shiftreg5-1

numerics aggregations set_partitioning cardinality equation_knapsack binpacking knapsack mixed_binary

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Domenico Salvagnin	48736	31424	1.02844e-04	open	shiftreg	522.1155479894852*	shiftreg5-1.mps.gz

Multi-activity shift scheduling problem with 5 activities and 24 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	48736	46048
Constraints	31424	31424
Binaries	10608	7920
Integers	0	0
Continuous	38128	38128
Implicit Integers	0	0
Fixed Variables	2688	0
Nonzero Density	0.000102844	0.000105132
Nonzeroes	157504	152128

Constraint Classification Properties
	Original	Presolved
Total	31424	31424
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	11280	12432
Precedence	0	0
Variable Bound	0	0
Set Partitioning	2304	1152
Set Packing	0	0
Set Covering	0	0
Cardinality	24	24
Invariant Knapsack	0	0
Equation Knapsack	24	24
Bin Packing	24	24
Knapsack	24	72
Integer Knapsack	0	0
Mixed Binary	17744	17696
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	3.618362
Constraint %		0.00318	0.0105218	0.00636	0.700102
Variable %		0.00434	0.0116240	0.00651	0.873002
Score	0.435379

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	Int. Viol	Cons. Viol	Submitter	Date	Description
4	522.1155	522.5230	0e+00	4e-07	Edward Rothberg	2020-11-25	Found with Gurobi 9.1 NoRel heuristics
3	522.4711		9e-07	9e-07	Edward Rothberg	2019-12-13	Obtained with Gurobi 9.0
2	522.5793		0e+00	0e+00	Robert Ashford and Alkis Vazacopoulus	2019-12-18	Found using ODH\|CPlex
1	524.1003	524.1003	0e+00	0e+00	-	2018-10-13	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to shiftreg5-1 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
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
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
ns2124243	open	156083	16447	139636	139280	429032	Timo Berthold	neos-pseudoapplication-93	77460*	decomposition aggregations variable_bound set_partitioning cardinality mixed_binary general_linear
binkar10_1	easy	2298	170	2128	1026	4496	H. Mittelmann	–	6742.1998835	benchmark benchmark_suitable aggregations 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}}