THE IMPACT OF PULL SYSTEM
STRUCTURE AND CONFIGURATION
ON PRODUCTION LINE PERFORMANCE
UNDER STATE DEPENDENT BEHAVIOR
Master’s Thesis
By:
Hariadhi Wicaksono Student number: S2699338
MSc Technology & Operations Management
i Abstract
Purpose: Pull system design is defined by its structure and configuration, which are the pattern of work in process (WIP) limit and the level of the work in process limit, respectively. WIP limitation allows the occurrence of starving and blocking in the production system, where empirical evidence shows that human workers adjusts their work processing time to minimize the occurrence of starving and blocking. This processing time adjustment behavior, referred to as the state-dependent behavior, is incorporated into the study of pull system structures and configurations to analyze their effect on line performance. By studying simulation models, this research aims to provide a more accurate understanding in designing an efficient pull system with human workers.
Method: A pull system production line simulation model is made by incorporating a state-dependent behavior model made by Powell and Schultz (2004) and a pull system design model made by Gaury, Kleijnen, and Pierreval (2001). Different pull system structures and pull system configurations are used as the experimental input for the simulation study to analyze the relation between pull system structures and pull system configurations to line performance under the influence of state-dependent behavior.
Findings: Increasing the occurrence of workflow disturbance through the pull system structure increases the system throughput. Increasing the pull system configuration also increases throughput, but with a diminishing rate of throughput increase.
State-dependent behavior alters the initially balanced work allocation pattern into an imbalanced allocation pattern. This occurrence increases the throughput of the production line further when the higher workloads are distributed to the workstation with faster average processing time and the lower workloads on the slower workstations. In extended production lines, throughput decrease from higher stochastic interference is minimized under state-dependent behavior due to more interior workers that have faster processing times.
Recommendations: There are various possible pull system structures that can be studied under state-dependent behavior, which might have a better cost efficiency than the performance of the Kanban, POLCA, or CONWIP pull system structure.
ii Preface
This project is the final project that is done to obtain my Master of Science in Technology and Operations Management degree. This project incorporates the principle of the program itself by practicing how efficiency in a system can be attained through an appropriate management of both technology and the people who run the operation.
The objective of the project is to understand the two most important parts of a pull system design, that is the structure and the configuration, that implements limitation of work in process in the production system. The result of the simulation study achieves the objective of the study as well as providing new insights and interests of both operations management practitioners and researchers.
I would like to thank my supervisor for his patience and continuous effort in providing reviews and feedbacks throughout the project. Without his help in building the code, as well as providing the facility to run the simulation, I could not finish the simulation on time.
I would also like to thank my co-assessor for his input on the initial stage of the project. I also want to give the most gratitude to my fellow Technology and Operations Management master students for providing me feedbacks during the initial poster presentation and final presentation, especially to those who personally helps me with the writing of the report. Finally, I thank every single person that has given me the knowledge and support up to this point, so that I could finish this project in time.
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TABLE OF CONTENTS
1 Introduction ... 1
2 Theoretical Background ... 3
2.1 State-Dependent Behavior ... 3
2.2 Pull System Structure and Configuration ... 5
2.3 How Structure and Configuration Contributes to State-Dependent Behavior .. 7
2.4 Conceptual Model ... 7
3 Methodology ... 8
3.1 Production Line Model ... 9
3.2 State-Dependent Behavior Model ... 9
3.3 Simulation Program ... 10
4 Simulation ... 11
4.1 Model Summary ... 11
4.2 Simulation Setup ... 14
4.3 Simulation Model Validation ... 15
4.4 Simulation Results ... 16
4.4.1 Structure, Configuration, and Speedup Constant ... 16
4.4.2 Structure, Configuration, and Work Allocation ... 18
4.4.3 Structure, Configuration, and Line Length ... 20
5 Discussion ... 22
5.1 Pull System Configuration ... 22
5.2 Pull System Structure ... 23
5.3 Work In Process ... 25
6 Conclusion ... 26
6.1 Conclusion ... 26
6.2 Recommendations ... 27
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References ... 29
APPENDIX A: WIP Movement Flowchart ... 31
APPENDIX B: Workers processing time adjustment model ... 32
APPENDIX C: Warm-Up length, Replication, and Run Length ... 33
APPENDIX D: Summary of Simulation Result ... 37
3 Workstations: Throughput ... 37
3 Workstations: Average Cycle Time ... 38
3 Workstations: Average WIP ... 39
5 Workstations: Throughput ... 40
5 Workstations: Average Cycle Time ... 41
5 Workstations: Average WIP ... 42
TABLE OF FIGURES Figure 2.1 Kanban pull system structure (Ziengs et al., 2012) ... 6
Figure 2.2 CONWIP pull system structure (Germs and Riezebos, 2009) ... 6
Figure 2.3 POLCA pull system structure (Germs and Riezebos, 2009) ... 6
Figure 2.4 Conceptual model of the study ... 7
Figure 4.1 Generic pull system structure (Gaury, Kleijnen, and Pierreval, 2001) ... 12
Figure 4.2 Efficiency on different speedup constants ... 15
Figure 4.3 Efficiency of each structure on increasing configuration ... 16
Figure 4.4 Production line efficiency under different work allocation pattern ... 18
Figure 4.5 Efficiency on different line lengths ... 20
Figure 5.1 Efficiency on excessively higher pull system configurations ... 22
Figure 5.2 Average processing times and average WIP of CONWIP, POLCA, and Kanban in balanced work allocation ... 24
Figure.Appendix 1 WIP movement flowchart ... 31
Figure.Appendix 2 Processing time adjustment flowchart ... 32
Figure.Appendix 3 Welch’s Method Calculation Result for 3 Workstations ... 33
Figure.Appendix 4 Run Length Calculation Graph for 3 Workstations ... 34
Figure.Appendix 5 Welch’s Method Calculation Result for 5 Workstations ... 35
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TABLE OF TABLES
Table 4.1 Model summary ... 11
Table 4.2 Worker processing time for different line length ... 13
Table 4.3 Efficiency of different structures under the same maximum WIP ... 17
Table 4.4 Efficiency of different structures under the same maximum WIP ... 19
Table 5.1 Average WIP With Equal Level Of Maximum WIP ... 25
Table 5.2 Production Line Efficiency Relative to Their Average WIP ... 26
Table.Appendix 1 Confidence Interval Calculation Result for 3 Workstations ... 33
Table.Appendix 2 Run Length Calculation Result for 3 Workstations ... 34
Table.Appendix 3 Confidence Interval Calculation Result for 5 Workstations ... 35
Table.Appendix 4 Run Length Calculation Result for 5 Workstations ... 36
Table.Appendix 5 Throughput of each simulation in 3 workstation setting ... 37
Table.Appendix 6 Average cycle time of each simulation in 3 workstation setting .... 38
Table.Appendix 7 Average WIP of each simulation in 3 workstation setting ... 39
Table.Appendix 8 Throughput of each simulation in 5 workstation setting ... 40
Table.Appendix 9 Average cycle time of each simulation in 5 workstation setting .... 41
1 1 Introduction
Studies in operations management categorized the production systems into push and pull production systems. A pull system is a production system that explicitly limits the amount of work in process (WIP) in the system (Hopp & Spearman 2004). WIP can be limited through the structure and the configuration of the pull system (Gaury, Pierreval & Kleijnen 2000).The pull system structure is the specific pattern of control loops which regulates the workload of a certain area in the production line, while pull system configuration is the WIP limit on each of the control loops (Germs & Riezebos 2009).
By maintaining the level of WIP, pull systems are more cost effective compared to push systems (Hopp & Spearman 2004). This advantage has triggered both practitioners and researchers to tailor pull system designs for specific kinds of manufacturing conditions (Hopp & Spearman 2008:356). This has resulted in several types of pull system structures such as CONstant Work In Process or CONWIP (Spearman et al. 1990) and Paired-cell Overlapping Loops of Cards or POLCA (Krishnamurthy & Suri 2009). Gaury, Pierreval and Kleijnen (2000) studies the performance of various pull system designs by simulating a generic pull system design that incorporates any possible types of pull system structure and pull system configuration. They concluded that the CONWIP structure leads to better performance compared to other pull system structures.
Pull system structures and pull system configurations are known to critically affect the performance of the pull system (Khojasteh-Ghamari 2009). Coupling, a workflow disturbance caused by starving and blocking of the buffer, is operationalized by the pull system structure and configuration (Heimbach, Grahl & Rothlauf 2012). A tightly coupled pull system strictly limits WIP which causes higher occurrence of starving and blocking. On the other hand, a loosely coupled pull system like CONWIP, allows more WIP in the system to prevent starving and blocking.
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Empirical evidence shows that workers processing time adjustment are strengthened in lower pull system configurations because starving and blocking are more likely to happen, and workers adjust their processing time to avoid starving and blocking to happen (Schultz, Juran & Boudreau 1999). These studies show that pull systems could benefit from the response of production workers to the state of their production line and that performance deterioration has been overstated.
Powell and Schultz (2004) coined the term state-dependent behavior to define the workers processing time adjustment behavior that opposes the independence assumption. In their paper which examines the effect of state-dependent behavior on line performance and line length, they mention that other aspects of line design would be a promising extension for research in dependent behavior. Heimbach, Grahl, and Rothlauf (2012) extend the state-dependent behavior research by including work allocation in their experiment. Both of the literatures conclude that a production line design that induces tighter coupling has more benefit from state-dependent behavior compared to a line with loose coupling. This effect caused the state-dependent pull system, under certain levels of speedup constant, to outperform the state-independent push system which has no interference from the coupling.
This is surprising because the studies in pull system structures and pull system configurations suggest that the loosely coupled pull system design results in better line performance, while studies in state-dependent behavior suggest the opposite. It is intriguing to see how state-dependent behavior will alter the performance of various pull system structures and pull system configurations with different degrees of coupling. This interest leads to the following research question.
RQ: What is the impact of pull system structure and configuration on line performance given state-dependent behavior?
Based on the research question, this study aims to provide a better understanding to design an efficient pull system with human workers. The analyses are based on the line performance of different pull system structures and pull system configurations that are compared to the performance of a state-independent push system, which is used as the reference point.
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and pull system configurations under the state-dependent behavior. More importantly, this study facilitates practitioners with a practical tool to efficiently search for pull system structures and pull system configurations that fits with their individual needs.
2 Theoretical Background 2.1 State-Dependent Behavior
Relation between workers’ processing time and their workload has been studied for decades. Edie (1954) studies service times of toll booths and finds that workers work faster when the queue is longer, while Franks and Sury (1966) shows that workers in conveyor work adjust their processing time according to the pace of arrival times. The interest to study state-dependent behavior continues to develop and extended to today’s retail industry, such as the service speed of restaurant workers and amount of tables being served (Tan & Netessine 2014), or the service times of checkout in retails and the queue design (Shunko, Niederhoff & Rosokha 2014). However, this state-dependent behavior effect has more complexity in a serial production line where the workers processing time is affected by both his/her own workload and the workload of the subsequent workstation.
Because of the WIP limit, a pull system can be starved or blocked. A workstation becomes starved when it cannot work because there is no inventory in the upstream buffer, and it becomes blocked when it cannot work because there is no space to put the finished goods in the downstream buffer. The lower the WIP limit in the system, the higher the probability of workflow disturbance from starving and blocking. Meanwhile, push system can never experience blocking because it does not implement a WIP limit.
The study of Doerr et al. (1996) is the first to determine the relation between the states of the production line to the behavior of the workers. The result of their experiment on comparing unlimited inventory push system and the low inventory pull system shows that both production systems result in similar processing rates, even though there are more interruptions in the lower inventory pull system. They conclude that the workers put more effort when they are producing in the pull system, since they experience short breaks from the starving and blocking.
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the state of the buffer, or the independence assumption, might not be true in low inventory settings. They show that the assumption does not hold, by providing concrete empirical evidences of state-dependent behavior in the result of their study. This result sheds a new light in the study of behavioral operations management, especially, on the fact that workers speed up if others are starving.
Having clear evidence on the effect of state-dependent behavior in pull production systems, the focus of the studies shifted to the design of the pull production system line. Powell and Schultz (2004) pioneered this by exploring the relation between throughput and the length of the serial line. They modeled the effect of state-dependent behavior in processing time adjustment through a speedup constant. This speedup constant mechanizes the adjustment of processing times by decreasing it according to the state of the adjacent buffers. Their study shows that state-dependent behavior causes the increase of production line performance along with the increase in line length under high level speedup constant. This result shows contradiction with the classic assumption where line performance deteriorates when the production line is extended.
Empirical evidences on state-dependent behavior, encourage researchers to explore its implication on practical settings, especially in the design of a production system. Heimbach, Grahl, and Rothlauf (2012) took this chance to explore the different work allocations of the serial line. Through a similar method to those of previous studies, they modeled the effect of state-dependent behavior on the adjustment of workers processing time in different types of work allocations, line length, and buffer size. Their main conclusion is that optimal line performance in different state-dependent behavior levels are achieved through different work allocation patterns.
5 2.2 Pull System Structure and Configuration
Germs and Riezebos (2010) define the structure of the pull system as the pattern of control loops among the production line which limits the movement of the WIP, while the configuration of the pull system is the number of cards which limits the amount of the WIP within the control loop. The basic pull production system, namely the Kanban system, used two types of cards to define that the WIP attached with the card has to be moved or has to be operated (Sugimori et al. 1977). Different types of card-based pull system are distinguished by their unique placement of control loops and the number of cards within the control loops in the production line (Gaury, Kleijnen & Pierreval 2001).
Pull system structures and pull system configurations define the coupling level of a pull system. A tightly coupled pull system strictly limits WIP by having a structure with less workstations in each control loop and low configuration level in each control loop, inducing higher likelihood of starving and blocking. A loosely coupled pull system has less chance of blocking due to a larger area of control loops and high configuration level in each control loop.
In the following section, three pull system structures with different coupling levels are explained. The first one, Kanban, represents the tightly coupled pull system. CONWIP represents the loosely coupled pull system since it has a structure that disables blocking and starving except for the first and last workstations. Lastly, POLCA represents the pull system design that has moderate coupling level, combining the benefit of Kanban and CONWIP. The behaviors of these structures are used as main examples to study various pull system structures and configurations that are generated by the generic pull system design (Gaury, Pierreval & Kleijnen 2000).
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CONstant Work In Progress (CONWIP) is a pull system structure that intends to combine the advantage of Kanban in minimizing inventory and the throughput maximization of push production systems (Spearman et al. 1990). This characteristic is operationalized by the use of cards, in which the control loop structure consists of the entire production line. This way, the configuration of the cards applies to the whole production line, as shown in figure 2.2 (Germs & Riezebos 2009). Compared to Kanban, CONWIP performs better in inventory minimization when processing times between stations are imbalanced (Khojasteh-Ghamari 2009).
Paired-cell Overlapping Loops of Cards with Authorization (POLCA) is a pull system structure that claims the best features of card-based pull systems and push systems (Krishnamurthy & Suri 2009). Different from CONWIP, the structure of POLCA covers the entire line with several different control loops that overlap each other, presented in figure 2.3 (Germs & Riezebos 2010). The fundamental difference between POLCA and other card-based pull system policies is that the card used in POLCA does not represent a request to operate a product, but a signal representing available capacity at a downstream loop.
Figure 2.1 Kanban pull system structure (Ziengs et al., 2012)
Figure 2.2 CONWIP pull system structure (Germs and Riezebos, 2009)
Figure 2.3 POLCA pull system structure (Germs and Riezebos, 2009)
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simulation study, they concluded that the loosely coupled CONWIP is the best pull system structure in general.
2.3 How Structure and Configuration Contributes to State-Dependent Behavior
None of the past studies in state-dependent behavior has considered the pull system structures and pull system configurations in their experiment (Powell & Schultz 2004; Heimbach, Grahl & Rothlauf 2012). In state-independent serial line with stochastic processing times, the loosely coupled CONWIP is generally deemed as the best strategy among other pull systems considering its performance in maintaining service level and minimizing inventory (Gaury, Pierreval, & Kleijnen 2001). However, loose coupling leads to less interdependence between the workers who interact through the production line and weakens the awareness of the workers to adjust their processing time. This causes CONWIP to have little benefit from state-dependent behavior, while Kanban has the most benefit.
2.4 Conceptual Model
The conceptual model (Figure 2.4) describes the framework of the study. To incorporate the interest of understanding the manner of state-dependent behavior under different pull system structures and pull system configurations, a model is built for the simulation. The magnitude of the state-dependent behavior in the model is represented by a speedup constant, a mechanism that represents the processing time adjustment of workers under state-dependent behavior (Powell & Schultz 2004). This speedup constant is embedded in a mathematical function that changes the processing time of a worker, according to the state of the upstream and the downstream buffer (Heimbach, Grahl & Rothlauf 2012).
Pull System Structure and Configurations
Line Performance
State of Production : Blocked, About to be blocked, Producing, About to be starved,
Starved Model · Speed-up Constant · Line Length · Structure and Configuration
· Work Allocation Pattern
· Efficiency
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The experiment also includes line length and work allocation pattern as part of the experimental inputs. Conway et al. (1988) claims that longer line length in a pull system suffers from increasing stochastic interference which leads to a reduced throughput, which is later shown to be not true in a state-dependent pull system model with a high level of speedup constant (Powell & Schultz 2004). Hillier and Boling (1979) define a ‘bowl’ shaped work allocation pattern that allocates slower processing time at the first and the last workstation in a serial production line, which works better than a balanced production line. Heimbach, Grahl and Rothlauf (2012) studied the effect of the bowl pattern, reverse bowl pattern, and the balanced pattern under state-dependent behavior and found that each pattern increases line performance differently at different state-dependent behavior level. Line lengths and work allocation patterns are included as input variables in this study to validate the model used in this study with the state-dependent model in previous studies, as well as extending the knowledge on how different pull system structure and pull system configuration will relate to different line lengths and work allocation patterns.
The model simulates the movement and the processing of WIP throughout the production line, according to the different experimental inputs. Following Powell and Schultz (2004), line performance is measured in efficiency, which is the throughput of the state-dependent pull system model compared to the throughput of the state-instate-dependent push system in the same line length. This is done to further contrast the effect of state-dependent behavior on pull system, which is considered to be less productive than a push system in past literatures.
3 Methodology
9 3.1 Production Line Model
The production line model is modeled according to the generic pull system structure proposed by Gaury, Kleijnen, and Pierreval (2001). When the WIP enters the model, its movement through buffers and workstations in the production line is guided by cards. The cards cycle in a certain loop according to the setting of the pull system structure, while the number of cards in the loop is defined by the setting of the pull system configuration. In this section, the steps that have to be taken for every movement of the WIP is explained, which can be seen as a flowchart in appendix A.
First, the WIP arrives into a buffer prior to the production line. It does not require a card to authorize its movement into the production line; therefore it could proceed to the first buffer of the production line directly. After the WIP enters the production line, it is examined for two conditions, the availability of cards required to advance and the availability of the workstation ahead. If the cards required are not available, the WIP has to wait in the buffer until the card becomes available. After the card is available, the status of the workstation next to the buffer is examined. If the upcoming workstation is unavailable, then the WIP has to wait until the workstation becomes available.
When the WIP arrives in a workstation, it will be processed with a processing time that is adjusted according to the state-dependent behavior model explained in the next section. The WIP continues to the next buffer after it has finished being processed. If the pull system structure requires the WIP to release an attached card, the card will be released after the WIP has entered the next buffer. If the subsequent buffer is not available, the WIP will block the machine from working. This blocking mechanism is referred as blocking-after service, which is also used in other pull system state-dependent behavior models (Powell and Schultz 2004; Heimbach, Grahl, Rothlauf 2012).
3.2 State-Dependent Behavior Model
This study adapted the state-dependent behavior model made by Heimbach, Grahl and Rothlauf (2012). In this study, workers are modeled to have an initial average processing time that is exponentially distributed. This processing time is then adjusted according to the state of the system, and calculated by the following mathematical model:
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In equation 1, wi is the average initial processing time of the worker at workstation i,
while wiadj is the workers processing time after they adjust according to the state of the
buffers. C is the maximum capacity of the buffers between the stations, ci,i+1 is the amount of
WIP in buffer bi,i+1 between stations i and i+1, and ci-1 is the amount of WIP in bufferbi-1,i.
Powell and Schultz (2004) facilitate further processing time adjustment in the model, assuming that workers change their processing time when the WIP level in the adjacent buffer changes. To implement similar mechanism, Heimbach, Grahl and Rothlauf (2012) implement this assumption in an additional model, where wirem is the remaining processing time after a
WIP leaves the downstream buffer or arrived in the upstream buffer, and wirem,adj is the
adjusted remaining processing time:
( )
In this study, the maximum capacity of the buffer is decided by the pull system structure and the pull system configuration level. Assuming that workers are aware of the maximum allowed WIP that moves throughout their workstation, the maximum buffer capacity is equal to the lowest pull system configuration that covers the area of the buffer. For example, a CONWIP pull system structure with 5 configuration levels has the maximum capacity of 5 for all the buffers. This is because the maximum possible number of WIP queuing in a buffer is 5, even though a CONWIP structure does not have a buffer limit in the buffers aside from the first and the last buffers. This mechanism of deciding maximum buffer capacity also applies to different pull system structures and pull system configurations in the same way. The implementation logic of the processing time adjustment model is defined in the flowchart in appendix B.
3.3 Simulation Program
11 4 Simulation
Prior to the execution of the simulation study, the model is carefully prepared in order to properly attain the objective of the study. The simulation input defines the scope that is observed through simulation, while the simulation setup keeps the obtained data to be accurate and valid. Each simulation scenario is composed of different experimental inputs. The result from simulating these scenarios is analyzed to understand the answer to the research question.
4.1 Model Summary
Table 4.1 shows the summary of the model used in the simulation. Input variables for the simulation model are divided into fixed and experimental.
Fixed input variables
Inter-arrival time 0.5
Utilization 0.9
Experimental input variables
Structure Kanban, CONWIP, POLCA
Configuration 1,2,3,4,5,6,7,8,9,10
Speedup constant 0.1, 0.5, 1
Workstation length 3 and 5 workstations Processing time distribution 1. Bowl pattern
2. Balanced
3. Reverse bowl pattern Output
Line performance Efficiency
Table 4.1 Model summary
The simulation model assumes that the production line has an unlimited supply and demand to demonstrate the maximum potential of the production line (Heimbach, Grahl & Rothlauf 2012). In order to do so, the model is set in an inter-arrival time of 0.5 units of time and 90% utilization, and an unlimited space to store the finished goods after being processed by the last workstation. This ensures that a work is released to the system every 0.556 units of time, which is considered enough to generate WIP to feed the system for the entire run length. The inter-arrival time is set at constant. This input is fixed for every model built with different combinations of experimental variables.
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Kanban pull system structure is modeled by assigning pull system configurations into the C11, C22, and C33. In the same way, the CONWIP pull system structure is represented by allocating pull system configurations into C31, while the same is done to the POLCA pull system structure by assigning pull system configurations into C21, and C32. These three pull system structures are chosen to analyze how their different coupling levels affect line performance. The rest of the control loop in the model that does not have a certain configuration are given an unlimited configuration to nullify its restriction.
W1 B1 W2 B2 W3 B3 C11 C21 C31 C22 C32 C33
Figure 4.1 Generic pull system structure (Gaury, Kleijnen, and Pierreval, 2001)
Pull system configuration level defines the WIP limit, which affects the state-dependent behavior. A range from 1 to 10 with the increment of 1 is implemented to observe the effect of increasing the configuration level to line performance.
In implementing the pull system configuration, identical configuration level is assigned for each control loop, except the loops with unlimited configurations. For example, based on the 3 workstation model above, a Kanban structure with the configuration level of 5 is modeled by assigning control loops C11, C22, and C33 with an identical WIP limit of 5. A CONWIP structure with a configuration level of 5 is modeled by assigning a WIP limit of 5 in control loop C31, while POLCA is modeled by assigning WIP limit of 5 in control loops C21 and C32. Configuration of a control loop within a larger control loop is restricted by the larger control loop. For example, if control loop C31 is assigned with a configuration of 5, control loop C22 can only have 5 WIP in maximum even though it is assigned with a configuration higher than 5.
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configuration for the 3 workstations and 5 workstations setting, respectively. Having the highest configuration of 10 in the experimental design makes the chosen numbers that replaced the unlimited configuration to not restrain the WIP movement. Hence, the simulation model can still be represented accurately.
Line length of 3 workstations is chosen because it is the shortest line length that enables a model to observe different processing time adjustment for workers at the end of the line and the interior of the line. Line length of 5 workstations is selected to represent the longer line setting for it is considered to be sufficient to examine the impact of extended line length, without excessive use of time to execute the simulation.
According to Hillier and Boling (1966 cited by Heimbach, Grahl & Rothlauf 2012) work allocation pattern is applied based on the degree of unbalance, or δ. With N as the number of workstations and wi is the processing time of workstation i, the degree of
unbalance is calculated as:
∑ | |
Three different work allocation patterns are used as the experimental input. A balanced work allocation pattern has a δ of 0, while both of the bowl and reverse bowl pattern is assigned with a same δ value of 1.04. The study of Heimbach, Grahl and Rothlauf (2012), shows that an unbalance degree above 1 is enough to give a distinct effect to line performance.
For each different line length, table 4.2 shows the distribution of the work allocation pattern of initial average worker processing time according to equation 3.
Line length Work Allocation Pattern
Average worker processing time (unit of time) First Workstation Middle Workstations Last Workstation 3 Reverse Bowl 0.74 1.52 0.74 Balanced 1 1 1 Bowl 1.26 0.48 1.26 5 Reverse Bowl 0.74 1.173 0.74 Balanced 1 1 1 Bowl 1.26 0.82667 1.26
Table 4.2 Worker processing time for different line length
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magnitude of state-dependent behavior, 0.5 for the moderate level and 1 for the maximum effect of state-dependent behavior.
The performance of each scenario is based on the efficiency of the pull system simulation model over the state-independent push system with a balanced work allocation pattern and equal line length. This rate is obtained through the following calculation:
A result with an efficiency rate lower than 1 means that the design of the state-dependent pull system performs lower than a push system setting used as the benchmark, while efficiency rate more than 1 means the opposite.
4.2 Simulation Setup
Five different experimental input variables are implemented into the basic simulation model. To conduct a full factorial design of all levels in the experimental input, 540 unique scenarios are run. Each of the scenarios is simulated and the results are analyzed to understand the impact of each experimental variable, focusing on pull system structure and configuration to line performance.
To obtain accurate data, appropriate simulation warm-up period, replications, and run length have to be decided carefully. A state-independent push system is used instead of the state-dependent pull system model in calculating the setup, because a model with higher variation needs a longer period to reach the steady state. Benchmarking the simulation setup for all scenarios to the model with the most variation is considered the safest decision to produce accurate simulation results.
A warm-up period is needed to prevent inaccurate data collection that happens during initialization bias (Robinson 2004:142). To calculate the appropriate warm-up period for the simulation, Welch’s Method is used (Heidelberger & Welch 1983). The Welch’s Method is used to calculate the warm-up period for both settings of line length 3 and 5 workstations, and the longer period between the two is selected. 600 units of time are selected and implemented for each model with different line length.
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obtain a better accuracy. Using the state-independent push system model with line length of 3 and 5 as the input, a confidence interval method described in Robinson (2004:154) determined that 4 replications are enough to achieve a 95% confidence interval. Graphical method is used to decide the run length for each of the simulation replication (Robinson 1995). As the result, 900 units of time is decided to be a sufficient run length for providing accurate simulation result. The calculation of each warm-up time, run length, and replications can be found in Appendix C.
4.3 Simulation Model Validation
The result of the simulation model is compared with the result of previous state-dependent model by Powell and Schultz (2004), which is used as the foundation for the current state-dependent model.
Figure 4.2 Efficiency on different speedup constants
The result produced by the model has similar interaction between speedup constant and line performance with the result produced by the past model (figure 4.2), even though the model used in this study has a slightly higher efficiency. This higher performance is caused by a different mechanism of processing time adjustment. Powell and Schultz (2004) modeled the processing time adjustment based on Markov models, while the current study adapted the mathematical model proposed by Heimbach, Grahl and Rothlauf (2012). Adjusting processing time based on the different state of the system is less sensitive compared to a mathematical model that continuously adjusts according to the slightest changes in the system.
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Eff ic ie n cy Speed up constant (f)
16 4.4 Simulation Results
The explanation of each simulation result in this section is done according to each of the experimental variables. The impact of pull system structures and pull system configurations to line performance under state-dependent behavior is outlined first, followed by the effect of work allocation patterns and line lengths. Most of the results shown to study the impact are taken from 3 workstations instead of 5 workstations to simplify and give a clearer view of the effect. The complete summary of the simulation result can be found in Appendix D.
4.4.1 Structure, Configuration, and Speedup Constant
Figure 4.3 Efficiency of each structure on increasing configuration
It can be observed in the graphs in figure 4.3 that the increase in configuration also increases the line performance, with a diminishing rate of increase. The slope of the graph shows that lower configuration induces higher increase in line performance, compared to the higher configuration. The effect on production performance resulting from the increase of the speedup constant differs among structures. This different increase rate shows that line performance of a pull system structure might reach an optimal level at higher pull system configurations.
To understand how different pull system structures affect line performance, the 3 different structures are compared. However, it is not fair to directly compare the line performance of the different pull system structures at the same configuration level. In 3
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workstations settings, a configuration of 5 in CONWIP structure with 1 control loop has the maximum WIP of 5. POLCA structure with the same configuration level allows a maximum of 10 WIP, because there are 2 control loops that are assigned with configuration of 5 in each of the control loops. A Kanban structure that has 3 control loops has a maximum of 15 WIP in the production line.
In order to make an equal comparison, a level of 6 maximum WIP is used. The line performance of the Kanban structure outperforms CONWIP and POLCA (table 4.3). The gap of the line performance between the different structures gets wider as the effect of state-dependent behavior gets stronger.
Speedup constant CONWIP (Configuration = 6, Max WIP = 6) POLCA (Configuration = 3, Max WIP = 6) Kanban (Configuration = 2, Max WIP = 6) 0.1 0.80 0.72 0.85 0.5 0.94 0.83 1.04 1 1.12 1.03 1.33
Table 4.3 Efficiency of different structures under the same maximum WIP
18 4.4.2 Structure, Configuration, and Work Allocation
Figure 4.4 Production line efficiency under different work allocation pattern
19
According to figure 4.4, the line performance of different structures tends to behave similarly under the influence of different work allocation patterns. Under low speedup constant, balanced pattern works better than the bowl and reverse bowl pattern. But, the production performance of the reverse bowl pattern slowly outperforms the bowl pattern along the increase of speedup effect, and finally tops the other patterns on the highest speedup constant.
Similar results are also shown by Heimbach, Grahl and Rothlauf (2012) in comparing the best work allocation pattern with different speedup constant on low configuration settings. On low and moderate speedup constant, the bowl shaped work allocation pattern and the balanced line works best. As the speedup constant increases, reverse bowl work allocation pattern becomes the best.
Work Allocation Pattern Speedup Constant CONWIP (Configuration = 6, Max WIP = 6) POLCA (Configuration = 3, Max WIP = 6) Kanban (Configuration = 2, Max WIP = 6) Reverse Bowl 0.1 0.69 0.63 0.71 0.5 0.91 0.73 0.95 1 1.16 0.91 1.32 Bowl 0.1 0.72 0.69 0.79 0.5 0.86 0.84 0.95 1 1.05 1.06 1.24
Table 4.4 Efficiency of different structures under the same maximum WIP
20 4.4.3 Structure, Configuration, and Line Length
Figure 4.5 Efficiency on different line lengths
21
22 5 Discussion
The results demonstrated in the previous section reveal that difference in pull system structures and pull system configurations play a role in affecting line performance. Still, the experimental design used in this study only shows a limited view on the effect. In this section, further analysis is done on the effect of pull system structure and pull system configuration on line performance, and their implications on other pull system designs.
5.1 Pull System Configuration
The diminishing rate of line performance increase from increasing the configuration level indicates that there might be an optimal performance level. The different rate of increase also shows that a possibility of a certain structure might outperform the other at a higher configuration level. To address this issue, additional simulations in the higher configuration for each pull system structure are done.
Figure 5.1 Efficiency on excessively higher pull system configurations
In higher configuration levels, line performance of the different pull system structures seems to reach a certain level that is close to equal (figure 5.1). This shows that flooding the pull system with WIP will lead to the different pull system structures to behave similarly. This is explained by the formula used to model the processing time adjustment (Equation 1).
Assuming that the maximum capacity of each buffer used as the benchmark to adjust processing time is the pull system configuration, putting a large number as the capacity will
23
bring the average processing time of the system to almost half of the initial average processing time. The first station will work half of the average initial processing time since the large capacity makes the model treat the downstream buffer as empty and has to be filled. On the other hand, the last station will work at the normal processing time because the large capacity leads to the model behave as if there is only a very small number of WIP queuing in the buffer. Meanwhile, the middle workstations are having a combined effect of the previous two assumptions.
The result of the 5 workstations shows a decreasing line performance in higher pull system configuration levels, which does not happen to the 3 workstations setting. This happens due to the high variation in longer line length (Conway et al. 1988). More stages allow more variability to happen, which decreases the effect from state-dependent behavior. When the adverse effect of variability is stronger than the benefit of state-dependent behavior, increasing the configuration will decrease line performance instead of increasing it.
Increasing the buffer capacity of the pull system excessively in the real world would transform the pull system into a push system. Workers that are initially aware of the buffer state will cease to be concerned with the state when the buffer limit is too high to be noticeable, and return to their initial average processing time. The model used in this study has not yet facilitated this diminishing effect of state-dependent behavior that occurs when buffer capacity increases. To be able to incorporate this effect and create a more accurate processing time adjustment model, supporting empirical data would be needed.
5.2 Pull System Structure
24
Figure 5.2 Average processing times and average WIP of CONWIP, POLCA, and Kanban in balanced work allocation
The smaller the area of a control loop, the more sensitive it gets to processing time variability. Under state-dependent behavior, this occurrence increases the frequency of processing time adjustment which minimizes processing time variability (Powell and Schultz, 2004). This effect is less emphasized in the CONWIP and the POLCA which have less control loops in their structure. The CONWIP structure does not strictly limit the middle workstation, while the POLCA structure limits it by controlling from the beginning of the first workstation. This difference in structure creates a higher processing time of the middle workstation in CONWIP and POLCA structure, because of the lagged adjustment of the processing times variability.
Powell and Schultz (2004) mentioned in their study of a single Kanban structure production line, that the middle workstation would have the most speedup effect of state-dependent behavior since it is affected by both the upstream and downstream buffer. The exact result is obtained from the Kanban structure in this study, while other pull system structures have different processing time distribution. This makes it reasonable to implement a certain work allocation pattern according to the average processing time distribution, which is a reversed bowl pattern in the case of Kanban pull system structure.
Beside processing time distribution, different pull system structures have different WIP level distribution among the buffers. The simulation results show that POLCA has the lowest performance, however, it also has the lowest average and most balanced WIP level in each buffer compared to the other structures. This fact may not be interesting in the case that
0.00 0.50 1.00 1.50 2.00 2.50 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 Avg. processing time workstation 1 Avg. WIP in Buffer 1 Avg. processing time workstation 2 Avg. WIP in Buffer 2 Avg. processing time workstation 3 A ve rag e WI P in B u ff e r Pr o ce ssi n g tim e
CONWIP Processing Time POLCA Processing Time Kanban Processing Time
25
only throughput is considered as the performance measure. But, WIP is an important measure for a pull system because preventing WIP explosion and reducing WIP level is one of the most important features of pull system (Hopp & Spearman 2004).
5.3 Work In Process
It is difficult to monitor the average WIP directly from the simulation model. However, the average WIP of the simulation model can be obtained through Little’s law (Hopp and Spearman 2008:239) with the formula:
This method of calculating average WIP is less accurate than direct measurement because of the variation in throughput and cycle time. Throughput in this calculation is the average output per unit time, while cycle time is the average time from when a job is released into the station until it exits (Hopp and Spearman 2008:239). In this model, the cycle time is calculated after a work enters the pull system structure and becomes a WIP.
Speedup constant CONWIP (Configuration = 6, Max WIP = 6) POLCA (Configuration = 3, Max WIP = 6) Kanban (Configuration = 2, Max WIP = 6) 0.1 5.98 4.21 6.13 0.5 6.05 4.37 6.55 1 6.00 4.77 6.89
Table 5.1 Average WIP with equal level of maximum WIP
Table 5.1 shows the POLCA structure has the lowest average WIP, while CONWIP and Kanban structures used the maximum WIP on average. This means that the Kanban and CONWIP structures are blocked at most of the time during the process but still manage to perform efficiently. The fact that Kanban has slightly higher WIP also contradicts with the earlier finding by Khojasteh-Ghamari (2009) that claims Kanban has a better WIP minimization ability in a balanced work allocation pattern in state-independent settings.
26 Speedup constant CONWIP (Configuration = 6, Max WIP = 6) POLCA (Configuration = 3, Max WIP = 6) Kanban (Configuration = 2, Max WIP = 6) 0.1 0.134 0.171 0.139 0.5 0.155 0.190 0.159 1 0.187 0.216 0.193
Table 5.2 Production line efficiency relative to their average WIP
From the result in table 5.2, POLCA has the highest throughput efficiency over average WIP compared to Kanban and CONWIP. It can be said that POLCA is the best structure to use WIP efficiently to produce throughput under state-dependent behavior.
This is a discovery of one out of hundred different possible pull system structures. Through the generic structure proposed by Gaury, Kleijnen and Pierreval (2001), further research on different pull system structures and configurations under state-dependent behavior can discover other optimal pull system designs.
6 Conclusion
Through the simulation, analysis, and discussions, the objective of the research has been achieved. This study has done its intended contribution, although still limited. These limitations are considered as an insight for future research in state-dependent behavior.
6.1 Conclusion
Aiming to provide a better understanding of pull system design under the influence of state-dependent behavior, this study has been done to answer the initial research question:
What is the impact of pull system structure and configuration on line performance given state-dependent behavior? There are two main findings that answer the research question directly.
Pull system structures with tighter coupling effect have more benefit of increasing line performance compared to other pull system structures with loose coupling. However, tighter coupling means more sensitivity to variation, which means that it is more prone to line performance decrease in longer line length.
27
processing times. Pull system structures with tighter coupling are more prone to experience line performance decrease on longer line length, because of the higher sensitivity to workflow disturbance from variations.
Aside from pull system structures and pull system configurations, this study also discovered several side findings on other aspects of pull system design. These side findings provide further explanation on the main research question and complement the study.
Pull system structure under state-dependent behavior has a self-balancing mechanism (Powell & Schultz 2004), but also alters the initially balanced work allocation pattern into an imbalanced allocation pattern. Allocating higher workload to workstations with faster work processing time, and lower workload to the workstations with slower processing time, will result in higher line performance.
Analyzing the average WIP shows that different pull system structures have different performance in minimizing WIP under state-dependent behavior. The POLCA structure has the highest line performance-to-average WIP ratio compared to other pull system structures, showing that it has better capability to minimize WIP usage while efficiently processing it into finished goods.
6.2 Recommendations
The Kanban pull system structure provides the best performance under state-dependent behavior. On the other hand, the POLCA pull system structure is one example that provides both sufficiently high throughput compared to the push system, and low average WIP level.
It is more feasible for management to manipulate the pull system structures and configurations compared to manipulate the length of the line or work allocation pattern in order to achieve higher line performance. Pull system structures and pull system configurations have the capability to distribute workload. Designing the pull system production line to distribute a higher workload to faster workstations, and lower workload to slower workstation, will result in higher line performance.
28 6.3 Limitations and suggestions for future research
Cost efficiency can be used instead of throughput to measure line performance, which is able to incorporate important aspects of a production system. Designing a cost effective pull system does not only focus in the capability to provide a high throughput. The capability of a pull system to minimize WIP is an important part that has to be paid attention to, to minimize operating expense.
From thousands of different possible pull system structure, only three structures are studied in this research. These other possible structures might be able to provide more cost efficient pull system design than the Kanban, POLCA, and CONWIP pull system structures. On the other hand, non-identical configuration between control loops in a production line should also be considered in future research to accommodate workload distribution with varying intensity. To perform a study with a vast search space, a heuristic method is needed to perform the simulation effectively. Evolutionary algorithm that is used in the study by Gaury, Kleijnen and Pierreval (2001) is an example of a heuristic method with the capability to efficiently search the optimal result.
The state-dependent behavior model that is used to adjust workers’ processing time has not completely incorporates the propensity of decreasing state-dependent behavior effect on higher buffer capacity. Increasing the buffer capacity of a pull system would disproportionately reduce or even erase the state-dependent behavior effect, and alters the pull system into a state-independent push system. This further development of the model has to be based on concrete empirical research in a real production system.
The pull system model should facilitate stochastic inter-arrival times. In most industries, order does not come at a constant rate, and this increases the variation in the system even further. On the other hand, the processing time of each workstation should be distributed with a Coefficient of Variation (CV) around 0.35, to represent the actual variations of a human worker according to an empirical study (Schultz et al. 1998).
29 References
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31 APPENDIX A: WIP Movement Flowchart
The movement of the WIP in the simulation model is coded into the simulation software according to the following flowchart. Pull system structures and pull system configurations affect the WIP movement through the number of cards in every stage of the movement.
Start
WIP
Any card required to move to the next workstation ?
Wait for the required card to be available
YES Is the required card available ?
YES NO
NO
Wait in the buffer until workstation ahead becomes available
NO Is the workstation ahead available ? YES
Move to workstation ahead and start processing according to the processing time adjustment model
YES Is this the last workstation in
the line ?
Any attached card that has to be released ? Release card
YES
End Block the current machine until the next buffer is availavle
NO Is the next buffer available?
Move to the next buffer
YES Attach the required card
NO
NO
32
APPENDIX B: Workers processing time adjustment model
The processing times of each workstation in the simulation model is coded according to the following flowchart. Initially, the WIP is processed according to the initial state of the buffer before the processing starts. During the process, the state of the buffers is continuously monitored, and adjustments are made to the remaining processing time for every change of WIP level in the upstream or the downstream buffer.
Start
Mean processing times
Is the downstream buffer in full capacity?
YES
(C-ci,i+1) = 0
NO
Is the upstream buffer empty?
(ci-1,i)/C = 0 YES
NO
Process inventory according to the following formula:
wiadj =wi – f * (wi /2) * ((ci-1,i)/C)- f * (wi /2) * ((C-ci,i+1)/C)
Is there a new WIP entering the upstream buffer ? YES
Adjust remaining processing time into wi+1rem,adj =wi+1rem -f * (1/C)*wi+1rem
NO
Is there a WIP leaving the downstream buffer ?
NO
Adjust remaining processing time into wirem,adj =wirem -f * (1/C)*wirem
NO
End
Has the workstation finished processing?
YES
YES
33
APPENDIX C: Warm-Up length, Replication, and Run Length
In calculating the required warm-up length, replications, and run length, a period of 60 units of time is used. The average result of each period is recorded and used as the data to calculate the required warm-up length, replications, and run length.
Warm-up Length Calculation for 3 Workstations
Figure.Appendix 3 Welch’s method calculation result for 3 workstations
A window of 5 in the Welch’s method calculation is implemented to show the appropriate length for the warm-up period. 10 periods are considered to be enough to ensure an accurate simulation result in a steady state.
Number of Runs Calculation for 3 Workstations
Replication Throughput Cumulative
mean Standard deviation 95 % Confidence interval Lower interval Upper interval % deviation 1 58.82 58.82 2 59.93 59.37 0.55 54.42 64.33 8.35% 3 60.41 59.72 0.66 58.07 61.37 2.76% 4 60.93 60.02 0.77 58.78 61.26 2.06% 5 61.13 60.24 0.82 59.22 61.27 1.70% 6 58.13 59.89 1.08 58.75 61.03 1.91% 7 61.03 60.05 1.08 59.05 61.06 1.67% 8 62.65 60.38 1.32 59.27 61.49 1.84% 9 59.17 60.24 1.30 59.24 61.25 1.67% 10 62.31 60.45 1.38 59.46 61.44 1.64%
Table.Appendix 1 Confidence interval calculation result for 3 workstations
Through a confidence interval method, 3 replication is decided to be sufficient, because the result does not deviate higher than the 5% limit for longer replications. 10 replications are done to produce the required calculation.
34 Run Length Calculation for 3 Workstations
Replication 1 Replication 2 Replication 3
Period Result Cum.mean
average Result Cum.mean average Result Cum.mean average Convergence 1 49 49 92 92 94 94 91.84% 2 56 52.50 52 58.42 62 65.69 25.13% 3 63 56.00 66 59.50 56 63.83 13.98% 4 60 57.00 66 59.88 50 62.51 9.67% 5 66 58.80 44 59.15 60 61.53 4.64% 6 57 58.50 54 58.71 56 60.75 3.84% 7 63 59.14 61 59.04 74 61.10 3.49% 8 61 59.38 52 58.85 56 60.65 3.06% 9 55 58.89 63 58.86 57 60.41 2.64% 10 48 57.80 63 58.60 66 60.24 4.22% 11 64 58.36 52 58.56 51 59.93 2.68% 12 48 57.50 57 58.19 60 59.61 3.67% 13 59 57.62 64 58.35 80 59.93 4.02% 14 49 57.00 44 57.75 50 59.33 4.09% 15 81 58.60 61 58.36 67 59.72 2.34% 16 56 58.44 65 58.45 59 59.70 2.16% 17 58 58.41 53 58.33 61 59.59 2.15% 18 64 58.72 57 58.42 59 59.58 1.98% 19 55 58.53 66 58.49 70 59.69 2.04% 20 59 58.55 58 58.50 62 59.66 1.99%
Table.Appendix 2 Run length graphical method calculation results for 3 workstations
Figure.Appendix 4 Run length graphical method calculation graph for 3 workstations
In the graphical method, convergence level less than 3% is chosen instead of 5% to ensure accuracy of the data. 15 periods or 900 units of time are considered sufficient since the convergence level remains at the same even for a longer time period.
35 Warm-up Length Calculation for 5 Workstations
Figure.Appendix 5 Welch’s method calculation result for 5 workstations
Using the same window value to calculate the length of the warm-up period for the 5 workstation setting, 10 periods of time are considered stable to provide an accurate simulation result.
Number of Runs Calculation for 5 Workstations
Replication Mean time in system Cumulative mean Standard deviation 95 % Confidence interval Lower interval Upper interval % deviation 1 59.97 59.97 2 60.20 60.08 0.11 59.05 61.12 1.73% 3 57.12 59.10 1.39 55.62 62.57 5.88% 4 58.44 58.93 1.24 56.95 60.91 3.36% 5 59.61 59.07 1.14 57.65 60.49 2.41% 6 58.97 59.05 1.04 57.95 60.15 1.86% 7 60.07 59.20 1.03 58.24 60.15 1.61% 8 60.20 59.32 1.02 58.47 60.18 1.44% 9 59.23 59.31 0.96 58.57 60.05 1.25% 10 61.66 59.55 1.15 58.72 60.37 1.39%
Table.Appendix 3 Confidence interval calculation result for 5 workstations
Based on this calculation, 4 replications are needed to provide accurate results in simulation with a 5 workstation setting. It is decided to implement 4 replications for both the 3 and 5 workstations, assuming that more replications will provide a more accurate data.
