Model based optimization of reservoir water flooding is an ill-posed problem where significantly different control strategies deliver near identical Net Present Values (NPVs). Discovering and exploiting the existence of "redundant" control strategies - particularly those in close proximity to an optimal strategy - is valuable since this offers operational flexibility in reservoir management. To identify such 'flexible strategies' this thesis proposes a workflow to characterize the space of feasible solutions. The feasible region or feasible solution space consists of all control strategies that deliver an NPV within some threshold from an optimal value. Ensemble-based optimization is performed with strong Wolfe line search to identify an optimal control strategy. The BFGS scheme is used to iteratively approximate the Hessian matrix. One dimensional exploration is performed along the singular vector directions that characterize the null space of the Hessian. A thorough exploration results in an accurate characterization of the feasible region. Such an approach however is computationally intractable in case of realistic reservoirs with multiple hundred controls. To address this, a high-dimensional polytope is first defined using the end points from the exploration step. Subsequently, an innovative cross-section constrained maximum volume ellipsoid is inscribed within this polytope to generate an ellipsoidal approximation of the feasible region. Validation results are then presented which show that even one ellipsoid centred at the optimum control vector coordinate provides a conservative description of the feasible solution space.