This paper attempts to provide a better understanding of the facial structure of polyhedra previously investigated separately. It introduces the notion of transitive packing and the transitive packing polytope. Polytopes that turn out to be special cases of the transitive packing polytope include the node packing, acyclic subdigraph, bipartite subgraph, planar subgraph, clique partitioning, par...

In this paper, we study the strength of aggregation cuts for sign-pattern integer programs (IPs). Sign-pattern IPs are a generalization of packing IPs and are of the form {x ∈ Z+ | Ax ≤ b} where for a given column j, Aij is either non-negative for all i or non-positive for all i. Our first result is that the aggregation closure for such sign-pattern IPs can be 2-approximated by the original 1-r...

The aim of this article is to apply the methodology of genetic algorithms to the packing problem encountered in a sticker company. Owing to the nature of the packing operation in this company the problem is not easily solved with exact integer linear programming algorithms (Gilmore and Gomory, 1963). Industrial applications of packing methodology can be found in (Dyson and Gregory, 1974), (Farl...

We propose a framework to model general guillotine restrictions in two-dimensional cutting problems formulated as Mixed Integer Linear Programs (MIP). The modeling framework requires a pseudo-polynomial number of variables and constraints, which can be effectively enumerated for medium-size instances. Our modeling of general guillotine cuts is the first one that, once it is implemented within a...

Many systems can be modeled with hard and various size spheres, therefore packing and geometrical structures of such sets are of great importance. In this paper, rigid spherical particles distributed in different sizes are randomly packed in confined spaces, using a parallel algorithm. Mersenne Twister algorithm was used to generate pseudorandom numbers for initial coordination of particles. Di...

A recurrent task in mathematical programming requires optimizing polytopes with prohibitivelymany constraints, e.g., the primal polytope in cutting-plane methods or the dual polytope in Column Generation (CG). This paper is devoted to the ray projection technique for optimizing such polytopes: start from a feasible solution and advance on a given ray direction until intersecting a polytope face...

in a graph g = (v,e), a subset s  v is said to be an open packing set if no two vertices of s have a common neighbour in g. the maximum cardinality of an open packing set is called the open packing number and is denoted by rho^o. this paper further studies on this parameter by obtaining some new bounds.

the main issues in nasal surgery are to stabilize the nose in the good position after surgery and preserve the cartilages and bones in the favorable situation and reduce the risk of deviation recurrence. also it is necessary to avoid the synechia formation, nasal valve narrowing, hematoma and bleeding. due to the above mentioned problems and in order to solve and minimize them nasal packing, na...