Author(s)

B. F. Lamond & P. Lang

Abstract

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. Keywords: multi-reservoir system, hydro-power production, turbined outflow routing, spilled outflow routing, arborescent network, incidence matrix, stochastic optimization model, stochastic dynamic programming, convex analysis, monotone optimal policy. 1 Introduction The problem of optimizing long-term production for a hydroelectric system with multiple reservoirs is notoriously difficult, and most optimization models assume a planning horizon in which time is discretized into a finite number of fixed length intervals or periods. Due to the large variability of weather systems, the natural hydraulic inflows are represented by random variables, thus forming a stochastic process whose evolution laws are investigated by statistical analysis of time series data from historical records. Because typical inflow processes were found to

Keywords

multi-reservoir system, hydro-power production, turbined outflow routing, spilled outflow routing, arborescent network, incidence matrix, stochastic optimization model, stochastic dynamic programming, convex analysis, monotone optimal policy.