splan1

numerics aggregations variable_bound set_partitioning set_packing cardinality invariant_knapsack knapsack integer_knapsack mixed_binary general_linear

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
C. Helmberg, A. Lau	1317382	572800	6.93595e-06	open	–	-194336.3443844448*	splan1.mps.gz

University course timetabling instance 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	1317382	1288613
Constraints	572800	557387
Binaries	90810	92731
Integers	1978	50791
Continuous	1224594	1145091
Implicit Integers	0	50734
Fixed Variables	0	0
Nonzero Density	6.93595e-06	7.19297e-06
Nonzeroes	5233840	5166390

Constraint Classification Properties
	Original	Presolved
Total	574272	557444
Empty	0	0
Free	0	0
Singleton	9271	0
Aggregations	15468	17563
Precedence	100	0
Variable Bound	23466	21243
Set Partitioning	0	46819
Set Packing	14034	14034
Set Covering	0	0
Cardinality	105	105
Invariant Knapsack	390	390
Equation Knapsack	0	0
Bin Packing	0	0
Knapsack	215	215
Integer Knapsack	1472	57
Mixed Binary	508279	451631
General Linear	1472	5387
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
Constraint %
Variable %
Score

Best Known Solution(s)

Find solutions below. Download the archive containing all solutions from the Download page.

## Warning in lapply(df["exactobjval"], as.numeric): NAs introduced by coercion

ID	Objective	Exact	Cons. Viol	Obj. Viol	Submitter	Date	Description
5	-194336.3	-194336.3	5e-07	0.0e+00	Ed Rothberg	2023-05-23	Found with the NoRel heuristic.
4	-193995.0	-193995.0	5e-07	6.5e-06	Ed Rothberg	2023-05-19	Found with the NoRel heuristic.
3	341753.1		0e+00	0.0e+00	Edward Rothberg	2020-02-17	Obtained with Gurobi 9.0 using the solution improvement heuristic
2	6630536.6		0e+00	0.0e+00	Edward Rothberg	2019-12-13	Obtained with Gurobi 9.0
1	6771695.2	6766599.7	0e+00	0.0e+00	-	2018-10-12	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to splan1 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
neos-2987202-jeir	hard	146700	9045	0	137655	120209	1979663	Jeff Linderoth	neos-pseudoapplication-82	-1836136351.2	numerics aggregations precedence mixed_binary
lr1dr12vc10v70b-t360	open	193525	90670	93480	9375	56160	587100	Dimitri Papageorgiou	maritime	1166516.57270949*	aggregations variable_bound set_partitioning set_packing integer_knapsack mixed_binary general_linear
gasprod2-2	easy	29568	6826	0	22742	72728	280740	Andrew Stamps	gasprod	1375631.6625	numerics aggregations precedence variable_bound set_packing invariant_knapsack binpacking mixed_binary
ns2124243	open	156083	16447	0	139636	139280	429032	Timo Berthold	neos-pseudoapplication-93	77460*	decomposition aggregations variable_bound set_partitioning cardinality mixed_binary general_linear
unitcal_7	easy	25755	2856	0	22899	48939	127595	R. O’Neill	–	19635558.244	benchmark benchmark_suitable precedence variable_bound mixed_binary general_linear

Reference

@mastersthesis{Lau2008,
 author = {Anja Lau},
 school = {Technische Universit{\"a}t Chemnitz},
 title = {Erstellen von wegeoptimierten {S}tundenpl{\"a}nen mit
{D}iskreten {M}ethoden},
 type = {Diploma thesis},
 year = {2008}
}