Relaxations of linear programming problems with first order stochastic dominance constraints

Authors:
Nilay Noyan;GáBor Rudolf;Andrzej RuszczyńSki
Affiliations:
RUTCOR, Rutgers University, 640 Bartholomew Rd., Piscataway, NJ 08854, USA;RUTCOR, Rutgers University, 640 Bartholomew Rd., Piscataway, NJ 08854, USA;Department of Management Science and Information Systems, Rutgers University, 640 Bartholomew Rd., Piscataway, NJ 08854, USA
Venue:
Operations Research Letters
Year:
2006

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Abstract

Linear stochastic programming problems with first order stochastic dominance (FSD) constraints are non-convex. For their mixed 0-1 linear programming formulation we present two convex relaxations based on second order stochastic dominance (SSD). We develop necessary and sufficient conditions for FSD, used to obtain a disjunctive programming formulation and to strengthen one of the SSD-based relaxations.