brazil3

benchmark decomposition benchmark_suitable aggregations precedence variable_bound set_partitioning set_packing set_covering cardinality invariant_knapsack equation_knapsack mixed_binary general_linear

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
George Fonseca	23968	14646	3.79403e-04	easy	timetabling	24	brazil3.mps.gz

Educational timetabling problems from several real schools/universities around the world. These instances were originally expressed in the xhstt file format [1] and formulated as Integer Programming models as described at [2].

[1] https://www.sciencedirect.com/science/article/pii/S0377221717302242 [2] https://link.springer.com/article/10.1007/s10479-011-1012-2

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	23968	17802
Constraints	14646	10345
Binaries	23874	17708
Integers	94	94
Continuous	0	0
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.000379403	0.000497324
Nonzeroes	133184	91588

Constraint Classification Properties
	Original	Presolved
Total	14646	10345
Empty	82	0
Free	0	0
Singleton	114	0
Aggregations	360	192
Precedence	1080	576
Variable Bound	1274	677
Set Partitioning	1270	1211
Set Packing	1170	1101
Set Covering	275	269
Cardinality	693	272
Invariant Knapsack	1217	662
Equation Knapsack	6987	5312
Bin Packing	0	0
Knapsack	0	0
Integer Knapsack	0	0
Mixed Binary	16	16
General Linear	108	57
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	1.230449
Constraint %		3.29338	5.34627	5.98753	6.35292
Variable %		3.08938	5.91821	6.66336	7.13696
Score	0.802666

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	24	24	0	0	0	-	2018-10-15	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to brazil3 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
woodlands09	hard	382147	382119	28	0	194599	2646003	George Fonseca	timetabling	0	aggregations variable_bound set_partitioning set_packing set_covering cardinality invariant_knapsack equation_knapsack general_linear
kosova1	open	614253	609591	4662	0	304931	3414761	George Fonseca	timetabling	6.0*	aggregations precedence variable_bound set_partitioning set_packing set_covering cardinality invariant_knapsack equation_knapsack binpacking general_linear
highschool1-aigio	hard	320404	319686	718	0	92568	1562168	George Fonseca	timetabling	0	benchmark benchmark_suitable aggregations variable_bound set_partitioning set_packing set_covering cardinality invariant_knapsack equation_knapsack general_linear
neos-3045796-mogo	easy	11016	11016	0	0	2226	44442	Jeff Linderoth	neos-pseudoapplication-22	-175	binary decomposition set_partitioning set_packing set_covering invariant_knapsack equation_knapsack
csched007	easy	1758	1457	0	301	351	6379	Tallys Yunes	csched	350.9999999999955	benchmark benchmark_suitable aggregations variable_bound set_partitioning mixed_binary general_linear

Reference

@article{FONSECA201728,
title = "Integer programming techniques for educational timetabling",
journal = "European Journal of Operational Research",
volume = "262",
number = "1",
pages = "28 - 39",
year = "2017",
note = "",
issn = "0377-2217",
doi = "http://dx.doi.org/10.1016/j.ejor.2017.03.020",
url = "http://www.sciencedirect.com/science/article/pii/S0377221717302242",
author = "George H.G. Fonseca and Haroldo G. Santos and Eduardo G. Carrano and Thomas J.R. Stidsen",
keywords = "Timetabling",
keywords = "Integer Programming",
keywords = "Formulation"
}