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Show X Qw, * Dk, k- 1 K, t= l N ( 3.8) wek where D^ is the demand for the km water supply agency in year t 2. Drawdown control One of the management objectives is to restrict drawdowns in the aquifer ( or maintain heads Hyt at node ( ij) for year t above prescribed values). The most severe drawdown at each node of interest at any time will occur at the well nodes and only constraints on the drawdowns at the well nodes thus need to specified. For each well node w, then the minimum head over an N year planning period should be higher than a minimum allowable head Hw min at that node. Note that this constraint may be alternately stated as a limit on the maximum drawdown at the node. m i n H ^ H ™ n w- 1 W ( 3.9) Usually these constraints are specified for each year and often for all the nodes. It is rather obvious that considering these constraints only at the wells, which are the points of maximum drawdown, affords a considerable saving in the mathematical size of the optimization problem, without any loss of generality. Often head maintenance at other selected nodes may be desirable. In such a case those nodes could also be included in the specification of this constraint. By constraining only the minimum head over the N year period at each well, further savings are achieved over a model that explicitly specifies constraints for each year. This specification is infeasible in the linear formulation of the problem adopted by other modelers. The only disadvantage is the likelihood of some discontinuities in the evaluation of the gradients of this constraint with respect to the decision variables. 3. Water rights ( Preservation of flow across agency boundaries) The water rights of an agency are preserved by requiring that the average annual groundwater flow entering/ leaving its boundaries be at a prescribed level. Procedures for computing the flow F^ across a boundary in year t were presented earlier. The constraint for preservation of flow across each boundary may then be specified as N ( 1- TOL^ < u l £ ( l+ TOLb) F£ b - 1.... B ( 3.10) where TOLb is some acceptable tolerance for deviation in the flow across the boundary b. Fv is the prescribed flow across boundary b. 49 |