Medium Term Hydroelectric Production Planning - A Multistage Stochastic Optimization Model

Document Type: Research Papers


1 PhD Candidate, Institute of Statistics and Operations Research (ISOR), University of Vienna, Vienna, Austria.

2 PhD, Institute of Statistics and Operations Research (ISOR), University of Vienna, Vienna,Austria.


Multistage stochastic programming is a key technology for making decisions over time in an uncertain environment. One of the promising areas in which this technology is implementable, is medium term planning of electricity production and trading where decision makers are typically faced with uncertain parameters (such as future demands and market prices) that can be described by stochastic processes in discrete time. We apply this methodology to hydrosystem operation assuming random electricity prices and random inflows to the reservoir system. After describing the multistage stochastic model a simple case study is presented. In particular we use the model for pricing an electricity delivery contract in the framework of indifference pricing.


Bühlmann, H. (1972). Mathematical methods in risk theory, Die Grundlehren der Mathematischen Wissenschaften. New York: Springer.

Carmona, R. (2009). Indifference pricing: Theory and applications, Princeton University Press.

Eichhorn, A. and Römisch, W. (2005). “Polyhedral risk measures in stochastic programming”, SIAM Journal of Optimization, 16(1), 69-95.

Eichhorn, A., Römisch, W. and Wegner, I. (2005). “Mean risk optimization of electricity portfolios using multi period polyhedral risk measures”, IEEE Power Tech Proceedings, St.Petersburg, Russia, 1-7.

Giacometti, R., Vespucci, M.T., Bertocchi, M. and Adesi, G.B. (2001). “Hedging electricity portfolio for a hydro-energy producer via stochastic programming” Proceedings of Stochastic Optimization Methods in Finance and Energy, Springer, 163-179.

Heitsch, H. and Römisch, W. (2005). “Generation of multivariate scenario trees to model stochasticity in power management”, IEEE Power Tech proceedings, St. Petersburg, Russia.

Kovacevic, R.M. and Paraschiv, F. (2013). “Medium-Term planning for thermal electricity production”, OR Spectrum, DOI:10.1007/s00291-013-0340-9.

Kovacevic, R.M. and Pflug, G.C. (2013). “Pricing of energy contracts - from replication pricing to swing options”, In: R.M. Kovacevic, G.C. Pflug and M.T. Vespucci (eds.), Handbook of Risk Management for Energy Production and Trading, New York: Springer, pp. 393-418.

Labadie, J.W. (2004). “Optimal operation of multi reservoir system: State of the art review”, Water Resources Planning and Management, 130(2), 93-111.

Ledolter, J. (1978). “A general class of stochastic models for hydrological sequences”, Journal of Hydrology, 2(36), 309-325.

Papamichail, D.M. and Georgiou, P.E. (2001). “Seasonal ARIMA inflow models for reservoir sizing”, Journal of American Water Resource Association, 37(4), 877-885.

Pflug, G.C. and Römisch, W. (2007). Modeling, measuring and managing risk,  Singapore: World Scientific.

Rockafellar, R.T. and Uryasev, S. (2000). “Optimization of conditional value-at-risk”, Journal of Risk, 2(3), 21-42.

Ruszczynski, A. and Shapiro, A. (2003). Stochastic programming, 1st Edition, Handbooks in Operations Research and Management Science, Amsterdam: Elsevier.