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Parametric Stochastic Programming with One Chance Constraint: Gaining Insights from Response Space Analysis

In: Harvey J. Greenberg

Author

Listed:
  • Harvey J. Greenberg

    (University of Colorado)

  • Jean-Paul Watson

    (Lawrence Livermore National Laboratory)

  • David L. Woodruff

    (University of California Davis)

Abstract

We consider stochastic programs with discrete scenario probabilities where scenario-specific constraints must hold with some probability, which we vary parametrically. We thus obtain minimum cost as a function of constraint-satisfaction probability. We characterize this trade-off using Everett’s response space and introduce an efficient construction of the response space frontier based on tangential approximation, a method introduced for one specified right-hand side. Generated points in the response space are optimal for a finite set of probabilities, with Lagrangian bounds equal to the piece-wise linear functional value. We apply our procedures to a number of illustrative stochastic mixed-integer programming models, emphasizing insights obtained and tactics for gaining more information about the trade-off between solution cost and probability of scenario satisfaction. Our code is an extension of the PySP stochastic programming library, included with the Pyomo (Python Optimization Modeling Objects) open-source optimization library.

Suggested Citation

  • Harvey J. Greenberg & Jean-Paul Watson & David L. Woodruff, 2021. "Parametric Stochastic Programming with One Chance Constraint: Gaining Insights from Response Space Analysis," International Series in Operations Research & Management Science, in: Allen Holder (ed.), Harvey J. Greenberg, chapter 0, pages 99-124, Springer.
    • Handle: RePEc:spr:isochp:978-3-030-56429-2_6
    DOI: 10.1007/978-3-030-56429-2_6
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