Stochastic programming in water management: A case study and a comparison of solution techniques

Dupačová, Jitka; Gaivoronski, Alexei A.; Kos, Z.; Szántai, Tamás

doi:10.1016/0377-2217(91)90333-q

Cited by 72 publications

(29 citation statements)

References 10 publications

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“…Contrary to penalty models, probabilistic programs capture the reliability requirements or risk restrictions even in cases which do not allow for reasonably accurate evaluation of penalties, e.g. Dupačová et al (1991). A suggestion of Prékopa (1973) is to apply probabilistic constraints (4), (5) or (6) and at the same time, to extend the objective function for an expected penalty term which is active whenever the original constraints g k (x, ω) ≤ 0 are not fulfilled: Prékopa (1973) ".…”

Section: Probabilistic Constraintsmentioning

confidence: 99%

“…For a numerical evidence see also Dupačová et al (1991) where a piecewise linear nonseparable penalty function N [max j (x j − ω j )] + was applied and the results compared with those obtained for a joint probabilistic constraint of the type P {x j ≤ ω j , j = 1, . .…”

Section: Probabilistic Programs and Their Recourse Reformulationsmentioning

confidence: 99%

“…Two special penalty functions are readily available: ϑ 1 (u) = m k=1 [u k ] + applied in Ermoliev et al (2000) and ϑ 2 (u) = max 1≤k≤m [u k ] + applied in Dupačová et al (1991).…”

Section: Remarkmentioning

confidence: 99%

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Approximation and contamination bounds for probabilistic programs

Branda

Dupačová

2010

Ann Oper Res

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Development of applicable robustness results for stochastic programs with probabilistic constraints is a demanding task. In this paper we follow the relatively simple ideas of output analysis based on the contamination technique and focus on construction of computable global bounds for the optimal value function. Dependence of the set of feasible solutions on the probability distribution rules out the straightforward construction of these concavity-based global bounds for the perturbed optimal value function whereas local results can still be obtained. Therefore we explore approximations and reformulations of stochastic programs with probabilistic constraints by stochastic programs with suitably chosen recourse or penalty-type objectives and fixed constraints. Contamination bounds constructed for these substitute problems may be then implemented within the output analysis for the original probabilistic program.Keywords Stochastic programs with probabilistic constraints · Output analysis · Contamination technique Modeling issuesClassical stochastic programming (SP) models aim at hedging against consequences of possible realizations of random parameters-scenarios-so that the expected final outcome or position is the best possible.Modeling part of realistic applications consists of a clear declaration of random factors to be taken into account, of distinguishing between hard and soft constraints and of a choice of a sensible optimality criterion. The starting point may be formulation of a deterministic

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Section: Probabilistic Constraintsmentioning

confidence: 99%

Section: Probabilistic Programs and Their Recourse Reformulationsmentioning

confidence: 99%

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Approximation and contamination bounds for probabilistic programs

Branda

Dupačová

2010

Ann Oper Res

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“…For a theoretical background we may refer to Prékopa [2] where an extensive list of references can be found. Applications of chance constrained programming include, e.g., water management [3] and optimization of chemical processes [4], [5].…”

Section: Introductionmentioning

confidence: 99%

Sample Average Approximation Method for Chance Constrained Programming: Theory and Applications

Pagnoncelli

Ahmed

Shapiro

2009

J Optim Theory Appl

450

304

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We study sample approximations of chance constrained problems. In particular, we consider the sample average approximation (SAA) approach and discuss the convergence properties of the resulting problem. We discuss how one can use the SAA method to obtain good candidate solutions for chance constrained * ( )Departamento de Matemática, Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, RJ Brazil 22453-900, e-mail: bernardo@mat.puc-rio.br, research supported by CAPES and FUNENSEG.† Georgia Institute of Technology, Atlanta, Georgia 30332, USA, e-mail: sahmed@isye.gatech.edu, research of this author was partly supported by the NSF award DMI-0133943.‡ Georgia Institute of Technology, Atlanta, Georgia 30332, USA, e-mail: ashapiro@isye.gatech.edu, research of this author was partly supported by the NSF award DMI-0619977. 1 problems. Numerical experiments are performed to correctly tune the parameters involved in the SAA. In addition, we present a method for constructing statistical lower bounds for the optimal value of the considered problem and discuss how one should tune the underlying parameters. We apply the SAA to two chance constrained problems. The first is a linear portfolio selection problem with returns following a multivariate lognormal distribution. The second is a joint chance constrained version of a simple blending problem.

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“…Consequently, in the past decades, many inexact optimization methods were advanced for addressing uncertainties presented as different formats in water resources management systems (Slowinski 1986;Camacho et al 1987;Morgan et al 1993;Srinivasan and Simonovic 1994;Curi et al 1995;Rangarajan 1995;Chang et al 1996a, b;Dupačová et al 1991;Russell and Campbell 1996;Huang 1996Huang , 1998ReVelle 1999;Anderson et al 2000;Jairaj and Vedula 2000;Edirisinghe et al 2000;Watkins et al 2000;Seifi and Hipel 2001;Ji and Chang 2005;Maqsood et al 2005;Li et al 2007a; Guo and Huang 2008;Zarghami and Szidarovszky 2008). Among them, a number of chance-constrained programming (CCP) and multistage stochastic programming (MSP) methods were developed for decision problems whose coefficients (input data) are uncertain but can be represented as chances or probabilities.…”

Section: Introductionmentioning

confidence: 99%

Multistage scenario-based interval-stochastic programming for planning water resources allocation

Huang

Chen

2008

Stoch Environ Res Risk Assess

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In this study, a multistage scenario-based interval-stochastic programming (MSISP) method is developed for water-resources allocation under uncertainty. MSISP improves upon the existing multistage optimization methods with advantages in uncertainty reflection, dynamics facilitation, and risk analysis. It can directly handle uncertainties presented as both interval numbers and probability distributions, and can support the assessment of the reliability of satisfying (or the risk of violating) system constraints within a multistage context. It can also reflect the dynamics of system uncertainties and decision processes under a representative set of scenarios. The developed MSISP method is then applied to a case of water resources management planning within a multi-reservoir system associated with joint probabilities. A range of violation levels for capacity and environment constraints are analyzed under uncertainty. Solutions associated different risk levels of constraint violation have been obtained. They can be used for generating decision alternatives and thus help water managers to identify desired policies under various economic, environmental and system-reliability conditions. Besides, sensitivity analyses demonstrate that the violation of the environmental constraint has a significant effect on the system benefit.

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Stochastic programming in water management: A case study and a comparison of solution techniques

Cited by 72 publications

References 10 publications

Approximation and contamination bounds for probabilistic programs

Approximation and contamination bounds for probabilistic programs

Sample Average Approximation Method for Chance Constrained Programming: Theory and Applications

Multistage scenario-based interval-stochastic programming for planning water resources allocation

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