δ-Form approximating problem for a conjunctive water resource management model

A nonlinear coupled simulation and optimization model is formulated to find the optimal operating policies with a minimal cost for the conjunctive management of hydraulically interacting surface and ground water supplies. The term representing the pumpage cost in the objective function of the management model causes nonlinearity that cannot be put in a quadratic form as in the traditional approach, since drawdown in that term is a function of well pumpage and other parameters. To eliminate the nonlinearity, delta-form approximating model is formulated with a particular emphasis on the concave function of the transformed objective function. The original problem in a nonlinear form is solved by coupling the solver with a random number generator to provide the model with a different initial guess each time. However, the delta-form approximating problem is formulated as a linear mixed integer programming model. Optimal operating policies and the operation costs obtained from both models are found to be in good agreement. (C) 1999 Elsevier Science Ltd. All rights reserved.