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 507 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).

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.

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 Integers Continuous Constraints Nonz. Submitter Group Objective Tags
neos-480878 easy 534 189 0 345 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 0 252 447 10277 J. Aronson ran 3712 benchmark benchmark_suitable variable_bound set_covering mixed_binary
g503inf easy 48 24 0 24 41 144 MIPLIB submission pool Infeasible infeasible variable_bound binpacking knapsack mixed_binary
gr4x6 easy 48 24 0 24 34 96 MIPLIB submission pool 202.349999999998 variable_bound mixed_binary
ns1830653 easy 1629 1458 0 171 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"
}

Last Update Apr 09, 2019 by Gregor Hendel
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