Stochastic Optimization Models for Lake Eutrophication Management

We develop a general framework for the study and the control of the eutrophication process of (shallow) lakes. The randomness of the environment (variability in hydrological and meteorological conditions) is an intrinsic characteristic of such systems that cannot be ignored in the analysis of the process or by management in the design of control measures. The models that we suggest take into account the stochastic aspects of the eutrophication process. An algorithm, designed to handle the resulting stochastic optimization problem, is described and its implementation is outlined. A second model, based on expectation-variance considerations, that approximates the "full" stochastic model can be handled by standard linear or nonlinear programming packages. A case study illustrates the approach; we compare the solutions of the stochastic models, and examine the effect that randomness has on the design of good management programs.
KEYWORDS: lake eutrophication; eutrophication management; stochastic programming; recourse model; water quality management; probabilistic constraints

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