Invited Session Mon.3.MA 141

Monday, 15:15 - 16:45 h, Room: MA 141

Cluster 22: Stochastic optimization [...]

Solution methods for constrained stochastic optimization

 

Chair: Sumit M. Kunnumkal

 

 

Monday, 15:45 - 16:10 h, Room: MA 141, Talk 2

Sumit M. Kunnumkal
Randomization approaches for network RM with choice behavior

 

Abstract:
We present new approximation methods for the network RM problem with customer choice. We have a fairly general model of customer choice behavior; we assume that customers are endowed with an ordered list of preferences among the products and choose the most preferred alternative among the available ones. The starting point for our methods is a dynamic program that allows randomization. An attractive feature of this dynamic program is that the size of its action space is linear in the number of itineraries. We present two approximation methods that build on this dynamic program and use ideas from the independent demands setting.

 

 

Monday, 16:15 - 16:40 h, Room: MA 141, Talk 3

Gabor Rudolf
Optimization with multivariate conditional-value-at-risk constraints

Coauthor: Nilay Noyan

 

Abstract:
For decision making problems under uncertainty it is crucial to specify the decision makers' risk preferences based on multiple stochastic performance measures. Incorporating multivariate preference rules into optimization models is a recent research area. Existing studies focus on extending univariate stochastic dominance rules to the multivariate case. However, enforcing such dominance constraints can be overly conservative in practice. As an alternative, we focus on the risk measure conditional value-at-risk (CVaR), introduce a multivariate CVaR relation, and propose an optimization model with multivariate CVaR constraints based on polyhedral scalarization. For finite probability spaces we develop a cut generation algorithm, where each cut is obtained by solving a mixed integer problem. We show that a multivariate CVaR constraint reduces to finitely many univariate CVaR constraints, which proves the finite convergence of our algorithm. We also show that our results can be extended to the wider class of coherent risk measures. The proposed approach provides a novel, flexible, and computationally tractable way of modeling preferences in stochastic multi-criteria decision making.

 

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