a u-shape assembly line balancing by usingmax-min ant ... · . . 2556 16-18 2556 -a u-shape...
TRANSCRIPT
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-
A U-Shape Assembly Line Balancing by UsingMax-Min Ant System
And Random Technique
1* 2 1,2
E-mail: [email protected]*
Amonpong Sa-nguansin1*JakrawarnKunadilok 1,2Department of Industrial Engineering, Faculty of Engineering,Burapha University, Chonburi
E-mail: [email protected]
- (Max-Min Ant System; MMAS) (Random Permutation; RP) RP
MMAS -
- UALB 5 Scholl (2006)
Comsoal 81.99%
-
Abstract
This paper presents the solving the U-Shape assembly line balancing (UALB) by using the Max-Min Ant
System (MMAS) and Random Permutation optimization (RP). The RP technique is used for assigning the groups of inflow tasks to workstation and outflow tasks from workstation. The MMAS method is used for
address the number of tasks to be assigned for each workstation according to precedence constraints. The workload variance is set as the objective function. The proposed method was tested against five UALB
problems collected by Scholl (2006). The results showed that the proposed method is capable of producing better solutioncompared to the COMSOAL method. The maximum reduction of the workload variance is of
81.99%.
Keyword: U-Shape Assembly Line Balancing, Max-Min Ant System, Random Permutation
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1.
(Assembly Line Balancing: ALB)
(Task) (Station)
(Idle Time)
(Cycle Time)
- (Precedence)
[1] (ALB)
. . 1955 [2] ALB
(Combinationaloptimization) (NP-Hard)
(Exact methods)
(Optimal solution)
� �(Metaheuristic methods) [3], [4]
-
(Local Serach)
[5]
-
-
[6]
[7]
1
1
Miltenburg and
zwijingaard,199
4 [8]
DP
formulation
RPWT-based
heuristic
Single
model
up to 11
tasks
up to 111
tasks
m(
)
Miltenburg,1998
[9]
DP-based
exact alg.
U-line
facility
with
several
individual
U-line
individual
U-line
with up to
22 tasks
m and idle
time in a
single st.
GÖkÇen and
Agpak,2006
[10]
Ip formation
and GP
Single
model
up to
30tasks
m
Chaing and
Uran, 2006 [11]
Hybrid
heuristic
Single
model
Up to 111
tasks
m
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1
[8], [9], [10], [11]
[5],[9] -
(UALBP)
(RP)
- - (MMAS)
-
5 Scholl [12]
COMSOAL
2.
(UALB)
(SALB) - (Precedence constraint)
(Precedence) j 1,�, k
1
(Successors) j 1,�k 1
2
(Forward)
(Precedence diagram) (Backward)
(Line Efficiency)
[13]
(1) �
(4) m = w/Ct (1) Tid = (2)
wv = (3)
E = (4)
n , m , wv
, ct
, cr , w , ts
Tid
(UALB) [14]
1 SALB
F F = {i|i = 1,2,�,n}, P
- (Precedence) P = {(x,y)| x y}, T
T = {i|i = 1,2,�,n}, c m
F, (S1,S2,�,Sn) Sk = {i| i
k} (5)-(8)
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1 [15]
(5) (6)
(7)
For each task y, If (x,y) ,
If (y,z) , (8) (5)
(6) (7)
8
-
[15]
3. UALB
UALB MMAS RP
RP MMAS
3.1
r
r! A = {1,2,3,4} A
r = 4 A 24 24 (a1 a24)
2 [16], [17]
2 A = {1,2,3,4}
3.2 MAX-MIN Ant System
(MMAS)
MMAS
Stüzle [18]
(Priority rule)
- (Precedence)
(Station oriented precedence) (k=1)
- (9)-(11)
j
, j k Sk
k, j = tj (9)
pkj = (10)
(k+1) = (1- ) (t) + (11)
pkj
0 <1 Stüzle [18]
(TSP)
= 1/ �(sbest) �(sbest)
3.3
1
-
- (RP)
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2 RP
(Factorial; !)
3 MMAS MMAS
(Alpha : ) , (Beta ; ) ,
(Evaporate ; ) , 4 (L = 0),
(L = RPmax) 5
�(sbest)
6
7
(11)
8 L RPmax L = L+1
5
UALB
- 2
MMAS
4
3
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2 -
1
2
g
*g =
4 MMAS
4.
UALB Scholl [4] 5 Jaeschke, Jackson, Mitchell, Roszieg,
Buxey 3 5 Jaeschke
MMAS Microsoft Visual
C++ ( ) = 0.02
RPmax
5 - Jaeschke
UALB 3-4
3 UALB
n W ct
1. Jaeschke 9 37 18
2. Jackson 11 46 21
3. Mitchell 21 105 21
4. Roszieg 25 125 25
5. Buxey 29 324 54
4
COMSOAL
COMSOAL
Tid wv E (%) Tid wv E (%)
1. 17 64.22 68.52 17 11.56 72.55
2. 17 64.22 73.02 17 16.89 76.67
3. 21 48.25 83.33 21 8.92 83.33
4. 25 37.47 83.33 25 21.81 83.33
5. 54 146.78 85.71 54 113.63 85.71
5
COMSOAL
UALB
1 2 3 4 5
wv
(%) 81.99 73.69 81.51 41.79 22.58
5.
(UALB)
MAX-MIN Ant System (MMAS)
RP
-
MMAS
- UALB 5
COMSOAL
81.99%
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UALB
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