Submitter | Variables | Constraints | Density | Status | Group | Objective | MPS File |
---|---|---|---|---|---|---|---|

Sam Allen | 754 | 1561 | 1.17851e-02 | easy | pigeon | -12000 | pigeon-13.mps.gz |

Instance of 3D packing (container loading) problem. The problem was solved by the Gurobi Optimizer version 5.0.1. It took approximately 22 hours.

Imported from MIPLIB2010.

Detailed explanation of the following tables can be found here.

Original | Presolved | |
---|---|---|

Variables | 754 | 637 |

Constraints | 1561 | 1560 |

Binaries | 637 | 598 |

Integers | 0 | 0 |

Continuous | 117 | 39 |

Implicit Integers | 0 | 0 |

Fixed Variables | 0 | 0 |

Nonzero Density | 0.0117851 | 0.0139456 |

Nonzeroes | 13871 | 13858 |

Original | Presolved | |
---|---|---|

Total | 1561 | 1560 |

Empty | 0 | 0 |

Free | 0 | 0 |

Singleton | 0 | 0 |

Aggregations | 0 | 0 |

Precedence | 0 | 0 |

Variable Bound | 0 | 0 |

Set Partitioning | 0 | 13 |

Set Packing | 0 | 0 |

Set Covering | 0 | 0 |

Cardinality | 78 | 65 |

Invariant Knapsack | 468 | 468 |

Equation Knapsack | 0 | 0 |

Bin Packing | 0 | 0 |

Knapsack | 1 | 0 |

Integer Knapsack | 0 | 0 |

Mixed Binary | 1014 | 1014 |

General Linear | 0 | 0 |

Indicator | 0 | 0 |

Available nonzero structure and decomposition information. Further information can be found here.

Decomposed structure of original problem (dec-file)

Decomposed structure after trivial presolving (dec-file)

value | min | median | mean | max | |
---|---|---|---|---|---|

Components | 0.602060 | ||||

Constraint % | 21.6667 | 21.6667 | 21.6667 | 21.6667 | |

Variable % | 32.6531 | 32.6531 | 32.6531 | 32.6531 | |

Score | 0.437755 |

Find solutions below. Download the archive containing all solutions from the Download page.

ID | Objective | Exact | Int. Viol | Cons. Viol | Obj. Viol | Submitter | Date | Description |
---|---|---|---|---|---|---|---|---|

1 | -12000 | -12000 | 0 | 0 | 0 | - | 2018-10-12 | Solution found during MIPLIB2017 problem selection. |

The following instances are most similar to pigeon-13 in the collection. This similarity analysis is based on 100 scaled instance features describing properties of the variables, objective function, bounds, constraints, and right hand sides.

Instance | Status | Variables | Binaries | Integers | Continuous | Constraints | Nonz. | Submitter | Group | Objective | Tags |
---|---|---|---|---|---|---|---|---|---|---|---|

pigeon-16 | easy | 1072 | 928 | 0 | 144 | 2353 | 21104 | Sam Allen | pigeon | -15000 | benchmark_suitable set_partitioning cardinality invariant_knapsack mixed_binary |

pigeon-10 | easy | 490 | 400 | 0 | 90 | 931 | 8150 | Sam Allen | pigeon | -9000 | benchmark_suitable set_partitioning cardinality invariant_knapsack mixed_binary |

pigeon-20 | easy | 1580 | 1400 | 0 | 180 | 3661 | 33100 | Sam Allen | pigeon | -19000 | benchmark_suitable set_partitioning cardinality invariant_knapsack mixed_binary |

pigeon-08 | easy | 344 | 272 | 0 | 72 | 601 | 5176 | Sam Allen | pigeon | -7000 | benchmark_suitable set_partitioning cardinality invariant_knapsack mixed_binary |

supportcase41 | open | 4725 | 2000 | 0 | 2725 | 28923 | 221321 | Domenico Salvagnin | – | 32.03376809388* | precedence variable_bound mixed_binary |

```
@article{AllenBurkeMarecek2010,
author = {Sam D. Allen and Edmund K. Burke and Jakub Marecek},
journal = {Technical Report, University of Nottingham},
title = {A Space-Indexed Formulation of Packing Boxes into a Larger Box},
year = {2010}
}
@article{AllenBurkeMarecek2011,
author = {Sam D. Allen and Edmund K. Burke and Jakub Marecek},
journal = {Oper. Res. Lett.},
number = {1},
pages = {20--24},
title = {A Space-Indexed Formulation of Packing Boxes into a Larger Box},
volume = {40},
year = {2012}
}
```

Last Update Aug 13, 2020 by Gabriel Kressin

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