Submitter Variables Constraints Density Status Group Objective MPS File
Manuel Iori 1456 111 1.48277e-01 easy bppc 53 bppc4-08.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 1456 1455
Constraints 111 111
Binaries 1454 1454
Integers 0 0
Continuous 2 1
Implicit Integers 0 0
Fixed Variables 1 0
Nonzero Density 0.148277 0.148379
Nonzeroes 23964 23964
Constraint Classification Properties
Original Presolved
Total 111 111
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 91 91
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 % 0.900901 0.900901 0.900901 0.900901
Variable % 3.024050 4.996560 5.085910 5.841920
Score 0.171177

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 53 53 0 0 0 - 2018-10-12 Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to bppc4-08 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
bppc6-02 4784 4782 0 2 309 188143 Manuel Iori bppc open 116*
bppc8-09 431 423 6 2 67 9051 Manuel Iori bppc easy 472
bppc6-06 3922 3920 0 2 273 181510 Manuel Iori bppc open 212*
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 09, 2018 by Gregor Hendel
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