bppc8-02

aggregations set_partitioning mixed_binary

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Manuel Iori	232	59	3.205e-01	easy	bppc	506.9999999999998	bppc8-02.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	232	230
Constraints	59	58
Binaries	229	229
Integers	1	0
Continuous	2	1
Implicit Integers	0	0
Fixed Variables	1	0
Nonzero Density	0.320500	0.325937
Nonzeroes	4387	4348

Constraint Classification Properties
	Original	Presolved
Total	60	58
Empty	0	0
Free	0	0
Singleton	1	0
Aggregations	1	1
Precedence	0	0
Variable Bound	0	0
Set Partitioning	17	18
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	1	0
Mixed Binary	33	39
General Linear	7	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	1.301030
Constraint %		1.724140	1.72414	1.72414	1.72414
Variable %		0.865801	5.21759	6.06061	10.38960
Score	0.310494

Best Known Solution(s)

Find solutions below. Download the archive containing all solutions from the Download page.

ID	Objective	Exact	Int. Viol	Cons. Viol	Obj. Viol	Submitter	Date	Description
1	507	507	0	0	0	-	2018-10-12	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to bppc8-02 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
neos-480878	easy	534	189	345	1321	44370	NEOS Server Submission	neos-pseudoapplication-76	492.5144492879	benchmark_suitable variable_bound set_partitioning set_packing invariant_knapsack mixed_binary
ran14x18-disj-8	easy	504	252	252	447	10277	J. Aronson	ran	3712	benchmark benchmark_suitable variable_bound set_covering mixed_binary
g503inf	easy	48	24	24	41	144	MIPLIB submission pool	–	Infeasible	infeasible variable_bound binpacking knapsack mixed_binary
gr4x6	easy	48	24	24	34	96	MIPLIB submission pool	–	202.3499999999979	variable_bound mixed_binary
ns1830653	easy	1629	1458	171	2932	100933	NEOS Server Submission	neos-pseudoapplication-110	20622	benchmark benchmark_suitable variable_bound set_partitioning set_packing cardinality invariant_knapsack knapsack 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"
}