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Joint chance-constrained programs and the intersection of mixing sets through a submodularity lens

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Title
Joint chance-constrained programs and the intersection of mixing sets through a submodularity lens
Author(s)
Kilinc-Karzan, Fatma; Kucukyavuz, Simge; Dabeen Lee
Publication Date
2022-09
Journal
MATHEMATICAL PROGRAMMING, v.195, no.1-2, pp.283 - 326
Publisher
SPRINGER HEIDELBERG
Abstract
A particularly important substructure in modeling joint linear chance-constrained programs with random right-hand sides and finite sample space is the intersection of mixing sets with common binary variables (and possibly a knapsack constraint). In this paper, we first revisit basic mixing sets by establishing a strong and previously unrecognized connection to submodularity. In particular, we show that mixing inequalities with binary variables are nothing but the polymatroid inequalities associated with a specific submodular function. This submodularity viewpoint enables us to unify and extend existing results on valid inequalities and convex hulls of the intersection of multiple mixing sets with common binary variables. Then, we study such intersections under an additional linking constraint lower bounding a linear function of the continuous variables. This is motivated from the desire to exploit the information encoded in the knapsack constraint arising in joint linear CCPs via the quantile cuts. We propose a new class of valid inequalities and characterize when this new class along with the mixing inequalities are sufficient to describe the convex hull.
URI
https://pr.ibs.re.kr/handle/8788114/12866
DOI
10.1007/s10107-021-01688-1
ISSN
0025-5610
Appears in Collections:
Pioneer Research Center for Mathematical and Computational Sciences(수리 및 계산과학 연구단) > Discrete Mathematics Group(이산 수학 그룹) > 1. Journal Papers (저널논문)
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