Response matrix minimization used in groundwater management with mathematical programming: A case study in a transboundary aquifer in Northern Greece

Groundwater has always been considered to be a readily available source of water for domestic, agricultural and industrial use. The last decades, the lack of policymaking for the utilization of groundwater, has led to overexploitation in many areas. The cooperation of a wide range of scientists such as mathematicians, engineers, computer scientists, environmentalists and economists–operation researchers, has led to the design and construction of commercial computer programs concerned on water management and specifically on the optimal distribution of limited water resources using groundwater management models. These combined models, via simulation and optimization algorithms, result in one optimal solution through operations research and mathematical programming methods. The groundwater management models are based on the method of space superposition or the combination of space and time superposition for steady and unsteady state problems, respectively. In the present study, an algorithm is presented, which minimizes the dimension of the response matrix, concerning on two assumptions: the first is the added fixed cost which represents the water supply pumping well and the second is the removal of time superposition. The study area is a transboundary phreatic aquifer in Northern Greece, in the area of Eidomeni, a small Hellenic village just on the borderline with FYROM. The aquifer has a total area of 10.84 km², 26 operating–pumping wells, of which 9 are control points of the hydraulic head. The number of the management periods is 12 months.