Model of Spine Configuration
Assembly Line Design for a
Product Family
By
Dida D Damayanti (ITTelkom, Indonesia)
Isa Setiasyah Toha (ITB, Indonesia)
Outline
Introduction
Sub-lines Networking
Model of spine
assembly line design
Conclusion
INTRODUCTION
Product Family
PLATFORM
VARIANT PRODUCTS
Produk A
Produk B
MIXED-MODEL ASSEMBLY LINE
Produk C
The Drawbacks of Mixed-model
line
Increasing variation and assembly operations,
caused:
Increasing in line management complexity
Decreasing in line efficiency
Decreasing in line flexibility
Spine Assembly Line
A layout consisting of a main aisle used as a
designed skeleton with some cells located in other
sides [Langevin, et. al, 1994; Benjafar, et. al, 2006]
Designed to connect some sub-assembly lines as
the modular structure of a product family
Variation and line length problem in mixed model
assembly line, can be solved by taking the benefits
of assembly operation commonality in a product
family [He and Kusiak, 1997].
Objective
Develop a model of spine assembly line design
based on the modular structure of a product family
SUB LINES NETWORKING
Family Product Subassemblies
Common subassemblies (CS): basic subassembly
Unique subassemblies (US): used in a certain
variant products
Variant subassemblies (VS): have a similar
function, but may be different in shape or quality to
differentiate each variant product
Example of Product Family
Architecture
VS
CS
US-1
US-2
Combined Precedence Diagram
VS
US-2
1
6
4
Start
CS
2
7
3
US-1
5
8
Finish
Connection Between Lines
St
1
St
2
St
3
US
St 1
St 2
St 3
St 4
-2
Lin
e
St 1
1
CS Line
2
St
1
St
U
ine
L
S-1
St 2
2
4
St 3
3
5
VS Line
St 4
6
7
8
MODEL OF SPINE ASSEMBLY LINE
DESIGN
Spine Assembly Line Modelling Process
V
Makespan
CE 
Q
C C
B
q
 q
E b 1
b
b
b
Model of VS line design
•
•
•
•
It is a mixed model assembly line
The line is controlled as unpaced line
The MPS is sequenced by the STPT rule.
Decision variables of the model are assembly
operations allocation, number of
workstations, and time between minimal part
set (MPS).
Model of VS line design
• The objective function: to minimize the total operational
costs, consist of operation costs, idle time cost in each
workstation, and waiting cost for each product.
M
M
P
Min. TOE   βyk  
k 1
k 1 i  2
 f
ik
f
 D  f  δ   
M
dum
k
1k
P
k 1 i  2
ik
Dλ
• The model constraints: allocation constraint, precedence
constraint, station time constraint, cycle time constraint,
idle time and waiting time constraint, and workstation
constraint.
Model of VS line design
Objective function:
M
M
P

Min. TOE   βyk   fik  f
k 1
k 1 i  2
 D  f  δ   
M
dum
k
1k
P
k 1 i  2
ik
Dλ
(1)
Constraints:
M
x
k 1
 1 , j=1,2,...N
jk
M
 k .x
hk
k 1
V
M
  k .x jk , j=1,2,...N and h  Gj
b 1 j 1
(3)
k 1
N
 w
(2)
bj
x jk  ib  aik  0, i = 1,2,...,P and k=1,2,...M
(4)
akdum  a1k , k=1,2,...M
(5)
Model of VS line design


 P
dum 
f

 1k   (aik  fik )  f1k  f k  D  Q  C ,
 i 1
 

k=1,2,...M
fi1  0, i = 1,2,...,P
k 1
a
s 1
1s
 f1k  0,
(8)
i 1
a
i
r ( k 1)
r 1
k=2,...M
 f r ( k 1)     ark  f rk    ik  aik ,
r 1
k=2,...M, r = 1,...,i and i = 2,...,P
dum
( k 1)
a
f
dum
( k 1)
(9)
P
P
i 1
i 1
   ai ( k 1)  fi ( k 1)     aik  fik   f kdum
k=2,...M and i = 2,...,P
N
x
j 1
jk
(6)
(7)
 Nyk  0,
k=1,2,...M
ys  ys 1  0, s=1,2,...(k-1) and k=2,...M
x jk , yk ,  ib 0,1 , j=1,2,...N and k=1,2,...M
(10)
(11)
(12)
(13)
Model of CS line design
• CS line is a single assembly line and it is assumed that
buffer is always available in CS line.
• The objective function of CS line design: to minimize the
total operational costs, consist of operation costs, idle
time cost in each workstation, and waiting cost to VS line.
M
M
k 1
k 1
Min. TOS   βyk   f k Qδ   Qλ
• The model constraints: allocation constraint, precedence
constraint, idle time constraint, cycle time and waiting
time constraint, and workstation constraint.
Model of US line design
• US line is a single assembly line, its demand depends on
the variant using the US.
• The objective function of US line design: to minimize the
total operational costs, consist of operation cost, idle
time cost in each workstation, waiting cost in the first
production and waiting cost to VS line.
M
M
M
k 1
k 1
k 2
Min. TOS   βyk   f k Qδ   (k  1)dδyk   Qλ
• The model constraints: allocation constraint, precedence
constraint, idle time constraint, cycle time and waiting
time constraint, and workstation constraint.
Numerical Example
• Numerical example is provided to illustrate the
operational of the model.
• Data Product Family A: demand, cost, and combined
precedence diagram
i
1
2
3
Variant Product
V1
V2
V3
Total
Demand
100
50
50
200
Numerical Example
11,11,11
1
7,7,7
4,4,4
2
6
3,3,3
8,8,8
3
4
CS
10,10,10
0,4,6
11,11,11
9
14
7
5,5,5
11,8,13
7,6,9
6,10,0
11
18
15
5
6,4,7
6,6,6
12
8
10,10,12
10
Start
9,9,0
10,10,0
7,7,0
16
20
21
5,5,0
15,15,0
19
18
12,12,0
17
US
VS
a,b,c
n
: Assembly operation n,
a,b,c: operation time V1, V2,
dan V3
Finish
Numerical Example
St1 13,12,12,10
St2
8
VS
St1
13
2
St2
14
5
1
7
St1
17
17
13
14
15
St3
14
6
9
St2
17
St3
15
20
19
16
9,13,13,16
11
4
3
US
St4
10
12
Eff-1
CS
St3 19,11,11,12
12,10,10,10
21
18
Numerical Example
CS
1
2
3
VS
1
1
US
2
2
3
3
4
Discussion
• Spine assembly line:
– Shorten a mixed-model (VS) assembly line: lessen
complexity
– More flexible to variation changes
– Increase the operation efficiency: mass production (CS
Line), adjusted cycle time (US)
– Support the issue of mass customization, postpone for
differentiation, and reconfigurable assembly line
Conclussion
• The spine assembly line for a product family consist of
common subassembly (CS) lines, unique subassembly (US)
lines, and a variant subassembly (VS) line.
• The spine assembly line is designed in three sequential stages:
design of VS line, design of CS and US lines, and connect CS
and US to VS to make the spine assembly line configuration.
• By this line configuration, the complexity of the mixed model
line is declined. The assembly operation similarities at the CS
and US line could contribute to a more simple, flexible and
efficient product family assembly line.
References
•
•
•
•
•
•
•
•
•
•
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