bin packing problem

(classic problem)

Definition:
Determine how to put the most objects in the least number of fixed space bins. More formally, find a partition and assignment of a set of objects such that a constraint is satisfied or an objective function is minimized (or maximized). There are many variants, such as, 3D, 2D, linear, pack by volume, pack by weight, minimize volume, maximize value, fixed shape objects, etc.

Note:
A common form of the problem is, what is the least number of bins (containers of fixed volume) needed to hold a set of objects. This problem often appears in manufacturing. For instance, suppose we need a number of pipes of different, specific lengths to plumb a house and we can buy pipe stock in 5 meter lengths. How can we cut the 5 meter pipes to waste as little as possible (minimize the cost of pipe)?

Everyone likes to cut a little pipe now and then.