Best Permutations for the Dynamic Plant Layout Problem

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Best Permutations for the Dynamic Plant Layout
Problem

• Jose M. Rodriguez, F. Chris MacPhee, David J.
  Bonham, Joseph D. Horton, Virendrakumar C.
  Bhavsar
• Department of Mechanical Engineering
• Faculty of Computer Science
• University of New Brunswick
• Fredericton, N.B., Canada, E3B 5A3
• bhavsar_at_unb.ca

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Outline

• Introduction
• Problem Statement
• Description of the Algorithm
• Experimental Results
• Conclusions

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Introduction

• Plant layout an engineering design problem

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Facilities Planning Process

• Strategic Planning stages
• Planning (strategic level)
• Design (tactical level)
• Implementation (operational level).

• Plant layout objectives are determined according
  to
• Selection of a strategy to manufacture the
  products (i.e., Manufacturing strategy)
• Definition of the products (i.e., Product
  design)
• Specification of the process plan (i.e., Process
  design)
• Definition of the production plan (i.e.,
  Schedule design).

S ? Objectives are determined T ? Other plant
layout requirements are determined O ? Plant
layout is selected and maintained.
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Problem Statement
The Dynamic PlantLayout Problem (DPLP)as an
optimization problem J. Balakrishnan and C. H.
Cheng, Dynamic Layout Algorithms A
State-of-the-art Survey, International Journal
of Management Science, vol. 264, pp. 507-521,
1998.
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DPLP Formulation
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DPLP Formulation
Ytijl - 0,1 dependant variable for including cost
of shifting facility i from location j to
location l in period t Atijl - fixed cost of
shifting facility i from location j to location l
in period t Ctijkl - cost of material flow
between facility i located at j and facility k
located at l in period t djl - distance from
location j to location l ftik - flow of material
between facility i and facility k in period t
P - number of periods n - number of facilities
and locations t - a given period of the planning
horizon i,k - facilities in the layout j,l -
locations in the layout
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Genetic and Tabu Search Algorithm (GATS)

• Overview of the GATS code
• The GATS search space
• The triangular evolutionary technique used by
  GATS
• Research questions

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Overview of the GATS Code
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The GATS Search Space

• Location of a DPLP instance cost in the GATS
  search space is defined by (P, CF, N), where
• Population (P) refers to the number of
  chromosomes or layouts in the parent pool
• Convergence factor (CF) is the evolution
  threshold a better solution must be found every
  CF generations or the tabu search parameters are
  modified
• Mutation (N) refers to the number of mutations
  to be performed between the crossover and tabu
  search routines

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The Triangular Evolutionary Technique Used by GATS
Synergetic Evolution (i.e., improving population
quality at each generation)
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Research Questions

• How many optimal layout sets are there and
  what are they?
• How many times is the layout changed during
  the five periods (i.e., re-layouts) and at what
  cost?

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Flow/Distance matrices shifting costs for the
Rosenblatt (1986) Instance
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GATS Early Convergence
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GATS Final Convergence
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GATS End of Evolution
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An Optimal Layout Set
Optimal --gt Cost 71187 , NUM_MOVE 4 ,
TABU_LEN 1 , G 138 , Real G 38 The Layout
is P 11, cost 71187 No.1 Period 6 4 2 5 3 1
No.2 Period 6 4 2 5 3 1 No.3 Period 6 4 2 3 5
1 No.4 Period 4 6 2 3 5 1 No.5 Period 4 1 2 3
5 6  
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All Layout Sets Found by GATS
                   
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Experimental Results
The GATS site http//acrl.cs.unb.ca/research/gat
s/ Experiments were performed on infrastructure
managed by the Advanced Computational Research
Laboratory at the University of New Brunswick
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ACRL Infrastructure
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ACRL Usage
From April 2003 - March 2004, GATS utilized over
11 CPU years of compute time on the ACRL chorus
cluster.
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DPLP Algorithms

• Genetic Algorithms
• CVGA - Conway, D.G. and Venkataramanan, M.A.
• NLGA - Balakrishnan, J. and Cheng, C.H.
• GADP - Balakrishnan, J., Cheng, C.H., Conway,
  D.G., and Lau, C.M.
• CCGA - Chang, M., Sugiyama, M., Ohkura, K., and
  Ueda, K.
• SymEA - Chang, M., Ohkura, K., Ueda, K., and
  Sugiyama, M.
• Simulated Annealing Algorithms
• SA - Baykasoglu, A. and Gindy, N.N.Z. SA, GA, DP
• Dynamic Programming, Genetic, and Simulated
  Annealing Algorithms
• DP-GA-SA - Erel, E., Ghosh, J.B., Simon, J.T.

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DPLP ResultsTotal cost of 6 department / 5
period instances
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DPLP ResultsTotal cost of 6 department / 10
period instances
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DPLP ResultsTotal cost of 15 department / 5
period instances
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DPLP ResultsTotal cost of 15 department / 10
period instances
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DPLP ResultsTotal cost of 30 department / 5
period instances
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DPLP ResultsTotal cost of 30 department / 10
period instances
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Conclusions Results

• GATS has been developed to solve QAP and DPLP
  instances. We have challenged the well-known
  QAPLIB, a selected DPLP dataset, and other
  difficult instances.
• Optimum or best-known permutations have been
  generated for over 82 of 210 available QAP and
  DPLP instances.
• Better solutions than those known to date for the
  DPLP have been found. Of the attempted 51 DPLP
  instances, 29 now have new best-known solution
  found by GATS.

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Conclusions Benefits

• Multiple global optima provide many benefits
• equally optimal layouts by different qualitative
  criteria
• solutions can be chosen that may have fewer
  layout changes, requiring fewer interruptions in
  the production system.
• Most results published in the literature include
  only the layout cost (no permutation). This has
  lead to false best known solutions and
  retractions. Published results should always
  include both costs and permutations for
  verification purposes.

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Conclusions Future Work

• A provisional patent regarding GATS has been
  filed with the United States Patent and Trademark
  Office . Next steps
• Although the design of a factory is a planning
  problem, response time is as important as
  solution quality. The concept of iterative
  design is implicit in GATS and can only be
  realized with a high performance computing (HPC)
  infrastructure.