Tighter reformulations using classical Dawson and Sankoff bounds for approximating two-stage chance-constrained programs

Singh, Bismark

doi:10.1007/s11590-020-01592-1

Tighter reformulations using classical Dawson and Sankoff bounds for approximating two-stage chance-constrained programs

Journal Article · Mon May 25 00:00:00 EDT 2020 · Optimization Letters

DOI:https://doi.org/10.1007/s11590-020-01592-1· OSTI ID:1634781

^[1]

Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen (Germany). Discrete Mathematics

We extend and improve recent results given by Singh and Watson on using classical bounds on the union of sets in a chance-constrained optimization problem. Specifically, we revisit the so-called Dawson and Sankoff bound that provided one of the best approximations of a chance constraint in the previous analysis. Next, we show that our work is a generalization of the previous work, and in fact the inequality employed previously is a very relaxed approximation with assumptions that do not generally hold. Computational results demonstrate on average over a 43% improvement in the bounds. As a byproduct, we provide an exact reformulation of the floor function in optimization models.

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

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

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1634781

Report Number(s):: SAND--2019-9568J; 678512

Journal Information:: Optimization Letters, Journal Name: Optimization Letters Journal Issue: 2 Vol. 15; ISSN 1862-4472

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

References (10)

Approximating two-stage chance-constrained programs with classical probability bounds Singh, Bismark; Watson, Jean-Paul Optimization Letters, Vol. 13, Issue 6 https://doi.org/10.1007/s11590-019-01387-z	journal	March 2019
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Complexity of some graph-based bounds on the probability of a union of events Scozzari, Andrea; Tardella, Fabio Discrete Applied Mathematics, Vol. 244 https://doi.org/10.1016/j.dam.2018.03.012	journal	July 2018
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