Groundwater quantity management problems with fixed charges have been formulated in the past as mixed integer and linear programming problems. In this paper a new methodology is presented where the fixed charges are incorporated into the objective function in an exponential form and the problem is solved as a concave minimization problem. The principal difficulty in the minimization of a concave function over a linear or nonlinear set of constraints is that the local minima which are determined by the classical minimization algorithms may not be global. In an effort to circumvent this problem the outer approximation method is introduced. This method is applicable to the global minimization of a concave function over a compact set of constraints. In the present work the outer approximation is applied to concave minimization problems over a convex compact set of constraints. Two applications of the method to groundwater management problems are presented herein, and the results are compared with an existing solution obtained using a different optimization approach.