A Generalization of Odd Set Inequalities for the Set Packing Problem

Savelsbergh The Mixed Vertex Packing Problem

We study a generalization of the vertex packing problem having both binary and bounded continuous variables, called the mixed vertex packing problem (MVPP). The wellknown vertex packing model arises as a subproblem or relaxation of many 0-1 integer problems, whereas the mixed vertex packing model arises as a natural counterpart of vertex packing in the context of mixed 0-1 integer programming. ...

The Mixed Vertex Packing Problem 1

We study the polyhedral structure of a new model for various bottleneck resource allocation problems in which the resource consumption is determined by the activity with the maximum usage. The model, called the mixed vertex packing problem, is a generalization of the vertex packing problem having both binary and bounded continuous variables. We give valid inequalities and separation algorithms ...

Characterizing Noninteger Polyhedra with 0-1 Constraints

We characterize when the intersection of a set-packing and a set-covering polyhedron or of their corresponding minors has a noninteger vertex. Our result is a common generalization of Lovász’s characterization of ‘imperfect’ and Lehman’s characterization of ‘nonideal’ systems of inequalities, furthermore, it includes new cases in which both types of inequalities occur and interact in an essenti...

The mixed vertex packing problem

We study a generalization of the vertex packing problem having both binary and bounded continuous variables, called the mixed vertex packing problem (MVPP). The well-known vertex packing model arises as a subproblem or relaxation of many 0-1 integer problems, whereas the mixed vertex packing model arises as a natural counterpart of vertex packing in the context of mixed 0-1 integer programming....

 Abstract: Packing rectangular shapes into a rectangular space is one of the most important discussions on Cutting & Packing problems (C;P) such as: cutting problem, bin-packing problem and distributor's pallet loading problem, etc. Assume a set of rectangular pieces with specific lengths, widths and utility values. Also assume a rectangular packing space with specific width and length. The obj...