1. Bin Packing Algorithms

2. Bin Packing Consider a set of bins, all the same cross section and height. The bin packing problem is to pack into the bins a number of boxes of the same cross section as the bins, but of varying height so as to use the minimum possible bins.

3. Example: suppose bins are 15m tall and boxes are:- Box A B C D E F G H I J Height 8 6 7 5 9 4 3 6 5 6

4. Example: suppose bins are 15m tall and boxes are:- Box A B C D E F G H I J Height 8 6 7 5 9 4 3 6 5 6 Total size of all bins = 59, 59/15 = 3 and 14/15 So best solution could be 4???? But this may or may not be possible

5. Full Bin Combinations For problems with only a few bins it is possible to look for combinations that will fill a bin. For example if we look at the example mentioned before:-

6. Example: suppose bins are 15m tall and boxes are:- Box A B C D E F G H I J Height 8 6 7 5 9 4 3 6 5 6 Here we can spot some full bin combinations B + E ----- Full bin 1 A + C ----- Full bin 2 G + H + J -----Full bin 3 This leaves D, F and I = 14, almost fills bin 4

7. This is best summarised using a diagram