Unbalanced Assignment Problem

The Unbalanced Assignment Problem is a variation of the classic Assignment Problem in Operations Research, where the number of tasks (jobs) does not equal the number of agents (workers or machines). This imbalance can occur in two ways: either there are more tasks than agents, or more agents than tasks. To solve it using standard assignment methods (like the Hungarian Algorithm), the problem is first converted into a balanced form by adding dummy rows or columns with zero cost. These dummy entries represent fictitious tasks or agents, ensuring that each real agent is assigned to exactly one task, and vice versa. The objective remains to minimize the total cost or time of assignments while maintaining feasibility.

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