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Type: Journal article
Title: A novel solution for stochastic dynamic game of water allocation from a reservoir using collocation method
Author: Homayounfar, Mehran
Ganji, Arman
Martinez, C. J.
Citation: Water Resources Management, 2011; 25(13):3427-3444
Publisher: Kluwer Academic Publishing
Issue Date: 2011
ISSN: 0920-4741
School/Discipline: School of Civil, Environmental and Mining Engineering
Statement of
Mehran Homayounfar & Arman Ganji & C. J. Martinez
Abstract: In this study, a continuous model of stochastic dynamic game for water allocation from a reservoir system was developed. The continuous random variable of inflow in the state transition function was replaced with a discrete approximant rather than using the mean of the random variable as is done in a continuous model of deterministic dynamic game. As a result, a new solution method was used to solve the stochastic model of game based on collocation method. The collocation method was introduced as an alternative to linear-quadratic (LQ) approximation methods to resolve a dynamic model of game. The collocation method is not limited to the first and second degree approximations, compared to LQ approximation, i.e. Ricatti equations. Furthermore, in spite of LQ related problems, consideration of the stochastic nature of game on the action variables in the collocation method would be possible. The proposed solution method was applied to the real case of reservoir operation, which typically requires considering the effect of uncertainty on decision variables. The results of the solution of the stochastic model of game are compared with the results of a deterministic solution of game, a classical stochastic dynamic programming model (e.g. Bayesian Stochastic Dynamic Programming model, BSDP), and a discrete stochastic dynamic game model (PSDNG). By comparing the results of alternative methods, it is shown that the proposed solution method of stochastic dynamic game is quite capable of providing appropriate reservoir operating policies.
Keywords: Stochastic model; Reservoir operation; Game theory; Collocation method
Rights: © Springer Science+Business Media B.V. 2011
RMID: 0020121543
DOI: 10.1007/s11269-011-9863-5
Appears in Collections:Civil and Environmental Engineering publications

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