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Practicable robust stochastic optimization under divergence measures with an application to equitable humanitarian

Aakil M Caunhye1, Douglas Alem1

  • 1Business School, The University of Edinburgh, 29 Buccleuch Place, Edinburgh, EH8 9JU UK.

OR Spectrum : Quantitative Approaches in Management
|June 26, 2023
PubMed
Summary

This study introduces new divergence functions for robust stochastic optimization, making complex models more practical. These methods improve decision-making in humanitarian logistics by balancing effectiveness and equity.

Keywords:
AmbiguityEquitable humanitarian logisticsMoreau-Yosida regularizationRobust stochastic optimizationStochastic programmingf-divergence

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Area of Science:

  • Operations Research
  • Optimization Theory
  • Decision Science

Background:

  • Robust stochastic optimization models are crucial for decision-making under uncertainty.
  • Existing f-divergence-based models present significant numerical challenges, especially with mixed-integer decisions.
  • Practicable approximations are needed to enhance the applicability of these models.

Purpose of the Study:

  • To develop novel divergence functions for tractable approximations of two-stage robust stochastic optimization models.
  • To maintain versatility in modeling diverse ambiguity aversions while ensuring numerical tractability.
  • To implement and validate these new methods in a humanitarian logistics context.

Main Methods:

  • Proposal of novel divergence functions that yield robust counterparts with manageable numerical difficulties.
  • Development of techniques to mimic existing f-divergences without compromising practicability.
  • Application within a realistic location-allocation model for humanitarian operations, incorporating an effectiveness-equity trade-off.

Main Results:

  • Demonstrated significant improvements in the practicability of robust counterparts compared to existing f-divergences.
  • Achieved greater equity in humanitarian response through a novel objective function.
  • Enhanced robustness of operational plans against variations in probability estimations.

Conclusions:

  • The proposed divergence functions offer a practical approach to robust stochastic optimization.
  • The methodology effectively balances effectiveness and equity in humanitarian operations.
  • The approach enhances the reliability of planning under uncertainty.