pigeon-13

benchmark_suitable set_partitioning cardinality invariant_knapsack mixed_binary

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.

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
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
Constraint Classification Properties
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

Structure

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

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

Best Known Solution(s)

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.

Similar instances in collection

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

Reference

@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}
}

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