- Email: [email protected]
Performance of Reliable and Unreliable Unpaced Production Lines with Uneven Buffer Allocation
Proceedings of the 14th IFAC Symposium on Information Control Problems in Manufacturing Bucharest, Romania, May 23-25, 2012
Performance of Reliable and Unreliable Unpaced Production Lines with Uneven Buffer Allocation Sabry Shaaban*, Tom McNamara*, Sarah Hudson*
* ESC Rennes School of Business 2 Rue Robert d'arbrissel, Rennes France (E-mail: [email protected]). Abstract: We compare the efficiency of reliable and unreliable unpaced production lines that are unbalanced in terms of their buffer storage capacities to a corresponding line with equal sized buffers. The lines were simulated with different values of line length, buffer storage size, mean buffer capacity, and configuration of buffer imbalance. The results show that, for both reliable and unreliable lines the best buffer allocation patterns in terms of generating lower idle times as compared to a balanced line are those where total available buffer capacity is allocated as evenly as possible between workstations, whereas concentrating more buffer capacity towards the end of the line gives best average buffer level results. Keywords: Unpaced reliable and unreliable production lines, simulation; uneven buffer sizes, idle time, average buffer level.
1. INTRODUCTION Research into unpaced production line design is a growing area because of the complexity of the decisions to be made in several areas. One of the major factors affecting line performance, and one which has been more extensively studied in the literature is the buffer allocation problem. Lines unbalanced with respect to their buffer capacities are of great interest as technical considerations often restrict the amount of space available in the line, thereby making it difficult to allocate total buffer capacity evenly amongst individual buffers. The paper will first provide a review of the relevant literature followed by a presentation of the motivation and objectives of the study. Subsequent sections discuss the methodology and experimental design and provide the simulation results and analyses. The last two parts provide a summary of the results along with a discussion and some conclusions. 2. LITERATURE REVIEW There is a significant body of literature on the effects of buffer allocation on line performance. The literature deals with a variety of line types, for example balanced and unbalanced serial production lines, where workload allocation and variability are kept constant or vary along the line, respectively. In addition to considerations of balance, research investigating buffer placement in unreliable lines, assembly closed-loop or rework loop lines have also been carried out (Helber, 2001; Sabuncuoglu et al, 2006). Some of the earliest work on the influence of buffer allocation on WIP and throughput (El-Rayah, 1979) found that uneven buffering had a detrimental effect on output, but that conversely, WIP could be reduced in some cases if buffer space was distributed unevenly in some particular configurations. The 978-3-902661-98-2/12/$20.00 © 2012 IFAC
conclusion was that if unbalancing the buffers was unavoidable, more buffer space should be allocated to the central stations and less to the end stations. In the following decade this idea was developed, and some studies (Chow, 1987; Conway et al, 1988) showed that unbalanced buffering could be managed in order to maintain, or even improve the performance of the line in terms of output and WIP when compared to the balanced line. These ideas were interesting in that in general the belief was that a balanced line i.e. a line where all stations have equal operating times, equal variability and buffer is evenly allocated would provide the best performance. In particular, Conway et al (1988) proposed that buffer capacity should be placed as evenly as possible along the line, but any small additional amount of buffer should be allocated to the line’s centre. In the case of limited buffer space, preference should be given to the middle stations, and one notable result of this work was that the proper assignment of buffers along the line is as equally important as their number. Following on from this, there were a number of articles investigating buffer allocation and its effects on throughput (TR) with the aim of optimisation. Studies by Powell (1994), Hillier and So (1991) and Hillier, So & Boling (1993) found that for a limited total buffer capacity, a balanced allocation is best, whereas as more buffer space became available, the best results were obtained by concentrating more buffer capacity towards the centre of the line. This tendency became more marked when operator variability (coefficient of variation, CV) was higher. Hillier, So & Boling (1993) termed this the “storage bowl phenomenon”. Further work (Hillier and So (1995); Powell and Pyke (1996); Hillier (2000); Hillier and Hillier, (2006)) has also tended to support this idea. Other authors extended this work to looking at other indicators of performance such
384
10.3182/20120523-3-RO-2023.00285
INCOM 2012, May 23-25, 2012 Bucharest, Romania
as WIP levels. Papadopoulos and Vidalis (2001) developed a heuristic buffer allocation algorithm to find the minimum amount of average WIP for a predetermined throughput. They concluded that a trade-off has to be made. If the interest was to maximize TR, then an inverted bowl (or a close approximation) is generally the preferred arrangement. On the other hand, if the objective was a reduction in average WIP level, then it is better to allocate more buffers towards the end of the line. This idea that the optimal buffer allocation pattern differs for different performance indicators has found support in the work of Grosfeld-Nir and Magazine (2005), but in their case it was observed that for lines where the buffer was allocated evenly, throughput was maximised, whereas unbalancing the buffer allocation gave better results in terms of WIP, ascending buffer patterns being superior to descending patterns. Several studies have investigated unreliable lines with a single source of imbalance in the form of uneven buffer allocation. Vouros and Papadopoulos (1998) investigated the buffer allocation problem in terms of TR and presented a method that uses an established list of generic procedures, including simulation. They looked at lines of 3, 4 and 5 stations with balanced mean operating times and various machine reliability rates across the stations. The probability distributions utilized were exponential and Erlang for mean processing times (MT), exponential for the mean time between failures (MTBF) and exponential or Erlang-m for repair rates. They observed that their solution procedure is fairly accurate for small line lengths, but for longer lines the accuracy declines. However, the focus in general is not on the effects of imbalance, but rather an interest in generating algorithms for operating characteristics and determining performance outcomes (see recebt work for example by Papadopoulos and Vidalis (1999); Gershwin and Schor (2000); Helber (2001); Kim and Lee (2001); Enginarlar et al (2001); Nahas et al (2006)). There are several differences between the work carried out previously and the investigation presented in this paper. We can see that for most of the studies the aim is not to compare reliable and unreliable lines, but is mostly concerned with optimization of some performance indicator, be it throughput or buffer capacity. The approach used is often mathematical analysis or algorithm generation and testing in order to reach this optimal solution. In addition, the performance indicator used is for the most part throughput, and the question of WIP or idle time has not been very much looked at in these types of line. Finally, there are no studies to our knowledge that use simulation to observe the effects of various patterns of buffer allocation (and not simply total buffer capacity) on idle time and average buffer levels in unpaced lines. 3. STUDY OBJECTIVES We investigate reliable and unreliable, unpaced, serial production lines where buffer space is allocated unequally (unbalanced) between workstations. The results are then compared with those from the equivalent simulated balanced line where total buffer capacity is distributed evenly between workstations. Mean operation times (MT) and the coefficient of variation (CV) are kept constant, with MT= 10 time units per station and CV = 0.274 in all experiments. The main goals of the study are to: 1) Compare the efficiency of the
reliable and unreliable unbalanced lines and to those of a corresponding balanced line to find out if improvement in performance is attainable. 2) Assess the merits of various patterns of unequal buffer sizes and identify the ones with the most potential in terms of performance. 3) Evaluate the effects of line design factors, namely line length and mean buffer capacity on the measures of performance; idle time and average buffer level. 4. METHODOLOGY AND EXPERIMENTAL DESIGN There is no mathematical procedure presently capable of handling the unbalanced steady-state characteristics of such lines, so computer simulation was utilized as the most suitable technique for this type of experiment. 4.1 Factorial Design Complete factorial design was chosen for the current investigation. In the context of the particular lines being simulated, the independent variables are: Total number of stations in the line, N; Total amount of buffer capacity for the line, TB, also expressed as Mean capacity of each buffer, MB (= TB divided by the number of buffers).; Pattern of buffer capacity imbalance, Pi. The dependent performance measures were:1. Average Buffer Level, ABL for the whole line. Idle time (percentage of total working time that the line is idle), IT. Line Performance Length Indicators N
Total Buffer Capacity (TB)
Buffer Allocation Policy (Pi)
ABL
5 stations 8&24 units
4 policies
IT
8 stations 14& 42 units
(see section 4.6)
* All these compared to the balanced line with buffer evenly allocated along the line. Table 1. Summary of reliable and unreliable lines simulated 4.2 Simulation Run Parameters The work time probability distribution used in the simulations followed a Weibull distribution with a CV value averaging around 0.274 following Slack (1982). A sufficiently long warm up period was used in accordance with the technique proposed by Law and Kelton (2000), observing WIP as they suggest. A trial procedure established that after an initial run of 20,000 minutes, acceptable autocorrelation values of between -0.163 and +0.153 were achieved within the -0.20 and +0.20 range suggested by Harrell et al (2004). All data collected during the first 30,000 minutes initial period were discarded and measurements from a production run of 20,000 minutes, broken down into 50 blocks (subruns) of 400 minutes each were gathered. Therefore mean IT and ABL values were collected every 400 minutes and the average of these 50 means (the grand mean) was computed Finally, in order to generate an identical event sequence for all the designs and highlight the contrast amongst the configurations, all the experiments used
385
INCOM 2012, May 23-25, 2012 Bucharest, Romania
the same random number seed. The data presented in tables 3-6 are the grand means.
o
P4: Bowl shape (V): position smaller amounts of buffer towards the centre – patterns D1 & D2.
o
P5: General: no concentration of TB at any area of the line – patterns E1 & E2.
4.4 Failure and Repair Parameters – Unreliable Lines
For this investigation the failure rate was set at 0.01 breakdowns per minute, with the repair rate being 0.10 repairs per minute, so that the mean time between failures was 100 minutes and the mean time until repair was 10 minutes in accordance with the rates used in the literature (Altiok and Stidham (1983); Hopp and Simon (1993)). As a result, line efficiency was determined to be 91% (MTBF 100 / (MTBF 100 + MTTR 10)).
The line configurations for the experimental design are exhibited in Table 2 below, where policies 1 through 5 are represented respectively by patterns A1 – A2, B1 - B, C1 – C2, D1 – D2 and E1 – E2 for the 5 and 8-station lines. Line Length N = 5 8
24
Mean Buffer
2
6
4, 2, 1, 1 3,3,1,1 1, 1, 2, 4 1,1,1,5 1, 3, 3, 1 1,2,4,1 3, 1, 1, 3 4, 1, 1, 2 2,2,3,1 2,3,2,1 14
12, 6, 3, 3 9,9,3,3 3, 3, 6, 12 3,3,3,15 3, 9, 9, 3 3,6,12,3 9, 3, 3, 9 12, 3, 3, 6 6,6,9,3 6,9,6,3 42
P1 A1 \ A2 P2 B1 / B2 P3 C1 C2 P4 D1 D2 V P5 E1 E2 Total Buffer c
It was also assumed that both the failure and repair rates were independent, exponentially distributed random variables and as suggested by Law (2007), all downtimes were considered to be usage rather than clock based. 4.5 Simulation Model Assumptions The basic operating assumptions for the asynchronous flow line simulated are 1) The first station is never starved and the last station is never blocked. 2) No defective parts are produced. 3) Only one type of product flows in the system, with no changeovers. 4) Time to move the work units in and out of the storage buffers is considered to be small enough in comparative terms to be assumed t be negligible. 5) No breakdowns occur for the reliable lines and in the case of the unreliable lines, breakdown and repair rates are the same for each station.
Total Buffer
Buffer Allocation Policy Pi and Patterns(A – E)
An exponential probability distribution with regard to both the mean time between failure and mean time to repair is considered to be most representative of what is observed in actual manufacturing systems according to an empirical study of unreliable lines by Inman (1999).
o
P1: Descending order (\): concentrate the available buffer capacity nearer the beginning of the line – patterns A1 & A2.
In this study a total of 2 line lengths * 2 mean buffer capacities * 5 policies * 2 patterns each * 2 line reliability types = 80 configurations were simulated.
o
P2: Ascending order (/): concentrate the available buffer capacity nearer the end of the line – patterns B1 & B2.
5. RESULTS
4.6 Specific Design Features Line length: N values of 5 and 8 were specified in this study, and a total buffer capacity: TB values of 8 and 24 (for N = 5), and 14 and 42 (for N = 8) were selected, giving rise to mean buffer capacities MB = 2, 4 and 6 for both N = 5 and 8. Buffer allocation policies
o
P3: Inverted bowl shape (): concentrate the available buffer capacity nearer the middle of the line – patterns C1 & C2. .
Buffer Allocation Policy Pi and Patterns(A – E)
Five policies (Pi) were investigated for the total allocation of buffer size:
Mean Buffer N = 82 6 Line Length P1 A1 6, 2, 2, 1, 1, 18, 6, 6, 3, 3, \ A2 4,4,2,1,1,1,1 12,12,6,3,3,3,3 1, 1, 1, 1, 6, 3, 3, 3, 3, 18, P2 B1 / 1,1,1,1,1,1,8 3,3,3,3,3,3,24 B2 P3 C1 1, 1, 4, 4, 2, 3, 3, 12, 12, 6, C2 1,1,6,2,2,1,1 3,3,18,6,6,3,3 P4 D1 4, 2, 1, 1, 3, 12, 6, 3, 3, 9, D2 4, 2, 1, 1, 1, 12, 6, 3, 3, 3, V 2,2,2,3,3,1,1 6,6,6,9,9,3,3 P5 E1 2,2,3,3,2,1,1 6,6,9,9,6,3,3 E2 Table 2. Unequal buffer size allocation policies (Pi) and patterns Ai - Ei for reliable and unreliable lines.
The results of the simulations are presented below. Section 5.1 presents the findings in terms of idle time (IT) performance and section 5.2 looks at the results found for average buffer levels (ABL). Due to space limitations, only IT and ABL results for the best, some good, and the worst patterns will be shown. Full data are available from the authors.
386
INCOM 2012, May 23-25, 2012 Bucharest, Romania
5.1 Idle Time (IT) Data
•
The total idle time calculated for the reliable and unreliable line patterns chosen are exhibited in Tables 3 and 4 below. The results for the balanced line are shown in the bottom line for purposes of comparison, and the cases that show decreased idle time when compared to the balanced line control are marked in bold.
In terms of whether better idle time results are obtained for a policy- (ascending, descending, inverted bowl or no strong concentration), we can see that none of the policies can be labelled as the best or the worst one for both of its constituent patterns.
•
Generally speaking, the data indicate that patterns E2 (N = 5) and E1 (N = 8) for the reliable line and pattern E2 for the unreliable line can be viewed as the best configurations, i.e. the best arrangement is one where the available capacity is distributed as uniformly as possible along the line.
•
The same patterns with different line lengths; E1 (N = 5), E2 (N = 8) in the case of reliable lines and E2 for unreliable lines can also be deemed as good configurations.
•
Pattern B2 (concentrate the available buffer capacity nearer the end of the line) can be regarded as the worst pattern, which shows the highest idle times across the board both with respect to the other patterns and compared to the balanced line.
•
The influence of line length is negative, as one would expect, with IT tending to increase with the number of workstations. The degree of increase becomes more substantial for lower mean buffer values in the case of the best pattern.
•
The effect of mean buffer: IT decreases as MB goes up.
•
As expected, the IT data for unreliable lines are clearly much higher than their reliable line counterpart, which reflects the system inefficiency resulting from somewhat prolonged breakdown and repair delays.
Line Length N
5
8
Mean Buffer 2
6
2
6
7.661 7.380 7.978 9.104 6.007 6.240 7.721 6.175 5.707 5.598
2.906 2.682 3.094 3.499 2.342 2.463 3.099 3.030 2.082 1.733
9.976 10.110 9.315 10.982 7.846 7.542 7.663 7.501 7.112 7.497
3.511 3.918 3.571 4.123 3.260 2.949 2.230 2.352 2.212 3.492
4.985
2.066
5.935
2.174
P1 \ P2 / P3 P4 V P5
Balanced Results
A1 A2 B1 B2 C1 C2 D1 D2 E1 E2 Line
Table 3. IT data for reliable 5- and 8-station lines, policies 1 - 5, patterns Ai - Ei and a balanced line Line Length N
5
8
Mean Buffer 2
6
2
6
20.259 20.627 22.728 23.831 20.584 20.632 20.254 21.146 20.009 19.954
15.680 16.374 13.988 16.105 14.714 14.547 16.785 14.678 13.736 13.375
25.575 26.260 23.663 26.866 22.916 22.751 22.855 26.258 22.941 21.909
18.205 17.096 16.473 18.062 16.610 14.658 17.771 15.734 15.242 15.703
19.352 13.432 21.530
13.581
Buffer Allocation Policy Pi and Patterns(Ai – Ei)
Capacity MB P1 \ P2 / P3 P4 V P5
Balanced Results
A1 A2 B1 B2 C1 C2 D1 D2 E1 E2 Line
5.2 Average Buffer Level (ABL) Data Tables 5 and 6 summarise the ABL results. The results for the balanced line are shown in the bottom line for purposes of comparison, and the patterns which outperform those of the balanced line are marked in bold.
Table 4. IT data for unreliable 5- and 8-station lines, policies 1 - 5, patterns Ai - Ei and a balanced line 5.1.1 Ranking Patterns and Effects of N & TB on IT The following conclusions can be drawn from the results shown above for the reliable and unreliable lines:
Line Length N 5 8 Mean Buffer 2 6 2 6 P1 A1 1.507 2.506 1.136 1.965 2.480 A2 1.468 4.417 1.577 P2 B1 0.534 1.679 0.513 1.417 B2 0.531 1.457 0.531 1.444 2.689 P3 C1 1.090 3.341 1.076 2.664 C2 0.798 2.170 0.962 3.258 P4 D1 1.025 2.741 1.144 3.140 D2 1.284 4.135 1.198 3.458 P5 E1 1.235 2.758 1.314 4.248 E2 1.218 2.792 1.411 2.601 Balanced Line 1.033 3.321 0.970 Table 5. ABL data for reliable 5- and 8-station lines, policies 1-5, patterns Ai-Ei and a balanced line
387
Buffer Allocation Policy Pi and Patterns(Ai – Ei)
Buffer Allocation Policy Pi and Patterns(Ai – Ei)
Capacity MB
INCOM 2012, May 23-25, 2012 Bucharest, Romania
Buffer Allocation Policy Pi and Patterns(Ai – Ei)
Line Length N 5 8 Mean Buffer 2 6 2 6 4.486 P1 A1 1.382 4.388 1.420 4.316 A2 1.297 4.185 1.455 P2 B1 0.598 1.810 0.683 1.485 B2 0.560 1.678 0.568 1.755 4.155 P3 C1 1.046 2.308 1.052 3.270 C2 0.999 2.058 1.230 3.457 P4 D1 1.027 3.002 1.165 3.330 D2 1.242 3.363 1.101 V 3.792 P5 E1 1.049 3.529 1.194 3.815 E2 1.098 3.692 1.167 3.201 Balanced Line 0.976 3.265 1.001 Table 6 ABL data for unreliable 5- and 8-station lines, policies 1 - 5, patterns Ai - Ei and a balanced line 5.2.1 Ranking of Patterns and Effects of Design Variables on ABL An examination of the results shown in Tables 9 and 10 yields the following noteworthy conclusions for reliable and unreliable lines: •
Policy P2, (patterns B1 and B2), where buffers are allocated in an ascending order, with capacity concentrated towards the end of the line consistently outperforms both the balanced line and all other configurations simulated in terms of average buffer levels.
•
Pattern C2 (the inverted bowl shape configuration) can also be regarded as a good pattern, with results showing improved ABL performance for most of its patterns.
•
For unreliable lines, the worst results in terms of average buffer levels are seen for the descending order policy P1, with available buffer space concentrated towards the beginning of the line. However, there was no discernible worst configuration for reliable lines.
•
The influence of line length seems not to be important; there is no directly observable consistent pattern of change of ABL levels with N.
•
On the other hand, there is an influence due to mean buffer capacity which is that average buffer levels increase with the availability of space, i.e. higher MB.
•
The unreliability of the line has no effect on ABL
5.3 Best Pattern Savings We can compare the results yielded in terms of percentage change from the balanced line. 5.3.1 Best Pattern Savings in IT Table 7 summarises the % difference in IT for the best reliable and unreliable unbalanced line patterns in comparison with those of the balanced line. The results where IT is lower than for the control are in bold.
N=5 N= 8 MB Reliable Unreliable Reliable Unreliable 12.30 3.11 1.76 2 -16.14 19.83 1.75 15.62 6 -0.42 Table 7. % change in the best patterns’ IT compared to the control for reliable and unreliable lines MB= 2 &,6. It can be noted from the table that MB and N have no impact on the change in IT compared to the balanced line. 5.3.2 Best Pattern Savings in ABL Table 8 summarises the % saving in ABL for the best reliable and unreliable unbalanced patterns in comparison with those of the balanced line: N=5 N= 8 MB Reliable Unreliable Reliable Unreliable Pattern B1 48.31 -38.73 -47.11 -31.77 2 -49.44 -44.56 -45.52 -53.61% 6 Pattern B2 -48.60 -42.62 -45.26 -43.26 2 -56.13 -48.61 -44.48 -45.17 6 Table 8.Percentage % change in ABL for the two best patterns compared to the balanced line. We can see from table8 that for both reliable and unreliable lines: Patterns B1 and B2 show consistent improvement over the control for all values of line length and mean buffer capacity considered. Buffer space availability (MB) has no a generally consistent impact on the degree of improvement in ABL performance. On the other hand, for reliable lines, we can see that as N increases, the % saving in ABL declines, but for unreliable lines ABL does not appear to be influenced by the number of stations. Furthermore, unbalancing buffers can yield savings in terms of idle time for specific configurations (16.4% for the best reliable line configuration and 0.42 for the best unreliable line pattern), but the imbalance is having a much stronger impact on the savings in ABL (56.13% for the best reliable line configuration and 53.61%. for the unreliable line). 6. SUMMARY 6.1 Effects of Buffer Allocation Policy and Patterns From the results presented above, we can say that for both reliable and unreliable lines policy five (P5) with buffer space allocated fairly evenly performed better in terms of idle time than any of the others, when compared to the balanced line. On the other hand, for both reliable and unreliable lines the best patterns with respect to decreasing average buffer level was found to be an ascending BC order (policy P2), where more buffer capacity is positioned towards the end of the line. It was also found that the less extreme the buffer capacity allocation, i.e. the more evenly spread it is, the better are the results as far as idle time is concerned. This is generally in line with the finding of Conway et al (1988) and Hillier and So (1991) Support was also found for the results obtained by El-Rayah (1979) and Papadopoulos and Vidalis (2001) in that for ABL, the most advantageous configuration is to
388
INCOM 2012, May 23-25, 2012 Bucharest, Romania
concentrate the available buffer capacity towards the end of the line. 6.2 Effects of Line Design Factors: Length and Buffer Capacity If we consider line length, the reliable and unreliable line results show that as N increases, so does idle time, whereas no overall effect of line length on average buffer levels is observed. When mean buffer capacity is increased, however, enhanced performance in terms of idle time is observed. On the other hand, the effects of increased buffer capacity on performance in terms of average buffer level are negative, i.e. ABL rises with increased MB. It should be noted that for the best patterns, where buffer capacity is concentrated at the end of the line, the performance in terms of ABL consistently outperforms the control, where buffers are allocated evenly between workstations. An unreliable line generates much higher IT values than a reliable line counterpart. This obviously is a clear indication of line inefficiency which results from waiting time delays, caused by breakdowns and repairs. No tangible effect of breakdown on ABL, however, is seen. This is somewhat surprising, as we would expect buffers to be filling up more for lines which are subject to breakdown. We could speculate that the impact of the imbalanced buffer allocation may be overcoming the negative effects of the downtime, a result that may be worth following up in future work. 6.3 Line Performance Results Unbalanced buffer allocation under the various conditions simulated, had varying effects on performance. In terms of idle time, the vast majority of the unbalanced patterns performed less well than the balanced line, whereas buffer imbalance gave improved average buffer level performance for many of the lines simulated. For each performance indicator, however, there were certain configurations that gave enhanced performance over the balanced control, and the highest % savings in IT and ABL over the corresponding balanced line are IT: 16.14% (reasonable) and ABL: 56.13% (considerable) for reliable lines and IT: 0,42% (v.small) and ABL 53.61% (considerable) for unreliable lines. From the above, there seems to be a great deal of similarity in the behaviour of reliable and unreliable BC unbalanced lines that needs to be explored in more depth in the future. 7. DISCUSSION AND CONCLUSIONS One of the principal conclusions of this study is that the One of the principal conclusions of this study is that the decision of how to allocate different sized buffers between workstations will depend on the particular objectives of the production facility. There is a choice to be made as to whether low inventory is the aim or whether IT needs to be reduced. In this context, although our results show that buffer imbalance in unreliable lines generally causes a decline in performance; we also see that superior performance to that achieved by a balanced line counterpart in terms of idle time or average buffer level is attainable for particular reliable and unreliable line designs. Even though the improvements in idle times are not large in size (16.14%
for reliable and 0.42% for unreliable lines), they can result in substantial savings over the expected lifespan of a production line. On the other hand the superiority in ABL is considerable (around 56% in the case of reliable and 54% for unreliable lines), which indicates that it may be worthwhile to purposely allocate buffers unevenly, with more capacity assigned to the end of the line. Possible future research could for example investigate the effects of the buffer capacity imbalance for reliable and unreliable merging (assembly) lines and also for unreliable lines with two sources of imbalance, which would enable managers to make more accurate decisions in line design in the future. REFERENCES Altiok Altiok, T. and Stidham, S. (1983), “The Allocation of Inter-Stage Buffer Capacities in Production Lines”, IIE Transactions, Vol. 15, No. 4, pp. 292 - 299. Chow, W. M. (1987), “Buffer Capacity Analysis for Sequential Production Lines with Variable Process Times”, International Journal of Production Research, Vol. 25 pp. 1183 - 1196. Conway, R., Maxwell, W., McClain, J. and Thomas, L. J. (1988), “The Role of Work in Progress Inventory in Serial Production Lines”, Operations Research, Vol. 36, pp. 229 - 241. El-Rayah, T. (1979), “The Effect of Inequality of Inter-Stage Buffer Capacities and Operation Time Variability on the Efficiency of Production Line Systems” International Journal of Production Research, Vol. 17, pp. 77 - 89. Enginarlar, E., Li, J. and Meerkov, S. M. (2001), “A Potpourri on the Theme of Lean Buffering”, Proceedings of 3rd Aegean International Conference on Design and Analysis of Manufacturing Systems, Tinos Island, Greece, pp. 249 - 258,. Enginarlar, E., Li, J. and Meerkov, S. M. (2005), “Lean Buffering in Serial Production Lines With NonExponential Machines”, OR Spectrum, Vol. 27, pp. 195 219. Enginarlar, E., Li, J., Meerkov, S. M. and Zhang R. Q. (2002), “Buffer Capacity for Accommodating Machine Downtime in Serial Production Lines”, International Journal of Production Research, Vol. 40, No. 3, pp. 601 - 624. Gershwin,S.B. & Schor, J.E. (2000) ‘Efficient algorithms for buffer space allocation’, Annals of Operations Research, Vol.93, pp.117-144. Grosfeld-Nir, A. and Magazine, M. (2005), “A Simulation Study of Pull Systems with Ascending/Descending Buffers and Stochastic Processing Times”, International Journal of Production Research, Vol. 43, pp. 3529 – 3541. Helber, S. (2001), “Cash-Flow-Orientated Buffer Allocation in Stochastic Flow Lines”, International Journal of Production Management, Vol. 39, No. 14, pp. 3061 3083. Hillier, M.S (2000), “Characterizing the Optimal Allocation of Storage Space in Production Line Systems. IIE Transactions, Vol. 32, pp. 1 - 8. Harrell, C., Ghosh, B., K., & Bowden, R., O. (2004) Simulation using ProModel, New York, McGraw- Hill.
389
INCOM 2012, May 23-25, 2012 Bucharest, Romania
Helber,S. (2001) “Cash-Flow-Orientated Buffer Allocation in Stochastic Flow Lines” International Journal of Production Management, Vol. 39, No. 14, pp. 3061 3083. Hillier, M. S. and Hillier, F. S. (1991), “Simultaneous Optimization of Work and Buffer Space in Hillier, F. S., So, K.C., The Effect of the Coefficient of Variation of Operation Times on the Allocation of Storage Space in Production Line Systems”, IIE Transactions, Vol. 23, pp. 198 - 206. Hillier, F. S., So, K. C. (1995), “On the Optimal Design of Tandem Queuing Systems with Finite Buffers”, Queuing Systems, Vol. 21, pp. 245 – 266. Hillier, F. S. and So, K. C. (1991), “The Effect of Machine Breakdowns and Interstage Storage on the Performance of Production Line Systems”, International Journal of Production Research, Vol. 29, No. 10, pp. 2043 - 2055. Hillier, F. S., So, K. C., Boling, R. W. (1993), “Notes: Toward Characterizing the Optimal Allocation of Storage Space in Production Line Systems with Variable Processing Times”, Management Science, Vol. 39, pp. 126 - 133. Hopp, W. J. and Simon, J. T. (1993), “Estimating Throughput in an Unbalanced Assembly Like Flow System”, International Journal of Production Research, Vol. 31, No. 4, pp. 851 -868. Inman, R. R. (1999), “Empirical Evaluation of Exponential and Independence Assumptions in Queuing Models of Manufacturing Systems”, Production and Operations Management, Vol. 8, No. 4, pp. 409 - 432. Kim, S. and Lee, H. J. (2001), “Allocation of Buffer Capacity to Minimize Average Work-in-Process”, Production Planning & Control, Vol. 12, No. 7, pp. 706 - 716. Law, A., M. (2007), “Simulation Modeling and Analysis”, Irwin / McGraw Hill. Law, A., M. and Kelton, W. D. (2000), “Simulation Modeling and Analysis”, Irwin / McGraw Hill. Nahas, N., Ait-Kadi, D. and Nourelfath, M. (2006), “A New Approach for Buffer Allocation in Unreliable Production Lines”, International Journal of Production Economics, Vol. 103, pp. 873 - 881. Papadopoulos, H. T., Vidalis, M. I. (2001), “Minimizing WIP Inventory in Reliable Production Lines”, International Journal of Production Economics, Vol. 26, pp. 185 197. Papadopoulos, H. T. and Vidalis, M. I. (1999), “Optimal Buffer Allocation in Short -Balanced Unreliable Production Lines”, Computer and Industrial Engineering, Vol. 37, pp. 691 - 710. Powell, S. G. (1994), “Buffer Allocation in Unbalanced Three - Station Serial Lines”, International Journal of Production Research, Vol. 32, pp. 2201 - 2217. Powell, S. G., Pyke, D. F. (1996), “Allocation of Buffers to Serial Production Lines with Bottlenecks”, IIE Transactions, Vol. 28, pp. 18 - 29. Sabuncuoglu, I., Erel, E. and Gocgun, Y. (2006), AAnalysis of Serial Production Lines: Characterisation Study and a New Heuristic Procedure for Optimal Buffer Allocation”, International Journal of Production Research, Vol. 44, No. 13, pp. 2499 - 2523.
Slack, N. (1982), “Work Time Distributions in Production System Modelling”, Research Paper, Oxford Centre for Management Studies. Vouros, G. A.and Papadopoulos, H. T. (1998), “Buffer Allocation in Unreliable Production Lines Using a Knowledge Based System”, Computers and Operations Research, Vol. 25, No. 12, pp. 1055 - 1067.
390
Performance of Reliable and Unreliable Unpaced Production Lines with Uneven Buffer Allocation Sabry Shaaban*, Tom McNamara*, Sarah Hudson*
* ESC Rennes School of Business 2 Rue Robert d'arbrissel, Rennes France (E-mail: [email protected]). Abstract: We compare the efficiency of reliable and unreliable unpaced production lines that are unbalanced in terms of their buffer storage capacities to a corresponding line with equal sized buffers. The lines were simulated with different values of line length, buffer storage size, mean buffer capacity, and configuration of buffer imbalance. The results show that, for both reliable and unreliable lines the best buffer allocation patterns in terms of generating lower idle times as compared to a balanced line are those where total available buffer capacity is allocated as evenly as possible between workstations, whereas concentrating more buffer capacity towards the end of the line gives best average buffer level results. Keywords: Unpaced reliable and unreliable production lines, simulation; uneven buffer sizes, idle time, average buffer level.
1. INTRODUCTION Research into unpaced production line design is a growing area because of the complexity of the decisions to be made in several areas. One of the major factors affecting line performance, and one which has been more extensively studied in the literature is the buffer allocation problem. Lines unbalanced with respect to their buffer capacities are of great interest as technical considerations often restrict the amount of space available in the line, thereby making it difficult to allocate total buffer capacity evenly amongst individual buffers. The paper will first provide a review of the relevant literature followed by a presentation of the motivation and objectives of the study. Subsequent sections discuss the methodology and experimental design and provide the simulation results and analyses. The last two parts provide a summary of the results along with a discussion and some conclusions. 2. LITERATURE REVIEW There is a significant body of literature on the effects of buffer allocation on line performance. The literature deals with a variety of line types, for example balanced and unbalanced serial production lines, where workload allocation and variability are kept constant or vary along the line, respectively. In addition to considerations of balance, research investigating buffer placement in unreliable lines, assembly closed-loop or rework loop lines have also been carried out (Helber, 2001; Sabuncuoglu et al, 2006). Some of the earliest work on the influence of buffer allocation on WIP and throughput (El-Rayah, 1979) found that uneven buffering had a detrimental effect on output, but that conversely, WIP could be reduced in some cases if buffer space was distributed unevenly in some particular configurations. The 978-3-902661-98-2/12/$20.00 © 2012 IFAC
conclusion was that if unbalancing the buffers was unavoidable, more buffer space should be allocated to the central stations and less to the end stations. In the following decade this idea was developed, and some studies (Chow, 1987; Conway et al, 1988) showed that unbalanced buffering could be managed in order to maintain, or even improve the performance of the line in terms of output and WIP when compared to the balanced line. These ideas were interesting in that in general the belief was that a balanced line i.e. a line where all stations have equal operating times, equal variability and buffer is evenly allocated would provide the best performance. In particular, Conway et al (1988) proposed that buffer capacity should be placed as evenly as possible along the line, but any small additional amount of buffer should be allocated to the line’s centre. In the case of limited buffer space, preference should be given to the middle stations, and one notable result of this work was that the proper assignment of buffers along the line is as equally important as their number. Following on from this, there were a number of articles investigating buffer allocation and its effects on throughput (TR) with the aim of optimisation. Studies by Powell (1994), Hillier and So (1991) and Hillier, So & Boling (1993) found that for a limited total buffer capacity, a balanced allocation is best, whereas as more buffer space became available, the best results were obtained by concentrating more buffer capacity towards the centre of the line. This tendency became more marked when operator variability (coefficient of variation, CV) was higher. Hillier, So & Boling (1993) termed this the “storage bowl phenomenon”. Further work (Hillier and So (1995); Powell and Pyke (1996); Hillier (2000); Hillier and Hillier, (2006)) has also tended to support this idea. Other authors extended this work to looking at other indicators of performance such
384
10.3182/20120523-3-RO-2023.00285
INCOM 2012, May 23-25, 2012 Bucharest, Romania
as WIP levels. Papadopoulos and Vidalis (2001) developed a heuristic buffer allocation algorithm to find the minimum amount of average WIP for a predetermined throughput. They concluded that a trade-off has to be made. If the interest was to maximize TR, then an inverted bowl (or a close approximation) is generally the preferred arrangement. On the other hand, if the objective was a reduction in average WIP level, then it is better to allocate more buffers towards the end of the line. This idea that the optimal buffer allocation pattern differs for different performance indicators has found support in the work of Grosfeld-Nir and Magazine (2005), but in their case it was observed that for lines where the buffer was allocated evenly, throughput was maximised, whereas unbalancing the buffer allocation gave better results in terms of WIP, ascending buffer patterns being superior to descending patterns. Several studies have investigated unreliable lines with a single source of imbalance in the form of uneven buffer allocation. Vouros and Papadopoulos (1998) investigated the buffer allocation problem in terms of TR and presented a method that uses an established list of generic procedures, including simulation. They looked at lines of 3, 4 and 5 stations with balanced mean operating times and various machine reliability rates across the stations. The probability distributions utilized were exponential and Erlang for mean processing times (MT), exponential for the mean time between failures (MTBF) and exponential or Erlang-m for repair rates. They observed that their solution procedure is fairly accurate for small line lengths, but for longer lines the accuracy declines. However, the focus in general is not on the effects of imbalance, but rather an interest in generating algorithms for operating characteristics and determining performance outcomes (see recebt work for example by Papadopoulos and Vidalis (1999); Gershwin and Schor (2000); Helber (2001); Kim and Lee (2001); Enginarlar et al (2001); Nahas et al (2006)). There are several differences between the work carried out previously and the investigation presented in this paper. We can see that for most of the studies the aim is not to compare reliable and unreliable lines, but is mostly concerned with optimization of some performance indicator, be it throughput or buffer capacity. The approach used is often mathematical analysis or algorithm generation and testing in order to reach this optimal solution. In addition, the performance indicator used is for the most part throughput, and the question of WIP or idle time has not been very much looked at in these types of line. Finally, there are no studies to our knowledge that use simulation to observe the effects of various patterns of buffer allocation (and not simply total buffer capacity) on idle time and average buffer levels in unpaced lines. 3. STUDY OBJECTIVES We investigate reliable and unreliable, unpaced, serial production lines where buffer space is allocated unequally (unbalanced) between workstations. The results are then compared with those from the equivalent simulated balanced line where total buffer capacity is distributed evenly between workstations. Mean operation times (MT) and the coefficient of variation (CV) are kept constant, with MT= 10 time units per station and CV = 0.274 in all experiments. The main goals of the study are to: 1) Compare the efficiency of the
reliable and unreliable unbalanced lines and to those of a corresponding balanced line to find out if improvement in performance is attainable. 2) Assess the merits of various patterns of unequal buffer sizes and identify the ones with the most potential in terms of performance. 3) Evaluate the effects of line design factors, namely line length and mean buffer capacity on the measures of performance; idle time and average buffer level. 4. METHODOLOGY AND EXPERIMENTAL DESIGN There is no mathematical procedure presently capable of handling the unbalanced steady-state characteristics of such lines, so computer simulation was utilized as the most suitable technique for this type of experiment. 4.1 Factorial Design Complete factorial design was chosen for the current investigation. In the context of the particular lines being simulated, the independent variables are: Total number of stations in the line, N; Total amount of buffer capacity for the line, TB, also expressed as Mean capacity of each buffer, MB (= TB divided by the number of buffers).; Pattern of buffer capacity imbalance, Pi. The dependent performance measures were:1. Average Buffer Level, ABL for the whole line. Idle time (percentage of total working time that the line is idle), IT. Line Performance Length Indicators N
Total Buffer Capacity (TB)
Buffer Allocation Policy (Pi)
ABL
5 stations 8&24 units
4 policies
IT
8 stations 14& 42 units
(see section 4.6)
* All these compared to the balanced line with buffer evenly allocated along the line. Table 1. Summary of reliable and unreliable lines simulated 4.2 Simulation Run Parameters The work time probability distribution used in the simulations followed a Weibull distribution with a CV value averaging around 0.274 following Slack (1982). A sufficiently long warm up period was used in accordance with the technique proposed by Law and Kelton (2000), observing WIP as they suggest. A trial procedure established that after an initial run of 20,000 minutes, acceptable autocorrelation values of between -0.163 and +0.153 were achieved within the -0.20 and +0.20 range suggested by Harrell et al (2004). All data collected during the first 30,000 minutes initial period were discarded and measurements from a production run of 20,000 minutes, broken down into 50 blocks (subruns) of 400 minutes each were gathered. Therefore mean IT and ABL values were collected every 400 minutes and the average of these 50 means (the grand mean) was computed Finally, in order to generate an identical event sequence for all the designs and highlight the contrast amongst the configurations, all the experiments used
385
INCOM 2012, May 23-25, 2012 Bucharest, Romania
the same random number seed. The data presented in tables 3-6 are the grand means.
o
P4: Bowl shape (V): position smaller amounts of buffer towards the centre – patterns D1 & D2.
o
P5: General: no concentration of TB at any area of the line – patterns E1 & E2.
4.4 Failure and Repair Parameters – Unreliable Lines
For this investigation the failure rate was set at 0.01 breakdowns per minute, with the repair rate being 0.10 repairs per minute, so that the mean time between failures was 100 minutes and the mean time until repair was 10 minutes in accordance with the rates used in the literature (Altiok and Stidham (1983); Hopp and Simon (1993)). As a result, line efficiency was determined to be 91% (MTBF 100 / (MTBF 100 + MTTR 10)).
The line configurations for the experimental design are exhibited in Table 2 below, where policies 1 through 5 are represented respectively by patterns A1 – A2, B1 - B, C1 – C2, D1 – D2 and E1 – E2 for the 5 and 8-station lines. Line Length N = 5 8
24
Mean Buffer
2
6
4, 2, 1, 1 3,3,1,1 1, 1, 2, 4 1,1,1,5 1, 3, 3, 1 1,2,4,1 3, 1, 1, 3 4, 1, 1, 2 2,2,3,1 2,3,2,1 14
12, 6, 3, 3 9,9,3,3 3, 3, 6, 12 3,3,3,15 3, 9, 9, 3 3,6,12,3 9, 3, 3, 9 12, 3, 3, 6 6,6,9,3 6,9,6,3 42
P1 A1 \ A2 P2 B1 / B2 P3 C1 C2 P4 D1 D2 V P5 E1 E2 Total Buffer c
It was also assumed that both the failure and repair rates were independent, exponentially distributed random variables and as suggested by Law (2007), all downtimes were considered to be usage rather than clock based. 4.5 Simulation Model Assumptions The basic operating assumptions for the asynchronous flow line simulated are 1) The first station is never starved and the last station is never blocked. 2) No defective parts are produced. 3) Only one type of product flows in the system, with no changeovers. 4) Time to move the work units in and out of the storage buffers is considered to be small enough in comparative terms to be assumed t be negligible. 5) No breakdowns occur for the reliable lines and in the case of the unreliable lines, breakdown and repair rates are the same for each station.
Total Buffer
Buffer Allocation Policy Pi and Patterns(A – E)
An exponential probability distribution with regard to both the mean time between failure and mean time to repair is considered to be most representative of what is observed in actual manufacturing systems according to an empirical study of unreliable lines by Inman (1999).
o
P1: Descending order (\): concentrate the available buffer capacity nearer the beginning of the line – patterns A1 & A2.
In this study a total of 2 line lengths * 2 mean buffer capacities * 5 policies * 2 patterns each * 2 line reliability types = 80 configurations were simulated.
o
P2: Ascending order (/): concentrate the available buffer capacity nearer the end of the line – patterns B1 & B2.
5. RESULTS
4.6 Specific Design Features Line length: N values of 5 and 8 were specified in this study, and a total buffer capacity: TB values of 8 and 24 (for N = 5), and 14 and 42 (for N = 8) were selected, giving rise to mean buffer capacities MB = 2, 4 and 6 for both N = 5 and 8. Buffer allocation policies
o
P3: Inverted bowl shape (): concentrate the available buffer capacity nearer the middle of the line – patterns C1 & C2. .
Buffer Allocation Policy Pi and Patterns(A – E)
Five policies (Pi) were investigated for the total allocation of buffer size:
Mean Buffer N = 82 6 Line Length P1 A1 6, 2, 2, 1, 1, 18, 6, 6, 3, 3, \ A2 4,4,2,1,1,1,1 12,12,6,3,3,3,3 1, 1, 1, 1, 6, 3, 3, 3, 3, 18, P2 B1 / 1,1,1,1,1,1,8 3,3,3,3,3,3,24 B2 P3 C1 1, 1, 4, 4, 2, 3, 3, 12, 12, 6, C2 1,1,6,2,2,1,1 3,3,18,6,6,3,3 P4 D1 4, 2, 1, 1, 3, 12, 6, 3, 3, 9, D2 4, 2, 1, 1, 1, 12, 6, 3, 3, 3, V 2,2,2,3,3,1,1 6,6,6,9,9,3,3 P5 E1 2,2,3,3,2,1,1 6,6,9,9,6,3,3 E2 Table 2. Unequal buffer size allocation policies (Pi) and patterns Ai - Ei for reliable and unreliable lines.
The results of the simulations are presented below. Section 5.1 presents the findings in terms of idle time (IT) performance and section 5.2 looks at the results found for average buffer levels (ABL). Due to space limitations, only IT and ABL results for the best, some good, and the worst patterns will be shown. Full data are available from the authors.
386
INCOM 2012, May 23-25, 2012 Bucharest, Romania
5.1 Idle Time (IT) Data
•
The total idle time calculated for the reliable and unreliable line patterns chosen are exhibited in Tables 3 and 4 below. The results for the balanced line are shown in the bottom line for purposes of comparison, and the cases that show decreased idle time when compared to the balanced line control are marked in bold.
In terms of whether better idle time results are obtained for a policy- (ascending, descending, inverted bowl or no strong concentration), we can see that none of the policies can be labelled as the best or the worst one for both of its constituent patterns.
•
Generally speaking, the data indicate that patterns E2 (N = 5) and E1 (N = 8) for the reliable line and pattern E2 for the unreliable line can be viewed as the best configurations, i.e. the best arrangement is one where the available capacity is distributed as uniformly as possible along the line.
•
The same patterns with different line lengths; E1 (N = 5), E2 (N = 8) in the case of reliable lines and E2 for unreliable lines can also be deemed as good configurations.
•
Pattern B2 (concentrate the available buffer capacity nearer the end of the line) can be regarded as the worst pattern, which shows the highest idle times across the board both with respect to the other patterns and compared to the balanced line.
•
The influence of line length is negative, as one would expect, with IT tending to increase with the number of workstations. The degree of increase becomes more substantial for lower mean buffer values in the case of the best pattern.
•
The effect of mean buffer: IT decreases as MB goes up.
•
As expected, the IT data for unreliable lines are clearly much higher than their reliable line counterpart, which reflects the system inefficiency resulting from somewhat prolonged breakdown and repair delays.
Line Length N
5
8
Mean Buffer 2
6
2
6
7.661 7.380 7.978 9.104 6.007 6.240 7.721 6.175 5.707 5.598
2.906 2.682 3.094 3.499 2.342 2.463 3.099 3.030 2.082 1.733
9.976 10.110 9.315 10.982 7.846 7.542 7.663 7.501 7.112 7.497
3.511 3.918 3.571 4.123 3.260 2.949 2.230 2.352 2.212 3.492
4.985
2.066
5.935
2.174
P1 \ P2 / P3 P4 V P5
Balanced Results
A1 A2 B1 B2 C1 C2 D1 D2 E1 E2 Line
Table 3. IT data for reliable 5- and 8-station lines, policies 1 - 5, patterns Ai - Ei and a balanced line Line Length N
5
8
Mean Buffer 2
6
2
6
20.259 20.627 22.728 23.831 20.584 20.632 20.254 21.146 20.009 19.954
15.680 16.374 13.988 16.105 14.714 14.547 16.785 14.678 13.736 13.375
25.575 26.260 23.663 26.866 22.916 22.751 22.855 26.258 22.941 21.909
18.205 17.096 16.473 18.062 16.610 14.658 17.771 15.734 15.242 15.703
19.352 13.432 21.530
13.581
Buffer Allocation Policy Pi and Patterns(Ai – Ei)
Capacity MB P1 \ P2 / P3 P4 V P5
Balanced Results
A1 A2 B1 B2 C1 C2 D1 D2 E1 E2 Line
5.2 Average Buffer Level (ABL) Data Tables 5 and 6 summarise the ABL results. The results for the balanced line are shown in the bottom line for purposes of comparison, and the patterns which outperform those of the balanced line are marked in bold.
Table 4. IT data for unreliable 5- and 8-station lines, policies 1 - 5, patterns Ai - Ei and a balanced line 5.1.1 Ranking Patterns and Effects of N & TB on IT The following conclusions can be drawn from the results shown above for the reliable and unreliable lines:
Line Length N 5 8 Mean Buffer 2 6 2 6 P1 A1 1.507 2.506 1.136 1.965 2.480 A2 1.468 4.417 1.577 P2 B1 0.534 1.679 0.513 1.417 B2 0.531 1.457 0.531 1.444 2.689 P3 C1 1.090 3.341 1.076 2.664 C2 0.798 2.170 0.962 3.258 P4 D1 1.025 2.741 1.144 3.140 D2 1.284 4.135 1.198 3.458 P5 E1 1.235 2.758 1.314 4.248 E2 1.218 2.792 1.411 2.601 Balanced Line 1.033 3.321 0.970 Table 5. ABL data for reliable 5- and 8-station lines, policies 1-5, patterns Ai-Ei and a balanced line
387
Buffer Allocation Policy Pi and Patterns(Ai – Ei)
Buffer Allocation Policy Pi and Patterns(Ai – Ei)
Capacity MB
INCOM 2012, May 23-25, 2012 Bucharest, Romania
Buffer Allocation Policy Pi and Patterns(Ai – Ei)
Line Length N 5 8 Mean Buffer 2 6 2 6 4.486 P1 A1 1.382 4.388 1.420 4.316 A2 1.297 4.185 1.455 P2 B1 0.598 1.810 0.683 1.485 B2 0.560 1.678 0.568 1.755 4.155 P3 C1 1.046 2.308 1.052 3.270 C2 0.999 2.058 1.230 3.457 P4 D1 1.027 3.002 1.165 3.330 D2 1.242 3.363 1.101 V 3.792 P5 E1 1.049 3.529 1.194 3.815 E2 1.098 3.692 1.167 3.201 Balanced Line 0.976 3.265 1.001 Table 6 ABL data for unreliable 5- and 8-station lines, policies 1 - 5, patterns Ai - Ei and a balanced line 5.2.1 Ranking of Patterns and Effects of Design Variables on ABL An examination of the results shown in Tables 9 and 10 yields the following noteworthy conclusions for reliable and unreliable lines: •
Policy P2, (patterns B1 and B2), where buffers are allocated in an ascending order, with capacity concentrated towards the end of the line consistently outperforms both the balanced line and all other configurations simulated in terms of average buffer levels.
•
Pattern C2 (the inverted bowl shape configuration) can also be regarded as a good pattern, with results showing improved ABL performance for most of its patterns.
•
For unreliable lines, the worst results in terms of average buffer levels are seen for the descending order policy P1, with available buffer space concentrated towards the beginning of the line. However, there was no discernible worst configuration for reliable lines.
•
The influence of line length seems not to be important; there is no directly observable consistent pattern of change of ABL levels with N.
•
On the other hand, there is an influence due to mean buffer capacity which is that average buffer levels increase with the availability of space, i.e. higher MB.
•
The unreliability of the line has no effect on ABL
5.3 Best Pattern Savings We can compare the results yielded in terms of percentage change from the balanced line. 5.3.1 Best Pattern Savings in IT Table 7 summarises the % difference in IT for the best reliable and unreliable unbalanced line patterns in comparison with those of the balanced line. The results where IT is lower than for the control are in bold.
N=5 N= 8 MB Reliable Unreliable Reliable Unreliable 12.30 3.11 1.76 2 -16.14 19.83 1.75 15.62 6 -0.42 Table 7. % change in the best patterns’ IT compared to the control for reliable and unreliable lines MB= 2 &,6. It can be noted from the table that MB and N have no impact on the change in IT compared to the balanced line. 5.3.2 Best Pattern Savings in ABL Table 8 summarises the % saving in ABL for the best reliable and unreliable unbalanced patterns in comparison with those of the balanced line: N=5 N= 8 MB Reliable Unreliable Reliable Unreliable Pattern B1 48.31 -38.73 -47.11 -31.77 2 -49.44 -44.56 -45.52 -53.61% 6 Pattern B2 -48.60 -42.62 -45.26 -43.26 2 -56.13 -48.61 -44.48 -45.17 6 Table 8.Percentage % change in ABL for the two best patterns compared to the balanced line. We can see from table8 that for both reliable and unreliable lines: Patterns B1 and B2 show consistent improvement over the control for all values of line length and mean buffer capacity considered. Buffer space availability (MB) has no a generally consistent impact on the degree of improvement in ABL performance. On the other hand, for reliable lines, we can see that as N increases, the % saving in ABL declines, but for unreliable lines ABL does not appear to be influenced by the number of stations. Furthermore, unbalancing buffers can yield savings in terms of idle time for specific configurations (16.4% for the best reliable line configuration and 0.42 for the best unreliable line pattern), but the imbalance is having a much stronger impact on the savings in ABL (56.13% for the best reliable line configuration and 53.61%. for the unreliable line). 6. SUMMARY 6.1 Effects of Buffer Allocation Policy and Patterns From the results presented above, we can say that for both reliable and unreliable lines policy five (P5) with buffer space allocated fairly evenly performed better in terms of idle time than any of the others, when compared to the balanced line. On the other hand, for both reliable and unreliable lines the best patterns with respect to decreasing average buffer level was found to be an ascending BC order (policy P2), where more buffer capacity is positioned towards the end of the line. It was also found that the less extreme the buffer capacity allocation, i.e. the more evenly spread it is, the better are the results as far as idle time is concerned. This is generally in line with the finding of Conway et al (1988) and Hillier and So (1991) Support was also found for the results obtained by El-Rayah (1979) and Papadopoulos and Vidalis (2001) in that for ABL, the most advantageous configuration is to
388
INCOM 2012, May 23-25, 2012 Bucharest, Romania
concentrate the available buffer capacity towards the end of the line. 6.2 Effects of Line Design Factors: Length and Buffer Capacity If we consider line length, the reliable and unreliable line results show that as N increases, so does idle time, whereas no overall effect of line length on average buffer levels is observed. When mean buffer capacity is increased, however, enhanced performance in terms of idle time is observed. On the other hand, the effects of increased buffer capacity on performance in terms of average buffer level are negative, i.e. ABL rises with increased MB. It should be noted that for the best patterns, where buffer capacity is concentrated at the end of the line, the performance in terms of ABL consistently outperforms the control, where buffers are allocated evenly between workstations. An unreliable line generates much higher IT values than a reliable line counterpart. This obviously is a clear indication of line inefficiency which results from waiting time delays, caused by breakdowns and repairs. No tangible effect of breakdown on ABL, however, is seen. This is somewhat surprising, as we would expect buffers to be filling up more for lines which are subject to breakdown. We could speculate that the impact of the imbalanced buffer allocation may be overcoming the negative effects of the downtime, a result that may be worth following up in future work. 6.3 Line Performance Results Unbalanced buffer allocation under the various conditions simulated, had varying effects on performance. In terms of idle time, the vast majority of the unbalanced patterns performed less well than the balanced line, whereas buffer imbalance gave improved average buffer level performance for many of the lines simulated. For each performance indicator, however, there were certain configurations that gave enhanced performance over the balanced control, and the highest % savings in IT and ABL over the corresponding balanced line are IT: 16.14% (reasonable) and ABL: 56.13% (considerable) for reliable lines and IT: 0,42% (v.small) and ABL 53.61% (considerable) for unreliable lines. From the above, there seems to be a great deal of similarity in the behaviour of reliable and unreliable BC unbalanced lines that needs to be explored in more depth in the future. 7. DISCUSSION AND CONCLUSIONS One of the principal conclusions of this study is that the One of the principal conclusions of this study is that the decision of how to allocate different sized buffers between workstations will depend on the particular objectives of the production facility. There is a choice to be made as to whether low inventory is the aim or whether IT needs to be reduced. In this context, although our results show that buffer imbalance in unreliable lines generally causes a decline in performance; we also see that superior performance to that achieved by a balanced line counterpart in terms of idle time or average buffer level is attainable for particular reliable and unreliable line designs. Even though the improvements in idle times are not large in size (16.14%
for reliable and 0.42% for unreliable lines), they can result in substantial savings over the expected lifespan of a production line. On the other hand the superiority in ABL is considerable (around 56% in the case of reliable and 54% for unreliable lines), which indicates that it may be worthwhile to purposely allocate buffers unevenly, with more capacity assigned to the end of the line. Possible future research could for example investigate the effects of the buffer capacity imbalance for reliable and unreliable merging (assembly) lines and also for unreliable lines with two sources of imbalance, which would enable managers to make more accurate decisions in line design in the future. REFERENCES Altiok Altiok, T. and Stidham, S. (1983), “The Allocation of Inter-Stage Buffer Capacities in Production Lines”, IIE Transactions, Vol. 15, No. 4, pp. 292 - 299. Chow, W. M. (1987), “Buffer Capacity Analysis for Sequential Production Lines with Variable Process Times”, International Journal of Production Research, Vol. 25 pp. 1183 - 1196. Conway, R., Maxwell, W., McClain, J. and Thomas, L. J. (1988), “The Role of Work in Progress Inventory in Serial Production Lines”, Operations Research, Vol. 36, pp. 229 - 241. El-Rayah, T. (1979), “The Effect of Inequality of Inter-Stage Buffer Capacities and Operation Time Variability on the Efficiency of Production Line Systems” International Journal of Production Research, Vol. 17, pp. 77 - 89. Enginarlar, E., Li, J. and Meerkov, S. M. (2001), “A Potpourri on the Theme of Lean Buffering”, Proceedings of 3rd Aegean International Conference on Design and Analysis of Manufacturing Systems, Tinos Island, Greece, pp. 249 - 258,. Enginarlar, E., Li, J. and Meerkov, S. M. (2005), “Lean Buffering in Serial Production Lines With NonExponential Machines”, OR Spectrum, Vol. 27, pp. 195 219. Enginarlar, E., Li, J., Meerkov, S. M. and Zhang R. Q. (2002), “Buffer Capacity for Accommodating Machine Downtime in Serial Production Lines”, International Journal of Production Research, Vol. 40, No. 3, pp. 601 - 624. Gershwin,S.B. & Schor, J.E. (2000) ‘Efficient algorithms for buffer space allocation’, Annals of Operations Research, Vol.93, pp.117-144. Grosfeld-Nir, A. and Magazine, M. (2005), “A Simulation Study of Pull Systems with Ascending/Descending Buffers and Stochastic Processing Times”, International Journal of Production Research, Vol. 43, pp. 3529 – 3541. Helber, S. (2001), “Cash-Flow-Orientated Buffer Allocation in Stochastic Flow Lines”, International Journal of Production Management, Vol. 39, No. 14, pp. 3061 3083. Hillier, M.S (2000), “Characterizing the Optimal Allocation of Storage Space in Production Line Systems. IIE Transactions, Vol. 32, pp. 1 - 8. Harrell, C., Ghosh, B., K., & Bowden, R., O. (2004) Simulation using ProModel, New York, McGraw- Hill.
389
INCOM 2012, May 23-25, 2012 Bucharest, Romania
Helber,S. (2001) “Cash-Flow-Orientated Buffer Allocation in Stochastic Flow Lines” International Journal of Production Management, Vol. 39, No. 14, pp. 3061 3083. Hillier, M. S. and Hillier, F. S. (1991), “Simultaneous Optimization of Work and Buffer Space in Hillier, F. S., So, K.C., The Effect of the Coefficient of Variation of Operation Times on the Allocation of Storage Space in Production Line Systems”, IIE Transactions, Vol. 23, pp. 198 - 206. Hillier, F. S., So, K. C. (1995), “On the Optimal Design of Tandem Queuing Systems with Finite Buffers”, Queuing Systems, Vol. 21, pp. 245 – 266. Hillier, F. S. and So, K. C. (1991), “The Effect of Machine Breakdowns and Interstage Storage on the Performance of Production Line Systems”, International Journal of Production Research, Vol. 29, No. 10, pp. 2043 - 2055. Hillier, F. S., So, K. C., Boling, R. W. (1993), “Notes: Toward Characterizing the Optimal Allocation of Storage Space in Production Line Systems with Variable Processing Times”, Management Science, Vol. 39, pp. 126 - 133. Hopp, W. J. and Simon, J. T. (1993), “Estimating Throughput in an Unbalanced Assembly Like Flow System”, International Journal of Production Research, Vol. 31, No. 4, pp. 851 -868. Inman, R. R. (1999), “Empirical Evaluation of Exponential and Independence Assumptions in Queuing Models of Manufacturing Systems”, Production and Operations Management, Vol. 8, No. 4, pp. 409 - 432. Kim, S. and Lee, H. J. (2001), “Allocation of Buffer Capacity to Minimize Average Work-in-Process”, Production Planning & Control, Vol. 12, No. 7, pp. 706 - 716. Law, A., M. (2007), “Simulation Modeling and Analysis”, Irwin / McGraw Hill. Law, A., M. and Kelton, W. D. (2000), “Simulation Modeling and Analysis”, Irwin / McGraw Hill. Nahas, N., Ait-Kadi, D. and Nourelfath, M. (2006), “A New Approach for Buffer Allocation in Unreliable Production Lines”, International Journal of Production Economics, Vol. 103, pp. 873 - 881. Papadopoulos, H. T., Vidalis, M. I. (2001), “Minimizing WIP Inventory in Reliable Production Lines”, International Journal of Production Economics, Vol. 26, pp. 185 197. Papadopoulos, H. T. and Vidalis, M. I. (1999), “Optimal Buffer Allocation in Short -Balanced Unreliable Production Lines”, Computer and Industrial Engineering, Vol. 37, pp. 691 - 710. Powell, S. G. (1994), “Buffer Allocation in Unbalanced Three - Station Serial Lines”, International Journal of Production Research, Vol. 32, pp. 2201 - 2217. Powell, S. G., Pyke, D. F. (1996), “Allocation of Buffers to Serial Production Lines with Bottlenecks”, IIE Transactions, Vol. 28, pp. 18 - 29. Sabuncuoglu, I., Erel, E. and Gocgun, Y. (2006), AAnalysis of Serial Production Lines: Characterisation Study and a New Heuristic Procedure for Optimal Buffer Allocation”, International Journal of Production Research, Vol. 44, No. 13, pp. 2499 - 2523.
Slack, N. (1982), “Work Time Distributions in Production System Modelling”, Research Paper, Oxford Centre for Management Studies. Vouros, G. A.and Papadopoulos, H. T. (1998), “Buffer Allocation in Unreliable Production Lines Using a Knowledge Based System”, Computers and Operations Research, Vol. 25, No. 12, pp. 1055 - 1067.
390