Final answer:
The special case that typically requires reformulation to solve an optimization problem is infeasibility. This occurs when there is no set of solution that satisfies all the constraints, necessitating changes to the constraints or objective function.
Step-by-step explanation:
When solving optimization problems, particularly in operations research and linear programming, you may encounter certain special cases that require special attention. The special case that typically requires reformulation of the problem to obtain a solution is infeasibility. Infeasibility occurs when the set of constraints in a problem can't be satisfied simultaneously, meaning there is no possible solution within the defined parameters.
Unlike feasibility, which indicates that there is at least one solution that satisfies all constraints, or slack, which refers to any surplus resources when an inequality constraint is not tight, or boundedness, which assures that the solution does not go to infinity, infeasibility cannot be resolved without changing the original problem statement.
In order to address infeasibility, one may need to relax or remove some constraints, change the values of constants, or even reevaluate and modify the objective function. Only through such reformulations can a previously infeasible problem become solvable.