bppc6-06

set_partitioning mixed_binary

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Manuel Iori	3922	273	1.69524e-01	open	bppc	208*	bppc6-06.mps.gz

The models that we attach solve the “bar-relaxation”, also known as the “Bin Packing Problem with Contiguity” or the “P||Cmax with contiguity”. This is one of the most interesting relaxations for two dimensional cutting and packing problems. Its solution by means of an ILP software is the bottleneck of the primal decomposition methods that we attempted in the paper cited below. In detail, the files correspond to model (12)-(15) in the paper, applied to the instances of the Classes 4, 6 and 8 by Martello and Vigo (Management Science, 1998).

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	3922	3921
Constraints	273	273
Binaries	3920	3920
Integers	0	0
Continuous	2	1
Implicit Integers	0	0
Fixed Variables	1	0
Nonzero Density	0.169524	0.169567
Nonzeroes	181510	181510

Constraint Classification Properties
	Original	Presolved
Total	273	273
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	0	0
Precedence	0	0
Variable Bound	0	0
Set Partitioning	20	20
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	253	253
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	1.322219
Constraint %		0.36630	0.36630	0.36630	0.36630
Variable %		3.06044	4.99872	5.07524	5.84035
Score	0.069598

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	208		Hans Mittelmann	2019-12-18	found with Gurobi 9.0 using 48 threads after approx. 11 hours of running time
2	210		Robert Ashford and Alkis Vazacopoulus	2019-12-18	Found using ODH\|CPlex
1	212	212	-	2018-10-12	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to bppc6-06 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
bppc6-02	hard	4784	4782	0	2	309	188143	Manuel Iori	bppc	116	set_partitioning mixed_binary
bppc4-08	easy	1456	1454	0	2	111	23964	Manuel Iori	bppc	53	benchmark benchmark_suitable set_partitioning mixed_binary
bppc8-09	easy	431	423	6	2	67	9051	Manuel Iori	bppc	471.9999999999998	benchmark_suitable set_partitioning mixed_binary
assign1-10-4	open	572	520	0	52	582	28280	Robert Fourer	assign1	422*	set_partitioning cardinality mixed_binary
assign1-5-8	easy	156	130	0	26	161	3720	Robert Fourer	assign1	211.999999999998	benchmark benchmark_suitable set_partitioning cardinality mixed_binary

Reference

@ARTICLE{CDI14,
    AUTHOR  = "C{\^o}t{\'e}, J.-F. and Dell'Amico, M. and Iori, M.",
    TITLE   = "Combinatorial {B}enders' Cuts for the Strip Packing Problem",
    JOURNAL = "Operations Research",
    YEAR    = 2014,
    VOLUME  = 62,
    NUMBER  = 3,
    PAGES   = "643--661"
}