shiftreg2-7

decomposition numerics aggregations set_partitioning cardinality equation_knapsack binpacking knapsack mixed_binary

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Domenico Salvagnin	11404	8540	3.58352e-04	hard	shiftreg	230.326187744737	shiftreg2-7.mps.gz

Multi-activity shift scheduling problem with 2 activities 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	11404	9628
Constraints	8540	8540
Binaries	4152	2376
Integers	0	0
Continuous	7252	7252
Implicit Integers	0	0
Fixed Variables	1776	0
Nonzero Density	0.000358352	0.000381255
Nonzeroes	34900	31348

Constraint Classification Properties
	Original	Presolved
Total	8540	8540
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	3504	4176
Precedence	0	0
Variable Bound	0	0
Set Partitioning	1152	480
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	3836	3812
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 %		8.27869	8.27869	8.27869	8.27869
Variable %		8.23639	8.23639	8.23639	8.23639
Score	0.911619

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	230.3262	230.8287	7e-07	4e-07	0	-	2018-10-12	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to shiftreg2-7 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
shiftreg1-4	easy	10008	3912	6096	8136	29976	Domenico Salvagnin	shiftreg	132.66969396	decomposition numerics aggregations set_partitioning cardinality equation_knapsack binpacking knapsack mixed_binary
shiftreg5-1	open	48736	10608	38128	31424	157504	Domenico Salvagnin	shiftreg	522.1155479894852*	numerics aggregations set_partitioning cardinality equation_knapsack binpacking knapsack mixed_binary
binkar10_1	easy	2298	170	2128	1026	4496	H. Mittelmann	–	6742.1998835	benchmark benchmark_suitable aggregations 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

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}}