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

Harvey J. Greenberg, Jean-Paul Watson () and David L. Woodruff ()
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Harvey J. Greenberg: University of Colorado
Jean-Paul Watson: Lawrence Livermore National Laboratory
David L. Woodruff: University of California Davis

Chapter Chapter 6 in Harvey J. Greenberg, 2021, pp 99-124 from Springer

Abstract: 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.

Date: 2021
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DOI: 10.1007/978-3-030-56429-2_6

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