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Title: Benders decomposition method in reservoir management
Author: Buchanan, Crawford S.
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 1999
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Multi-stage stochastic linear programming provides a framework in which to model and solve decision making problems that contain uncertain data. In this thesis the main stages in the process of modelling and solving a large-scale multi-stage stochastic linear programme (MSLP) are examined. The principal motivation for this research is the study of the electricity generation network of Southern Brazil. This network contains a high proportion of hydro-electric generation plants, and so the stochasticity of the future inflows has a large influence on decisions. The formulation of MSLPS is difficult within existing algebraic modelling languages. Many MSLPs can be formulation as a set of recurrences. We present a new algebraic modelling language, sMAGIC, that uses the recursive definition of sub-models to aid in the specification of MSLPs. The Benders Decomposition algorithm exploits the sparse structure of MSLPs, achieving a considerable reduction in the time taken to solve MSLPs over direct solution methods, such as the simplex method. In addition, the basic Benders Decomposition algorithm can be extended and is well suited to parallelisation. We present results that show that some of the extensions to the basic algorithm improve the performance of the solver in all cases, while others provide improvements only for particular test problems. The research from our parallel implementation on a network of workstations give near linear speedups. Sampling techniques can be incorporated within the Benders Decomposition method. This allows an approximation to the solution of MSLPs that are too large to solve using Benders Decomposition to be obtained. A Benders Decomposition algorithm that incorporates Monte Carlo is guaranteed to converge asymptotically to the actual solution. To improve the speed of this algorithm, an additive approximation to the cost function is used to guide an importance sampling technique.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available