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Show Aguado and Remson ( 1974) present linear programming management models for a number of aquifer systems. Finite difference approximations of the governing differential equations are included as constraints in the model. Hydraulic heads and pumping rates are considered directly as decision variables. Solutions are presented for 1) One- Dimensional Confined Aquifer with Fixed Head Boundaries, 2) One- Dimensional Unconfined Aquifer with Fixed Head Boundaries, 3) Two- Dimensional Confined Aquifer with Fixed Head Boundaries, 4) One- Dimensional Confined Aquifer Under Transient Conditions and 5) One- Dimensional Unconfined Aquifer Under Transient Conditions. The objective, in all cases, is to maximize hydraulic head at the well points with drawdown and pumping constraints. Unconfined conditions require the linearization of the steady- state equations with respect to the square of the hydraulic heads. Transient conditions were treated by discretizing overtime and space, and including separate sets of equations for each time step in the management model. Aguado et al ( 1974) conducted a dewatering study for a dry dock excavation site. An optimal plan is presented, including well locations and pumping rates to maintain ground water levels below specified maximums. The objective was to minimize pumping. Aguado and Remson ( 1980) extended the dewatering problem to consider fixed charges in the cost of the project. The objective was modified to minimize the sum of variable pumping costs and fixed costs incurred when wells are installed. This problem requires a mixed integer linear programming algorithm to obtain a solution. The solution in the latter study is less dependent on the finite difference grid; not all nodes along the excavation are well sites, as was the case in the study conducted by Aguado et al ( 1974). A further extension of ground water management models using the embedding method is contributed by Alley, Aguado and Remson ( 1976). Finite difference approximations for the partial differential equations governing two- dimensional transient flow are presented. The management model required separate linear programming models for each 5- day interval ( 20 day time period) to obtain head distributions and pumping requirements. Starting conditions for each model are obtained from the solution for the previous time step. This approach allows for short term objectives to differ in a long range management plan. Wanakule and Mays ( 1986) present an interesting application of the embedding approach to the Edwards aquifer in Texas that utilizes mathematical decomposition and augmented lagrangians for a solution of the optimization problem. Their computation times and mathematical problem sizes are, however, still quite large, and the degree of success of their approach with large problems is still rather doubtful. It is interesting to note that their decomposition of the embedded formulation is for all practical purposes a decoupling of the finite difference simulation from the optimization sequence. Where the problem is highly nonlinear, and/ or large, their algorithm shows a significant increase in the number of evaluations of the simulation ( finite difference) subprogram relative to the number of evaluations necessary for the response matrix formulations. Also, if a fine discretization of the physical problem domain is desired, their scheme fails to overcome the primary limitation of the embedding formulation, which is a greater than quadratic increase in the size of the mathematical problem to be solved. Tung and Koltermann ( 1985) also review computational experience with the embedding approach, and report that the computational and memory requirements increase rapidly and significantly as the problem size increases. 4 |