Nested Benders decomposition and dynamic programming for reservoir optimisation

Abstract

This paper presents a computational comparison of nested Benders decomposition and dynamic programming (DP) for stochastic optimisation problems arising from the optimisation of hydro-electric generation from hydraulically linked reservoirs. The examples considered have between 3 and 17 reservoirs, two weather states, three runoff patterns and five periods. The examples are solved exactly by the simplex method and nested Benders decomposition and solved approximately by discrete dynamic programming (DP). A full version of DP is used for examples with 3 and 4 reservoirs, and a decomposition method is used for all examples. The full DP results are within 1% of optimal and the DP decomposition results are within 3.2% of optimal. Timings are given for serial and parallel versions of the algorithms. An analysis is given of how the different methods scale with the number of periods, reservoirs, weather states and runoff patterns, and also how applicable they are to more general problems.