Abstract
In certain linear programs, especially those derived from integer programs, large numbers of constraints may have very simple form. Examples are:x ij ≤ 1 (simple upper bounds [SUB]),Σ i x ij = 1 (generalized upper bounds [GUB]) andx ij ≤ y i (variable upper bounds [VUB]). A class of constraints called generalized VUB [GVUB] is introduced which includes GUB and VUB as special cases. Also introduced is a method for representing GVUB constraints implicitly within the mechanics of the simplex method.
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References
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L.E. Schrage, “Implicit representation of variable upper bounds in linear programs”,Mathematical Programming Study 4 (1975) 118–132.
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Research supported in part by the Mobil Oil Corporation.
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Schrage, L. Implicit representation of generalized variable upper bounds in linear programming. Mathematical Programming 14, 11–20 (1978). https://doi.org/10.1007/BF01588948
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DOI: https://doi.org/10.1007/BF01588948