A study of the utilization of capacity constrained resources in drum-buffer-rope systems
Atwater, J Brian
A STUDY OF THE UTILIZATION OF CAPACITY CONSTRAINED RESOURCES IN DRUM-BUFFER-ROPE SYSTEMS*
Goldratt, the originator of the Theory of Constraints (TOC), maintains that only the system’s primary resource constraints) should be scheduled at 100% of capacity. All other resources should have excess capacity. This paper presents the results of a simulation experiment that studies how changes in the capacity utilization of a system’s two most heavily utilized resources affect the performance of a drum-buffer-rope (DBR)scheduling system. The research demonstrates that 100% utilization of the primary constraint is not optimal. It also shows that DBR responds well to relatively low levels of increased capacity at the operation’s second most heavily utilized resource. This research also highlights several other issues related to capacity utilization that need further investigation.
(CAPACITY MANAGEMENT; PRODUCTION SCHEDULING; BOTTLENECK MANAGEMENT; DRUM-BUFFER-ROPE; THEORY OF CONSTRAINTS)
Finite scheduling systems have become popular over the last several years. One such system developed by Elyahu Goldratt is widely known as drum-buffer-rope (DBR; Goldratt and Fox 1986). Several finite scheduling software programs based on the DBR logic have emerged since Goldratt introduced his first model. Although specific programs differ, the basics of a DBR system are the same. One reason DBR-type systems are so appealing is the approach they take to finite load orders into the schedule. Many scheduling programs that use finite loading policies attempt to develop detailed schedules for every machine in the shop (Wisner 1995). DBR systems only finite load the system’s long-term bottleneck while using buffers to protect against fluctuations occurring at nonbottleneck operations (Umble and Srikanth 1996).
Goldratt maintains that a balanced plant is undesirable and that some amount of capacity imbalance is necessary and virtually unavoidable (Goldratt and Cox 1984). Based on this belief, DBR systems operate by identifying the system’s long-term resource constraint and developing a detailed schedule for it. The system relies on the excess capacity at all other resources (i.e., nonconstraints) to help alleviate problems caused by disruptions throughout the operation so that the constraint resource stays on schedule and orders are shipped on time. Theory of constraints (Toc) vernacular refers to this extra capacity as protective capacity (PC).
Spearman (1997) raised two critical questions concerning the capacity imbalance used in DBR systems. His first question was “If capacity is not balanced, then how far out of balance should it be?” This is a critical question, especially in light of the lean manufacturing movement. In today’s operating environments, with the emphasis on minimizing waste, the protective capacity requirement needs to be better understood.
Spearman’s second question was equally important, “How does one find the proper utilization at a ‘constraint’?” Virtually all of the DBR literature focuses on situations where an operation has a resource with insufficient capacity to satisfy demand fully. Therefore, those resources are shown to operate 100% of the time. Although these situations are useful in demonstrating the application of DBR concepts, in real environments they represent temporary situations. Anyone with a basic understanding of queuing theory knows that if arrival rates always equal or exceed processing times work-in-process (WIP)and lead times will go to infinity. Therefore, if it is not realistic to operate the system’s primary constraint 100% of the time, what is a good utilization level?
The question of constraint utilization (CU) is related directly to the value of using DBR as a scheduling system. DBR scheduling systems assume that order due dates are the only constraint that must be met (Simmons et al. 1996). Orders are selected for release based on their due dates. A daily rough-cut capacity check is performed on each resource before each order’s release. If no constraint operation is identified during this capacity check, then the order is released. This process is repeated until a constraint resource is identified. At that time, a drum schedule is developed for the constraint resource and material release is subordinated to that schedule. Therefore, during periods when an operation has no resource constraint, DBR defaults to immediate release (IMM). Consequently, it is conceivable that DBR systems only outperform immediate release in environments with relatively high utilization of at least one resource. Because no resource can be utilized 100% of the time and DBR reverts to an immediate release system when there is no resource constraint, the question remains: What is the range of utilization on the system’s primary capacity constrained resource (ccR) that makes DBR systems maximally effective?
To date, none of the literature on DBR scheduling has addressed these issues. This study uses a simulation model, with features similar to a semiconductor plant, to provide some initial insights into these issues. The following are the specific research questions this study addresses:
* At what utilization levels of the system’s primary CCR do DBR systems outperform immediate release, with respect to manufacturing flow time (MFT) and on-time shipment of orders when due dates are exogenously assigned?
* How does the amount of protective capacity at the second most heavily utilized resource (i.e., the secondary CCR) affect the manufacturing flow time and due date performance of DBR systems when due dates are exogenously assigned?
* How do protective capacity at the secondary CCR and the utilization level of the primary CCR interact to effect the performance of DBR scheduling systems with respect to manufacturing flow time and on-time shipment of orders when due dates are exogenously assigned?
2. The Simulation Model and DBR Scheduling Logic
In this study we applied DBR scheduling logic to a 13-station job shop producing 10 different product lines. Bitran and Tirupati (1998) originally modeled this specific operation in 1988. We selected it for this study for two reasons. First, the system has fairly complex product flows, which create a good deal of bottleneck shifting (Lawrence and Buss 1994). An operation that experiences a good deal of natural bottleneck shifting provides an excellent environment to test the value of using a DBR scheduling system, as well as, the impact from varying resource utilization levels on its performance. The second reason we selected this model was because we could vary order arrival rates to change the utilization level of individual resources. This characteristic made it possible to manipulate resource utilization in a manner so that we could study the affects of protective capacity and constraint utilization separately. Table 1 provides order arrival distributions and their specific routings through the shop. Table 2 provides the processing time distribution for the work centers and their observed utilization levels. The order arrival distributions and utilization levels described in Tables 1 and 2 represent the initial condition for the operation used in the simulation experiments.
We developed two scheduling systems for this operation. The first system uses an immediate release method for order review and release (ORR). Under this system, when an order arrives, a due date is assigned using the constant time allowance method (Baker 1984). The size of the constant allowance was 61 time units. Based on preliminary runs, this value resulted in approximately 92% of the orders being completed on time. We used this lead-time value in all simulation runs. Once the due date was assigned, the order was released to the first work center in its routing.
The second scheduling system used a DBR approach to ORR. We operationalized the DBR system in the following manner. First, we established buffers. In the DBR system, buffers are used to ensure that disruptions at nonconstraint processes don’t adversely impact the ability to meet order due dates. Two time buffers are built into the system. One time buffer, referred to as the constraint buffer, is placed between material release and the primary CCR. This buffer provides sufficient processing time at nonconstraint resources preceding the bottleneck operation to ensure that any disruptions in the order’s flow don’t prevent it from arriving at the constraint in time to be processed there. The second time buffer, called the shipping buffer, allows sufficient time for orders to flow across nonconstraint operations after leaving the primary CCR so they arrive in shipping in time to meet their due dates.
Schragenheim and Ronen (1990) describe a process for setting these buffers, which starts by simply dividing the company’s current lead-time allowance in half and using one portion as the constraint buffer and one portion as the shipping buffer. Managers can use this approach to determine initial buffer sizes and make adjustments over time until optimal buffer sizes are identified. Initial simulation runs indicated that no significant change in performance resulted from adjusting these buffers. Consequently, we set both the constraint and the shipping buffers at one-half of the quoted lead time (i.e., 30.5 time units each) for the simulation experiments.
Next, we developed a detailed schedule for Work Center 9 (the system’s primary CCR). This detailed schedule is referred to as the drum in the DBR system because it sets the pace of the operation. Once the two time buffers have been developed, they can be used to tie the order’s due date to its constraint schedule and, continuing to work backward, tie the constraint schedule to the order’s release date. The rope analogy in the DBR system essentially comes from this idea of tying all of these scheduling dates together. Conceptually, the process of tying the rope is quite simple. First, the shipping buffer is added to the order’s processing time at the primary CCR. The resulting sum is subtracted from the order’s due date to establish its start time at the constraint (i.e., its place in the constraint schedule). If the scheduled processing times of two orders overlap at Work Center 9, a first-come-first-serve priority rules is used to push one order’s processing time back until the overlap is eliminated. Once the drum schedule is developed, the order’s release time can be established by subtracting the constraint buffer from the order’s start time at the constraint. By tying material release to the drum schedule, nonconstraints are not allowed to process at their own pace. Instead, they are subordinated to ensure the drum schedule is met with the least amount of work-in-process inventory necessary. Once the order’s release time is set, it is sent to a pre-shop queue where it waits to be released. If an order does not use Work Center 9, it is released to the shop immediately on arrival.
3. Research Methodology
3.1. The Independent Variables
Three independent variables were used in this study. The first independent variable was the type of scheduling system. As described in the previous section, the IMM and DBR scheduling systems were modeled. The IMM system was included in the study to serve as a base comparison for the value of changes in constraint utilization and protective capacity. The IMM system is particularly relevant as a base comparison because DBR reverts to an immediate release system when there are no internal resource constraints.
The second independent variable is the overall utilization of the system’s primary CCR (i.e., Work Center 9). This variable is referred to in this study as cu and was modeled at three levels. The third independent variable is the difference between the utilization level of the system’s primary CCR and the system’s secondary CCR (i.e., the second most heavily utilized resource). In this operation, the secondary CCR is Work Center 2. This variable is labeled Pc and is modeled at five levels.
We modeled the different levels for the cu and Pc variables by manipulating product arrival rates. We modeled the cu variable by changing the arrival rate of product 1. We selected product 1 because preliminary runs indicated that changes to its arrival rate altered the utilization levels of both Work Center 9 and Work Center 2 by approximately the same amount so that protective capacity was not changed. In addition, the changes in arrival rate for product 1, made in this study, ensured that Work Centers 2 and 9 remained the operation’s most heavily utilized resources. At the lowest level of the CU variable, Work Center 9 is used approximately 94% of the time. The other two levels of the CU variable are achieved by increasing the arrival rate for product 1 so that average utilization of Work Center 9 is about 96 and 98.5%.
The third independent variable used in this study is PC. The APICS Dictionary (The American Production and Inventory Controls Society 1995) defines PC as
A given amount of extra capacity at non-constraints above the system constraint’s capacity, used to protect against statistical fluctuations … Protective capacity provides non-constraints with the ability to catch up to protect throughput and due date performance.
In this study we specifically defined Pc as the difference in utilization between Work Center 9, the system’s primary resource constraint, and Work Center 2, which is the second most heavily utilized resource. Because of the way Pc is modeled, precise levels of this variable were not possible. Instead, the levels of Pc are defined in terms of a narrow range. Those ranges are
We modeled the PC variable by changing the arrival rate of product 7. We chose product 7 because Work Center 9 is not included in its routing. Consequently, changing the arrival rate of product 7 increases the utilization of Work Center 2 without changing the utilization of Work Center 9. In the initial model, Work Center 2 is utilized about 90% of the time and Work Center 9 has about a 94% utilization level. This scenario represents the case with 3-5% Pc. Next, we increased the arrival rate of product 7 so that the utilization levels of Work Center 2 were approximately 92 and 94% (1-3% Pc and
3.2. The Dependent Variables
The performance of DBR and the iM systems was measured using two criteria. One criterion was the average level of WIP inventory present in the system. The second criterion was the ability to deliver orders on time. These two criteria were selected because surveys have indicated that current managers regard these factors as very important in assessing effective shop floor control. In addition, past research on the use of controlled release systems has generated conflicting results surrounding these variables (Wisner 1995). All of these factors, machine utilization, mr inventory levels, and due date performance, are central to this research.
Three dependent variables were used in this study. To measure the performance of the ORR systems with regard to vap inventory, we used the mean manufacturing flow time (MFT). To measure the due date performance of the two ORR systems, we used two dependent variables. One variable was the percentage of orders that finished tardy (mean % tardy). We selected this variable because previous research suggests that DBR systems perform well with respect to minimizing maximum tardiness (Simmons et al. 1996). Woolsey and Swanson (1975) developed a principle that suggests that systems, which minimize maximum tardiness, should be evaluated on the number of jobs that are late. The second dependent variable based to assess due date performance was the average tardiness of orders (mean tardy). We included the mean tardy variable to investigate the amount of variability in the delivery performance of DBR systems.
We used a full factorial design to develop 30 simulation models (2 ORR X 3 cu X 5 PC). To be 95% confident of a 1% precision level on the dependent variables, 30 replications of each run were conducted. In addition, to ensure steady-state conditions, each simulation was run for 100,000 time units and then statistics were cleared and data were collected over the next 200,000 time units.
4. Data Analysis
To answer the research questions, three analysis of variance (ANOVA) models were constructed for each dependent variable using CU, PC, and ORR as the independent variables. The results of these ANOVA models are summarized in the following text. For those readers who are interested the actual ANOVA, models are provided in the Appendix at the end of the paper. In all cases where significant interactions were found, graphical analysis and the Bonferroni method for multiple comparisons were used to provide detailed insights into those interactions. The data analysis section of the paper is broken into three sections, one for each dependent variable.
4. 1. Mean Flow Time
To answer the research questions related to MFT, we developed an ANOVA model using it as the dependent variable. The table showed that a significant three-way interaction exists between the three independent variables. To answer the research questions related to mFr, we analyzed the three-way interaction.
Three graphs were developed by plotting the MFT for both ORR systems at each of the five PC levels. Figure 1a displays the MFT graph for both ORR systems under different PC levels when CU is at 98.5%. The graph shows that at all three PC levels, the DBR system has a lower MFr than the IMM system. In addition, the differences in MFT between the two ORR systems were significant at all five PC levels. The graph also shows that increases in Pc had a larger impact on the MFT performance of the DBR system then it did on the IMM system.
Similar graphs were developed for the second and third levels of the CU variable, which are shown in Figure 1, b and c. The interaction graphs for both levels of the CU variable show essentially the same relationship between the ORR and Pc as when CU is at 98.5%. The DBR’s MFT is significantly better than IMM’s at all five PC levels. Furthermore, increases in PC have a larger impact on DBR systems than on IMM. Here again all differences were found statistically significant.
It is important to note that despite the statistically significant differences in the MFr of these two systems, there is a clear convergence in the performance of the two ORR systems as cu is decreased. This convergence indicates that the advantage in MFT provided by a DBR system diminishes as the utilization level of the system’s primary CCR decreases.
Another interesting observation was noted from the graphs in Figure 1. The impact on mr from increasing PC is largest for smaller amounts of PC. Figure 1 shows this relationship to be true for all levels of the CU variable. This indicates that relatively small amounts of PC are needed to significantly improve the mr performance of DBR systems. Furthermore, in this study, increasing PC beyond 5% had relatively little impact.
To answer the third research question about how CU and PC interactions impact the DHR systems performance, with respect to MFT, the DBR data were used to construct an interaction graph for CU and PC. The graph of this interaction is provided in Figure 2. The graph displays an interaction between PC and CU for the DBR system. Here again, when CU is high, the largest impact from increasing PC occurs from the smallest amounts. As cu decreases, PC’s impact also decreases.
4.2. Mean Tardiness
To answer the research questions with regard to average tardiness, we developed another ANOVA model using mean tardiness as the dependent variable and ORR, CU, and PC as the independent variables. All three independent variables significantly impact average tardiness performance. In addition, there was a two-way interaction between ORR and CU.
To determine the relative performance of DBR and IMM systems with respect to mean tardiness, detailed analysis of the two-way interaction between ORR and CU was performed. A graph of the interaction is provided in Figure 3. The graph indicates that the IMM system has lower mean tardiness at all three levels of the CU variable. However, further analysis revealed that the differences in mean tardiness between the two systems were significant when cu was at 98.5 and 96%, but when CU is at 94% the difference was not statistically significant. Here again, the performances of DBR and IMM systems converge at lower levels of utilization for the system’s primary CCR. However, in the case of mean tardiness IMM systems perform better than DBR at high utilization levels for the primary CCR.
To answer the second research question, we used the DBR data to develop a graph showing the mean tardiness at each level of the PC variable. The graph is provided in Figure 4. The graph shows that increased levels of PC reduced the mean tardiness for the DBR system. Here again, further analysis revealed that the largest reductions in mean tardiness occurred when PC was increased from level one (
Detailed analysis was not required to answer the third research question with regard to mean tardiness. The ANOVA model showed no significant interaction between the cu and PC variables. Therefore, changes in CU levels do not alter the impact that PC has on the DBR system. So regardless of the utilization level of the system’s primary constraint, the largest reduction in mean tardiness occurs when PC is increased above 1% and maintained between 1 and 3%. Increases in PC above 3% do not decrease mean tardiness by a statistically significant amount.
4.3. Mean Percent Tardy
We developed a third ANOVA model using mean percent tardy as the dependent variable and ORR, CU, and PC as the independent variables. This ANOVA model showed that all the two-way interactions were significant but there was no significant three-way interaction. Detailed analyses of the two-way interactions were performed to answer the three research questions.
To determine if the utilization level of the system’s primary constraint impacts the relative performance of DBR and IMM systems with respect to mean percent tardy, we aggregated the data across the PC variable and developed a graph of the two-way interaction between ORR and cu. The graph is provided in Figure 5. It shows that the imm system has a lower mean percent tardy rate than the DBR system at all three cu levels. In addition, these differences were significant at all three levels of the cu variable. However, the relative performance difference diminished as the utilization level of the primary constraint decreased, once again indicating a convergence in the performance of the two systems at lower levels of utilization for the system’s primary constraint.
To analyze the impact of PC on the mean percent tardy performance of the two systems, we aggregated the data across the cu variable and graphed the interaction between ORR and PC. The graph is provided in Figure 6. The figure shows that the IMM system has a lower mean percent tardy rate than the DBR system at all five PC levels and these differences were all found to be significant. Although the graph does not reveal an obvious interaction, further analysis did show that the difference in the mean percent tardy performance of the two systems decreased as PC was increased. This indicates that PC has a larger impact on DBR systems than it does on IMM systems.
To determine the specific impact that PC has on the DBR system, we performed pairwise comparisons between each level of the PC variable. These comparisons showed that adding PC to the DBR system significantly reduced the mean percent tardy rate at every PC level. However, it is important to note that the reductions in the mean percent tardy rate decreased with each subsequent increase in the PC variable. Given this trend, it is reasonable to assume that further Pc increases eventually would fail to improve DBR’s performance significantly.
To analyze the impact of the interaction between CU and PC on the DBR system, we constructed a graph using only the data related to DBR. The graph is provided in Figure 7. Again, the graph does not reveal an obvious interaction. However, further analysis revealed that the impact of PC does vary with different cu levels. Specifically, when CU is at 98.5%, each increase in the PC variable resulted in a significant drop in the DBR’s mean percent tardy rate. When CU is at 96%, the mean percent tardy rate drops significantly as PC is increased from level 1-2, level 2-3, and level 3-4. However, increasing PC from level 4-5 did not significantly reduce the mean percent tardy. When cu was at 94%, increasing PC from levels 1-2 and 2-3 significantly reduced the mean percent tardy, but further increases did not.
This analysis indicates two things. First, the value of adding PC to a DBR system, with respect to mean percent tardy, decreases as the utilization level of the system’s primary constraint decreases. Second, regardless of the constraint’s utilization level, the largest reduction in the percentage of late orders shipped occurs from the smallest PC increases and diminishes as PC is increased.
5. Summary and Conclusions
First, the DBR system operates with significantly less MFT than the IMM system regardless of the level of utilization at the primary constraint. This faster MFT directly translates to lower inventory levels. Second, the IMM system generally has better due date performance than the DBR system. However, the performance of the two systems, with regard to due date performance, converges as the primary constraint’s utilization decreased. For example, at high primary constraint utilization levels, the im system has a significantly lower mean tardiness rate than the DBR system, but at the lowest CU level no significant difference in the mean tardiness rate exists between the two systems. Consequently, it appears that there is a level of utilization at the primary constraint that allows DBR to operate with essentially the same mean tardiness rate as an IMM system while maintaining its advantage with regard to MFT and WIP inventory.
This study also shows that for the manufacturing environment, PC has a larger impact on the DBR system than it does on the IMM system. In addition, it indicates that relatively low levels of PC generate the biggest benefits. For this environment, increasing PC from less than 1% to somewhere between land 3% always generated significant improvements in the DBR system’s performance. Further increases in PC did not always significantly improve the performance of the DBR system. In fact, there were diminishing returns from each incremental increase in PC. This finding indicates that, potentially, only a small capacity imbalance is required to achieve fairly good results from a DBR system.
In addition, the environment modeled in this study showed that an interaction occurs between PC and CU. This finding indicates that managers should consider the level of utilization for the primary and secondary CCR jointly. In this study DBR performed as well or better than IMM in terms of MFT, WIP, and mean tardiness rates when CU was at its lowest level. The study also shows a decreasing trend in the performance difference of the two systems with regard to mean percent tardy as cu was decreased. Furthermore, adding a small amount of PC (somewhere between 1 and 3%) also significantly improved DBR’S performance with regard to all the independent variables. This would indicate that there is a combination of CU and PC, which enables DBR to perform as well as imm in terms of due date performance (both mean tardiness and mean percent tardy) while still having a significantly faster MFT. Further research is needed to verify if such a combination of CU and PC exists and if it is consistent across different types of operations as well.
More research is needed investigating the role of resource utilization in the performance of scheduling systems. Research that extends this study to other resources could provide additional insights. For example, if an item bypasses the primary CCR and the secondary CCR, can orders for it be accepted and scheduled without any real consequences to the system’s overall performance? Does the impact of PC at other resources change with the constraint’s utilization level? Where do the diminishing returns occur as PC is added to other resources throughout the system? In addition, studies are needed that simulate other types of manufacturing environments to determine if these findings hold true for them as well.
* Received May 2000; revisions received September 2000 and February 2001; accepted August 2001.
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J. BRIAN ATWATER AND SATYA S. CHAKRAVORTY
Business Administration Department, College of Business,
Utah State University, Logan, Utah 84322-3510, USA
Department of Management and Entrepreneurship, Michael J. Coles College of
Business, Kennesaw State University, Kennesaw, Georgia 30144-5591, USA
J. Brian Atwater is an associate professor of operations management at Utah State University. He earned his Ph.D. in operations management at the University of Georgia. Dr. Atwater is certified in production and inventory management (CPIM) by the American Production and Inventory Control Society (APICS). He has received lead auditor training in ISO 9000 and is also a certified academic associate (JONAH) of the Goldratt Institute and he currently works as an examiner for the Shingo Prize for Excellence in Manufacturing. He has provided professional consulting services for several manufacturing operations including 3M, Apple Computers, Inc., Carrier, and Schuller/Manville Corporation. His research interests focus on the application of world-class manufacturing systems such as the Theory of Constraints, Six Sigma, and Lean Manufacturing Techniques. He has published several articles in various journals including the International Journal of Operations and Production Management, Productions Inventory Management Journal, and Cost Management Journal.
Satya S. Chakravorty, Ph.D., CFPIM, is Caraustar Professor of Operations Management at the Michael J. Coles College of Business at Kennesaw State University. He received his Ph.D. in Production/Operations Management from the University of Georgia. He also holds Bachelors and Masters degrees in Engineering and Sciences from BITS, Pilani (India). He has published in the Omega: The International Journal of Management Science, Quality Management Journal, International Journal of Operations and Production Management, International Journal of Production Research, Production and Inventory Management Journal, Industrial Management, International Journal of Technology Management, and Simulation and Gaming. He is a member of the Decision Sciences Institute (DSI), Production and Operations Management Society (POMS), American Production and Inventory Control Society (APICS), and National Association of Purchasing Management (NAPM). He has consulted with many companies in the United States, including 3M and AT&T. Before academia, he worked as a Manager/Engineer for 5 years in Escorts Ltd. (India).
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