physiciansched3-4

aggregations precedence variable_bound set_packing set_covering invariant_knapsack binpacking knapsack mixed_binary general_linear

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Pelin Damci-Kurt	74119	239780	5.11265e-05	easy	physiciansched	1480386.746666666	physiciansched3-4.mps.gz

Physician scheduling problem for hospitalist, radiology and kidney specialist groups. Solved in 5533s on 6 cores using Gurobi 9.0

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	74119	26715
Constraints	239780	74601
Binaries	65900	20124
Integers	0	2190
Continuous	8219	4401
Implicit Integers	0	2190
Fixed Variables	873	0
Nonzero Density	5.11265e-05	1.71646e-04
Nonzeroes	908634	342084

Constraint Classification Properties
	Original	Presolved
Total	239780	74601
Empty	10158	0
Free	0	0
Singleton	9499	0
Aggregations	0	30
Precedence	40372	20361
Variable Bound	139990	36647
Set Partitioning	0	0
Set Packing	2194	1121
Set Covering	543	1185
Cardinality	0	0
Invariant Knapsack	10763	4465
Equation Knapsack	0	0
Bin Packing	9128	3648
Knapsack	7794	1006
Integer Knapsack	0	0
Mixed Binary	9339	3197
General Linear	0	2941
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	2.800717
Constraint %		0.00134	0.1211050	0.00134	12.82420
Variable %		0.00523	0.0823235	0.00523	7.40256
Score	0.745952

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	Submitter	Date	Description
3	1480387	1480387	Ed Klotz	2022-05-25	Found with Gurobi v9.5.1rc2 using 8 threads in 40 minutes.
2	1480387		Edward Rothberg	2019-12-18	Optimal solution found with Gurobi 9.0 in 5500s on 6 cores
1	1480390		Robert Ashford and Alkis Vazacopoulos	2019-12-18	Found using ODH\|CPlex

Similar instances in collection

The following instances are most similar to physiciansched3-4 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	Integers	Continuous	Constraints	Nonz.	Submitter	Group	Objective	Tags
physiciansched3-3	easy	79555	72141	0	7414	266227	1062479	Pelin Damci-Kurt	physiciansched	2623271.326667	benchmark decomposition benchmark_suitable precedence variable_bound set_packing set_covering invariant_knapsack binpacking knapsack mixed_binary
physiciansched5-3	easy	14488	11501	0	2987	31925	156378	Pelin Damci-Kurt	physiciansched	21100	decomposition benchmark_suitable precedence variable_bound set_packing set_covering invariant_knapsack binpacking mixed_binary
neos-5193246-nerang	easy	14546	9792	0	4754	42256	175794	Jeff Linderoth	neos-pseudoapplication-32	0.03821976217279999	benchmark_suitable aggregations precedence variable_bound set_partitioning cardinality invariant_knapsack knapsack mixed_binary
neos-5195221-niemur	easy	14546	9792	0	4754	42256	176586	Jeff Linderoth	neos-pseudoapplication-32	0.0038354326	benchmark benchmark_suitable aggregations precedence variable_bound set_partitioning cardinality invariant_knapsack knapsack mixed_binary
neos-555884	easy	3815	3800	15	0	4331	19067	NEOS Server Submission	neos-pseudoapplication-32	1232700	decomposition benchmark_suitable aggregations precedence variable_bound set_partitioning cardinality equation_knapsack binpacking mixed_binary general_linear

Reference

No bibliographic information available