Perancangan Sistem Manufaktur
D0394 Perancangan Sistem
Manufaktur
Kuliah Ke XXIII - XXVI
Introduction to Assembly Systems
• Definition of the term assembly
– The aggregation of all processes by which various parts
and subassemblies are built together to form a
complete, geometrically designed assembly or product
either by an individual, batch, or continuous process.
• Assembly of manufactured goods accounts for:
– over 50% of total production time,
– 20% of the total unit production cost, and
– 33%-50% of labor costs
Product Assembly
• Virtually all end products go through some
assembly process.
• Approaches
– Craftsman approach

Output =  parts/unit time



Output = 3  parts/unit time
Product Assembly
• Virtually all end products go through some
assembly process.
• Approaches
– Craftsman approach
– Assembly line
3
3



Output = 3  parts/unit time
3
Output = 3  parts/unit time
Product Assembly
1

2

3

• = 2 part/hour each
• 3  = 6 parts/hour
•  = 1/  = 1/2 hour
Assume = 1 = 2 = 3 = 
v1
3 • = 2 part/hour each
v2
3
• 3  = 6 parts/hour
• v = 1/3  = 1/6 hour
v3
3
Assume = v1 = v2 = v3 = v
Assembly Line
• Each part moves sequentially
down the line, visiting each
workstation.
• Assembly (or inspection) tasks are
performed at each station.
• C is defined as the cycle time. At steady state, one unit is produced every
C time units (i.e., C = 1/required number of assemblies per unit time).
• Paced lines vs. unpaced lines.
• Single product vs. mixed lines.
• Flexible flow line.
Assembly Line Balancing
• Assembly line balancing problems:
– ALB-1 - Assign tasks to the minimum number of
stations such that the workload assigned to each station
does not exceed the cycle time, C.
– ALB-2 - Assign tasks to a fixed number of stations such
that the cycle time, C, is minimized.
• An assembly consists of a set of tasks.
• Task precedence relationships are described by a
graph G = (N, A) where nj  N represents task j,
and aijA indicates that task i is an immediate
predecessor of task j.
Example Problem
Task
Ti
Predecessor
a
b
c
d
3
2
3
2
a,b
a
e
1
d
d
a
c
e
b
Assembly Line Balancing
• Problem (ALB-1): Assign tasks to workstations
• Objective: Minimize assembly cost
– f(labor cost while performing tasks, idle time cost)
• Constraints:
– Total time for all tasks assigned to a workstation can
not exceed C.
– Precedence constraints between individual tasks.
– Zoning constraints
• Same workstation
• Different workstation
Parameter/Input
• Parameters / Inputs
–
–
–
–
–
–
P parts/unit time are required
m parallel lines are to be designed (usually 1)
C = m/P is the required cycle time
ti is the assembly time required by task i, i = 1,…,N
IP = {(u,v) | task u must preceed task v}
ZS = {(u,v) | tasks u and v must be assigned to
the samen workstation}
– ZD = {(u,v) | tasks u and v can not be assigned to
the same workstation}
– S(i) is the set of successors for task i.
Parameter / Decision Variables (cont.)
• Decision Variables
• k is the number of workstations required
(unknown).
1, if task i is assigned to station k
• xik  
0, otherwise
• cik is a set of cost coefficients such
that:
Nc  c
, k  1,2,... , n  1
ik
i , k 1
ALB-1 Problem Formulation
N
min
K
 c
i 1 k 1
N
t x
i 1
i ik
k
x
k 1
ik
x
ik ik
 C , k  1,..., K
 1,
i  1,..., N
h
x vh   xuj , h  1,..., K and (u , v)  IP
j 1
K
x
k 1
uk
xvk  1, (u , v)  ZS
xuk  xvk  1, k  1,..., K and (u , v)  ZD
xik  0,1i, k
Solving Problem
• Very difficult to solve optimally
– Integer variables
– Non-linear constraints
• Heuristic Solutions
– COMSOAL
– Ranked positional weight
• Enumeration Methods
– Tree Generation
• Naive approach
• Fathoming rules
Example Problem
j
Tj
Pj
1
5
-
2
35
1
3
25
1
4
60
2
5
30
2
6
10
2,3
7
60
6
8
25
4,5
9
35
8
10
70
7,9
11
30
10
5
8
2
4
9
1
6
3
10
7
11
C = 72
COMSOAL
• Random sequence generation procedure
– Sequentially generates solutions by randomly selecting from
a set of “fittable” tasks at each stage.
– Stops the current solution when:
a) a complete solution is generated, or
b) an upper bound is violated
– Continues until the user says “stop.”
• Benefits
– Easy to implement
– Improvement method - Quickly generates feasible solutions
and continues to improve with additional computer time.
– General solution procedure is very useful for similar
problem
COMSOAL Procedure
1.
2.
3.
4.
5.
6.
7.
8.
Form a list A of tasks. Set the trial station s=1 and remaining cycle
time =C
Promote all tasks from list A that have no immediate predecessors to
list B, the “candidate list.”
Scan list B, promoting each task, j, with tj <= to list C, the “fit
list.”
If C is empty, increment the trial station s = s+1, set =C, and goto
step 3.
Select task j from list C and assign it to station s. Set =-tj.
Eliminate task j from all lists.
If all lists are empty, STOP.
Update the immediate successors of task j on list A and goto step 2.
Example Problem
j
Tj
Pj
All Pred,
1
5
-
2
35
1
1
3
25
1
1
4
60
2
1,2
5
30
2
1,2
6
10
2,3
1,2,3
7
60
6
1,2,3.6
8
25
4,5
1,2,4,5
9
35
8
1,2,4,5,8
10
70
7,9
1,2,3,4,5,6,7,8,9
11
30
10
1,2,3,4,5,6,7,8,9,10,11
5
8
2
4
9
1
6
3
10
7
11
C = 72
Ranked Positional Weight (RPW)
• Ranks tasks according to their positional weight and
assigns tasks to workstations sequentially according
to the ranking.
• The positional weight of a task is a measure of the
total time required for the task and all succeeding
tasks.
PWi  ti 
 t
jS i
j
where: ti is the time required for task i , and
S(i) is the set tasks which follow task
Ranked Positional Weight
Example
j
Tj
Pj
All Pred,
S(j)
PW(j)
Rank
Sts
1
5
-
-
2,3,4,5,6,7,8,9,10,11
385
1
1
2
35
1
1
4,5,6,7,8,9,10,11
355
2
1
3
25
1
1
6,7,10,11
195
3
1
4
60
2
1,2
8,9,10,11
220
4
2
5
30
2
1,2
8,9,10,11
190
5
3
6
10
2,3
1,2,3
7,10,11
170
6
2
7
60
6
1,2,3.6
10,11
160
7
4
8
25
4,5
1,2,4,5
9,10,11
160
8
3
9
35
8
1,2,4,5,8
10,11
135
9
5
10
70
7,9
1,2,3,4,5,6,7,8,9
11
100
10
6
11
30
10
1,2,3,4,5,6,7,8,9,10,11
30
11
7
-
Tree Generation
• Generate a decision tree containing all possible
sequences of tasks that obey the precedence
constraints (this version doesn’t consider zoning
constraints).
• Askin and Standridge describe a general tree
generation procedure that examines all N!
sequences of N tasks.
• FABLE - Fast Algorithm for Balancing Lines
Effectively
• Uses tree generation with a set of fathoming rules
to reduce the solution space and speed
evaluation.
FABLE
• Preprocessing
• – Task renumbering
• Renumber a task only after all of it’s predecessors have
been renumbered
• Break ties in favor of tasks with the largest tj.
• Break second level ties in favor of the task with the
largest number of successors
• Break third level ties arbitrarily
– Increase task times where possible to facilitate
fathoming.
if t j  min
k  jtk
 C, then set t j  C
Example Tree Generation
2
Task
Tj
Pred.
a
3
-
b
2
-
c
3
a,b
d
2
a
e
1
d
a
d
b
c
C=4
1
3
6
0
11
e
15
16
12
7
4
5
8
9
10
13
14
17
18
20
21
22
19