When the number of agents exceeds the number of tasks in an assignment problem,one or more dummy tasks must be introduced in the LP formulation or else the LP will not have a feasible solution.

Question

Quizplus · Accepted Answer

In an assignment problem, if the number of agents exceeds the number of tasks, introducing dummy tasks (with zero cost) ensures that the problem remains balanced and every agent is assigned to a task, but not having dummy tasks does not mean the LP will not have a feasible solution; it just means some agents will not be assigned tasks.

When the Number of Agents Exceeds the Number of Tasks