Abstract
We are given finitely many polyhedra defined by linear constraints, using the same constraint matrix and different right-hand sides. We consider a simple constraint system and give necessary and sufficient conditions for this system to define the union of the polyhedra. We also show that deciding whether the system does define the union is NP-hard.
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E. Balas, “Disjunctive programming and a hierarchy of relaxations for discrete optimization problems,”SIAM Journal on Discrete Mathematics 6 (1985) 466–486.
R. Jeroslow, “A simplification for some disjunctive formulations,”European Journal of Operations Research 36 (1988) 116–121.
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Dedicated to the memory of Robert Jeroslow
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Blair, C. Representation for multiple right-hand sides. Mathematical Programming 49, 1–5 (1990). https://doi.org/10.1007/BF01588775
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DOI: https://doi.org/10.1007/BF01588775