Economics at your fingertips  

Robust multicriteria risk-averse stochastic programming models

Xiao Liu (), Simge Küçükyavuz () and Nilay Noyan ()
Additional contact information
Xiao Liu: The Ohio State University
Simge Küçükyavuz: University of Washington
Nilay Noyan: Sabancı University

Annals of Operations Research, 2017, vol. 259, issue 1, No 12, 259-294

Abstract: Abstract In this paper, we study risk-averse models for multicriteria optimization problems under uncertainty. We use a weighted sum-based scalarization and take a robust approach by considering a set of scalarization vectors to address the ambiguity and inconsistency in the relative weights of each criterion. We model the risk aversion of the decision makers via the concept of multivariate conditional value-at-risk (CVaR). First, we introduce a model that optimizes the worst-case multivariate CVaR and show that its optimal solution lies on a particular type of stochastic efficient frontier. To solve this model, we develop a finitely convergent delayed cut generation algorithm for finite probability spaces. We also show that the proposed model can be reformulated as a compact linear program under certain assumptions. In addition, for the cut generation problem, which is in general a mixed-integer program, we give a stronger formulation than the existing ones for the equiprobable case. Next, we observe that similar polyhedral enhancements are also useful for a related class of multivariate CVaR-constrained optimization problems that has attracted attention recently. In our computational study, we use a budget allocation application to benchmark our proposed maximin type risk-averse model against its risk-neutral counterpart and a related multivariate CVaR-constrained model. Finally, we illustrate the effectiveness of the proposed solution methods for both classes of models.

Keywords: Stochastic programming; Risk aversion; Robust optimization; Multicriteria optimization; Stochastic Pareto optimality; Conditional value-at-risk; Cut generation; Mixed-integer programming; McCormick envelopes; RLT technique (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed

Downloads: (external link) Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link:

Ordering information: This journal article can be ordered from

DOI: 10.1007/s10479-017-2526-z

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla ().

Page updated 2020-04-28
Handle: RePEc:spr:annopr:v:259:y:2017:i:1:d:10.1007_s10479-017-2526-z