On probabilistic constraints induced by rectangular sets and multivariate normal distributions

Wim Van Ackooij, René Henrion (), Andris Möller and Riadh Zorgati

Mathematical Methods of Operations Research, 2010, vol. 71, issue 3, 535-549

Abstract: In this paper, we consider optimization problems under probabilistic constraints which are defined by two-sided inequalities for the underlying normally distributed random vector. As a main step for an algorithmic solution of such problems, we prove a derivative formula for (normal) probabilities of rectangles as functions of their lower or upper bounds. This formula allows to reduce the calculus of such derivatives to the calculus of (normal) probabilities of rectangles themselves thus generalizing a similar well-known statement for multivariate normal distribution functions. As an application, we consider a problem from water reservoir management. One of the outcomes of the problem solution is that the (still frequently encountered) use of simple individual probabilistic constraints can completely fail. By 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. Copyright Springer-Verlag 2010

Keywords: Stochastic programming; Probabilistic constraints; Chance constraints; Derivative of probabilities of rectangles; Water reservoir management; MSC 90C15; MSC 90C90 (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (11)

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DOI: 10.1007/s00186-010-0316-3

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