English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We present an exact method, based on an arc-flow formulation with sideconstraints, for solving bin packing and cutting stock problems --- includingmulti-constraint variants --- by simply representing all the patterns in a verycompact graph. Our method includes a graph compression algorithm that usuallyreduces the size of the underlying graph substantially without weakening themodel. As opposed to our method, which provides strong models, conventionalmodels are usually highly symmetric and provide very weak lower bounds.  Our formulation is equivalent to Gilmore and Gomory's, thus providing a verystrong linear relaxation. However, instead of using column-generation in aniterative process, the method constructs a graph, where paths from the sourceto the target node represent every valid packing pattern.  The same method, without any problem-specific parameterization, was used tosolve a large variety of instances from several different cutting and packingproblems. In this paper, we deal with vector packing, graph coloring, binpacking, cutting stock, cardinality constrained bin packing, cutting stock withcutting knife limitation, cutting stock with binary patterns, bin packing withconflicts, and cutting stock with binary patterns and forbidden pairs. Wereport computational results obtained with many benchmark test data sets, allof them showing a large advantage of this formulation with respect to thetraditional ones.

Bin Packing and Related Problems: General Arc-flow Formulation with Graph Compression