The present work proposes new heuristics and algorithms for the 3D Cutting and Packing class of problems. Specifically the cutting stock problem and a real-world application from the retail steel distribution industry are addressed. The problem being addressed for the retail steel distribution industry is the retail steel cutting problem, which is how to cut steel in order to satisfy the custom...

Here, we focus on a generalized version of the strip packing problem; namely have several open-end strips with different widths, and wish to pack rectangular items into these without overlapping such that minimize either makespan (i.e. top topmost item), or total area used. We investigate online variant problem, where are arriving one-by-one, make irrevocable decisions their packing. A similar ...

The Three Dimensional Bin Packing Problem (3DBPP) is within one of the broad categories of the Bin Packing Problem. The other broad categories include the One Dimensional and the Two Dimensional Bin Packing Problem. As we live in a three dimensional world, the 3DBPP can model a variety of real world problems. Some of the popular applications of the 3DBPP include the Container Loading Problem an...

At large packing fraction, disordered packings of particles with repulsive contact interactions jam into a rigid state where they withstand finite shear stresses before yielding. For frictionless particles at zero temperature, the Jamming transition coincides with the onset of iso-staticity. Various geometrical and mechanical properties exhibit critical behavior with the distance to Jamming. Wh...

The ordered open-end bin packing problem is a variant of the bin packing problem in which the items to be packed are sorted in a given order and the capacity of each bin can be exceeded by the last item packed into the bin. We present a branch-and-price algorithm for its exact optimization. The pricing subproblem is a special variant of the binary knapsack problem, in which the items are ordere...

We consider problems of distributing a number of points within a polygonal region P, such that the points are \far away" from each other. Problems of this type have been considered before for the case where the possible locations form a discrete set. Dispersion problems are closely related to packing problems. While Hochbaum and Maass (1985) have given a polynomial time approximation scheme for...

We prove that the First Fit bin packing algorithm is stable under the input distribution U {k − 2, k} for all k ≥ 3, settling an open question from the recent survey by Coffman, Garey, and Johnson [3]. Our proof generalizes the multi-dimensional Markov chain analysis used by Kenyon, Rabani, and Sinclair to prove that Best Fit is also stable under these distributions [11]. Our proof is motivated...

BACKGROUND Hereditary hemorrhagic telangiectasia (HHT) is an autosomal dominant disease that results in telangiectasia of the sinonasal tract, gastro-intestinal tract as well as possible arteriovenous malformations of the lung, liver and brain. One of the most common disease manifestations of HHT is epistaxis. Severe recurrent epistaxis necessitating iron therapy and blood transfusion is often ...

In the CUT PACKING problem, given an undirected connected graph G, it is required to nd the maximum number of pairwise edge disjoint cuts in G. It is an open question if CUT PACKING is NP-hard on general graphs. In this paper we prove that the problem is polynomially solvable on Seymour graphs which include both all bipar-tite and all series-parallel graphs. We also consider the weighted versio...