple zeroes in any columns or rows in the final (Optimal) table in the Assignment problem.

Like a transportation problem, an assignment model can be unbalanced when supply exceeds demand or demand exceeds supply. For example, assume that, instead of four teams of officials, there are five teams to be assigned to the four games. In this case a dummy column is added to the assignment tableau to balance the model. In solving this model, one team of officials would be assigned to the dummy column. If there were five games and only four teams of officials, a dummy row would be added instead of a dummy column. The addition of a dummy row or column does not affect the solution method.