Packing Problem

The integer-programming problem defined as follows:

$$ \begin{array}{ll} \quad\,\,\, {{\rm Maximize}\quad \boldsymbol{c^T} \boldsymbol {x}} \\ \mathrm{\rm subject}\ \mathrm{\rm to}\quad \boldsymbol {Ex}\leq \boldsymbol{e} \end{array} $$

where the components of E are either 1 or 0, the components of the column vector e are all ones, and the variables are restricted to be either 0 or 1. The idea of the problem is to choose among items or combinations of items that can be packed into a container and to do so in the most effective way.

See

Bin-Packing

Set-covering Problem

Set-partitioning Problem