Approximating two-stage chance-constrained programs with classical probability bounds
Approximating two-stage chance-constrained programs with classical probability bounds
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.
1403-1416
Singh, Bismark
9d3fc6cb-f55e-4562-9d5f-42f9a3ddd9a1
Watson, Jean-Paul
a9781540-b93b-4cfa-9d7a-4f6d046a380b
16 March 2019
Singh, Bismark
9d3fc6cb-f55e-4562-9d5f-42f9a3ddd9a1
Watson, Jean-Paul
a9781540-b93b-4cfa-9d7a-4f6d046a380b
Singh, Bismark and Watson, Jean-Paul
(2019)
Approximating two-stage chance-constrained programs with classical probability bounds.
Optimization Letters, 13 (6), .
(doi:10.1007/s11590-019-01387-z).
Abstract
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.
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Accepted/In Press date: 2 January 2019
Published date: 16 March 2019
Identifiers
Local EPrints ID: 471299
URI: http://eprints.soton.ac.uk/id/eprint/471299
ISSN: 1862-4480
PURE UUID: d628c7c0-abee-479d-bf58-89a774d3d326
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Date deposited: 02 Nov 2022 17:41
Last modified: 17 Mar 2024 04:16
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Author:
Bismark Singh
Author:
Jean-Paul Watson
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