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.

Location of instance in collection

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.

Nonzero entries of original problem

Nonzero entries after trivial presolving

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

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	Continuous	Constraints	Nonz.	Submitter	Group	Objective	Tags
pigeon-16	easy	1072	928	144	2353	21104	Sam Allen	pigeon	-15000	benchmark_suitable set_partitioning cardinality invariant_knapsack mixed_binary
pigeon-10	easy	490	400	90	931	8150	Sam Allen	pigeon	-9000	benchmark_suitable set_partitioning cardinality invariant_knapsack mixed_binary
pigeon-20	easy	1580	1400	180	3661	33100	Sam Allen	pigeon	-19000	benchmark_suitable set_partitioning cardinality invariant_knapsack mixed_binary
pigeon-08	easy	344	272	72	601	5176	Sam Allen	pigeon	-7000	benchmark_suitable set_partitioning cardinality invariant_knapsack mixed_binary
supportcase41	open	4725	2000	2725	28923	221321	Domenico Salvagnin	–	32.00076832127569*	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}
}