Assembly Line Balancing

1
Assembly Line Balancing

• The assembly line is a production line where
  material moves continuously through a series of
  workstations where assembly work is performed.

2
Assembly Lines

• Principle of Interchangeability
• individual components that make up a finished
  product should be interchangeable between product
  units
• Division of Labor complex activities divided
  into elemental tasks
• work simplification
• standardization
• specialization
• Mass Production

3
Production Systems

• Project Shop
• Job Shop
• Flow Shop
• Assembly Line
• Continuous Flow

• project networks
• job shop scheduling
• flow shop scheduling
• assembly line balancing
• e.g. cyclic scheduling
• single facility EOQ model

4
The Problem
Assign work elements (tasks) to workstations to
minimize unit assembly costs (e.g. labor cost).
flow of the line
station 3
station 1
station 2
Tasks
precedence requirements
precedence requirements
5
Cycle Time
The time between the completion of two successive
products, assumed constant for all products for
a given production line speed. The minimum
value of the cycle time must be greater than or
equal to the longest station time.
A group of engineering management students
discussing cycle times.
6
Problem Formulation
Assume production rate of P with m parallel
lines. Then each line must produce a unit every
m / P time units. Set Cycle time C lt m / P
the time between completion of two successive
units.
Example Planned order release requires a
production rate of 80 units per hours. Four (4)
assembly lines are available. Therefore cycle
time C ? 4/80 .05 hr. 3 minutes
7
Station Time
Sj lt C
8
Performance Measures
let k number of workstations 1 lt k lt n
dj C Sj delay (idle) time at station j
9
Minimizing Idle Timeminimizes assembly time per
unit
10
Precedence Relationships

• Precedence constraints
• some tasks may have to be completed in a
  particular sequence task i task j
• Zoning restrictions
• some tasks cannot be performed at the same
  workstation (divorces)
• some tasks may be required to be performed at the
  same workstation (marriages)

11
Our Very First Example
S5
S1
S2
S3
S4
1 5 min
2 7 min
3 10 min
4 6 min
5 8 min
k 5 C 10 min. P 6 per hr.
Performance Measures IT 5(10) 36 14 min. LE
36/50 72 SI 7.35
12
Our Very First Example
S1
S2
S3
S4
1 5 min
2 7 min
3 10 min
4 6 min
5 8 min
k 4 C 12 min. P 5 per hr.
Performance Measures IT 4(12) 36 12 min. LE
36/48 75 SI 7.48
13
Our Very First Example
S1
S3
S2
1 5 min
2 7 min
3 10 min
4 6 min
5 8 min
k 3 C 14 min. P 4.286 per hr.
Performance Measures IT 3(14) 36 6 min. LE
36/42 85.7 SI 4.47
14
Our Very First Example
S1
S2
1 5 min
2 7 min
3 10 min
4 6 min
5 8 min
k 2 C 22 min. P 2.72 per hr.
Performance Measures IT 2(22) 36 8 min. LE
36/44 81.8 SI 8
15
Our Very First Example
S1
1 5 min
2 7 min
3 10 min
4 6 min
5 8 min
k 1 C 36 min. P 1.67 per hr.
Look, a perfectly balanced line.
Performance Measures IT 1(36) 36 0 min. LE
36/36 100 SI 0
16
Chuck. Could you summarize all this for me?
Just tell me what I need to know!
17
Our Very Next Example Problem
Task 1 2 3 4 5 6 7 ti 5 3 4 3 6 5 2 Task 8 9 10
11 12 ti 6 1 4 4 7
precedence relationships
18
Trial and Error Approach

• Find minimum number of stations for a given cycle
  time
• Repeat for various cycle times
• Select solution that minimizes idle time

cycle times feasible? min k 50 yes 1
25 yes 2 10 yes 5 5 no 10 tmax
7 2 no 25
19
I II III IV V VI VII
station task ti column sum cumulative
sum I 1 5 5 5 II 2 3 4 3 6 11 III 3 4 5 6 10
21 IV 6 5 5 26 V 7 2 9 1 10 4 7 33 VI 8 6 11
4 10 43 VII 12 7 7 50
C 10 IT 7(10) 50 20 LE 50/70 71 SI
9.16
20
Heuristic

• place each task as far to the left as possible
• no restriction of movement within a column
• can move tasks further to the right
• assign tasks to work stations such that the sum
  of the times does not exceed C
• always select task with longest time when forming
  a workstation

21
I II III IV V VI

• task ti pred
• 1 5 0
• 2 3 1
• 3 4 2
• 4 3 1
• 6 2
• 6 5 5
• 7 2 6
• 8 6 7
• 9 1 6
• 10 4 6
• 11 4 7
• 12 7 11

X
station task ti column sum cumulative
sum I 1 5 2 3 8 8 II 4 3 5 6 9 17 III 3
4 6 5 9 26 IV 7 2 9 1 10 4 7 33 V 8 6 11 4
10 43 VI 12 7 7 50
C 10 IT 6(10) 50 10 LE 50/60 83 SI
4.89
22
I II III IV V VI
Can move tasks to the right.
station task ti column sum cumulative
sum I 1 5 2 3 8 8 II 4 3 5 6 9 17 III 3
4 6 5 9 26 IV 7 2 8 6 8 34 V 10 4 11 4 8 4
2 VI 9 1 12 7 8 50
C 9 IT 6(9) 50 4 LE 50/54 92.6 SI 2
23
Positional Weight Method

• Find positional Weight (PW) for each task
• Rank tasks based upon PW
• highest first
• Assign tasks to stations with highest rank first
• Continue to assign tasks as long as time remains
• task does not violate precedence relationship
• station time does not exceed cycle time
• Repeat until all tasks are assigned
• Each task is assigned to the first feasible
  station
• greedy algorithm

24
Positional Weight
PWi time of the longest path from beginning of
task i through the remainder of network.
2
6
3
4
5
5
7
1
3
6
4
4
Task 1 2 3 4 5 6 7 PWi 34 27 24 29 26 20 15 Tas
k 8 9 10 11 12 PWi 13 8 15 11 7
25
Task 1 2 3 4 5 6 7 PWi 34 27 24 29 26 20 15 Tas
k 8 9 10 11 12 PWi 13 8 15 11 7

• task ti pred
• 1 5 0
• 2 3 1
• 3 4 2
• 4 3 1
• 6 2
• 6 5 5
• 7 2 6
• 8 6 7
• 9 1 6
• 10 4 6
• 11 4 7
• 12 7 11

• Rank Task PW
• 1 34
• 4 29
• 2 27
• 5 26
• 3 24
• 6 20
• 7 15
• 10 15
• 8 13
• 11 11
• 9 8
• 12 7

Assume CT 10
26
station task ti column sum cumulative I 1 5
4 3 8 8 II 2 3 5 6 9 17 III 3 4 6 5 9 26 IV 7
2 10 4 6 32 V 8 6 11 4 10 42 VI 9 1 12 7 8 50

• task ti pred
• 1 5 0
• 2 3 1
• 3 4 2
• 4 3 1
• 6 2
• 6 5 5
• 7 2 6
• 8 6 7
• 9 1 6
• 10 4 6
• 11 4 7
• 12 7 11

• Rank Task PW
• 1 34
• 4 29
• 2 27
• 5 25
• 3 24
• 6 20
• 7 15
• 10 15
• 8 13
• 11 11
• 9 8
• 12 7

I have long advocated the positional weight
method in order to achieve the best balance.
C 10 IT 6(10) 50 10 LE 50/60 83.3 SI
5.09
27
An Integer Programming Approach
let xik 1 if task i assigned to station k 0
otherwise ci,k cost coefficient of xi,k where
cik lt ci,k1
precedence relationship when task j precedes task
i
28
Some Final Considerations

• If significant idle time remains
• consider parallel lines with larger cycle times
• use more than one worker per station (group
  stations)
• task variability
• max station time ESi 2.33 STDSi lt C
• probability all stations complete on time .99k
• provide rework area
• add buffers
• use unpaced (asynchronous) lines
• Max profit rather then minimize idle time

These are some very good final considerations.