Model of Spine Configuration Assembly Line Design for a

Product FamilyBy

Dida D Damayanti (ITTelkom, Indonesia)

Isa Setiasyah Toha (ITB, Indonesia)

OutlineIntroduction

Sub-lines Networking

Conclusion

Model of spine assembly line design

INTRODUCTION

MIXED-MODEL ASSEMBLY LINE

PLATFORM VARIANT PRODUCTS

Produk A Produk B Produk C

Product Family

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 LineA 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 SubassembliesCommon 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

CS VS

US-1 US-2

Combined Precedence Diagram

6 8

7

4

2Start FinishCS

US-2

US-1

1

3

5

VS

Connection Between Lines

St 1

St 2

US-1 Line

St 1

St 2

St 3US-2 Line

St 1 St 2 St 3 St 4

CS Line

12 3

4 5

6

7 8

St 1 St 2 St 3 St 4

VS Line

MODEL OF SPINE ASSEMBLY LINE DESIGN

Spine Assembly Line Modelling Process

QE MakespanC

bb

V

bb

EB

q

qCC 1

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.

• The model constraints: allocation constraint, precedence constraint, station time constraint, cycle time constraint, idle time and waiting time constraint, and workstation constraint.

PM M M P

11 1 2 1 2

. β D δ Dλdumk ik k k ik

k k i k i

Min TOE y f f f

Model of VS line designObjective function:

PM M M P

11 1 2 1 2

. β D δ Dλdumk ik k k ik

k k i k i

Min TOE y f f f

(1) Constraints:

M

1

1jkk

x

, j=1,2,...N (2)

M M

1 1

. . ,hk jkk k

k x k x

j=1,2,...N and h Gj (3)

V N

1 1

w 0,bj jk ib ikb j

x a

i = 1,2,...,P and k=1,2,...M

(4)

1 ,dumk ka a k=1,2,...M (5)

Model of VS line designP

1 11

( ) D Q Cdumk ik ik k k

i

f a f f f

,

k=1,2,...M (6)

1 0,if i = 1,2,...,P (7) 1

1 11

0,k

s ks

a f

k=2,...M (8)

1

( 1) ( 1)1 1

i i

r k r k rk rk ik ikr r

a f a f a

,

k=2,...M, r = 1,...,i and i = 2,...,P (9)

P P

( 1) ( 1) ( 1) ( 1)1 1

dum dum dumk k i k i k ik ik k

i i

a f a f a f f

k=2,...M and i = 2,...,P (10)

N

1

N 0,jk kj

x y

k=1,2,...M (11)

1 0,s sy y s=1,2,...(k-1) and k=2,...M (12)

, , 0,1jk k ibx y , j=1,2,...N and k=1,2,...M (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.

• The model constraints: allocation constraint, precedence constraint, idle time constraint, cycle time and waiting time constraint, and workstation constraint.

M M

1 1

. β Qδ Qλk kk k

Min TOS y f

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.

• The model constraints: allocation constraint, precedence constraint, idle time constraint, cycle time and waiting time constraint, and workstation constraint.

M M M

1 1 2

. β Qδ ( 1) δ Qλk k kk k k

Min TOS y f k d y

Numerical Example• Numerical example is provided to illustrate the

operational of the model. • Data Product Family A: demand, cost, and combined

precedence diagrami Variant Product Demand 1 V1 100 2 V2 50 3 V3 50

Total 200

Numerical Example

1

2

12

11,11,11

10,10,12 18

7,6,9

15

6,10,0

11

11,8,13

14

0,4,6

10

18

15,15,0

20

10,10,0

21

7,7,0

19

5,5,0

17

12,12,0

16

9,9,0

8

11,11,11

7

6,6,66,4,7

3 4

8,8,8

6

4,4,4

5

3,3,39

10,10,10

5,5,5

7,7,7

Start

Finish

Assembly operation n, a,b,c: operation time V1, V2, dan V3

a,b,c

n :

CS

VS

US

Numerical Example

Eff-1

St1 St213,12,12,10 12,10,10,10 St3 St419,11,11,12 9,13,13,16

12

8

1011

14

13

15

St1 St213 14 St3 14

52

3

67

4 9

1

St1 St217 17 St3 15

161819

21

2017

VS

US

CS

Numerical Example

1 2 3 4

1 2

1 2 3

CS

US

VS

3

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.

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