New Formulations for Optimization under Stochastic Dominance Constraints

Luedtke, James

doi:10.1137/070707956

Cited by 80 publications

(57 citation statements)

References 20 publications

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“…A linear formulation for the second-order stochastic dominance constrained optimization problem is introduced by Luedtke (26). Following Theorem 3.2 of Luedtke's work, the authors obtain the formulation in Equations 12 through 15 for the dominance constraint in Equation 7:…”

Section: Second-order Stochastic Dominance Constraintsmentioning

confidence: 99%

Modeling of Bus Transit Driver Availability for Effective Emergency Evacuation in Disaster Relief

Morgul

Çavuş

Özbay

et al. 2013

Transportation Research Record: Journal of the Transportation R

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Potential evacuees without access to personal automobiles are expected to use transit, especially buses, to reach safer regions. For a transit agency, operation problems to be considered include establishing bus launch areas, positioning the minimum number of required buses, and coordinating transit operators, especially determining whether the number of drivers will be sufficient to cover the number of vehicles (i.e., buses) to be used during the evacuation. It is also highly probable that during an emergency, absenteeism rates for bus drivers might increase. In this study, the authors developed two stochastic models to determine the need for extra drivers during an emergency evacuation and to provide optimal solutions using well-established concepts in mathematical programming. First, the authors reviewed the literature to develop an effective methodology for the development of optimal extraboard management strategies. The authors found that although several recent reports clearly mentioned the problem of not having enough bus drivers during emergency evacuation operations, no analytical study incorporated the optimal extraboard size problem into emergency evacuation operations. Second, two mathematical models are presented in this paper. The aim of the developed models is to fill the gap in the literature for determining optimal extraboard size for transit operations during emergency evacuations. The models are specifically designed to capture risk-averse behavior of decision makers. Finally, these models were tested with hypothetical examples from real-world data from New Jersey. Results show that both models give reasonable extraboard size estimates, and under different conditions, these models are responsive to the changes in cost and quality of service preferences. The results are encouraging in terms of the models' usefulness for real-world applications.

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Section: Second-order Stochastic Dominance Constraintsmentioning

confidence: 99%

Modeling of Bus Transit Driver Availability for Effective Emergency Evacuation in Disaster Relief

Morgul

Çavuş

Özbay

et al. 2013

Transportation Research Record: Journal of the Transportation R

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show abstract

“…Based on the general theoretical result in Strassen (1965), Luedtke (2008) recently developed the majorization test (9) further by explicitly including the probabilities of the states (which are assumed equal in (9)) and suggested a branching heuristic for solving the method. His linear programming formulation, however, closely resembles (9), particularly in terms of the computational complexity.…”

Section: Majorization Approachmentioning

confidence: 99%

Stochastic dominance efficiency analysis of diversified portfolios: classification, comparison and refinements

Lizyayev

2012

Ann Oper Res

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For more than three decades, empirical analysis of stochastic dominance was restricted to settings with mutually exclusive choice alternatives. In recent years, a number of methods for testing efficiency of diversified portfolios have emerged, which can be classified into three main categories: 1) majorization, 2) revealed preference and 3) distribution-based approaches. Unfortunately, some of these schools of thought are developing independently, with little interaction or crossreferencing among them. Moreover, the methods differ in terms of their objectives, the information content of the results and their computational complexity. As a result, the relative merits of alternative approaches are difficult to compare. This paper presents the first systematic review of all three approaches in a unified methodological framework. We examine the main developments in this emerging literature, critically evaluating the advantages and disadvantages of the alternative approaches. We also point out some misleading arguments and propose corrections and improvements to some of the methods considered.

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“…Much of the work on optimization with stochastic dominance has focused on the case where the underlying random quantities being compared are unidimensional [5,6,18,21]. More recently, Dentcheva and Ruszczyński [7] proposed the concept of positive linear second order stochastic dominance which is a special case of multivariate stochastic dominance and obtained necessary conditions of optimality for non-convex problems.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Programming with Multivariate Second Order Stochastic Dominance Constraints with Applications in Portfolio Optimization

Meskarian

Fliege

2014

Appl Math Optim

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In this paper we study optimization problems with multivariate stochastic dominance constraints where the underlying functions are not necessarily linear. These problems are important in multicriterion decision making, since each component of vectors can be interpreted as the uncertain outcome of a given criterion. We propose a penalization scheme for the multivariate second order stochastic dominance constraints. We solve the penalized problem by the level function methods, and a modified cutting plane method and compare them to the cutting surface method proposed in the literature. The proposed numerical schemes are applied to a generic budget allocation problem and a real world portfolio optimization problem.AMS Classification: 90C15 and 90C90

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New Formulations for Optimization under Stochastic Dominance Constraints

Cited by 80 publications

References 20 publications

Modeling of Bus Transit Driver Availability for Effective Emergency Evacuation in Disaster Relief

Modeling of Bus Transit Driver Availability for Effective Emergency Evacuation in Disaster Relief

Stochastic dominance efficiency analysis of diversified portfolios: classification, comparison and refinements

Stochastic Programming with Multivariate Second Order Stochastic Dominance Constraints with Applications in Portfolio Optimization

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