Unpaced Lines - Module 4

1. 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 - 5 minutes • Conclusion - 5 minutes • Total Lecture Time - 50 minutes

5. Readiness Assessment Test (RAT) • Differentiate between Paced and Unpaced Lines

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): 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.

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 0 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-1is 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) 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.

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.