This is a program, which reads an instance of an bpp and solves the bpp with the following BIP model with the SCIP-Framework and soplex as solver.
| Indizes und Mengen |
|
| $i \in \mathcal{I}$ |
Items |
| $j \in \mathcal{J}$ |
Bins |
| Parameter |
|
| $w_{i}$ |
Weight of item $i$
|
| $b$ |
Capacity of a single bin |
| Entscheidungsvariablen |
|
| $X_{ij} \in{0, 1}$ |
= 1 if we pack item $i$ into bin $j$, 0 otherwise |
| $Y_{j} \in{0, 1}$ |
=1 if we use bin $j$, 0 otherwise |
$$\min \sum_{j \in \mathcal{J}} Y_{j} \\\
s.t. \\\
\sum_{j \in \mathcal{J}} X_{ij} = 1; \forall i \in \mathcal{I} \\\
\sum_{i \in \mathcal{I}} w_{i} \cdot X_{ij} \leq b\cdot Y_{j}; \forall j \in \mathcal{J} \\$$