Submitter Variables Constraints Density Status Group Objective MPS File
Manuel Iori 431 67 3.13433e-01 easy bppc 472 bppc8-09.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 431 430
Constraints 67 67
Binaries 423 429
Integers 6 0
Continuous 2 1
Implicit Integers 0 0
Fixed Variables 1 0
Nonzero Density 0.313433 0.314162
Nonzeroes 9051 9051
Constraint Classification Properties
Original Presolved
Total 73 67
Empty 0 0
Free 0 0
Singleton 0 0
Aggregations 0 0
Precedence 0 0
Variable Bound 0 0
Set Partitioning 12 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 6 0
Mixed Binary 25 49
General Linear 30 0
Indicator 0 0

Structure

Available nonzero structure and decomposition information. Further information can be found here.

value min median mean max
Components 1.278754
Constraint % 1.49254 1.49254 1.49254 1.49254
Variable % 1.16279 5.54264 5.23256 8.37209
Score 0.253766

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
1 472 472 0 0 0 - 2018-10-12 Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to bppc8-09 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 Variables Binaries Integers Continuous Constraints Nonz. Submitter Group Status Objective
bppc4-08 1456 1454 0 2 111 23964 Manuel Iori bppc easy 53
bppc6-06 3922 3920 0 2 273 181510 Manuel Iori bppc open 212*
bppc6-02 4784 4782 0 2 309 188143 Manuel Iori bppc open 116*
assign1-10-4 572 520 0 52 582 28280 Robert Fourer assign1 open 422*
assign1-5-8 156 130 0 26 161 3720 Robert Fourer assign1 easy 211.999999999998

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 Nov 19, 2018 by Gregor Hendel
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