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

G. Astfalk | 8904 | 823 | 9.95703e-03 | easy | air | 56137 | air04.mps.gz |

Airline crew scheduling set partitioning problem

Imported from MIPLIB2010.

Detailed explanation of the following tables can be found here.

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

Variables | 8904 | 8904 |

Constraints | 823 | 823 |

Binaries | 8904 | 8904 |

Integers | 0 | 0 |

Continuous | 0 | 0 |

Implicit Integers | 0 | 0 |

Fixed Variables | 0 | 0 |

Nonzero Density | 0.00995703 | 0.00995703 |

Nonzeroes | 72965 | 72965 |

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

Total | 823 | 823 |

Empty | 0 | 0 |

Free | 0 | 0 |

Singleton | 0 | 0 |

Aggregations | 2 | 2 |

Precedence | 0 | 0 |

Variable Bound | 0 | 0 |

Set Partitioning | 821 | 821 |

Set Packing | 0 | 0 |

Set Covering | 0 | 0 |

Cardinality | 0 | 0 |

Invariant Knapsack | 0 | 0 |

Equation Knapsack | 0 | 0 |

Bin Packing | 0 | 0 |

Knapsack | 0 | 0 |

Integer Knapsack | 0 | 0 |

Mixed Binary | 0 | 0 |

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 | 0.301030 | ||||

Constraint % | 0.2457000 | 0.2457000 | 0.2457000 | 0.2457000 | |

Variable % | 0.0341647 | 0.0341647 | 0.0341647 | 0.0341647 | |

Score | 0.002456 |

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 | 56137 | 56137 | 0 | 0 | 0 | - | 2018-10-12 | Solution found during MIPLIB2017 problem selection. |

2 | 56137 | 56137 | 0 | 0 | 0 | - | 2018-10-12 | Solution imported from MIPLIB2010. |

The following instances are most similar to air04 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 |
---|---|---|---|---|---|---|---|---|---|---|---|

air05 | easy | 7195 | 7195 | 0 | 0 | 426 | 52121 | G. Astfalk | air | 26374 | benchmark binary benchmark_suitable set_partitioning |

air03 | easy | 10757 | 10757 | 0 | 0 | 124 | 91028 | G. Astfalk | air | 340160 | binary aggregations set_partitioning |

mod010 | easy | 2655 | 2655 | 0 | 0 | 146 | 11203 | MIPLIB submission pool | mod | 6548 | binary set_partitioning cardinality binpacking |

10teams | easy | 2025 | 1800 | 0 | 225 | 230 | 12150 | MIPLIB submission pool | -- | 924 | binary set_partitioning set_packing invariant_knapsack |

ds | hard | 67732 | 67732 | 0 | 0 | 656 | 1024059 | MIPLIB submission pool | -- | 93.52 | binary set_partitioning |

```
@article{BaruttHull1990,
author = {J. Barutt and T. Hull},
instance = {air04,air05},
journal = {SIAM News},
language = {English},
number = {6},
title = {Airline Crew Scheduling: Supercomputers and Algorithms},
volume = {23},
year = {1990}
}
```

Last Update Mai 20, 2021 by Philipp Wellner

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