fhnw-schedule-paira400

variable_bound mixed_binary

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Simon Felix	80600	160000	3.71824e-05	open	schedule	-35.4988125672093*	fhnw-schedule-paira400.mps.gz

Continuous-time project scheduling and selection, inspired by an industry use-case. Each project has a value, the sum should be maximized. Each project has a deadline, and an earliest start date. Three formulations of the same problem (“Pair A”, “Pair B” and “Slot”) - we expect “Pair B” to be the best formulation.

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	80600	80504
Constraints	160000	159904
Binaries	80200	80104
Integers	0	0
Continuous	400	400
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	3.71824e-05	3.72416e-05
Nonzeroes	479504	479408

Constraint Classification Properties
	Original	Presolved
Total	160000	159904
Empty	0	0
Free	0	0
Singleton	96	0
Aggregations	0	0
Precedence	0	0
Variable Bound	304	304
Set Partitioning	0	0
Set Packing	0	0
Set Covering	0	0
Cardinality	0	0
Invariant Knapsack	0	0
Equation Knapsack	0	0
Bin Packing	0	0
Knapsack	0	0
Integer Knapsack	0	0
Mixed Binary	159600	159600
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	0.301030
Constraint %		99.8099	99.8099	99.8099	99.8099
Variable %		99.6224	99.6224	99.6224	99.6224
Score	0.003769

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	Obj. Viol	Submitter	Date	Description
3	-35.49881		6.9e-06	0.0000000	0.0e+00	Edward Rothberg	2019-12-13	Obtained with Gurobi 9.0
2	-20.49320	-20.49319	0.0e+00	0.0007593	8.6e-06	Frederic Didier	2020-01-22	Obtained with Google OR-tools using 8 Threads through generating subproblems by fixing part of the current solution and trying to solve them with a sub CP-SAT solver
1	-11.31802		1.0e-05	0.0000000	0.0e+00	-	2018-10-10	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to fhnw-schedule-paira400 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
fhnw-schedule-paira200	open	20300	20100	0	200	40000	119746	Simon Felix	schedule	-19.2298568218154*	variable_bound mixed_binary
fhnw-schedule-paira100	open	5150	5050	0	100	10000	29873	Simon Felix	schedule	-15.1131226682367*	variable_bound mixed_binary
nh97_potential	easy	1180	630	328	222	1916	5748	MIPLIB submission pool	–	1418	benchmark_suitable mixed_binary general_linear
pg	easy	2700	100	0	2600	125	5200	M. Dawande	–	-8674.34260712	benchmark decomposition benchmark_suitable mixed_binary
pg5_34	easy	2600	100	0	2500	225	7700	M. Dawande	–	-14339.35345	benchmark decomposition benchmark_suitable mixed_binary

Reference

No bibliographic information available