air04

binary benchmark_suitable aggregations set_partitioning

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.

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	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

Constraint Classification Properties
	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

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	0.301030
Constraint %		0.2457000	0.2457000	0.2457000	0.2457000
Variable %		0.0341647	0.0341647	0.0341647	0.0341647
Score	0.002456

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
2	56137	56137	0	0	0	-	2018-10-12	Solution imported from MIPLIB2010.
1	56137	56137	0	0	0	-	2018-10-12	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

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	Continuous	Constraints	Nonz.	Submitter	Group	Objective	Tags
air05	easy	7195	7195	0	426	52121	G. Astfalk	air	26374	benchmark binary benchmark_suitable set_partitioning
air03	easy	10757	10757	0	124	91028	G. Astfalk	air	340160	binary aggregations set_partitioning
mod010	easy	2655	2655	0	146	11203	MIPLIB submission pool	mod	6548	binary set_partitioning cardinality binpacking
10teams	easy	2025	1800	225	230	12150	MIPLIB submission pool	–	923.9999999999997	binary set_partitioning set_packing invariant_knapsack
ds	hard	67732	67732	0	656	1024059	MIPLIB submission pool	–	93.52	binary set_partitioning

Reference

@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}
}