shiftreg1-4

decomposition numerics aggregations set_partitioning cardinality equation_knapsack binpacking knapsack mixed_binary

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Domenico Salvagnin	10008	8136	3.68142e-04	easy	shiftreg	132.66969396	shiftreg1-4.mps.gz

Multi-activity shift scheduling problem with 1 activity and 12 employees, using an implicit model based on a regular language.

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	10008	8376
Constraints	8136	8136
Binaries	3912	2280
Integers	0	0
Continuous	6096	6096
Implicit Integers	0	0
Fixed Variables	1632	0
Nonzero Density	0.000368142	0.000391975
Nonzeroes	29976	26712

Constraint Classification Properties
	Original	Presolved
Total	8136	8136
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	4248	4968
Precedence	0	0
Variable Bound	0	0
Set Partitioning	1152	432
Set Packing	0	0
Set Covering	0	0
Cardinality	12	12
Invariant Knapsack	0	0
Equation Knapsack	12	12
Bin Packing	12	12
Knapsack	12	36
Integer Knapsack	0	0
Mixed Binary	2688	2664
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	1.113943
Constraint %		8.27188	8.27188	8.27188	8.27188
Variable %		8.26170	8.26170	8.26170	8.26170
Score	0.910618

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	132.6697	132.6697	0	0	0	-	2018-10-12	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to shiftreg1-4 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
shiftreg2-7	hard	11404	4152	7252	8540	34900	Domenico Salvagnin	shiftreg	230.326187744737	decomposition numerics aggregations set_partitioning cardinality equation_knapsack binpacking knapsack mixed_binary
shiftreg5-1	hard	48736	10608	38128	31424	157504	Domenico Salvagnin	shiftreg	520.2562364680399	numerics aggregations set_partitioning cardinality equation_knapsack binpacking knapsack mixed_binary
ns2122698	open	155103	16447	138656	139280	424272	Timo Berthold	neos-pseudoapplication-93	68749.99988531263*	decomposition aggregations set_partitioning set_packing cardinality mixed_binary general_linear
neos-1396125	easy	1161	129	1032	1494	5511	NEOS Server Submission	neos-pseudoapplication-96	3000.0453373	benchmark_suitable precedence variable_bound set_partitioning set_packing cardinality invariant_knapsack knapsack mixed_binary
ns2124243	open	156083	16447	139636	139280	429032	Timo Berthold	neos-pseudoapplication-93	77460*	decomposition aggregations variable_bound set_partitioning cardinality mixed_binary general_linear

Reference

@article{CGR11,
    Author = {Marie-Claude C{\^o}t{\'e} and Bernard Gendron and Louis-Martin Rousseau},
    Journal = {Management Science},
    Number = {1},
    Pages = {151--163},
    Title = {Grammar-Based Integer Programming Models for Multiactivity Shift Scheduling},
    Volume = {57},
    Year = {2011}}

@article{CGQR11,
    Author = {Marie-Claude C{\^o}t{\'e} and Bernard Gendron and Claude-Guy Quimper and Louis-Martin Rousseau},
    Journal = {Constraints},
    Number = {1},
    Pages = {54--76},
    Title = {Formal languages for integer programming modeling of shift scheduling problems},
    Volume = {16},
    Year = {2011}}

@article{QuimperRousseau10,
    Author = {Quimper, Claude-Guy and Rousseau, Louis-Martin},
    Journal = {Journal of Heuristics},
    Pages = {373--392},
    Title = {A large neighbourhood search approach to the multi-activity shift scheduling problem},
    Volume = {16},
    Year = {2010}}

@inproceedings{SalvagninWalsh12,
    Author = {Domenico Salvagnin and Toby Walsh},
    Booktitle = {CP},
    Pages = {633--646},
    Title = {A hybrid MIP/CP approach for multi-activity shift scheduling},
    Year = {2012}}