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Paint line sequencing in mixed-model assembly lines Xie, H.; Shen, W.

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Paint line sequencing in mixed-model

assembly lines

Hui Xie and Weiming Shen

Integrated Manufacturing Technologies Institute 15 May 2007

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Outline

• Background

• Problem statement

• Iterated local search

• Numerical example

• Future work

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Background

Mixed-model assembly lines

– A variety of similar product models with multiple dimensions of product characteristics – such as product complexity and paint colours

– Different complexity: processing time tij of job i on station j

– Different paint colours: change over cost (setup times and paint waste)

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Assembly line layout

model

B3 B2 Assembly Station Buf f er Up Stream Down Stream Line B Line A Line C Line D B1 Buf f er Buffer Paint line Subassembly line

Main assembly line

(6)

Sequence analysis

• Assembly/subassembly line sequence

– Level work load on each station

– Keep a constant rate of usage of parts

=> Even distributing the same model products into the sequence

• Paint line sequence

– Reduce setup time

– Reduce paint change waste cost => A large color block size

• Two sequences are not identical

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Paint line performance

measures

• Production throughputs

– reducing setup times => increasing throughputs

• Work-in-process

– reducing setup times => increasing buffer inventories

• Trade-off

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Problem Statement (1)

• Given:

n jobs with k colours to be processed on a single paint station and m-1 other stations

– station order for all job is identical – same job order on all stations

– an optimized sequence in assembly/subassembly lines – a buffer

• Find:

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Problem Statement (2)

• Objective function:

– Minimize the paint change over cost and inventory cost minimize c = ws cs+ wb cb

where

ci = 0, when CLi = CLi+1

ci = 1, when CLi ≠ CLi+1

ws, wb – weight factor of paint change over cost, and inventory cost p n i i tj m j n i i s cc cc c

∑∑

− = = − = + = 1 1 1 1 1 n i p p cb = max{| ii' |}, =1,...,

(10)

Iterated local search

procedure

Iterated Local Search

s0 ← GenerateInitialSolution () s* ← LocalSearch(s0) repeat s’ ← Perturbation (s*, history) s*’ ← LocalSearch (s’) s* ← Acceptance (s*’, history)

until termination condition met

end

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Initial solution

• Optimized sequence on the assembly line

– with a random swap – or an exchange

– or an insertion

• Avoid always beginning with the assembly line sequence in the

loop

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Local search

• Insertion move:

– Remove a job at the ith position and insert it in the jth position – Find the best insertion move during the neighbourhood scan – Neighbourhood size is (n-1)(n-1)

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Perturbation

• Swap move

– Swaps of two neighbouring jobs at position i and i+1

• Exchange move

– Exchanges of jobs at the ith and the jth position

• Limit the distance of the two jobs for swap and exchange

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Acceptance Criteria

• Better criteria

– Only better local minima are accepted

• Simulated annealing criteria

– New solution s” is accepted with a probability of exp{(Cmin

(s”)-Cmin(s))/T} in case s” is worse than s;

– s” is always accepted in case s” is better than s

– T is called temperature and it is lowed during the run of the algorithm

• Found simulated annealing criteria better for moving out of the

local minima

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Numerical example

• 120 jobs, 7 colours

• blue, black, green, orange, gray, black, green, yellow, red, gray

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Numerical results

fitness setup cost inventory cost

88.25 92 77 88.75 109 28 84.5 93 59 85.75 97 52 86.75 106 29 87.5 106 32 82.25 99 32 85.5 97 51 87.25 96 61 88 106 34 90.5 102 56 85 91 67 85.5 94 60 89.25 110 27 81.75 99 30 86 99 47 84 98 42 86 97 53

fitness on multiple runs

0 50 100 1501 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 fitness setup cost inventory cost

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Future work

• Try different combination among choices of four subroutines

• Given a minimum buffer size, and move job into the same

colour cluster

• Optimize assembly line sequence taking paint change over cost

into account

(18)

Reference

• Thomas Stutzle. Applying iterated local search to the

permutation flow shop problem. Technical Report AIDA-98-04,

FG Intellektik, TU Darmstadt, 1998. 23

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