Data-driven chance constrained stochastic program

Ruiwei Jiang, Yongpei Guan

Research output: Contribution to journalArticle

108 Scopus citations

Abstract

In this paper, we study data-driven chance constrained stochastic programs, or more specifically, stochastic programs with distributionally robust chance constraints (DCCs) in a data-driven setting to provide robust solutions for the classical chance constrained stochastic program facing ambiguous probability distributions of random parameters. We consider a family of density-based confidence sets based on a general (Formula presented.)-divergence measure, and formulate DCC from the perspective of robust feasibility by allowing the ambiguous distribution to run adversely within its confidence set. We derive an equivalent reformulation for DCC and show that it is equivalent to a classical chance constraint with a perturbed risk level. We also show how to evaluate the perturbed risk level by using a bisection line search algorithm for general (Formula presented.)-divergence measures. In several special cases, our results can be strengthened such that we can derive closed-form expressions for the perturbed risk levels. In addition, we show that the conservatism of DCC vanishes as the size of historical data goes to infinity. Furthermore, we analyze the relationship between the conservatism of DCC and the size of historical data, which can help indicate the value of data. Finally, we conduct extensive computational experiments to test the performance of the proposed DCC model and compare various (Formula presented.)-divergence measures based on a capacitated lot-sizing problem with a quality-of-service requirement.

Original languageEnglish (US)
JournalMathematical Programming
DOIs
StateAccepted/In press - Jul 5 2015

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Keywords

  • Chance constraints
  • Semi-infinite programming
  • Stochastic programming

ASJC Scopus subject areas

  • Mathematics(all)
  • Software

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