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Paint line sequencing in mixed-model assembly lines Xie, H.; Shen, W.
Paint line sequencing in mixed-model
assembly lines
Hui Xie and Weiming Shen
Integrated Manufacturing Technologies Institute 15 May 2007
Outline
• Background
• Problem statement
• Iterated local search
• Numerical example
• Future work
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)
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 lineMain assembly line
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
Paint line performance
measures
• Production throughputs
– reducing setup times => increasing throughputs
• Work-in-process
– reducing setup times => increasing buffer inventories
• Trade-off
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:
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{| i − i' |}, =1,...,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
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
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)
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
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
Numerical example
• 120 jobs, 7 colours
• blue, black, green, orange, gray, black, green, yellow, red, gray
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