In an assignment problem if number of rows is greater than number of columns, then dummy .…. is added.

Answer

To solve the question: "In an assignment problem if the number of rows is greater than the number of columns, then dummy .... is added," we need to fill in the blank correctly. Here’s the step-by-step solution:

### Step-by-Step Solution:

1. **Understanding the Assignment Problem**:
- An assignment problem involves assigning resources (like workers, machines, etc.) to tasks in such a way that the total cost is minimized or the total profit is maximized.

**Hint**: Remember that an assignment problem typically involves a cost matrix where rows represent resources and columns represent tasks.

2. **Identifying the Condition**:
- The question states that the number of rows is greater than the number of columns. This means there are more resources than tasks.

**Hint**: Think about what happens when there are more workers than jobs.

3. **Balancing the Assignment Problem**:
- For an assignment problem to be solvable efficiently, it should be balanced. A balanced assignment problem has an equal number of rows and columns.

**Hint**: Consider how you can make the number of rows equal to the number of columns.

4. **Adding Dummy Elements**:
- To balance the assignment problem when there are more rows than columns, we add dummy columns. A dummy column represents a task that does not require any resources, effectively allowing us to balance the matrix.

**Hint**: What do we call a column that does not correspond to a real task but helps in balancing?

5. **Final Answer**:
- Therefore, the correct completion of the statement is: "In an assignment problem if the number of rows is greater than the number of columns, then dummy **column** is added."

### Final Answer:
In an assignment problem if the number of rows is greater than the number of columns, then dummy **column** is added.