A second-order cone programming approximation to joint chance-constrained linear programs

Authors:
Jianqiang Cheng;Céline Gicquel;Abdel Lisser
Affiliations:
Laboratoire de Recherche en Informatique (LRI), Université Paris Sud - XI, Orsay Cedex, France;Laboratoire de Recherche en Informatique (LRI), Université Paris Sud - XI, Orsay Cedex, France;Laboratoire de Recherche en Informatique (LRI), Université Paris Sud - XI, Orsay Cedex, France
Venue:
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Year:
2012

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Abstract

We study stochastic linear programs with joint chance constraints, where the random matrix is a special triangular matrix and the random data are assumed to be normally distributed. The problem can be approximated by another stochastic program, whose optimal value is an upper bound of the original problem. The latter stochastic program can be approximated by two second-order cone programming (SOCP) problems [5]. Furthermore, in some cases, the optimal values of the two SOCPs problems provide a lower bound and an upper bound of the approximated stochastic program respectively. Finally, numerical examples with probabilistic lot-sizing problems are given to illustrate the effectiveness of the two approximations.