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Show T, a~„ QP « ^ A n ™ 1 ™ m - 1 •••• M ( 2- 25) *- d mn ^ n m n The optimization model requires limiting values to a maximum pumping rate, and to a minimum drawdown in Girinski potential. Solutions of the dewatering problem were obtained for QPMAXn of 1, 2,4 and 6 nvVday, with Agminm value ranging from 5 to 150 ( see Table 2.2). A Successive Linear Programming ( SLP) model ( Zhang et al, 1985) was used to obtain solutions to the objectives represented by equations 2.15, 2.16 and 2.17. The program used allows for both linear & nonlinear optimization problems. The cost function used was CF( QPn) = X C* T* Y* QPn* E* Ln ( 2.25) n where C - cost coefficient T - the length of a time period y - unit weight of water E - the pumping efficiency the values of L^, the lift at the pump location, are computed by transforming the Girinski potential at n to the head hn, using equation 2.5. They are obtained by solving equation ( 2.5) for h in terms of G, the Girinski potential. The model was run with a cost coefficient of 1.82, a 1 year time period, and a pump efficiency of 0.9. A mixed integer solution algorithm is generally used for situations where fixed costs must be considered as in equation 2.17. The solution presented here utilized SLP and a heuristic to account for the mixed integer nature of the problem. Fixed costs ( FC) where included in the cost function as Cost = £ ( C* T* y* QPn* Ln* E) + FCn ( 2.27) J Table 2.1 summarizes the results from the three applications. Parametric applications with upper bounds on individual well pumpage varying from 1 to 6 m3/ day were performed, with the minimum drawdown in the Girinski potential varied from 5 to 150m3/ day. 20 |