markshare_5_0

benchmark_suitable integer_knapsack general_linear

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.

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	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

Constraint Classification Properties
	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

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 %		40.0000	40.0000	40.0000	40.0000
Variable %		93.3333	93.3333	93.3333	93.3333
Score	0.026667

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	1	1	0	0	0	-	2018-10-29	Solution found during MIPLIB2017 problem selection.
1	1	1	0	0	0	-	2018-10-11	Solution imported from MIPLIB2010.

Similar instances in collection

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	0.9999999999990905	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	–	21165.99999999978	set_packing integer_knapsack general_linear
neos-5045105-creuse	open	3848	0	3780	68	252	23108	Jeff Linderoth	neos-pseudoapplication-78	20.57124707548*	integer_knapsack general_linear

Reference

@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}
}