fhnw-schedule-pairb400

precedence variable_bound invariant_knapsack mixed_binary

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Simon Felix	160400	399096	1.87002e-05	open	schedule	-35.4584*	fhnw-schedule-pairb400.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	160400	92720
Constraints	399096	230280
Binaries	160000	92416
Integers	0	0
Continuous	400	304
Implicit Integers	0	0
Fixed Variables	96	0
Nonzero Density	1.87002e-05	3.04499e-05
Nonzeroes	1197100	650152

Constraint Classification Properties
	Original	Presolved
Total	399096	230280
Empty	0	0
Free	0	0
Singleton	96	0
Aggregations	0	0
Precedence	159600	101973
Variable Bound	0	10483
Set Partitioning	0	0
Set Packing	0	0
Set Covering	79800	0
Cardinality	0	0
Invariant Knapsack	0	46056
Equation Knapsack	0	0
Bin Packing	0	0
Knapsack	0	0
Integer Knapsack	0	0
Mixed Binary	159600	71768
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 %		68.8345	68.8345	68.8345	68.8345
Variable %		67.7922	67.7922	67.7922	67.7922
Score	0.221701

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	Cons. Viol	Obj. Viol	Submitter	Date	Description
4	-35.45840	-35.45841	8e-07	6.1e-06	Mou Sun, Tao Li, Wotao Yin	2023-12-22	Results computed using an adapted CPLEX with a 2-hour limit; details in the report “MindOpt Adapter for CPLEX Benchmarking Performance Analysis” (arXiv preprint: 2312.13527, 2023).
3	-35.45718	-35.45718	0e+00	0.0e+00	Edward Rothberg	2020-04-22	Obtained with Gurobi 9.0 using the solution improvement heuristic
2	-34.19035		0e+00	0.0e+00	Edward Rothberg	2019-12-13	Obtained with Gurobi 9.0
1	-28.78138	-28.78138	0e+00	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-pairb400 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
fhnw-schedule-pairb200	open	40200	40000	200	99554	298554	Simon Felix	schedule	-19.24094384259708*	precedence variable_bound invariant_knapsack mixed_binary
ns1828997	open	27275	27275	0	81725	190670	NEOS Server Submission	neos-pseudoapplication-13	7.99999999999967*	binary precedence variable_bound cardinality invariant_knapsack
neos-4300652-rahue	easy	33003	20900	12103	76992	183616	Jeff Linderoth	neos-pseudoapplication-13	2.1416	benchmark decomposition benchmark_suitable aggregations precedence variable_bound set_partitioning cardinality knapsack mixed_binary
neos-3283608-agout	easy	26256	26224	32	108649	301792	Jeff Linderoth	neos-pseudoapplication-84	Unbounded	precedence variable_bound set_partitioning set_covering invariant_knapsack mixed_binary
neos-3209462-rhin	hard	56453	383	56070	170226	447473	Jeff Linderoth	neos-pseudoapplication-98	12	aggregations precedence variable_bound set_partitioning set_covering cardinality invariant_knapsack mixed_binary

Reference

No bibliographic information available