This problem involves maximizing the number of pipes that can be fit into a storage container (but it’s a pipe fitting problem, not a bin packing problem).
A company manufactures pipes of uniform diameter. All pipes are stored in rectangular storage containers, but the containers come in several different sizes. Pipes are stored in rows within a container so that there is no space between pipes in any row (there may be some space at the end of a row), i.e., all pipes in a row are tangent, or touch. Within a rectangular cross-section, pipes are stored in either a grid pattern or a skew pattern as shown below: the two left-most cross-sections are in a grid pattern, the two right-most cross-sections are in a skew pattern.
Note that although it may not be apparent from the diagram, there is no space between adjacent pipes in any row. The pipes in any row are tangent to (touch) the pipes in the row below (or rest on the bottom of the container). When pipes are packed into a container, there may be “left-over” space in which a pipe cannot be packed. Such left-over space is packed with padding so that the pipes cannot settle during shipping.
3 3 2.9 10 2.9 10.5 11 11
9 grid 29 skew 30 skew 126 skew