fhnw-schedule-pairb200

precedence variable_bound invariant_knapsack mixed_binary

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Simon Felix	40200	99554	7.45999e-05	open	schedule	-19.24094384259708*	fhnw-schedule-pairb200.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	40200	21462
Constraints	99554	52925
Binaries	40000	21316
Integers	0	0
Continuous	200	146
Implicit Integers	0	0
Fixed Variables	54	0
Nonzero Density	7.45999e-05	1.31883e-04
Nonzeroes	298554	149803

Constraint Classification Properties
	Original	Presolved
Total	99554	52925
Empty	0	0
Free	0	0
Singleton	54	0
Aggregations	0	0
Precedence	39800	23425
Variable Bound	0	2231
Set Partitioning	0	0
Set Packing	0	0
Set Covering	19900	0
Cardinality	0	0
Invariant Knapsack	0	10585
Equation Knapsack	0	0
Bin Packing	0	0
Knapsack	0	0
Integer Knapsack	0	0
Mixed Binary	39800	16684
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 %		68.4761	68.4761	68.4761	68.4761
Variable %		67.4335	67.4335	67.4335	67.4335
Score	0.223003

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	-19.24094	-19.24094	8e-07	3e-06	Edward Rothberg	2020-04-22	Obtained with Gurobi 9.0 using the solution improvement heuristic
3	-19.20221		0e+00	0e+00	Edward Rothberg	2019-12-13	Obtained with Gurobi 9.0
2	-17.76836		0e+00	0e+00	Robert Ashford and Alkis Vazacopoulus	2019-12-18	Found using ODH\|CPlex
1	-17.50880	-17.50880	0e+00	0e+00	-	2018-10-10	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to fhnw-schedule-pairb200 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-pairb400	open	160400	160000	400	399096	1197096	Simon Felix	schedule	-35.4584*	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-1337307	easy	2840	2840	0	5687	30799	NEOS Server Submission	neos-pseudoapplication-13	-202319	binary decomposition benchmark_suitable precedence set_partitioning invariant_knapsack knapsack mixed_binary

Reference

No bibliographic information available