Assignment Problem XII

What is an unbalanced assignment problem?

• A problem with more agents than tasks or vice versa

• A problem with only profit entries

• A problem with missing steps

• A problem where assignment is optional

What is the basic requirement to apply the Hungarian Method?

• Matrix must be unbalanced

• Only profit values must be present

• Matrix must be square (same number of rows and columns)

• Matrix should have no restrictions

When do we add a dummy row or column to the assignment matrix?

• When matrix is square

• When there are restricted assignments

• When matrix is unbalanced

• When optimal solution is not found

True or False: The Hungarian Method can be used for both minimization and maximization problems.

Why do we convert a profit matrix to a cost matrix in maximization problems?

• To simplify calculations

• Because Hungarian Method is a minimization method

• Because cost is always less than profit

• To change the matrix shape

How are restricted assignments handled in the matrix?

• Replace the restricted cell with 0

• Leave it blank

• Replace the cell with a large number or ∞

• Ignore that row

Why must an assignment matrix be square before applying the Hungarian Method?

• To allow equal comparison

• So every task can be assigned to exactly one agent

• Because software requires it

• To remove restrictions

You are given a 3×4 cost matrix. What is your first step to apply the Hungarian Method?

• Add a dummy column

• Add a dummy row

• Begin column-wise subtraction

• Multiply values by -1

In a 3×3 matrix, Task 2 cannot be done by Agent B. How will you handle this?

• Delete Task 2

• Assign it to someone else directly

• Replace cell (B,2) with a large number

• Replace cell with 0

How do you know if alternate optimal solutions exist?

• When the matrix is not square

• When multiple assignments give the same total cost

• When cost is very high

• When restricted assignments are present