academictimetablesmall

benchmark binary decomposition benchmark_suitable aggregations precedence variable_bound set_partitioning set_packing cardinality invariant_knapsack equation_knapsack binpacking knapsack

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Joshua Friedman	28926	23294	3.98262e-04	easy	–	0	academictimetablesmall.mps.gz

Academic timetabling integer program

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	28926	25964
Constraints	23294	18016
Binaries	28926	25964
Integers	0	0
Continuous	0	0
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.000398262	0.000530255
Nonzeroes	268350	248036

Constraint Classification Properties
	Original	Presolved
Total	23294	18016
Empty	2940	0
Free	0	0
Singleton	27	0
Aggregations	87	17
Precedence	142	131
Variable Bound	4481	3771
Set Partitioning	87	741
Set Packing	1455	2500
Set Covering	3630	0
Cardinality	880	56
Invariant Knapsack	826	9754
Equation Knapsack	298	286
Bin Packing	420	570
Knapsack	356	190
Integer Knapsack	0	0
Mixed Binary	7665	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	1.863323
Constraint %		0.0166519	1.13341	0.133215	5.91141
Variable %		0.0306960	1.25363	0.207198	4.15548
Score	0.792248

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	0	0	0	0	0	-	2018-10-10	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to academictimetablesmall 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	Constraints	Nonz.	Submitter	Group	Objective	Tags
academictimetablebig	hard	168974	168974	0	167661	1545375	Joshua Friedman	–	427	binary aggregations precedence variable_bound set_partitioning set_packing set_covering cardinality invariant_knapsack equation_knapsack binpacking knapsack
nursesched-medium-hint03	hard	34248	34170	78	14062	622800	Haroldo Gambini Santos	nursescheduling	115	benchmark decomposition benchmark_suitable set_partitioning set_packing cardinality invariant_knapsack general_linear
nursesched-sprint-late03	easy	11690	11670	20	5032	208410	Haroldo Gambini Santos	nursescheduling	48	decomposition benchmark_suitable set_partitioning set_packing cardinality invariant_knapsack general_linear
nursesched-sprint-hidden09	easy	11650	11630	20	4872	208050	Haroldo Gambini Santos	nursescheduling	338	benchmark_suitable set_partitioning set_packing cardinality invariant_knapsack general_linear
neos-960392	easy	59376	59376	0	4744	189503	NEOS Server Submission	neos-pseudoapplication-94	-238	benchmark binary benchmark_suitable precedence variable_bound set_partitioning set_packing invariant_knapsack binpacking knapsack

Reference

@article{Friedman16,
  title={Automated timetabling for small colleges and high schools using huge integer programs},
  author={Friedman, Joshua S},
  journal={arXiv preprint arXiv:1612.08777},
  year={2016}
}