TY - JOUR
T1 - Tighter representations for set partitioning problems
AU - Sherali, Hanif D.
AU - Lee, Youngho
N1 - Funding Information:
This materiali s basedu pon work supportedb y the National ScienceF oundation under Grant No. DMII-9121419 and by the Air Force Office of ScientificR esearch underG rant No. AFOSR-90-0191.T he authorsw ould also like to thank an anonymous refereef or suggestiontso improvet he presentationin this paper.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 1996/6/12
Y1 - 1996/6/12
N2 - In this paper, we consider the set partitioning polytope and we begin by applying the reformulation-linearization technique of Sherali and Adams (1990, 1994) to generate a specialized hierarchy of relaxations by exploiting the structure of this polytope. We then show that several known classes of valid inequalities for this polytope, as well as related tightening and composition rules, are automatically captured within the first-and second-level relaxations of this hierarchy. Hence, these relaxations provide a unifying framework for a broad class of such inequalities. Furthermore, it is possible to implement only partial forms of these relaxations from the viewpoint of generating tighter relaxations that delete the underlying linear programming solution to the set partitioning problem, based on variables that are fractional at an optimum to this problem.
AB - In this paper, we consider the set partitioning polytope and we begin by applying the reformulation-linearization technique of Sherali and Adams (1990, 1994) to generate a specialized hierarchy of relaxations by exploiting the structure of this polytope. We then show that several known classes of valid inequalities for this polytope, as well as related tightening and composition rules, are automatically captured within the first-and second-level relaxations of this hierarchy. Hence, these relaxations provide a unifying framework for a broad class of such inequalities. Furthermore, it is possible to implement only partial forms of these relaxations from the viewpoint of generating tighter relaxations that delete the underlying linear programming solution to the set partitioning problem, based on variables that are fractional at an optimum to this problem.
KW - Cutting planes
KW - Reformulation-linearization technique
KW - Set partitioning polytope
KW - Valid inequalities
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U2 - 10.1016/0166-218X(95)00060-5
DO - 10.1016/0166-218X(95)00060-5
M3 - Article
AN - SCOPUS:0006222852
VL - 68
SP - 153
EP - 167
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
SN - 0166-218X
IS - 1-2
ER -