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

Domenico Salvagnin | 11404 | 8540 | 3.58352e-04 | hard | shiftreg | 230.326187744737 | shiftreg2-7.mps.gz |

Multi-activity shift scheduling problem with 2 activities and 12 employees, using an implicit model based on a regular language.

Detailed explanation of the following tables can be found here.

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

Variables | 11404 | 9628 |

Constraints | 8540 | 8540 |

Binaries | 4152 | 2376 |

Integers | 0 | 0 |

Continuous | 7252 | 7252 |

Implicit Integers | 0 | 0 |

Fixed Variables | 1776 | 0 |

Nonzero Density | 0.000358352 | 0.000381255 |

Nonzeroes | 34900 | 31348 |

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

Total | 8540 | 8540 |

Empty | 0 | 0 |

Free | 0 | 0 |

Singleton | 0 | 0 |

Aggregations | 3504 | 4176 |

Precedence | 0 | 0 |

Variable Bound | 0 | 0 |

Set Partitioning | 1152 | 480 |

Set Packing | 0 | 0 |

Set Covering | 0 | 0 |

Cardinality | 12 | 12 |

Invariant Knapsack | 0 | 0 |

Equation Knapsack | 12 | 12 |

Bin Packing | 12 | 12 |

Knapsack | 12 | 36 |

Integer Knapsack | 0 | 0 |

Mixed Binary | 3836 | 3812 |

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 | 1.113943 | ||||

Constraint % | 8.27869 | 8.27869 | 8.27869 | 8.27869 | |

Variable % | 8.23639 | 8.23639 | 8.23639 | 8.23639 | |

Score | 0.911619 |

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 | 230.3262 | 230.8287 | 7e-07 | 4e-07 | 0 | - | 2018-10-12 | Solution found during MIPLIB2017 problem selection. |

The following instances are most similar to shiftreg2-7 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 |
---|---|---|---|---|---|---|---|---|---|---|---|

shiftreg1-4 | easy | 10008 | 3912 | 0 | 6096 | 8136 | 29976 | Domenico Salvagnin | shiftreg | 132.66969396 | decomposition numerics aggregations set_partitioning cardinality equation_knapsack binpacking knapsack mixed_binary |

shiftreg5-1 | open | 48736 | 10608 | 0 | 38128 | 31424 | 157504 | Domenico Salvagnin | shiftreg | 522.1155479894852* | numerics aggregations set_partitioning cardinality equation_knapsack binpacking knapsack mixed_binary |

binkar10_1 | easy | 2298 | 170 | 0 | 2128 | 1026 | 4496 | H. Mittelmann | – | 6742.1998835 | benchmark benchmark_suitable aggregations mixed_binary |

ns2122698 | open | 155103 | 16447 | 0 | 138656 | 139280 | 424272 | Timo Berthold | neos-pseudoapplication-93 | 68749.99988531263* | decomposition aggregations set_partitioning set_packing cardinality mixed_binary general_linear |

neos-1396125 | easy | 1161 | 129 | 0 | 1032 | 1494 | 5511 | NEOS Server Submission | neos-pseudoapplication-96 | 3000.0453373 | benchmark_suitable precedence variable_bound set_partitioning set_packing cardinality invariant_knapsack knapsack mixed_binary |

```
@article{CGR11,
Author = {Marie-Claude C{\^o}t{\'e} and Bernard Gendron and Louis-Martin Rousseau},
Journal = {Management Science},
Number = {1},
Pages = {151--163},
Title = {Grammar-Based Integer Programming Models for Multiactivity Shift Scheduling},
Volume = {57},
Year = {2011}}
@article{CGQR11,
Author = {Marie-Claude C{\^o}t{\'e} and Bernard Gendron and Claude-Guy Quimper and Louis-Martin Rousseau},
Journal = {Constraints},
Number = {1},
Pages = {54--76},
Title = {Formal languages for integer programming modeling of shift scheduling problems},
Volume = {16},
Year = {2011}}
@article{QuimperRousseau10,
Author = {Quimper, Claude-Guy and Rousseau, Louis-Martin},
Journal = {Journal of Heuristics},
Pages = {373--392},
Title = {A large neighbourhood search approach to the multi-activity shift scheduling problem},
Volume = {16},
Year = {2010}}
@inproceedings{SalvagninWalsh12,
Author = {Domenico Salvagnin and Toby Walsh},
Booktitle = {CP},
Pages = {633--646},
Title = {A hybrid MIP/CP approach for multi-activity shift scheduling},
Year = {2012}}
```

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