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We examine a stochastic optimization model of a multiple reservoir water resource system in which the spilled outflows may have a different routing than the turbined outflows. We extend some results about the monotonicity of optimal decision rules, which were known for particular routings, and we show their validity for arbitrary routings of spilled outflows, provided they satisfy an intuitive monotonicity condition. Special cases are when the spilled outflows are expelled from the system, or when the spilled outflows are routed to the next reservoir downstream. The monotonicity of optimal policies and of the corresponding future value function can be exploited to develop efficient computational algorithms based on a dynamic programming methodology, especially when the rewards are given by a concave, piecewise linear function of electricity generation.

Stochastic optimization of multi-reservoir systems with power plants and spillways