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Stochastic programming

About: Stochastic programming is a research topic. Over the lifetime, 12343 publications have been published within this topic receiving 421049 citations.


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Book ChapterDOI
01 Jan 2001
TL;DR: The suggested methodology can be used for optimizing of portfolios by investment companies, brokerage firms, mutual funds, and any businesses that evaluate risks, and can be applied to any financial or non-financial problems involving optimization of percentiles.
Abstract: A new approach for optimization or hedging of a portfolio of finance instruments to reduce the risks of high losses is suggested and tested with several applications. As a measure of risk, Conditional Value-at-Risk (CVaR) is used. For several important cases, CVaR coincides with the expected shortfall (expected loss exceeding Values-at-Risk). However, generally, CVaR and the expected shortfall are different risk measures. CVaR is a coh erent risk measure both for continuous and discrete distributions. CVaR is a more consistent measure of risk than VaR. Portfolios with low CVaR also have low VaR because CVaR is greater than VaR. The approach is based on a new representation of the performance function, which allows simultaneous calculation of VaR and minimization of CVaR. It can be used in conjunction with analytical or scenario based optimization algorithms If the number of scenarios is fixed, the problem is reduced to a Linear Programming or Nonsmooth Optimization Problem. These techniques allow optimizing portfolios with large numbers of instruments. The approach is tested with two examples: (1) portfolio optimization and comparison with the Minimum Variance approach; (2) hedging of a portfolio of options. The suggested methodology can be used for optimizing of portfolios by investment companies, brokerage firms, mutual funds, and any businesses that evaluate risks. Although the approach is used for portfolio analysis, it is very general and can be applied to any financial or non-financial problems involving optimization of percentiles.

120 citations

Journal ArticleDOI
TL;DR: This paper modifies the conventional Stochastic Branch-and-Bound, using a heuristic--instead of exact methods--to solve the deterministic subproblem, and spares computational time and provides an appropriate method for solving various related applications of combinatorial stochastic optimization.
Abstract: Many applications such as project scheduling, workflow modeling, or business process re-engineering incorporate the common idea that a product, task, or service consisting of interdependent time-related activities should be produced or performed within given time limits. In real-life applications, certain measures like the use of additional manpower, the assignment of highly-skilled personnel to specific jobs, or the substitution of equipment are often considered as means of increasing the probability of meeting a due date and thus avoiding penalty costs. This paper investigates the problem of selecting, from a set of possible measures of this kind, the combination of measures that is the most cost-efficient. Assuming stochastic activity durations, the computation of the optimal combination of measures may be very expensive in terms of runtime. In this article, we introduce a powerful stochastic optimization approach to determine a set of efficient measures that crash selected activities in a stochastic activity network. Our approach modifies the conventional Stochastic Branch-and-Bound, using a heuristic--instead of exact methods--to solve the deterministic subproblem. This modification spares computational time and by doing so provides an appropriate method for solving various related applications of combinatorial stochastic optimization. A comparative computational study shows that our approach not only outperforms standard techniques but also definitely improves conventional Stochastic Branch-and-Bound.

120 citations

Journal ArticleDOI
TL;DR: Under suitable normality assumptions this problem is amenable to a quadratic programming formulation and the objective function consists of the maximization of the probability that a realization (in terms of target variables) will lie in a confidence region of predetermined size.
Abstract: This paper deals with the problem of attaining a set of targets (goals) by means of a set of instruments (subgoals) when the relation between the two groups of variables can be expressed with a linear system of stochastic equations. The objective function consists of the maximization of the probability that a realization (in terms of target variables) will lie in a confidence region of predetermined size. Under suitable normality assumptions this problem is amenable to a quadratic programming formulation.

120 citations

Book ChapterDOI
01 Jan 2003
TL;DR: This chapter explores the use of concepts from stochastic programming in the context of resource allocation problems that arise in freight transportation and focuses on the degree to which some techniques exploit the natural structure of these problems.
Abstract: Freight transportation is characterized by highly dynamic information processes: customers call in orders over time to move freight; the movement of freight over long distances is subject to random delays; equipment failures require last minute changes; and decisions are not always executed in the field according to plan. The high-dimensionality of the decisions involved has made transportation a natural application for the techniques of mathematical programming, but the challenge of modeling dynamic information processes has limited their success. In this chapter, we explore the use of concepts from stochastic programming in the context of resource allocation problems that arise in freight transportation. Since transportation problems are often quite large, we focus on the degree to which some techniques exploit the natural structure of these problems. Experimental work in the context of these applications is quite limited, so we highlight the techniques that appear to be the most promising.

120 citations

Journal ArticleDOI
TL;DR: This paper addresses inventory policy for spare parts, when demand for the spare parts arises due to regularly scheduled preventive maintenance, as well as random failure of units in service.

119 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023175
2022423
2021526
2020598
2019578
2018532