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.
Bibliographical noteFunding 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.
- Cutting planes
- Reformulation-linearization technique
- Set partitioning polytope
- Valid inequalities
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics