4 Presentations

• 
  03:30 PM - 03:55 PM

  Random-Valued Scenario Trees Based on an Objective-Aware Criterion

  • David Munger, presenter, Polytechnique Montréal
  • Michel Gendreau, Polytechnique Montréal
  • Antoine Saucier, Polytechnique Montréal

  The stability and accuracy of the solution of a multistage stochastic program approximated on a scenario tree is highly dependent on the quality of the sampling provided by the tree. In order to conduct an educated search for "good" scenario trees, we propose to rank trees using a rigorous criterion based on a node-by-node decomposition of the error on the optimal objective. This criterion is parameterized to reflect various sensitivities in the objective. We also propose a method for populating the tree with structured random values in a way to produce a random estimator for the optimal objective value, so that one can assess its stability through, for example, its variance. We illustrate actual tree construction using simple search methods.

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  03:55 PM - 04:20 PM

  A New Progressive Hedging Algorithm for Linear Stochastic Optimization Problems

  • Shohre Zehtabian, presenter, Université de Montréal
  • Fabian Bastin, Université de Montréal

  Progressive Hedging Algorithm remains a popular method to deal with multistage stochastic problems. The performance can be poor due to the quadratic penalty terms associated with nonanticipativity constraints. In this work, we investigate its connection with the developments in augmented Lagrangian methods. To preserve linearity, we consider linear penalty terms and evaluate the numerical performance on various test problems.

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  04:20 PM - 04:45 PM

  Stochastic Dynamic Dual Programming for Asset Allocation Problem

  • Thuener Silva, presenter, Pontifical Catholic University of Rio de Janeiro
  • Marcus Poggi, Pontifical Catholic University of Rio de Janeiro
  • Davi Valladão, Pontifical Catholic University of Rio de Janeiro

  Some attempts have been made to model the asset allocation problem as a multistage stochastic problem. The propose approach uses Stochastic Dynamic Dual Programming to solve the asset allocation problem for multiple periods with Conditional Value at Risk. To analyze the risk averse approach behavior we present a test case.

• 
  04:45 PM - 05:10 PM

  A Policy-Based Recourse for the Vehicle Routing Problem with Stochastic Demands

  • Majid Salavati, presenter, Université de Montréal
  • Michel Gendreau, Polytechnique Montréal
  • Walter Rei, Université du Québec à Montréal

  Consider a transportation company that targets some operational conventions to selectively perform the predefined recourse actions. These rules are typically based on fixed policies, risk-based policies, and mixed policies. Regarding what policy is selected, a set of thresholds is generated associated with an a priori route. An integer L-shaped algorithm is implemented to solve the problem exactly.