Unpaced Lines - Module 4

Dr. Cesar Malave

Texas A & M University

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.

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.

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 - 5 minutes Conclusion - 5 minutes Total Lecture Time - 50 minutes

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

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

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

Unpaced Lines (contd..)

Coefficient of Variation of processing time (CV) CV determines the throughput CV = standard deviation / mean

Unpaced Lines (contd..)

1.0

0.9

0.8

0.7

0.6

0.5

0.41 2 3 4 5 6 7 8 9

Rel

ativ

e ou

tput

Number of stages

CV = 0.1

CV = 0.3

CV = 0.5

CV = 1.0

Effect of random processing time in balanced, unbuffered lines

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

Unpaced Lines (contd..)

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.

Solution Case (i):

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 From Conway’s findings, we find that for 4 stages, 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.

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

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

010 20 30 40 50 60 70 80

Z = Size of each buffer

ZCV

Proportion of lost output recovered by buffering in balanced lines

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

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

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)

Case 3 (contd..) Conway’s Findings Effect of Buffers with Random Failures and Repair Times

Z.b/(1 + CV2R) (EZ – E0) / (E - E0)

0 0.0 0.25 0.25 0.5 0.35 1 0.5 2 0.7 4 0.8 8 0.9

Note: CVR is 1 for an exponential distribution.

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

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.

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

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.

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.