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

G. Cornuéjols, M. Dawande | 45 | 5 | 9.02222e-01 | easy | markshare | 1 | markshare_5_0.mps.gz |

Market sharing problem

Imported from MIPLIB2010.

Detailed explanation of the following tables can be found here.

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

Variables | 45 | 45 |

Constraints | 5 | 5 |

Binaries | 40 | 40 |

Integers | 0 | 5 |

Continuous | 5 | 0 |

Implicit Integers | 0 | 5 |

Fixed Variables | 0 | 0 |

Nonzero Density | 0.902222 | 0.902222 |

Nonzeroes | 203 | 203 |

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

Total | 5 | 10 |

Empty | 0 | 0 |

Free | 0 | 0 |

Singleton | 0 | 0 |

Aggregations | 0 | 0 |

Precedence | 0 | 0 |

Variable Bound | 0 | 0 |

Set Partitioning | 0 | 0 |

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 | 5 |

Mixed Binary | 5 | 0 |

General Linear | 0 | 5 |

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 % | 40.0000 | 40.0000 | 40.0000 | 40.0000 | |

Variable % | 93.3333 | 93.3333 | 93.3333 | 93.3333 | |

Score | 0.026667 |

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 | 1 | 1 | 0 | 0 | 0 | - | 2018-10-11 | Solution imported from MIPLIB2010. |

2 | 1 | 1 | 0 | 0 | 0 | - | 2018-10-29 | Solution found during MIPLIB2017 problem selection. |

The following instances are most similar to markshare_5_0 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 |
---|---|---|---|---|---|---|---|---|---|---|---|

markshare1 | easy | 62 | 50 | 0 | 12 | 6 | 312 | G. Cornuéjols, M. Dawande | markshare | 0.9999999999991 | benchmark_suitable integer_knapsack general_linear |

markshare_4_0 | easy | 34 | 30 | 0 | 4 | 4 | 123 | G. Cornuéjols, M. Dawande | markshare | 1 | benchmark benchmark_suitable integer_knapsack general_linear |

markshare2 | hard | 74 | 60 | 0 | 14 | 7 | 434 | G. Cornuéjols, M. Dawande | markshare | 1 | benchmark benchmark_suitable integer_knapsack general_linear |

gt2 | easy | 188 | 24 | 164 | 0 | 29 | 376 | MIPLIB submission pool | -- | 21166 | set_packing integer_knapsack general_linear |

neos-5045105-creuse | open | 3848 | 0 | 3780 | 68 | 252 | 23108 | Jeff Linderoth | neos-pseudoapplication-78 | 20.5714290993* | integer_knapsack general_linear |

```
@article{AardalBixbyHurkensEtal2000,
author = {K. Aardal and R. E. Bixby and C. A. J. Hurkens and A. K. Lenstra and J. W. Smeltink},
instance = {markshare1,markshare2},
journal = {INFORMS Journal on Computing},
language = {English},
number = {3},
pages = {192--202},
title = {Market split and basis reduction: Towards a solution of the
{C}ornu{\'e}jols-{D}awande instances},
volume = {12},
year = {2000}
}
@article{CornuejolsDawande1999,
author = {G. Cornu{\'e}jols and M. Dawande},
instance = {markshare1,markshare2},
journal = {INFORMS Journal on Computing},
language = {English},
number = {2},
pages = {205--210},
title = {A Class of Hard Small 0-1 Programs},
volume = {11},
year = {1999}
}
```

Last Update Mai 20, 2021 by Philipp Wellner

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