Application of the Cutting Stock Problem

1

• Application of the Cutting Stock Problem
• to a Construction Company A Case Study
• Seda Alp, Gurdal Ertek, S.Ilker Birbil
• Sabanci Üniversitesi
• Mühendislik ve Doga Bilimleri Fakültesi
• Orhanli, Tuzla, Istanbul, 34956

2
Outline

• Introduction
• The Problem Setting
• The Company
• The 1D Cutting Stock Problem
• The Solution Approaches
• Solving within the GAMS Modeling System
• Developing an IP-based Optimization Program
• Benchmarking Results
• The Performance Data
• Insights
• A Visual Approach for Determining How to Batch
  Subprojects
• Conclusions

3
Introduction

• The goal of the 1 Dimensional cutting stock
  problem
• is to find the "optimal" cutting patterns,
  where the total number of long steel bars used is
  minimized, subject to the constraint that the
  desired shorter steel bars are cut in needed
  quantities.

4
Bar Length 1200 cm
..........
Bar Length 600 cm
1
..........
2
...
15
Bar Length 700 cm
Bar Length 300 cm
1
1
..........
..........
2
2
...
...
35
10
5
Pattern 1
300 cm
300 cm
300 cm
300 cm
Pattern 2
300 cm
300 cm
600 cm
Pattern 3
300 cm
700 cm
Trim Loss
Pattern 4
600 cm
600 cm
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The Construction Company

• Mimag Makina Ltd
• Designs, produces, supervises formwork
• and scaffolding systems
• For structures such as dams, bridges,
• business centers, and industrial plants.

• Sample Project 1 Diesel/Kerosene
  Hydroprocessing and CCR Reformer Project
  implemented in Izmit Refinery of Tupras, Turkey.
• Sample Project 2 Waste Water Treatment Plant
  in Adana, Turkey.

7

• The standard steel bars used in reinforced
  concrete steel bars are 1200 cm and have various
  diameters range from 6mm to 50mm.

8
Tupras, Izmit
9
The 1D Cutting Stock Problem

• SETS
• I set of patterns,
• J set of lengths,
• VARIABLES
• xi number of bars cut according to pattern i
• PARAMETERS
• aij number of pieces of length j within one bar
  cut according to pattern i
• bj required number of pieces of length j

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The Model
s.t.

• The goal of the model is
• To minimize the objective function, which
  consists of the total number of long steel bars
  used.
• Enough number of shorter bars are cut from long
  bars in required quantities.
• The decision variables are restricted to
  non-negative values.

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The Solution Approaches

• Solving within the GAMS Modeling System
• Gams ( http//www.gams.com )
• MS Excel
• C
• Developing an IP-based Optimization Program
• lp_solve ( http//groups.yahoo.com/group/lp_solve/
  )
• Java under Eclipse IDE ( http//www.eclipse.org )
• Using Commercial Software
• 1 dimensional cutting stock softwares

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BAR_LENGTH 1200 NO_OF_LENGTHS 17 LENGTHS_AND_REQU
IRED_QUANTITIES 1100 10 950 20 1200 162 350 241 93
5 147 240 48 800 96 550 147 1180 28 1020 39 830 8
875 8 1065 39 80 104 340 8 345 32 300 16
java code
datafile.txt
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results.txt
10 bars cut as 1x1100cm 20 bars cut as
1x950cm 162 bars cut as 1x1200cm 46 bars cut
as 3x350cm 68 bars cut as 1x935cm 48 bars
cut as 1x935cm 1x240cm 89 bars cut as
1x350cm 1x800cm 70 bars cut as 2x550cm 28
bars cut as 1x1180cm ... ... ... 7 bars cut
as 1x550cm 1x345cm 1x300cm
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comparison file
15
Benchmarking

• Q1 How effective is our program compared to the
  commercial packages that we downloaded?
• Q2 How do the commercial packages compared
  amongst them?

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Result - Comparison
17
Insights

• None of the commercial packages have achieved the
  optimal total number of bars
• The software packages are not implementing an
  optimal algorithm, but are implementing heuristic
  techniques.
• First five software packages give solutions very
  close to the optimal
• A construction company should choose amongst
  these five software packages based on criteria
  such as
• price
• on-line support
• usability
• data import/export capabilities
• reporting quality (including visualization of
  optimal cutting patterns and their quantities)

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Insights

• Software 6 and especially Software 7 perform
  poorly.
• A company should definitely avoid using Software
  7, which also happens to be the most expensive
  package amongst all.
• Software 7 is distinguished from all others by
  its capability to import/export to and from MS
  Excel.
• Software 6 has the best GUI amongst all packages.
  
• The software selection should be
• based on performance tests,
• rather than data import/export capabilities,
• GUI, or price.

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Benchmarking

• Q3 Would it be considerably more effective to
  use two different software packages at the same
  time for each subproject and implement the better
  of the two solutions that they provide?
• Q4 Does batching of two or more subprojects and
  determining the best solution for the batch
  increase performance (decrease the cost)?

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Benchmarking

• The software packages that perform well are
  extremely close to the optimal,
• there is no need to use two of those software
  packages

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A Visual Approach for Determining How to Batch
Subprojects

• Subprojects can be batched (combined) to be cut
  simultaneously, so that we can reduce the number
  of long bars cut
• As a future research, this approach can be
  implemented in software packages

22
Batching two projects by using Miner3D software
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Conclusions

• Result of the visual approach
• The two considered projects (Izmit and Adana) did
  not include great improvement opportunities
  through batching.
• We even observed that batching could result in a
  worse performance.
• The decision maker should be aware that batching
  is not always a good option.
• Even though we have not gained meaningful
  improvements by batching, when using our data, we
  believe that for other projects there can be
  significant savings.
• One could especially expect good opportunities
  when there are a large number of
  projects/subprojects managed simultaneously, and
  a large number of steel bars to be cut.
• We suggest carrying out more extensive tests as a
  future research area.

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Conclusion

• Available software packages should be tested with
  sample project data before adoption.
• Software packages with the best import/export
  capabilities and/or GUI can perform very poorly.
• A higher price does not guarantee a good
  performance, as the worst software in our study
  was also the most expensive one.

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Thank you