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Inventory and capacity trade-offs in a manufacturing cell
Int. J. Production Economics 59 (1999) 203—212
Inventory and capacity trade-offs in a manufacturing cell Simon F. Hurley , D. Clay Whybark * Process Improvement Manager, Sensis Corporation, Syracuse, NY, USA Kenan-Flagler School, University of North Carolina, Chapel Hill, NC 27599-3490, USA
Abstract This paper describes an investigation into the trade-off between capacity, inventory and variance reduction techniques for buffering against uncertainty and model mix fluctuations in a manufacturing cell. The cell is patterned after one that produces engine blocks which feed directly on to the assembly line at a plant manufacturing large diesel engines. A simulation model is used to evaluate the effect of different buffering techniques on capacity utilization, throughput time and output rate. Two production control systems are used in the cell, one based on a pull approach, the other on a push approach. The results show that variance reduction and capacity increases are serious alternatives to using inventory for buffering in either system. 1999 Elsevier Science B.V. All rights reserved. Keywords: Manufacturing cells; JIT; TOC; Buffering
1. Introduction The nature of manufacturing is changing. This is not only due to competitive forces that require firms to adapt new strategies in but is also due to technologies which enable managers to organize and run processes differently. New ways of thinking about manufacturing have led to developments ranging from manufacturing cells to new approaches to material control. Unfortunately, the new developments have not eliminated the uncertainty that exists in many manufacturing processes nor the variations induced by changes in product mix. Thus, even new processes may need mechanisms for buffering against process uncertainties. * Corresponding author. Tel.: #1 919 962 3206; fax: #1 919 962 4266; e-mail: clay—[email protected]. This work was supported by Massey University, Palmerston North, New Zealand.
Although alternatives have been suggested, the primary means for buffering against uncertainty is still inventory, even in firms that utilize some of the new manufacturing techniques. In this paper, the use of inventory is compared with increasing capacity and reducing variance as means of buffering in a manufacturing cell. A simulation of the cell is used to study the different techniques’ effect on output rate, capacity utilization and throughput time. The remaining sections of the paper describe the simulation model, buffering approaches, experimental design and the simulation results. The paper concludes with a discussion of the findings.
2. The simulation The simulation model for this research is based on a manufacturing cell in a diesel engine plant in
0925-5273/99/$ - see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 5 2 7 3 ( 9 8 ) 0 0 1 0 1 - 7
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Europe. The plant produces engines in several power ranges and assembles a variety of different models within each. The company buys rough engine block castings, machines the blocks, assembles and paints the engines, and packages them for shipping. Over the last few years the company has undertaken a number of steps to reduce lead time, improve quality and increase efficiency all of which have led to improved sales. With the reduced lead times, the engines can be produced to customer order. The company uses a combination of material requirements planning (MRP) and just-in-time (JIT) to schedule production in the factory. The overall demand is fairly constant at approximately 15 engines per two shift day and the average mix of product types is quite stable. The firm is now reaching the limit of its output capacity and the manufacturing cell studied in this research is the limiting resource in the production of diesel engines. Increasing the capacity of the bottleneck station in the cell is not a feasible alternative at this time, so the company is interested in improving output rates by other means.
2.1. Simulation model The part of the process simulated for this study is the machining of diesel engine blocks. It is done in a manufacturing cell that feeds directly onto the assembly line. Three engine blocks are used in the simulation to represent the different product types that are produced in the cell. The three blocks will represent the high, mid and low power ranges. The demand for these three product types averages 60% for the mid power range and 20% each for the other two. The cell works with very little raw material inventory as delivery of the rough castings for the engines is very reliable. For purposes of the simulation, therefore, the supplier will be considered perfectly reliable. Similarly, rework in the cell is not significant and usually takes a small amount of time at the station where the need was first observed, so rework will be considered negligible for the simulation. The engine blocks are combined with other parts on the assembly to complete an
engine. They are delivered to the plant in final assembly schedule order which is determined from the customer order promise date. Setting the parts aside to take another engine onto the line is very disruptive. Consequently, in the simulation, the assembly line will process engine blocks in final assembly schedule order. If the block required to produce the product next scheduled for assembly is not available, the line is held up until it becomes available. The manufacturing cell consists of five work stations with each engine block going through each of the five stations in a flow process. (The adequacy of using five stations in such a simulation has been demonstrated by the work of Conway et al. [1].) The first station uses rough castings as raw material and performs some initial machining that is common to all blocks. The second station also performs some machining that is common to all the blocks. The next three stations have different machining steps depending on which of the three product types is being produced. In the plant there is provision for raw material inventory, inventory between each of the stations and between the last station and the assembly line. (Fig. 1 is a schematic of the engine block manufacturing cell.) The raw material inventory is resupplied on a daily basis with the same number of castings as were used on the assembly line the previous day.
Fig. 1. Diesel engine block manufacturing cell.
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S.F. Hurley, D.C. Whybark/Int. J. Production Economics 59 (1999) 203—212 Table 1 Average processing times for each product type (min) Product type
Station 1
Station 2
Station 3
Station 4
Station 5
Low power Mid power High power
60 60 60
60 60 60
31 55 79
36 60 84
31 55 79
The first two stations have no set-up time, as they produce a common part. Even though a substantial amount of effort has been invested in set-up time reduction, set-up times are still incurred in the other three stations whenever the next block to be processed is for a different product type than the block just finished. Set-up times are roughly constant and essentially independent of the processing order. For the simulation, the set-up time is 10 min each time a station is to work on a different product type. Average processing times are the same in the first and second stations, as are the processing times for each product type. In the last three stations, however, the average processing times differ for the three product types. Table 1 is a summary of the average processing times for each product. The demand for engine blocks comes from the assembly line. When assembly of an engine is to start, the appropriate engine block is taken from the finished block inventory or the line waits until it is available. The time until the next block is required is determined by the assembly time in the first station on the assembly line. The average assembly time for each engine type is different and the variation in assembly times is normally distributed. (The mean and standard deviation of the assembly times for each product type are shown in Table 2.) The average output rate of the manufacturing cell is slightly less than the potential assembly rate. Thus the overall output rate of the plant is determined by the output rate of the block machining cell and station four of the cell is the process bottleneck. A complete description of the simulation, its validation, ex-post facto measures and analysis procedures can be found in Ref. [2].
Table 2 First assembly line station average times and standard deviation (min) Product
Average
Std. Dev.
Low power Mid power High power
50 60 70
10 12 14
2.2. Scheduling production Since there is the possibility that the alternative buffering techniques studied here might behave differently under different scheduling systems, two different scheduling approaches were used in the simulation. One of the approaches was based on the “pull” philosophy, while the other was based on the “push” approach. In the pull approach, production is initiated when a completed engine block is used on the assembly line. The pull terminology arises since production is geared to pulling a replacement product through the cell to the line. In contrast, the “push” system is geared to pushing product through the factory toward a schedule based on future customer orders. There are a variety of ways by which either of the approaches can be implemented, so the specific information that is used to make the production authorization decisions will be precisely defined for each. In addition, the other variables will be controlled so as not to ascribe any differences as due to the systems when they may, in fact, have other causes. To implement the pull approach to production scheduling in the simulation, a kanban mechanism is used [3]. Kanbans authorize the production of a specific product type at a station in the
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manufacturing cell. The material flow starts when a completed engine block is removed from the cell and transferred to the assembly line. At that time a kanban requesting a replacement block of the same type is issued to station five. When station five pulls a block from the inventory of blocks completed by station four to make the replacement, a kanban is sent to station four to replace the unit just removed. The kanban authorizations to replace engine blocks are passed on through the cell back to the first station where the authorization is to bring a rough block casting (raw material) into the process. Under the pull system, kanbans keyed to the actual use of completed blocks by the assembly line manage the flow of materials throughout the cell. When there is more than one kanban to work on, a first-come, first-served rule is used to set priorities. That is, when a station is available for work, if possible, it processes the kanban that has been at the station the longest. For example, if the oldest kanban at station five is for a low power product type and there is inventory of low power engine blocks to work on, production can commence. If, however, there are no low power blocks for station five to work on, production can only be done if there is another kanban authorizing another product type and if there is a unit of that product type available for station five to work on. If there is no kanban or if there is a kanban(s) but no matching product type block(s) waiting to be processed no work can be started. The same rules apply at all stations in the cell, with station one authorized to bring one unit of raw material into the cell whenever it has a kanban authorizing work. Thus, production is not authorized, even if there are blocks available at a station, unless a replacement unit is required at the next station. In the pull system, no use is made of the information available in the final assembly schedule. In contrast, the push system used here makes explicit use of this information and is an adaptation of the theory of constraints (TOC) described in Ref. [4]. The final assembly schedule is translated back to the bottleneck station (station four) which is the key point for controlling the production. As an example, suppose there are 14 units in production or in inventory between the bottleneck station and
the assembly line. These units are designated for the next 14 customers in the final assembly schedule. The schedule at the bottleneck station, therefore, would start with the specific block required for the 15th customer and would continue on from there. Station four authorizes the release of raw material into the cell at the first station, production at stations one, two and three, and produces blocks in final assembly schedule order. In the push system, production throughout the cell is keyed to the final assembly schedule. Whenever blocks are available in the cell, work proceeds from station to station, with all stations authorized to work as long as blocks are available to them. For stations one through four the processing order is taken from the schedule at the bottleneck and station five uses the final assembly schedule. Thus, as long as there is material available, each station “pushes” blocks through to the next station and, ultimately, to the finished block inventory ready to go on to the assembly line.
3. Buffering approaches Variability is introduced into the manufacturing cell from two broad sources. One source is the mix of products produced by the factory. The orders for the product types arrive randomly, averaging 60% for the mid power range and 20% for the other two. Even though the mix is stable, the differences in average processing time between the product types introduces variation,. The second source of variability is processing time uncertainty. This uncertainty is brought about by occasions when rework is necessary, delays in attending to problems and other sources of variability common in a manufacturing process. This research evaluates the tradeoffs between alternative methods of buffering the system against both sources of variability. Three alternatives for buffering against the uncertainty and product mix changes were evaluated. The first of these is work-in-process (WIP) inventory, the traditional way of buffering against uncertainty. The second is protective capacity, an idea from the theory of constraints that suggests that the bottleneck should be protected by having additional capacity at the non-bottleneck stations.
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Finally, an alternative that reduces the need for any type of buffering; variance reduction. As uncertainty is taken out of the system, the need for buffering of any type is decreased. The theories behind each of these three techniques are described next.
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the inventory. This, of course, provides one of the incentives for considering non-inventory means of buffering the manufacturing cell.
3.2. Protective capacity 3.1. Work in process inventory The traditional way of buffering production against variability is with work-in-process inventory. Most introductory textbooks will describe how to calculate the extra inventory (buffer stock) needed to provide specified levels of protection against the uncertainties in manufacturing processes. (See, for example, Ref. [5].) Similarly, they will show how to calculate the additional cycle stock required to permit the production of multiple products made on a single facility in order to account for product mix changes. Moreover, a considerable amount of research has gone into studying both the size and location of inventory buffers in manufacturing facilities. The positive relationship between overall levels of inventory and throughput time has been documented by many researchers, among them, Cook [6]. Similarly, the location [7] and size [8] of buffer stock has been researched. From these studies, it is clear that the trade-off between buffer inventory, throughput rate, throughput time and capacity utilization is complex and may vary with control system. It is also clear that when buffer inventory is used, for this simulation, it should be placed before the bottleneck (station four) and before assembly line. This study builds on these results and follows the principle of allocating buffer inventory mainly to the bottleneck and to the assembly line. The overall level of buffer inventory is treated as an experimental factor so considerable effort was devoted to assuring that the inventory levels were equal (or nearly so) for each of the other experimental treatments. The historical reliance on inventory to buffer manufacturing processes resulted in the accusation, by many JIT advocates, that inventory simply covers up fundamental problems. They argue that reducing the inventory exposes problems that, when addressed and solved, could lead to improvements in performance without restoring
Perhaps due to the historical focus on maximizing capacity utilization, the use of capacity as a buffer against variability has not been widely studied. Krajewski et al. [9] found that some Japanese managers provide additional capacity in their production systems. Atwater and Chakravorty [10] and So [11] pointed out that capacity is an effective alternative to inventory in buffering against variability. One clear principle that emerges from the research on protective capacity to date is that, when it is used, the buffer inventories at the nonbottleneck stations can be reduced. In this study, protective capacity will be an experimental factor. The concept of protective capacity is associated with the theory of constraints (TOC) but is not limited to situations in which TOC is used. Capacity is explicitly considered in TOC by focusing attention on the constraining station, the bottleneck in the production process. Of course, it would be best to simply expand capacity at the bottleneck station, if possible. Unfortunately, in the diesel engine factory, the constraint station (station four) had no short term expansion possibilities, since any new equipment would be both very expensive and very large. An alternative to purchasing another machine tool for the bottleneck station, however, is to provide additional capacity (protective capacity) at the other stations. This way material can be fed to the constraint quickly and be moved to the point of use quickly. In this study, protective capacity will be applied to the non-bottleneck stations.
3.3. Variance reduction A well-known result from queuing theory is that queues increase and average output decreases as the variance in a system increases. This suggests that an alternative to providing buffers is to reduce the variability with which the system has to cope. Indeed, variance reduction is a basic tenet of
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continual process improvement programs which identify causes of uncertainty and remove them. Not much research has gone into this alternative to date, but the work of Atwater and Chakravorty [10], indicates that removing uncertainty is a viable option to using inventory to buffer uncertainty. As one of the factors in this research, the variance reduction program will be focused on reducing the uncertainty in processing times at each of the stations in the manufacturing cell. For this study, the processing times will be normally distributed. By reducing the variation, process performance can be restored without resorting to inventory or capacity increases. In this sense, a variance reduction program is an alternative to a buffering technique. Process improvements that reduce variability require investments, as does inventory, but little is known about the relative improvements in performance between the two approaches. They might be quite different. This study will evaluate programs that reduce the uncertainty in processing times at each of the stations in the cell, but the variation introduced by the model mix will still exist.
4. Experimental design The experimental factors for the research are the amount of work-in-process (WIP) inventory, the amount of protective capacity, and the amount of variance reduction in the processing times. The evaluation of these factors is done under both the “push” and the “pull” control systems. Before conducting the experiment, however, the measure for each of the factors was specified and exactly how they would be changed to provide the factor settings for the experiment was established. Also the length of the simulation runs and number of replications was determined as well as the number of periods needed for the simulation to reach stability for purposes of taking measurements. The details of how each of these was done is discussed below.
4.1. Factor settings The work in process inventory is measured in physical units. It is counted from the time raw
material is authorized to enter the cell (hence, raw material is not counted) until the completed block is taken onto the assembly line. Three levels of WIP were used in the experiment. Since it was not possible to determine the exact levels of work-inprocess inventory before running the simulation, setting the levels required considerable experimentation. This experimentation started with the JIT production control system. Under JIT, the number of kanbans in the manufacturing cell is related to the average amount of work-process that will be held. Therefore, a number of runs were made with different numbers of kanbans to provide different levels of average WIP inventory. Choices were made for the “low”, “medium” and “high” levels of inventory that provided approximately a 10% increase in inventory between each level. These levels of inventory were then used as the target WIP inventory levels for the TOC production control system. Under the TOC system, work-in-process inventory is related to the size of the buffer at the bottleneck station (station four). This buffer is managed using the drum-buffer-rope technique from the theory of constraints [12]. Specifically, the schedule at the bottleneck station is used to authorize new material to enter the cell. The amount of work in process prior to station four is increased by authorizing production to start on blocks destined to become engines for customers with due dates further into the future. By specifying how far out into the future to look as the basis for the release of new material into the cell, the amount of work-inprocess inventory can be controlled. Since station four is the bottleneck, inventory tends to collect just before that station and when work is finished at station four it tends to move on through to the inventory in front of the assembly line. Experimentation with the TOC system enabled similar levels of average WIP inventory to be achieved as with the JIT system. Protective capacity is introduced by decreasing the average processing times at the non-bottleneck stations. This is equivalent to adding equipment and/or labor during the two shifts of operation as opposed to adding a third shift, for example. The processing times in Table 1 are the base values when no protective capacity is used. The middle
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level of protective capacity is achieved using a 10% reduction in the average processing times for stations one, two, three and five. The high level of protective capacity is represented by a 20% reduction in the average processing times at the same stations. Changing the capacity of the bottleneck station was not evaluated here, since this was not a viable alternative for the plant nor a bottleneck buffering alternative. Variance reduction is measured as the decrease in the coefficient of variation (CV) of the processing times at all work stations. Using the coefficient of variation as a factor in simulation research is quite common [10] but it can overstate uncertainty for some of the high processing times and understate uncertainty for some of the low processing times. Using the CV has the offsetting advantage, however, that when the uncertainty (standard deviation) in the processing times is decreased, it will change in proportion to the mean processing times. The variance reduction program is applied at all five stations in the cell. Levels of the coefficient of variation were chosen to restrict the range of uncertainty to reasonable values for all stations and products. In this experiment, the lowest variance reduction level (the highest amount of uncertainty) is represented by a coefficient of variation of 30%. The middle level treatment has a coefficient of variation of 20% and the highest level of uncertainty reduction has a CV of 10%. The final experimental design was full factorial with three settings of each factor for each of the control systems. Table 3 provides a summary of the factor settings for each of the factors. The WIP inventory values shown are the averages across all settings for each control system. Since it was not possible to match the WIP factor setting values exactly between control systems, the range is
shown. Ex-post facto analysis, however, indicated that this variation made no difference in the overall conclusions from the experiment. 4.2. Running the simulation For each experimental setting of the factors and control systems, the model was seeded with a starting work-in-process and was run for 300 simulated days to stabilize production. This is more than 200 days beyond the period when the cumulative mean utilization of all five stations changed by less than 1% per simulation day. Data were gathered for 40 days and five replications of each setting was run. Statistics were collected on capacity utilization at each station, output rate (the rate at which blocks are used on the assembly line) and throughput time (from the authorization to bring a rough casting into the cell to when the machined block is taken onto the assembly line). To reduce variance, common random numbers were used for each combination of factor settings. These procedures provide for a 95% chance that the estimates will be within 1% of the actual value for each setting of factors [13]. With five replications per factor setting, this results in a total of 54 experimental runs in addition to the runs required for establishing the inventory levels. Analysis of variance (ANOVA) was used to determine if there were statistically significant differences in output performance and cycle time among the buffering techniques for both of the control systems. 5. Results Table 4 presents a summary of the performance of the manufacturing cell for each of the factor
Table 3 Factor settings for the experiment Factor
Average WIP inventory — units Protective capacity — % change Variance reduction — CV
Level Low
Medium
High
6.39—6.47 0% 30%
7.08—7.09 10% 20%
7.69—7.98 20% 10%
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Table 4 Results for each factor setting, control system and performance criterion Technique
WIP Inventory Protective Capacity Variance Reduction
Criterion
Output rate (units) Cycle time (min.) Utilization (%) Output rate (units) Cycle time (min.) Utilization (%) Output rate (units) Cycle time (min.) Utilization (%)
Factor level — JIT
Factor level — TOC
Low
Medium
High
Low
Medium
High
13.51 741 0.80 13.24 828 0.85 12.97 803 0.77
13.68 784 0.82 13.69 782 0.81 13.70 785 0.82
13.69 828 0.82 13.95 744 0.77 14.20 765 0.85
14.45 589 0.85 14.38 664 0.92 14.24 644 0.84
14.45 629 0.85 14.47 624 0.86 14.54 620 0.86
14.48 660 0.85 14.53 590 0.79 14.60 613 0.86
settings and both control systems. In all cases the results confirm the basic theory. As inventory is added to the cell, output increases, cycle time increases and utilization increases (though nominally for the TOC control system). As protective capacity is added, output increases, cycle time decreases and utilization decreases (there is more capacity to be utilized). Finally, as uncertainty is removed, output increases, cycle time decreases and utilization increases. These results suggest that capacity buffering and variance reduction are effective alternatives to work-in-process inventory as buffering techniques. Moreover, the final assembly schedule information used by the theory of constraints control system provides performance benefits. The output is higher, cycle times lower and utilization higher than for the JIT system. Table 5 provides a summary of the ANOVA results for the output rates. For the JIT control system, all effects are highly significant. The firstorder interactions indicate, for example, that the variance reduction technique has a greater effect on output rate at low levels of protective capacity than at high levels of protective capacity. The results for the TOC control system indicate that the inventory effect on output rate, while positive, is not significant. Likewise, any interactions with inventory are not significant. (The results for the utilization criterion, while not reproduced here, are very similar to these for the output rate. The complete ANOVA tables can be found in Hurley and Whybark [2].) The largest contribution to changes in output rate (sum of squared errors) for both systems comes
Table 5 Summary of ANOVA results for output rate Source
Inventory — IN Capacity — PC Variance — VR IN*PC IN*VR PC*VR IN*PC*VR
JIT
TOC
SS error
p
SS error
p
1.9 22.7 69.3 1.04 1.12 3.64 0.55
0.00 0.00 0.00 0.00 0.00 0.00 0.01
0.05 1.10 6.51 0.08 0.11 0.54 0.09
0.46 0.00 0.00 0.69 0.52 0.00 0.95
Table 6 Summary of ANOVA results for cycle time Source
Inventory — IN Capacity — PC Variance — VR IN*PC IN*VR PC*VR IN*PC*VR
JIT
TOC
SS error
p
SS error
p
337657 316493 63880 10078 3347 24593 29290
0.00 0.00 0.00 0.00 0.00 0.00 0.00
227092 249888 47554 24243 15789 64060 38762
0.00 0.00 0.00 0.00 0.03 0.00 0.00
from the variance reduction technique followed by protective capacity. Again, this is evidence that they are effective alternatives to inventory. A summary of the ANOVA results for cycle time is provided in Table 6. Here the results are highly
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significant for all buffering techniques, interactions and control systems. The variance reduction technique, however, has less of an effect in reducing cycle time than either of the other two techniques. This can be seen from the sum of squared errors. In manufacturing firms for which cycle time reduction is an important activity, reducing inventory and/or increasing protective capacity seems to be more effective than variance reduction.
6. Discussion The results of this simulation study indicate that the use of variance reduction programs or protective capacity are effective techniques for buffering against uncertainties in manufacturing. Indeed, for this manufacturing cell they both look like preferred alternatives to the traditional use of work-inprocess inventory for increasing the output rate of the cell. This is illustrated in Figs. 2—4, which present graphs of the output rate for all three settings of each factor. For both control systems, the change in output rate is greatest using variance reduction, next with protective capacity and least with inventory. The relatively high rate of overall output for the TOC control system means that little change is evident for any of the techniques, though there is some. Another way of evaluating the effectiveness of the techniques is to compare the relative change in output rate as the levels of the buffering technique change. Figs. 5 and 6 are plots of the percentage
Fig. 3. Variance reduction and output rate.
Fig. 2. Average WIP inventory and output rate.
Fig. 5. Changes in output rate with the TOC control system.
Fig. 4. Protective capacity and output rate.
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tion and how much flexibility exists for making changes in the factors. Unfortunately, however, these techniques do not often occur to management when the issue of increasing output rate arises. Instead, the traditional solution of inventory is well known and easily accepted. If nothing else, this study should encourage managers to consider other alternatives before investing in inventory to increase output rate.
References
Fig. 6. Changes in output rate with the JIT control system.
change in output rate per percentage change in factor level for each of the control systems. Under both systems, the superiority of the variance reduction program is clearly seen. The figures also show that there is a much higher change in output rate per change in factor level under JIT than TOC. Of course these graphs do not tell the whole story. First, no data are available on the relative costs of the alternative buffering techniques so the improvement per unit cost is not available. It would only be by coincidence that the costs would be proportional to the factor settings chosen here. Moreover, the changes in factors and output cannot be linear. For example, the variance reduction technique can achieve no less than zero uncertainty and it is likely that the cost of reductions of uncertainty at the higher levels of uncertainty is much less per unit of standard deviation than at lower levels. On the other hand, the amount of inventory and protective capacity is unlimited, though the benefits of increasing levels of each are likely to be diminishing. The key conclusion from this research is that variance reduction programs and protective capacity should be considered as serious alternatives to work-in-process inventory for buffering a manufacturing cell. This work shows them to be effective for quite different production control systems. Of course, the managerial attraction of these techniques depends both upon the cost of implementa-
[1] R. Conway, W. Maxwell, J.O. McClain, L.J. Thomas, The role of work-in-process inventory in serial production lines, Operations Research 36 (2) (1988) 229—242. [2] S.F. Hurley, D.C. Whybark, A simulation study of tradeoffs in a manufacturing cell, Global Manufacturing Research Center Working Paper, Kenan—Flagler Business School, University of North Carolina, Chapel Hill, NC, 27599-3490, September, 1998. [3] Y. Monden, Adaptable Kanban system helps Toyota maintain just-in-time production, Industrial Engineering 13 (5) (1981) 29—46. [4] E.M. Goldratt, J. Cox, The Goal (rev. ed. Croton-onHudson), North River Press, New York, 1996. [5] T.E. Vollmann, W.L. Berry, D.C. Whybark, Manufacturing Planning and Control Systems, 4th ed., Irwin, Homewood, IL, 1997. [6] D.P. Cook, A simulation comparison of traditional, JIT and TOC manufacturing systems in a flow shop with bottlenecks, Production and Inventory Management Journal 35 (1) (1994) 53—59. [7] K.C. So, S.C. Pinault, Allocating buffer storage in a pull system, International Journal of Production Research 26 (12) (1988) 1959—1980. [8] T. Park, A two-phase heuristic algorithm for determining buffer sizes of production lines, International Journal of Production Research 31 (3) (1993) 613—631. [9] L.J. Krajewski, B.E. King, L.P. Ritzman, D.S. Wong, Kanban, MRP, and shaping the manufacturing environment, Management Science 33 (1) (1987) 39—57. [10] J.B. Atwater, S.S. Chakravorty, Does protective capacity assist managers in competing along time-based dimensions, Production and Inventory Management Journal 35 (3) (1994) 53—59. [11] K.C. So, On the efficiency of unbalancing production lines, International Journal of Production Research 27 (4) (1989) 717—729. [12] M.S. Spencer, J.F. Cox III, Master production scheduling development in a theory of constraints environment, Production and Inventory Management Journal 36 (1) (1995) 8—14. [13] A. Law, W.D. Kelton, Simulation Modeling and Analysis, 2nd ed., McGraw Hill, New York, 1991.
Inventory and capacity trade-offs in a manufacturing cell Simon F. Hurley , D. Clay Whybark * Process Improvement Manager, Sensis Corporation, Syracuse, NY, USA Kenan-Flagler School, University of North Carolina, Chapel Hill, NC 27599-3490, USA
Abstract This paper describes an investigation into the trade-off between capacity, inventory and variance reduction techniques for buffering against uncertainty and model mix fluctuations in a manufacturing cell. The cell is patterned after one that produces engine blocks which feed directly on to the assembly line at a plant manufacturing large diesel engines. A simulation model is used to evaluate the effect of different buffering techniques on capacity utilization, throughput time and output rate. Two production control systems are used in the cell, one based on a pull approach, the other on a push approach. The results show that variance reduction and capacity increases are serious alternatives to using inventory for buffering in either system. 1999 Elsevier Science B.V. All rights reserved. Keywords: Manufacturing cells; JIT; TOC; Buffering
1. Introduction The nature of manufacturing is changing. This is not only due to competitive forces that require firms to adapt new strategies in but is also due to technologies which enable managers to organize and run processes differently. New ways of thinking about manufacturing have led to developments ranging from manufacturing cells to new approaches to material control. Unfortunately, the new developments have not eliminated the uncertainty that exists in many manufacturing processes nor the variations induced by changes in product mix. Thus, even new processes may need mechanisms for buffering against process uncertainties. * Corresponding author. Tel.: #1 919 962 3206; fax: #1 919 962 4266; e-mail: clay—[email protected]. This work was supported by Massey University, Palmerston North, New Zealand.
Although alternatives have been suggested, the primary means for buffering against uncertainty is still inventory, even in firms that utilize some of the new manufacturing techniques. In this paper, the use of inventory is compared with increasing capacity and reducing variance as means of buffering in a manufacturing cell. A simulation of the cell is used to study the different techniques’ effect on output rate, capacity utilization and throughput time. The remaining sections of the paper describe the simulation model, buffering approaches, experimental design and the simulation results. The paper concludes with a discussion of the findings.
2. The simulation The simulation model for this research is based on a manufacturing cell in a diesel engine plant in
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Europe. The plant produces engines in several power ranges and assembles a variety of different models within each. The company buys rough engine block castings, machines the blocks, assembles and paints the engines, and packages them for shipping. Over the last few years the company has undertaken a number of steps to reduce lead time, improve quality and increase efficiency all of which have led to improved sales. With the reduced lead times, the engines can be produced to customer order. The company uses a combination of material requirements planning (MRP) and just-in-time (JIT) to schedule production in the factory. The overall demand is fairly constant at approximately 15 engines per two shift day and the average mix of product types is quite stable. The firm is now reaching the limit of its output capacity and the manufacturing cell studied in this research is the limiting resource in the production of diesel engines. Increasing the capacity of the bottleneck station in the cell is not a feasible alternative at this time, so the company is interested in improving output rates by other means.
2.1. Simulation model The part of the process simulated for this study is the machining of diesel engine blocks. It is done in a manufacturing cell that feeds directly onto the assembly line. Three engine blocks are used in the simulation to represent the different product types that are produced in the cell. The three blocks will represent the high, mid and low power ranges. The demand for these three product types averages 60% for the mid power range and 20% each for the other two. The cell works with very little raw material inventory as delivery of the rough castings for the engines is very reliable. For purposes of the simulation, therefore, the supplier will be considered perfectly reliable. Similarly, rework in the cell is not significant and usually takes a small amount of time at the station where the need was first observed, so rework will be considered negligible for the simulation. The engine blocks are combined with other parts on the assembly to complete an
engine. They are delivered to the plant in final assembly schedule order which is determined from the customer order promise date. Setting the parts aside to take another engine onto the line is very disruptive. Consequently, in the simulation, the assembly line will process engine blocks in final assembly schedule order. If the block required to produce the product next scheduled for assembly is not available, the line is held up until it becomes available. The manufacturing cell consists of five work stations with each engine block going through each of the five stations in a flow process. (The adequacy of using five stations in such a simulation has been demonstrated by the work of Conway et al. [1].) The first station uses rough castings as raw material and performs some initial machining that is common to all blocks. The second station also performs some machining that is common to all the blocks. The next three stations have different machining steps depending on which of the three product types is being produced. In the plant there is provision for raw material inventory, inventory between each of the stations and between the last station and the assembly line. (Fig. 1 is a schematic of the engine block manufacturing cell.) The raw material inventory is resupplied on a daily basis with the same number of castings as were used on the assembly line the previous day.
Fig. 1. Diesel engine block manufacturing cell.
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Station 1
Station 2
Station 3
Station 4
Station 5
Low power Mid power High power
60 60 60
60 60 60
31 55 79
36 60 84
31 55 79
The first two stations have no set-up time, as they produce a common part. Even though a substantial amount of effort has been invested in set-up time reduction, set-up times are still incurred in the other three stations whenever the next block to be processed is for a different product type than the block just finished. Set-up times are roughly constant and essentially independent of the processing order. For the simulation, the set-up time is 10 min each time a station is to work on a different product type. Average processing times are the same in the first and second stations, as are the processing times for each product type. In the last three stations, however, the average processing times differ for the three product types. Table 1 is a summary of the average processing times for each product. The demand for engine blocks comes from the assembly line. When assembly of an engine is to start, the appropriate engine block is taken from the finished block inventory or the line waits until it is available. The time until the next block is required is determined by the assembly time in the first station on the assembly line. The average assembly time for each engine type is different and the variation in assembly times is normally distributed. (The mean and standard deviation of the assembly times for each product type are shown in Table 2.) The average output rate of the manufacturing cell is slightly less than the potential assembly rate. Thus the overall output rate of the plant is determined by the output rate of the block machining cell and station four of the cell is the process bottleneck. A complete description of the simulation, its validation, ex-post facto measures and analysis procedures can be found in Ref. [2].
Table 2 First assembly line station average times and standard deviation (min) Product
Average
Std. Dev.
Low power Mid power High power
50 60 70
10 12 14
2.2. Scheduling production Since there is the possibility that the alternative buffering techniques studied here might behave differently under different scheduling systems, two different scheduling approaches were used in the simulation. One of the approaches was based on the “pull” philosophy, while the other was based on the “push” approach. In the pull approach, production is initiated when a completed engine block is used on the assembly line. The pull terminology arises since production is geared to pulling a replacement product through the cell to the line. In contrast, the “push” system is geared to pushing product through the factory toward a schedule based on future customer orders. There are a variety of ways by which either of the approaches can be implemented, so the specific information that is used to make the production authorization decisions will be precisely defined for each. In addition, the other variables will be controlled so as not to ascribe any differences as due to the systems when they may, in fact, have other causes. To implement the pull approach to production scheduling in the simulation, a kanban mechanism is used [3]. Kanbans authorize the production of a specific product type at a station in the
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manufacturing cell. The material flow starts when a completed engine block is removed from the cell and transferred to the assembly line. At that time a kanban requesting a replacement block of the same type is issued to station five. When station five pulls a block from the inventory of blocks completed by station four to make the replacement, a kanban is sent to station four to replace the unit just removed. The kanban authorizations to replace engine blocks are passed on through the cell back to the first station where the authorization is to bring a rough block casting (raw material) into the process. Under the pull system, kanbans keyed to the actual use of completed blocks by the assembly line manage the flow of materials throughout the cell. When there is more than one kanban to work on, a first-come, first-served rule is used to set priorities. That is, when a station is available for work, if possible, it processes the kanban that has been at the station the longest. For example, if the oldest kanban at station five is for a low power product type and there is inventory of low power engine blocks to work on, production can commence. If, however, there are no low power blocks for station five to work on, production can only be done if there is another kanban authorizing another product type and if there is a unit of that product type available for station five to work on. If there is no kanban or if there is a kanban(s) but no matching product type block(s) waiting to be processed no work can be started. The same rules apply at all stations in the cell, with station one authorized to bring one unit of raw material into the cell whenever it has a kanban authorizing work. Thus, production is not authorized, even if there are blocks available at a station, unless a replacement unit is required at the next station. In the pull system, no use is made of the information available in the final assembly schedule. In contrast, the push system used here makes explicit use of this information and is an adaptation of the theory of constraints (TOC) described in Ref. [4]. The final assembly schedule is translated back to the bottleneck station (station four) which is the key point for controlling the production. As an example, suppose there are 14 units in production or in inventory between the bottleneck station and
the assembly line. These units are designated for the next 14 customers in the final assembly schedule. The schedule at the bottleneck station, therefore, would start with the specific block required for the 15th customer and would continue on from there. Station four authorizes the release of raw material into the cell at the first station, production at stations one, two and three, and produces blocks in final assembly schedule order. In the push system, production throughout the cell is keyed to the final assembly schedule. Whenever blocks are available in the cell, work proceeds from station to station, with all stations authorized to work as long as blocks are available to them. For stations one through four the processing order is taken from the schedule at the bottleneck and station five uses the final assembly schedule. Thus, as long as there is material available, each station “pushes” blocks through to the next station and, ultimately, to the finished block inventory ready to go on to the assembly line.
3. Buffering approaches Variability is introduced into the manufacturing cell from two broad sources. One source is the mix of products produced by the factory. The orders for the product types arrive randomly, averaging 60% for the mid power range and 20% for the other two. Even though the mix is stable, the differences in average processing time between the product types introduces variation,. The second source of variability is processing time uncertainty. This uncertainty is brought about by occasions when rework is necessary, delays in attending to problems and other sources of variability common in a manufacturing process. This research evaluates the tradeoffs between alternative methods of buffering the system against both sources of variability. Three alternatives for buffering against the uncertainty and product mix changes were evaluated. The first of these is work-in-process (WIP) inventory, the traditional way of buffering against uncertainty. The second is protective capacity, an idea from the theory of constraints that suggests that the bottleneck should be protected by having additional capacity at the non-bottleneck stations.
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Finally, an alternative that reduces the need for any type of buffering; variance reduction. As uncertainty is taken out of the system, the need for buffering of any type is decreased. The theories behind each of these three techniques are described next.
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the inventory. This, of course, provides one of the incentives for considering non-inventory means of buffering the manufacturing cell.
3.2. Protective capacity 3.1. Work in process inventory The traditional way of buffering production against variability is with work-in-process inventory. Most introductory textbooks will describe how to calculate the extra inventory (buffer stock) needed to provide specified levels of protection against the uncertainties in manufacturing processes. (See, for example, Ref. [5].) Similarly, they will show how to calculate the additional cycle stock required to permit the production of multiple products made on a single facility in order to account for product mix changes. Moreover, a considerable amount of research has gone into studying both the size and location of inventory buffers in manufacturing facilities. The positive relationship between overall levels of inventory and throughput time has been documented by many researchers, among them, Cook [6]. Similarly, the location [7] and size [8] of buffer stock has been researched. From these studies, it is clear that the trade-off between buffer inventory, throughput rate, throughput time and capacity utilization is complex and may vary with control system. It is also clear that when buffer inventory is used, for this simulation, it should be placed before the bottleneck (station four) and before assembly line. This study builds on these results and follows the principle of allocating buffer inventory mainly to the bottleneck and to the assembly line. The overall level of buffer inventory is treated as an experimental factor so considerable effort was devoted to assuring that the inventory levels were equal (or nearly so) for each of the other experimental treatments. The historical reliance on inventory to buffer manufacturing processes resulted in the accusation, by many JIT advocates, that inventory simply covers up fundamental problems. They argue that reducing the inventory exposes problems that, when addressed and solved, could lead to improvements in performance without restoring
Perhaps due to the historical focus on maximizing capacity utilization, the use of capacity as a buffer against variability has not been widely studied. Krajewski et al. [9] found that some Japanese managers provide additional capacity in their production systems. Atwater and Chakravorty [10] and So [11] pointed out that capacity is an effective alternative to inventory in buffering against variability. One clear principle that emerges from the research on protective capacity to date is that, when it is used, the buffer inventories at the nonbottleneck stations can be reduced. In this study, protective capacity will be an experimental factor. The concept of protective capacity is associated with the theory of constraints (TOC) but is not limited to situations in which TOC is used. Capacity is explicitly considered in TOC by focusing attention on the constraining station, the bottleneck in the production process. Of course, it would be best to simply expand capacity at the bottleneck station, if possible. Unfortunately, in the diesel engine factory, the constraint station (station four) had no short term expansion possibilities, since any new equipment would be both very expensive and very large. An alternative to purchasing another machine tool for the bottleneck station, however, is to provide additional capacity (protective capacity) at the other stations. This way material can be fed to the constraint quickly and be moved to the point of use quickly. In this study, protective capacity will be applied to the non-bottleneck stations.
3.3. Variance reduction A well-known result from queuing theory is that queues increase and average output decreases as the variance in a system increases. This suggests that an alternative to providing buffers is to reduce the variability with which the system has to cope. Indeed, variance reduction is a basic tenet of
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continual process improvement programs which identify causes of uncertainty and remove them. Not much research has gone into this alternative to date, but the work of Atwater and Chakravorty [10], indicates that removing uncertainty is a viable option to using inventory to buffer uncertainty. As one of the factors in this research, the variance reduction program will be focused on reducing the uncertainty in processing times at each of the stations in the manufacturing cell. For this study, the processing times will be normally distributed. By reducing the variation, process performance can be restored without resorting to inventory or capacity increases. In this sense, a variance reduction program is an alternative to a buffering technique. Process improvements that reduce variability require investments, as does inventory, but little is known about the relative improvements in performance between the two approaches. They might be quite different. This study will evaluate programs that reduce the uncertainty in processing times at each of the stations in the cell, but the variation introduced by the model mix will still exist.
4. Experimental design The experimental factors for the research are the amount of work-in-process (WIP) inventory, the amount of protective capacity, and the amount of variance reduction in the processing times. The evaluation of these factors is done under both the “push” and the “pull” control systems. Before conducting the experiment, however, the measure for each of the factors was specified and exactly how they would be changed to provide the factor settings for the experiment was established. Also the length of the simulation runs and number of replications was determined as well as the number of periods needed for the simulation to reach stability for purposes of taking measurements. The details of how each of these was done is discussed below.
4.1. Factor settings The work in process inventory is measured in physical units. It is counted from the time raw
material is authorized to enter the cell (hence, raw material is not counted) until the completed block is taken onto the assembly line. Three levels of WIP were used in the experiment. Since it was not possible to determine the exact levels of work-inprocess inventory before running the simulation, setting the levels required considerable experimentation. This experimentation started with the JIT production control system. Under JIT, the number of kanbans in the manufacturing cell is related to the average amount of work-process that will be held. Therefore, a number of runs were made with different numbers of kanbans to provide different levels of average WIP inventory. Choices were made for the “low”, “medium” and “high” levels of inventory that provided approximately a 10% increase in inventory between each level. These levels of inventory were then used as the target WIP inventory levels for the TOC production control system. Under the TOC system, work-in-process inventory is related to the size of the buffer at the bottleneck station (station four). This buffer is managed using the drum-buffer-rope technique from the theory of constraints [12]. Specifically, the schedule at the bottleneck station is used to authorize new material to enter the cell. The amount of work in process prior to station four is increased by authorizing production to start on blocks destined to become engines for customers with due dates further into the future. By specifying how far out into the future to look as the basis for the release of new material into the cell, the amount of work-inprocess inventory can be controlled. Since station four is the bottleneck, inventory tends to collect just before that station and when work is finished at station four it tends to move on through to the inventory in front of the assembly line. Experimentation with the TOC system enabled similar levels of average WIP inventory to be achieved as with the JIT system. Protective capacity is introduced by decreasing the average processing times at the non-bottleneck stations. This is equivalent to adding equipment and/or labor during the two shifts of operation as opposed to adding a third shift, for example. The processing times in Table 1 are the base values when no protective capacity is used. The middle
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level of protective capacity is achieved using a 10% reduction in the average processing times for stations one, two, three and five. The high level of protective capacity is represented by a 20% reduction in the average processing times at the same stations. Changing the capacity of the bottleneck station was not evaluated here, since this was not a viable alternative for the plant nor a bottleneck buffering alternative. Variance reduction is measured as the decrease in the coefficient of variation (CV) of the processing times at all work stations. Using the coefficient of variation as a factor in simulation research is quite common [10] but it can overstate uncertainty for some of the high processing times and understate uncertainty for some of the low processing times. Using the CV has the offsetting advantage, however, that when the uncertainty (standard deviation) in the processing times is decreased, it will change in proportion to the mean processing times. The variance reduction program is applied at all five stations in the cell. Levels of the coefficient of variation were chosen to restrict the range of uncertainty to reasonable values for all stations and products. In this experiment, the lowest variance reduction level (the highest amount of uncertainty) is represented by a coefficient of variation of 30%. The middle level treatment has a coefficient of variation of 20% and the highest level of uncertainty reduction has a CV of 10%. The final experimental design was full factorial with three settings of each factor for each of the control systems. Table 3 provides a summary of the factor settings for each of the factors. The WIP inventory values shown are the averages across all settings for each control system. Since it was not possible to match the WIP factor setting values exactly between control systems, the range is
shown. Ex-post facto analysis, however, indicated that this variation made no difference in the overall conclusions from the experiment. 4.2. Running the simulation For each experimental setting of the factors and control systems, the model was seeded with a starting work-in-process and was run for 300 simulated days to stabilize production. This is more than 200 days beyond the period when the cumulative mean utilization of all five stations changed by less than 1% per simulation day. Data were gathered for 40 days and five replications of each setting was run. Statistics were collected on capacity utilization at each station, output rate (the rate at which blocks are used on the assembly line) and throughput time (from the authorization to bring a rough casting into the cell to when the machined block is taken onto the assembly line). To reduce variance, common random numbers were used for each combination of factor settings. These procedures provide for a 95% chance that the estimates will be within 1% of the actual value for each setting of factors [13]. With five replications per factor setting, this results in a total of 54 experimental runs in addition to the runs required for establishing the inventory levels. Analysis of variance (ANOVA) was used to determine if there were statistically significant differences in output performance and cycle time among the buffering techniques for both of the control systems. 5. Results Table 4 presents a summary of the performance of the manufacturing cell for each of the factor
Table 3 Factor settings for the experiment Factor
Average WIP inventory — units Protective capacity — % change Variance reduction — CV
Level Low
Medium
High
6.39—6.47 0% 30%
7.08—7.09 10% 20%
7.69—7.98 20% 10%
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Table 4 Results for each factor setting, control system and performance criterion Technique
WIP Inventory Protective Capacity Variance Reduction
Criterion
Output rate (units) Cycle time (min.) Utilization (%) Output rate (units) Cycle time (min.) Utilization (%) Output rate (units) Cycle time (min.) Utilization (%)
Factor level — JIT
Factor level — TOC
Low
Medium
High
Low
Medium
High
13.51 741 0.80 13.24 828 0.85 12.97 803 0.77
13.68 784 0.82 13.69 782 0.81 13.70 785 0.82
13.69 828 0.82 13.95 744 0.77 14.20 765 0.85
14.45 589 0.85 14.38 664 0.92 14.24 644 0.84
14.45 629 0.85 14.47 624 0.86 14.54 620 0.86
14.48 660 0.85 14.53 590 0.79 14.60 613 0.86
settings and both control systems. In all cases the results confirm the basic theory. As inventory is added to the cell, output increases, cycle time increases and utilization increases (though nominally for the TOC control system). As protective capacity is added, output increases, cycle time decreases and utilization decreases (there is more capacity to be utilized). Finally, as uncertainty is removed, output increases, cycle time decreases and utilization increases. These results suggest that capacity buffering and variance reduction are effective alternatives to work-in-process inventory as buffering techniques. Moreover, the final assembly schedule information used by the theory of constraints control system provides performance benefits. The output is higher, cycle times lower and utilization higher than for the JIT system. Table 5 provides a summary of the ANOVA results for the output rates. For the JIT control system, all effects are highly significant. The firstorder interactions indicate, for example, that the variance reduction technique has a greater effect on output rate at low levels of protective capacity than at high levels of protective capacity. The results for the TOC control system indicate that the inventory effect on output rate, while positive, is not significant. Likewise, any interactions with inventory are not significant. (The results for the utilization criterion, while not reproduced here, are very similar to these for the output rate. The complete ANOVA tables can be found in Hurley and Whybark [2].) The largest contribution to changes in output rate (sum of squared errors) for both systems comes
Table 5 Summary of ANOVA results for output rate Source
Inventory — IN Capacity — PC Variance — VR IN*PC IN*VR PC*VR IN*PC*VR
JIT
TOC
SS error
p
SS error
p
1.9 22.7 69.3 1.04 1.12 3.64 0.55
0.00 0.00 0.00 0.00 0.00 0.00 0.01
0.05 1.10 6.51 0.08 0.11 0.54 0.09
0.46 0.00 0.00 0.69 0.52 0.00 0.95
Table 6 Summary of ANOVA results for cycle time Source
Inventory — IN Capacity — PC Variance — VR IN*PC IN*VR PC*VR IN*PC*VR
JIT
TOC
SS error
p
SS error
p
337657 316493 63880 10078 3347 24593 29290
0.00 0.00 0.00 0.00 0.00 0.00 0.00
227092 249888 47554 24243 15789 64060 38762
0.00 0.00 0.00 0.00 0.03 0.00 0.00
from the variance reduction technique followed by protective capacity. Again, this is evidence that they are effective alternatives to inventory. A summary of the ANOVA results for cycle time is provided in Table 6. Here the results are highly
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significant for all buffering techniques, interactions and control systems. The variance reduction technique, however, has less of an effect in reducing cycle time than either of the other two techniques. This can be seen from the sum of squared errors. In manufacturing firms for which cycle time reduction is an important activity, reducing inventory and/or increasing protective capacity seems to be more effective than variance reduction.
6. Discussion The results of this simulation study indicate that the use of variance reduction programs or protective capacity are effective techniques for buffering against uncertainties in manufacturing. Indeed, for this manufacturing cell they both look like preferred alternatives to the traditional use of work-inprocess inventory for increasing the output rate of the cell. This is illustrated in Figs. 2—4, which present graphs of the output rate for all three settings of each factor. For both control systems, the change in output rate is greatest using variance reduction, next with protective capacity and least with inventory. The relatively high rate of overall output for the TOC control system means that little change is evident for any of the techniques, though there is some. Another way of evaluating the effectiveness of the techniques is to compare the relative change in output rate as the levels of the buffering technique change. Figs. 5 and 6 are plots of the percentage
Fig. 3. Variance reduction and output rate.
Fig. 2. Average WIP inventory and output rate.
Fig. 5. Changes in output rate with the TOC control system.
Fig. 4. Protective capacity and output rate.
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tion and how much flexibility exists for making changes in the factors. Unfortunately, however, these techniques do not often occur to management when the issue of increasing output rate arises. Instead, the traditional solution of inventory is well known and easily accepted. If nothing else, this study should encourage managers to consider other alternatives before investing in inventory to increase output rate.
References
Fig. 6. Changes in output rate with the JIT control system.
change in output rate per percentage change in factor level for each of the control systems. Under both systems, the superiority of the variance reduction program is clearly seen. The figures also show that there is a much higher change in output rate per change in factor level under JIT than TOC. Of course these graphs do not tell the whole story. First, no data are available on the relative costs of the alternative buffering techniques so the improvement per unit cost is not available. It would only be by coincidence that the costs would be proportional to the factor settings chosen here. Moreover, the changes in factors and output cannot be linear. For example, the variance reduction technique can achieve no less than zero uncertainty and it is likely that the cost of reductions of uncertainty at the higher levels of uncertainty is much less per unit of standard deviation than at lower levels. On the other hand, the amount of inventory and protective capacity is unlimited, though the benefits of increasing levels of each are likely to be diminishing. The key conclusion from this research is that variance reduction programs and protective capacity should be considered as serious alternatives to work-in-process inventory for buffering a manufacturing cell. This work shows them to be effective for quite different production control systems. Of course, the managerial attraction of these techniques depends both upon the cost of implementa-
[1] R. Conway, W. Maxwell, J.O. McClain, L.J. Thomas, The role of work-in-process inventory in serial production lines, Operations Research 36 (2) (1988) 229—242. [2] S.F. Hurley, D.C. Whybark, A simulation study of tradeoffs in a manufacturing cell, Global Manufacturing Research Center Working Paper, Kenan—Flagler Business School, University of North Carolina, Chapel Hill, NC, 27599-3490, September, 1998. [3] Y. Monden, Adaptable Kanban system helps Toyota maintain just-in-time production, Industrial Engineering 13 (5) (1981) 29—46. [4] E.M. Goldratt, J. Cox, The Goal (rev. ed. Croton-onHudson), North River Press, New York, 1996. [5] T.E. Vollmann, W.L. Berry, D.C. Whybark, Manufacturing Planning and Control Systems, 4th ed., Irwin, Homewood, IL, 1997. [6] D.P. Cook, A simulation comparison of traditional, JIT and TOC manufacturing systems in a flow shop with bottlenecks, Production and Inventory Management Journal 35 (1) (1994) 53—59. [7] K.C. So, S.C. Pinault, Allocating buffer storage in a pull system, International Journal of Production Research 26 (12) (1988) 1959—1980. [8] T. Park, A two-phase heuristic algorithm for determining buffer sizes of production lines, International Journal of Production Research 31 (3) (1993) 613—631. [9] L.J. Krajewski, B.E. King, L.P. Ritzman, D.S. Wong, Kanban, MRP, and shaping the manufacturing environment, Management Science 33 (1) (1987) 39—57. [10] J.B. Atwater, S.S. Chakravorty, Does protective capacity assist managers in competing along time-based dimensions, Production and Inventory Management Journal 35 (3) (1994) 53—59. [11] K.C. So, On the efficiency of unbalancing production lines, International Journal of Production Research 27 (4) (1989) 717—729. [12] M.S. Spencer, J.F. Cox III, Master production scheduling development in a theory of constraints environment, Production and Inventory Management Journal 36 (1) (1995) 8—14. [13] A. Law, W.D. Kelton, Simulation Modeling and Analysis, 2nd ed., McGraw Hill, New York, 1991.