1. Dr. Cesar Malave Texas A & M University
Unpaced Lines - Module 4
Dr. Cesar Malave
Texas A & M University

2. Background Material
Any Manufacturing systems book has a chapter that covers the introduction about the transfer lines and general serial systems.
Suggested Books:
Chapter 3(Section 3.5) of Modeling and Analysis of Manufacturing Systems, by Ronald G.Askin and Charles R.Stanridge, John Wiley & Sons, Inc, 1993.
Chapter 3 of Manufacturing Systems Engineering, by Stanley B.Gershwin, Prentice Hall, 1994.

3. Lecture Objectives At the end of the lecture, each student should be
able to
Estimate the throughput of a line in all the cases listed below
Identical workstations, random service, no buffers and no failures
Identical workstations, random service, equal buffers and no failures
Constant processing time, random failures and random repair times
Determine the optimal location of the buffer in a transfer line.

4. Time Management Readiness Assessment Test (RAT) - 5 minutes
Lecture on Unpaced Lines - 10 minutes
Spot Exercise on Unpaced Lines - 5 minutes
Lecture on Unpaced Lines (contd..) - 15 minutes
Team Exercise on Unpaced Lines - 5 minutes
Homework Discussion minutes
Conclusion minutes
Total Lecture Time minutes

5. Readiness Assessment Test (RAT)
Differentiate between Paced and Unpaced Lines
Paced Lines
Unpaced Lines
Also referred to as a synchronous line
Also referred to as an asynchronous line
Limit on time available to complete each task
No fixed time to complete a task
Cycle time determines the production rate
Buffers between workstations are necessary
Each workstation is given the same amount of time to perform a job, and as such they start and stop at the same time
The unpaced line moves the job either to the next workstation or buffer immediately upon completion

6. Unpaced Lines Introduction Each workstation acts independently
Random processing times are involved
Each job has its own requirements at each workstation
Upon completion of the task, each workstation attempts to pass its part on to the next workstation or the buffer
If the next workstation is idle or buffer space exists - part is passed
Else, the station becomes blocked
Upon passing the part, the workstation checks its input buffer
If a part is available, the station is active and begins working
Else, the station becomes starved

7. Unpaced Lines (contd..)
Identical Workstations, Random Processing Times, No Buffers, No Failures - Case 1
Consider a line with M stages and all workstations have the same processing time distribution
Processing times for each stage of each job are assumed to be independent and identically distributed
Workstations do not break down
No Buffer space exists
Workstations will be starved until the upstream station finishes its operation
Workstations will be blocked until the downstream station finishes its operation and is able to pass on its job

8. Unpaced Lines (contd..)
Coefficient of Variation of processing time (CV)
CV determines the throughput
CV = standard deviation / mean
Effect of random processing time in balanced, unbuffered lines
1.0
0.9
CV = 0.1
Relative output
0.8
CV = 0.3
0.7
CV = 0.5
0.6
0.5
CV = 1.0
0.4 1 2 3 4 5 6 7 8 9
Number of stages

9. Unpaced Lines (contd..) Analysis of Conway’s findings - Case 1
Throughput decreases as the number of stages increases, but levels off immediately.
A two-stage line with CV of 0.5 has only 80% of the throughput of a single-stage line
But a eight or higher stage line with the same CV will have 65% of the throughput of the single-stage line
After a certain number of stages, a further increase in the number of stages will only lead to a minor reduction in the throughput as compared to a single-stage line
For CV = 1, throughput levels off at 45% of the single-stage output and for CV = 0.5, throughput levels off at 65% of the single-stage output

10. Spot Exercise Suppose a serial processing unit has 3 stages and
each station requires a mean service time of about
10 minutes with an exponential distribution.
Find the production rate for the line if there are no buffers.
Suppose service time variability could be reduced to a
standard deviation of one minute (non-exponential), find
the production rate.

11. Solution Case (i): Case (ii):
CV for an exponential distribution = 1.0
From Conway’s findings, we find that for 4 stages,
the relative output value is 0.55.
Therefore, instead of 1 unit being produced every 10 minutes
i.e. a production rate of 0.1/min, we have a production rate
equal to 0.55*0.1 = 0.055/min = 3/hr
Case (ii):
New coefficient of variation (CV) = 1/10 = 0.1
the relative output value is 0.91.
Therefore, instead of 1 unit being produced every 10
minutes i.e. a production rate of 0.1/min, we have a
production rate equal to 0.91*0.1 = 0.091/min = 5.5/hr
Thus, there is a significant increase in the production rate
from Case 1 to Case 2.

12. Identical Workstations, Random Processing Times, Equal Buffers, No Failures - Case 2
Buffers of same capacity are placed between each pair of workstations
The first buffer will always be full since the first workstation is never starved
The last buffer will always be empty since the last workstation is never starved
The middle buffer will be half full or half empty on the average
Overall, the buffer utilization decreases from the front to the rear of the line

13. Case 2 (contd..)
Since buffers are involved in this case, throughput depends on the ratio of buffer capacity (Z for each buffer) to the processing time CV
1.0
0.8
0.6
0.4
0.2 10 20 30 40 50 60 70 80 Z
Z = Size of each buffer CV
Proportion of lost output recovered by buffering in balanced lines

14. Case 2 (contd..)
In this case, some percentage of the capacity lost can be recovered by the addition of buffers
This is marginally dependent on the length of the line
From Conway’s findings of the average recovery proportion graph, the following observations can be made:
For Z/CV = 10, about 80% of the capacity lost due to random processing times is recovered.
For Z/CV = 20, about 90% of the capacity lost due to random processing times is recovered.
First, we can find the capacity lost because of random processing times from Case 1 i.e., using CV
Second, we can find the portion of the loss that can be recovered by buffering from Case 2 i.e., using Z

15. Optimal Buffer Location
For one buffer (Z = 1), the optimal location is the center of the line such that all the upstream workstations will have the same availability as those of the downstream workstations
For lines with identical workstations, the best allocation is many buffers of nearly equal size.
The largest buffers should be in the middle
The difference between the largest and smallest buffers should be no more than one slot
Buffer sizes should be symmetric from the center moving to the front and rear of the line
For lines with unequal workstations, the less reliable workstations should have larger input and output buffers
In case of failures or high processing time variability at a workstation other than the bottleneck workstation, the input and output buffers play a significant role in maintaining its utilization

16. Constant Processing Times, Random Failures and Repair Times - Case 3
To avoid the possibility of the stages to lose synchronization, it is worthwhile to employ asynchronous part transfer even in a balanced, constant-processing-time environment
Assume identical workstations and buffers are placed between every pair of adjacent workstations
From Conway's findings, throughput is determinant on the ratio
Z.b/(1 + CV2R) where
CVR is the coefficient of variation of repair time distribution
b-1 is the average repair time measured in processing time cycles
Z.b is the size of the buffer measured in multiples of average repair time
Effect of the buffer (improvement) is measured by the proportion of possible improvement gained form the addition of the buffer i.e.,
(EZ – E0) / (E – E0)

17. Case 3 (contd..) Conway’s Findings
Effect of Buffers with Random Failures and Repair Times
Z.b/(1 + CV2R) (EZ – E0) / (E - E0)
Note: CVR is 1 for an exponential distribution.

18. Buffers and production control
If the availability of the portion of the line in front of the buffer is larger than that of the portion behind it, the buffer will tend to be full
If the availability of the portion of the line in front of the buffer is smaller than that of the portion behind it, the buffer will tend to be empty
If the availabilities are similar, the buffer will tend to be half-full
Buffering is closely related to the pull-push system
Output buffer capacities are limited in pull system (JIT) and workstations stop when these are full
In a push system (MRP), workstations continue to produce even when there is no pull for stock down the line i.e, when the downstream stations break down

19. Team Exercise Four automatic insertion machines are set up for series,
without intermediate buffers, to add components to printed
circuit boards. Each machine inserts 20 different
component types. Due to board design and component
requirements, automatic setup and insertion times for
machines vary from 2 minutes to 6 minutes per
workstation. Assuming that machines do not fail, estimate
the number of boards produced by this line/hr while the
machines are all operational.

20. Solution Number of reliable workstations = 4
Cycle time Є [2,6] and let us assume uniform distribution
Mean processing time (µ) = (2 + 6)/2 = 4 minutes
Standard deviation of processing time (σ) is given by
σ = (max–min)/√12 = (6 - 2)/√12 = 1.15 minutes
Hence, the coefficient of variation (CV) = σ/µ = 0.29
From Conway's findings (Figure 3.6, Askin & Stanridge), we find
that the relative output factor is 0.8.
Hence, output/hr = 0.8 * (1 cycle/4 min) * (60 min/1 hr)
= 12/hr

21. Homework
Consider a six-stage serial processing system with identical workstations and random processing times. Details about the unpaced line are given below:
Mean processing time at each workstation is 30 minutes
Standard deviation of processing times at each station is about 9 minutes
Find the production rate of the line while it is
operating.

22. Conclusion
Coefficient of variation is required to estimate the production rate in case of reliable workstations and random processing times.
To estimate the effect of buffers when workstations fail, average repair time and the coefficient of variation for repair time are needed.