Conditional chance‐constrained model for reservoir control

Abstract

This paper presents a model for designing the optimum control policies of a reservoir serving an agricultural demand area. Policies are designed to maximize the expected agricultural benefits to the area. The demand for irrigation water depends on both the crops planted and the rainfall in the area. Explicit account is taken of both, particularly the stochastic nature of the rainfall, which is characterized as a joint log normally distributed random variable. The problem lends itself to a conditional chance‐constrained formulation. However, the dependency of the rainfall distributions and agricultural functions does not lead to conveniently solvable deterministic equivalents. As a result, decision rules are defined for each of a series of sequences of rainfall intervals. The problem then reduces to linear programing form. The novelty of the approach lies in the fact that the decision rules are conditional rules whose parameters depend on previous observations of the random variable.