Abstract
This paper presents a methodology for the solution of multistage stochastic optimization problems, based on the approximation of the expected-cost-to-go functions of stochastic dynamic programming by piecewise linear functions. No state discretization is necessary, and the combinatorial “explosion” with the number of states (the well known “curse of dimensionality” of dynamic programming) is avoided. The piecewise functions are obtained from the dual solutions of the optimization problem at each stage and correspond to Benders cuts in a stochastic, multistage decomposition framework. A case study of optimal stochastic scheduling for a 39-reservoir system is presented and discussed.
Similar content being viewed by others
References
J.F. Benders, “Partitioning procedures for solving mixed variables programming problems,”Numerische Mathematik 4 (1962) 238–252.
J.R. Birge, “Solution methods for stochastic dynamic linear programs,” Report 80/29, Systems Optimization Laboratory, Department of Operations Research, Stanford University (Stanford, CA, 1980).
S. Gal, “Parameter iteration dynamic programming”,Management Science (1989).
J.L. Kennington and R.V. Helgason,Algorithms for Network Programming (Wiley, New York, 1984).
M.V.F. Pereira and L.M.V.G. Pinto, “Stochastic optimization of a multireservoir hydroelectric system—a decomposition approach”,Water Resources Research 21(6) (1985).
R. J.-B. Wets, “Large scale linear programming techniques,” in: Y. Ermoliev and R. Wets, eds.,Numerical Methods for Stochastic Optimization (Springer, Berlin, 1988) Chapter 3.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Pereira, M.V.F., Pinto, L.M.V.G. Multi-stage stochastic optimization applied to energy planning. Mathematical Programming 52, 359–375 (1991). https://doi.org/10.1007/BF01582895
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01582895