Optimal Path Problems with Second-Order Stochastic Dominance Constraints

Nie, Yu; Wu, Xing; Homem-de-Mello, Tito

doi:10.1007/s11067-011-9167-6

Cited by 52 publications

(23 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Optimization problems with stochastic dominance constraints are introduced in Ruszczyński (2003, 2004). Recently, univariate stochastic dominance in the optimization models have been used to model finance, energy and transportation problems Karoui and Meziou (2006), Roman et al (2006), Dentcheva and Ruszczyński (2006), Gollmer et al (2007), Luedtke (2008), Nie et al (2009). The notions of multivariate positive linear second order stochastic dominance is studied in Dentcheva and Ruszczyński (2009).…”

Section: Introductionmentioning

confidence: 99%

Risk-adjusted budget allocation models with application in homeland security

Homem-de-Mello

Mehrotra

2011

IIE Transactions

Self Cite

View full text Add to dashboard Cite

This paper presents and studies models for multi-criterion budget allocation problems under uncertainty. The proposed models incorporate uncertainties in decision maker's weights using a robust weighted sum approach. The risk averseness of the decision maker in satisfying random risk related constraints is ensured by using stochastic dominance. A sample average approximation approach together with a cutting surface method is used to solve this model. An analysis for the computation of statistical lower and upper bounds is also given. We use the proposed models to study the budget allocation to ten urban areas in the United States under the Urban Areas Security Initiative (UASI). Here the decision maker considers property losses, fatalities, air departures, and average daily bridge traffic as separate criteria. The properties of the proposed modeling and solution methodology are discussed using a RAND Corporation proposed allocation policy and the current government budget allocation as two benchmarks. The budget results are discussed under several parameter scenarios.

show abstract

Section: Introductionmentioning

confidence: 99%

Risk-adjusted budget allocation models with application in homeland security

Homem-de-Mello

Mehrotra

2011

IIE Transactions

Self Cite

View full text Add to dashboard Cite

show abstract

“…To the knowledge of the authors, the only related study in the literature is an optimal path problem formulated by using second-order stochastic dominance constraints for analyzing risk-averse driver behavior (22).…”

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

View full text Add to dashboard Cite

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.

show abstract

“…However, very few people considered applying the thought of stochastic dominant to SCP. Recently, optimization models with stochastic dominance constraints have increasingly been the subject of theoretical considerations and have been applied in many areas such as finance, energy, and transportation; see [8][9][10][11]. Stochastic dominance is one of the popular established ways to formalize preferences among random values.…”

Section: Introductionmentioning

confidence: 99%

A Smoothing Algorithm for a New Two-Stage Stochastic Model of Supply Chain Based on Sample Average Approximation

Liu¹,

Xiong²,

Tong³

2017

Mathematical Problems in Engineering

View full text Add to dashboard Cite

We construct a new two-stage stochastic model of supply chain with multiple factories and distributors for perishable product. By introducing a second-order stochastic dominance (SSD) constraint, we can describe the preference consistency of the risk taker while minimizing the expected cost of company. To solve this problem, we convert it into a one-stage stochastic model equivalently; then we use sample average approximation (SAA) method to approximate the expected values of the underlying random functions. A smoothing approach is proposed with which we can get the global solution and avoid introducing new variables and constraints. Meanwhile, we investigate the convergence of an optimal value from solving the transformed model and show that, with probability approaching one at exponential rate, the optimal value converges to its counterpart as the sample size increases. Numerical results show the effectiveness of the proposed algorithm and analysis.

show abstract

Optimal Path Problems with Second-Order Stochastic Dominance Constraints

Cited by 52 publications

References 41 publications

Risk-adjusted budget allocation models with application in homeland security

Risk-adjusted budget allocation models with application in homeland security

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

A Smoothing Algorithm for a New Two-Stage Stochastic Model of Supply Chain Based on Sample Average Approximation

Contact Info

Product

Resources

About