Optimal Capacities for a Multireservoir System Using the Linear Decision Rule

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Abstract
A chance constrained formulation of a multireservoir system is considered. Minimum and maximum release requirements, minimum pool level, and minimum freeboard capacity are specified by the management for each reservoir. The management also specifies the maximum probabilities beyond which these requirements are not violated. By proposing linear decision rules for the releases, the authors reduce the chance constrained formulation to an ordinary linear programing formulation. The linear decision rule states that the release from a reservoir during a given time period is defined by the difference between the ‘net initial storage’ and a ‘decision parameter’ for that reservoir during that period. The objective function considers only the total cost of reservoirs, because the primary objective is to meet the various given demands at a minimum cost. This model has been applied to the Minnesota River basin.