Volume 2009
http://edoc.hu-berlin.de/18452/366
Thu, 24 Jun 2021 11:59:21 GMT2021-06-24T11:59:21ZUncertainties in minimax stochastic programs
http://edoc.hu-berlin.de/18452/9059
Uncertainties in minimax stochastic programs
Dupacová, J.
Higle, Julie L.; Römisch, Werner; Sen, Surrajeet
When using the minimax approach one tries to hedge against the worst possible distribution belonging to a speciﬁed class P. A suitable stability analysis of results with respect to the choice of this class is an important issue. It has to be tailored to the type of the minimax problem, to the considered class of probability distributions and to the anticipated input perturbations. We shall focus on the effect of changes in input information for classes of probability distributions with support belonging to a given set and deﬁned by (possibly perturbed) generalized moments values.
Fri, 16 Oct 2009 00:00:00 GMThttp://edoc.hu-berlin.de/18452/90592009-10-16T00:00:00ZDay-Ahead Market Bidding for a NordicHydropower Producer: Taking the ElbasMarket into Account
http://edoc.hu-berlin.de/18452/9058
Day-Ahead Market Bidding for a NordicHydropower Producer: Taking the ElbasMarket into Account
Faria, E.; Fleten, St..-E.
Higle, Julie L.; Römisch, Werner; Sen, Surrajeet
In many power markets around the world the energy generation decisions result from two-sidedauctions in which producing and consuming agents submit their price-quantity bids. Thedetermination of optimal bids in power markets is a complicated task that has to be undertakenevery day. In the present work, we propose an optimization model for a price-taker hydropowerproducer in Nord Pool that takes into account the uncertainty in market prices and both productionand physical trading aspects. The day-ahead bidding takes place a day before the actual operation and energy delivery. After this round of bidding, but before actual operation, some adjustments in the dispatched power (accepted bids) have to be done, due to uncertainty in prices, inflow and load. Such adjustments can be done in the Elbas market, which allows for trading physical electricity up to one hour before the operation hour. This paper uses stochastic programming to determine the optimal bidding strategy and the impact of the possibility to participate in the Elbas.ARMAX and GARCH techniques are used to generate realistic market price scenarios taking intoaccount both day-ahead price and Elbas price uncertainty. The results show that considering Elbas when bidding in the day-ahead market does not significantly impact neither the profit nor the recommended bids of a typical hydro producer.
Fri, 16 Oct 2009 00:00:00 GMThttp://edoc.hu-berlin.de/18452/90582009-10-16T00:00:00ZRisk-Averse Two-Stage Stochastic LinearProgramming: Modeling and Decomposition
http://edoc.hu-berlin.de/18452/9057
Risk-Averse Two-Stage Stochastic LinearProgramming: Modeling and Decomposition
Miller, N.; Ruszczynski, A.
Higle, Julie L.; Römisch, Werner; Sen, Surrajeet
We formulate a risk-averse two-stage stochastic linear programming problem in which unresolved uncertainty remains after the second stage. The objective function is formulated as a composition of conditional risk measures.We analyze properties of the problem and derive necessary and sufﬁcientoptimality conditions. Next, we construct two decomposition methods forsolving the problem. The ﬁrst method is based on the generic cutting planeapproach, while the second method exploits the composite structure of the objective function. We illustrate their performance on a portfolio optimization problem.
Fri, 16 Oct 2009 00:00:00 GMThttp://edoc.hu-berlin.de/18452/90572009-10-16T00:00:00ZOn probabilistic constraints induced by rectangular sets and multivariate normal distributions
http://edoc.hu-berlin.de/18452/9056
On probabilistic constraints induced by rectangular sets and multivariate normal distributions
Ackooij, W. Van; Henrion, R.; Möller, A.; Zorgati, R.
Higle, Julie L.; Römisch, Werner; Sen, Surrajeet
In this paper, we consider optimization problems under probabilistic constraints which aredeﬁned by two-sided inequalities for the underlying normally distributed random vector. Asa main step for an algorithmic solution of such problems, we derive a derivative formula for(normal) probabilities of rectangles as functions of their lower or upper bounds. This formulaallows to reduce the calculus of such derivatives to the calculus of (normal) probabilitiesof rectangles themselves thus generalizing a similar well-known statement for multivariatenormal distribution functions. As an application, we consider a problem from water reservoirmanagement. One of the outcomes of the problem solution is that the (still frequentlyencountered) use of simple individual probabilistic can completely fail. In contrast, the (more diﬃcult) use of joint probabilistic constraints which heavily depends on the derivative formula mentioned before yields very reasonable and robust solutions over the whole time horizon considered.
Fri, 16 Oct 2009 00:00:00 GMThttp://edoc.hu-berlin.de/18452/90562009-10-16T00:00:00Z