Computational methods for solving two-stage stochastic linear programming problems

Kall, Peter

doi:10.1007/bf01601939

Cited by 71 publications

(25 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let us assume that some of the entries of the technology matrix A and the righthand side b in the linear model (1) are uncertain and that this uncertainty is crucial for the decision making. One of possible modelling approaches to such a situation (see, e.g., Kall et al, 1979) is to assume that A and b are random and may attain one of finite many realizations with some known probabilities:…”

Section: A= -Kmentioning

confidence: 99%

Aspiration based decision support systems

1990

European Journal of Operational Research

View full text Add to dashboard Cite

IntroductionIt is not easy to summarize -even in a volume -the results of a scientific study conducted by circa 30 researchers, in four different research institutions, though cooperating between them and jointly with the International Institute for Applied Systems Analysis, but working part-time, sponsored not only by IIASA's national currency funds, but also by several other research grants in Poland. The aims of this cooperative study were defined broadly by its title Theory, Software and Testing Examples for Decision Support Systems. The focusing theme was the methodology of decision analysis and support related to the principle of reference point optimization (developed by the editors of this volume and called also variously: aspiration-led decision support, quasi-satisfying framework of rationality, DIDAS methodology etc.). This focusing theme motivated extensive theoretical research -from basic methodological issues of decision analysis, through various results in mathematical programming (in the fields of large scale and stochastic optimization, nondifferentiable optimization, cooperative game theory) motivated and needed because of this theme, through methodological issues related to software development to issues resulting from testing and applications. We could not include in this volume all papers -theoretical, methodological, applied, software manuals and documentation -written during this cooperative study. The selection principle applied for this volume was to concentrate on advances of theory and methodology, related to the focusing theme, to supplement them by experiences and methodological advances gained through wide applications and tests in one particular application area -the programming of development of industrial structures in chemical industry, and finally to give a very: short description of various software products developed in the contracted study agreement. The material of this volume is thus divided correspondingly into three unequal parts (it must be noted, however, that the last and shortest part corresponds to the most extensive research effort).PART 1 is composed of 15 theoretical and methodological papers. It starts with two more general papers, the first explaining the focusing theme of this volume and the second describing the methodology of decision analysis in decision support systems (DSS) of the DIDAS family. The following five papers are devoted to various aspects of linear programming: three represent innovative approaches to large-scale programming problems and new mathematical and algorithmic results in this field, including a new idea of decomposition of augmented Lagrangian functions for large-scale problem -motivated and related to the work on DSS, next addresses basic problems of multiobjective dynamic trajectory optimization, a further one presents a more detailed methodological guide to a multiobjective mathematical programming package HYBRID. We present such a mixture of results on purpose, to show the broad scope of the study, its com-IV ponents of mathemati...

show abstract

Section: A= -Kmentioning

confidence: 99%

Aspiration based decision support systems

1990

European Journal of Operational Research

View full text Add to dashboard Cite

show abstract

“…Conversely, reducing the allocation targets results in lower risk of penalties under water scarcity and a higher risk of water-resources wastage. Such problems can often be formulated as two-stage stochastic programming (TSP) models (Anderson, 1968;Kall, 1979;Louveaux, 1980;Birge, 1985;Birge & Louveaux, 1988;Gassmann, 1990;Eiger & Shamir, 1991;Lustig et al, 1991;Sen, 1993;Ediris-inghe & Ziemba, 1994;Ruszczynski & Swietanowski, 1997;Beraldi et al, 2000;Dai et al, 2000;Darby-Dowman et al, 2000;Yoshitomi et al, 2000;Zhao, 2001). In TSP, a decision is made at the first stage before random variables are known and then, after the random events have happened and their values are known, a second decision should be made in order to minimize penalties that may appear due to any infeasibility (Loucks et al, 1981;Birge et al, 1988;Ruszczynski, 1993).…”

Section: Introductionmentioning

confidence: 99%

Adaption to Climate Change through Water Trading under Uncertainty - An Inexact Two-Stage Nonlinear Programming Approach

Luo¹

2003

J ENV INFORM

View full text Add to dashboard Cite

ABSTRACT. Shifting hydrological phenomenon under changing climate would lead to decreased water availability, and thus would worse water supply-demand conflicts resulting in penalties on local economy. To tackle water shortage problems, water trading has been proved as an efficient and economical method. However, complexities and uncertainties in water trading system may result in its poor efficiency and improper management. To address these concerns, an inexact two-stage stochastic nonlinear programming (ITSNP) model is proposed for water resources management through water trading under uncertainty. The ITSNP model can reflect nonlinearity of the problems, incorporate uncertainties expressed as probability distributions and discrete intervals, and provide linkages between predefined policies and associated economic implications. The developed model is applied to a case study of water resources management of an agricultural system with and without water trading schemes. The obtained modeling solutions indicate that water resources management is more efficient with water trading than without water trading particularly during dry seasons. Moreover, it is found that water trading is a suitable method for adaptation to climate change impacts under water scarcity.

show abstract

“…Exact methods include simplex-based algorithms that exploit special structure of bases [17], decomposition or L-shaped schemes [2,31], interior point methods [24], and the Progressive Hedging algorithm [29]. A classic approximation scheme involves calculating deterministic lower and upper bounds via the inequalities of Jensen and Edmundson-Madansky, respectively; see [3,4,11,21] for extensions and alternatives.…”

mentioning

confidence: 99%

“…Theorem 7 Assume (7), (11), (16) If, in addition, (IS), (17), (18) hold and < e' < c then P{T(e) < oo} = 1.…”

mentioning

confidence: 99%