Packing problems

Packing problems are a class of <a href="/facts/Optimization_problem/QzwJfFEE">optimization problems</a> in <a href="/facts/Mathematics/pxTouaz4">mathematics</a> that involve attempting to pack objects together into containers. The goal is to either pack a single container as <a href="/facts/Packing_density/NY81NF80">densely</a> as possible or pack all objects using as few containers as possible. Many of these problems can be related to real-life <a href="/facts/Packaging/QGRXJLjq">packaging</a>, storage and transportation issues. Each packing problem has a dual <a href="/facts/Covering_problem/4BIHqE9K">covering problem</a>, which asks how many of the same objects are required to completely cover every region of the container, where objects are allowed to overlap.
In a <a href="/facts/Bin_packing_problem/T67Qe934">bin packing problem</a>, people are given:

<ul><li>A container, usually a two- or three-dimensional <a href="/facts/Convex_region/vdAuJRJl">convex region</a>, possibly of infinite size. Multiple containers may be given depending on the problem.</li>
<li>A set of objects, some or all of which must be packed into one or more containers. The set may contain different objects with their sizes specified, or a single object of a fixed dimension that can be used repeatedly.</li></ul>
Usually the packing must be without overlaps between goods and other goods or the container walls. In some variants, the aim is to find the configuration that packs a single container with the maximal <a href="/facts/Packing_density/NY81NF80">packing density</a>. More commonly, the aim is to pack all the objects into as few containers as possible. In some variants the overlapping (of objects with each other and/or with the boundary of the container) is allowed but should be minimized.

Packing problems open-in-new

Packing problems