1. Perancangan Sistem Manufaktur
D0394 Perancangan Sistem Manufaktur
Kuliah Ke XXIII - XXVI

2. 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

3. Product Assembly
Virtually all end products go through some assembly process.
Approaches
Craftsman approach
Output =  parts/unit time    
Output = 3  parts/unit time

4. Product Assembly 3 3    3
Virtually all end products go through some assembly process.
Approaches
Craftsman approach
Assembly line 3 3    3
Output = 3  parts/unit time
Output = 3  parts/unit time

5. Product Assembly    3  = 2 part/hour each  = 2 part/hour each 31 2 3 v1    3
 = 2 part/hour each
3  = 6 parts/hour
v = 1/3  = 1/6 hour v2
 = 2 part/hour each
3  = 6 parts/hour
 = 1/  = 1/2 hour 3 v3 3
Assume = 1 = 2 = 3 = 
Assume = v1 = v2 = v3 = v

6. 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.

7. 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.

8. Example Problem d
Task Ti
Predecessor a 3 - b 2 c
a,b d e 1 a c e b

9. 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

10. 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.

11. Parameter / Decision Variables (cont.)
k is the number of workstations required (unknown).
cik is a set of cost coefficients such that:

12. ALB-1 Problem Formulation

13. Solving Problem Very difficult to solve optimally Heuristic Solutions
Integer variables
Non-linear constraints
Heuristic Solutions
COMSOAL
Ranked positional weight
Enumeration Methods
Tree Generation
Naive approach
Fathoming rules

14. Example Problem 1 2 3 4 5 6 7 8 11 10 9 C = 72 j Tj Pj 1 5 - 2 35 3 2560 30 6 10
2,3 7 8
4,5 9 70
7,9 11 1 2 3 4 5 6 7 8 11 10 9
C = 72

15. COMSOAL Random sequence generation procedure Benefits
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

16. COMSOAL Procedure
Form a list A of tasks. Set the trial station s=1 and remaining cycle time τ=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 <= τ to list C, the “fit list.”
If C is empty, increment the trial station s = s+1, set τ=C, and goto step 3.
Select task j from list C and assign it to station s. Set τ=τ-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.

17. Example Problem 1 2 3 4 5 6 7 8 11 10 9 C = 72 j Tj Pj All Pred, 1 5 -35 3 25 4 60
1,2 30 6 10
2,3
1,2,3 7
1,2,3.6 8
4,5
1,2,4,5 9
1,2,4,5,8 70
7,9
1,2,3,4,5,6,7,8,9 11
1,2,3,4,5,6,7,8,9,10,11 1 2 3 4 5 6 7 8 11 10 9
C = 72

18. 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.
where: ti is the time required for task i , and
S(i) is the set tasks which follow task

19. Ranked Positional Weight Examplej Tj Pj
All Pred,
S(j)
PW(j)
Rank
Sts 1 5 -
2,3,4,5,6,7,8,9,10,11
385 2 35
4,5,6,7,8,9,10,11
355 3 25
6,7,10,11
195 4 60
1,2
8,9,10,11
220 30
190 6 10
2,3
1,2,3
7,10,11
170 7
1,2,3.6
10,11
160 8
4,5
1,2,4,5
9,10,11 9
1,2,4,5,8
135 70
7,9
1,2,3,4,5,6,7,8,9 11
100
1,2,3,4,5,6,7,8,9,10,11

20. 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.

21. 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.

22. Example Tree Generation2 3 4 5
Task Tj
Pred. a 3 - b 2 c
a,b d e 1 1 6 7 8 9 10 11 12 13 14 a d e 15 16 17 18 19 b c 20 21 22
C = 4