The Bin-Packing Problem (BPP)

The problem consists of packing a set of items into a number of bins such that the total weight, volume, etc. does not exceed a maximum value. In a precise way, we define a bin-packing problem (BPP) as follows:

Mathematically the problem's formulation can be as follows: Given a finite set of elements $E=\{e_{1},\ldots ,e_{n}\}$ with associated weights $W=\{w_{1},\ldots ,w_{n}\}$ such that $0 \leq
w_{i} \leq w(bin)$. Partition $E$ into $N$ subsets such that the sum of weights in each partition is at most $w(bin)$ and that $N$ is the minimum.

A typical input for the BPP and its corresponding output are shown in figure 1 and 2, respectively.

BBP Input
BBP Output
Figure 1: Input for BBP
Figure 2: Output of BBP