Approximating Two-Stage Chance-Constrained Programs with Classical Probability Bounds

Singh, Bismark; Watson, Jean-Paul

doi:10.1007/s11590-019-01387-z

Approximating Two-Stage Chance-Constrained Programs with Classical Probability Bounds

Journal Article · Tue Jan 01 00:00:00 EST 2019 · Optimization Letters

DOI:https://doi.org/10.1007/s11590-019-01387-z· OSTI ID:1492794

Singh, Bismark ^[1]; Watson, Jean-Paul ^[2]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Discrete Math & Optimization
Sandia National Lab. (SNL-CA), Livermore, CA (United States). Data Science & Cyber Analytics

We consider a joint-chance constraint (JCC) as a union of sets, and approximate this union using bounds from classical probability theory. When these bounds are used in an optimization model constrained by the JCC, we obtain corresponding upper and lower bounds on the optimal objective function value. We compare the strength of these bounds against each other under two different sampling schemes, and observe that a larger correlation between the uncertainties tends to result in more computationally challenging optimization models. We also observe the same set of inequalities to provide the tightest upper and lower bounds in our computational experiments.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Sandia National Laboratories, Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1492794

Alternate ID(s):: OSTI ID: 1524700
OSTI ID: 1526145
OSTI ID: 1530935
OSTI ID: 1592353

Report Number(s):: SAND--2019-0432J; 671570

Journal Information:: Optimization Letters, Journal Name: Optimization Letters; ISSN 1862-4472

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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