A multiperiod approach to the solution of groundwater management problems using an outer approximation method

In the past few years several groundwater management models have been presented, related to the decision making process for an optimal remediation design. The majority of these models consider the remediation time as a single management period. Existing groundwater management models using a multiperiod design are based on a dynamic programming approach. Such models require extensive computational effort that increases drastically as the number of decision variables increases. In order to overcome this difficulty, a simpler multiperiod approach is presented in this work. The outer approximation (OA) method applies the cutting hyperplane optimization technique for the determination of a global optimal solution. In this work, the method is customized to accommodate a multiperiod design. This customization is based on the introduction of the decision variables (pumping rates) into the optimization model while the basic concept of the OA method remains unchanged. The main characteristic of this approach is that the management periods are independent of each other. The number of decision variables is equal to the number of wells times the number of management periods and all the constraints are evaluated at the end of the remediation horizon. This approach requires the derivative calculation of only one constraint at each optimization step which reduces the computational effort. The method is tested on a hypothetical aquifer remediation scenario and an actual large-scale contaminated site, illustrating the cost-effectiveness of the method.