bppc6-06

set_partitioning mixed_binary

Submitter Variables Constraints Density Status Group Objective MPS File
Manuel Iori 3922 273 1.69524e-01 open bppc 212* 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).

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.

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.

ID Objective Exact Int. Viol Cons. Viol Obj. Viol Submitter Date Description
1 212 212 0 0 0 - 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 open 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 472 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"
}

Last Update Apr 09, 2019 by Gregor Hendel
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