Exploring the applicability of Kanban in high variety environments
A simulation study in the manufacturing industry
Andela, H.J. (Hessel) University of Groningen
MSc Technology & Operations Management June 26, 2017
Exploring the applicability of Kanban in high variety environments
A simulation study in the manufacturing industry
University of Groningen Faculty of Economics and Business
Master of Science in Technology & Operations Management
June 26, 2017
Andela, H.J. (Hessel) Netelbosje 2 9747AE Groningen h.j.andela@student.rug.nl Student number: S2610949
Supervisor University of Groningen: Dr. J.A.C. Bokhorst Co-assessor University of Groningen: N. Ziengs MSc
Word Count: 12026
Preface
This master’s thesis is the final part of my master’s study in technology and operations management. I would like to thank my supervisor, Dr J.A.C. Bokhorst, for his significant support during the completion period. Supervision meetings were very helpful for setting up a clear structure for the thesis. Furthermore, I would like to thank Dr Bokhorst for his helpfulness and the time he invested to support me during the development of the simulation model. I would like to thank my co-assessor, Mr N. Ziengs MSC, in particular, for his input during the research proposal.
I am grateful to (confidential), my supervisor at the case company, for thesis guidance. I would also like to express my thanks to all the employees of the case company who contributed to this research, especially (confidential), (confidential), (confidential) and (confidential).
Conversations with them assisted greatly in my development of an effective model and my analysis of the results.
Hessel Andela
19 June 2017, Groningen
Content
Preface ... I List of Tables ... III List of figures ... IV Abstract ... V
1. Introduction ... 1
2. Theoretical background... 4
2.1 High variety environments ... 4
2.2 Shared resources ... 5
2.3 Production levelling ... 6
2.4 Kanban ... 9
2.5 Relationship between Kanban, high variety and shared resources ... 11
2.6 Conceptual model ... 12
3. Case description ... 14
3.1 Production department ... 14
3.2 Production control system ... 14
3.2.1 Kanban board (1) ... 15
3.2.2 Production process (2) ... 17
3.2.3 Inventory, retrieval board and internal customer (3, 4, 5) ... 17
3.3 Production machine ... 17
3.4 Problem description ... 17
3.5 Differences with theory ... 18
4. Methodology ... 19
4.1 Research design ... 19
4.2 Experimental design ... 19
4.3 Data collection ... 20
4.4 Data analysis ... 21
4.5 Assumptions ... 22
4.6 Simulation model ... 23
4.7 Model validity ... 24
4.8 Experimental Setting ... 25
4.9 Output analysis ... 26
5. Results ... 28
5.1 Interaction effect MANOVA ... 28
5.2 Backorders ... 29
5.3 Changeovers ... 34
5.4 WIP ... 36
5.5 Correlation variables ... 38
6. Discussion ... 39
6.1 Key results and theoretical implications ... 39
6.2 Practical implication ... 40
6.3 Limitations and further research ... 41
7. Conclusion ... 42
References ... 43
Appendix A Simulation Framework ... 46
Appendix B: Distribution Calculation ... 52
Appendix C: Simulation description ... 56
Appendix D Warm up period ... 61
Appendix E Replications ... 64
List of Tables
Table 1 Experimental design ... 20Table 2 Simulation model ... 26
Table 3 Durbin-Watson test ... 27
Table 4 Significance levels ... 28
Table 5 Correlations performance criteria... 38
Table 6 Model scope ... 49
Table 7 Level of detail ... 50
Table 8 Data requirements ... 51
Table 9 Valid distributions ... 53
Table 10 Deviation iteration 1 ... 54
Table 11 Deviation iteration 8 ... 54
Table 12 Minimal number of replications ... 67
List of figures
Figure 1 Non-levelled initial state ... 7
Figure 2 fixed repeating daily sequence ... 7
Figure 3 Formula EPEI calculation ... 8
Figure 4 Formula Kanban calculation ... 10
Figure 5 Interval and lead time ... 11
Figure 6 Conceptual model ... 13
Figure 7 Schematic overview Kanban... 14
Figure 8 Kanban board ... 15
Figure 9 EPEI calculations case company (fixed interval) ... 16
Figure 10 Calculation method case company... 16
Figure 11 General overview simulation ... 23
Figure 12 Screenshot simulation model ... 24
Figure 13 Backorders (variety) ... 29
Figure 14 Backorders (variety * interval) ... 30
Figure 15 Backorders (variety * Kanban) ... 30
Figure 16 Backorders (variety * interval * Kanban) ... 31
Figure 17 Backorders (variety * interval * sequence) ... 32
Figure 18 Backorders (variety * Kanban * sequence) ... 33
Figure 19 Changeovers (variety) ... 34
Figure 20 Changeovers (variety * interval) ... 34
Figure 21 Changeovers (variety * Kanban) ... 35
Figure 22 Changeovers (variety * interval * Kanban) ... 35
Figure 23 WIP (variety) ... 36
Figure 24 WIP (variety * interval) ... 36
Figure 25 WIP (variety * Kanban) ... 37
Figure 26 WIP (variety * interval * Kanban) ... 37
Abstract
Over the last ten years, changes in customer demand, including expectation of a greater variety of products, have meant that manufacturers must change their production strategies towards make-to-order production. Shared resources are often used for producing products cost- efficiently and to create more flexible production. Kanban is one of the production control systems that is frequently used in the manufacturing industry, because of its simplicity. The co- operation between Kanban control and shared resources demonstrates some limitations in practice, because lead times are required to calculate the number of Kanban cards. Production levelling techniques are used to calculate the product lead time for products which are produced with shared resources. Those lead times can only be used as an indication, because Kanban systems employ decentralized control by the employees at operational level. Operators can make decisions other than those expected in the production levelling calculation, which can cause shortages or overflow of work-in-progress (WIP). To ensure that all customers can be supplied, WIP levels are often increased, but this can overcrowd the supply chain. Many companies want to maintain the Kanban system due to the simplicity of the system and try to find a synergetic effect. This research investigates the effect of shared resources on the applicability of Kanban systems by performing a simulation study. A company has cooperated in the study, enabling the researcher to validate the simulation with a real case example. The output of the simulation shows that Kanban systems are difficult to use in high variety environments. Kanban is only applicable if one of the performance criteria (backorders or WIP) is less important for an organization, because a Kanban system in high variety environment creates more backorders or more WIP in comparison to low variety systems. Other control systems are better suitable in these environments.
Keywords: Kanban, shared resources, production levelling, high variety environments
1. Introduction
During the last decade, the power of customers has increased due to globalization.
Customers are more demanding as they expect greater variety in products, and have higher quality expectations (Thull, 2003). In order to be competitive in the market and to meet customer expectations, manufacturers have to produce more variety of products (Ramdas, 2003).
To cope with the increased variety, manufacturers have to find a trade-off between the amount of dedicated and shared resources (Becker & Stern, 2016). Increasing the product variety slightly increases the total demand due to price elasticity (Desmet & Parente, 2009), but the demand per product is lower if the product has the same functionality (Chang & Wang, 2007). The lower demand per product type makes shared resources more efficient to produce, because dedicated resources have a higher risk of lower utilization when variety increases (Hopp & Roof, 1998). Shared resources produce multiple product families and enable manufacturers to produce low demand in a cost-efficient way. Recent research has shown that the use of shared resources is growing in the industry in order to match developments in the market (Van Donk & Van Der Vaart, 2005).
The use of shared resources in supply chains can have some disadvantages. Most shared resources are coping with changeovers which makes planning more difficult. The inconvenience arises from the fact that changeovers result in more unpredictability about the availability of the machine. Besides that, some shared resources can only produce in a specific sequence and require backward planning methods, because sequences are fixed and make machines less flexible (Chopra & Sodhi, 2014; Hu, Zhu, Wang, & Koren, 2008). Not all changeovers are a problem for the performance of a supply chain. Only when utilization of the machine is above 85%, performance is negatively affected in terms of throughput and flexibility, because changeovers affect the machine availability (Hopp & Spearman, 2008).
It is argued that more variety of products on one machine leads to more changeovers, but in order to prevent changeovers from taking up large parts of the total available time, production levelling is required (Bicheno, Holweg, & Niessmann, 2001). Production levelling techniques calculate optimal product groups and run sizes with the purpose of lowering the number of changeovers and increasing the availability of machines (Hopp & Roof, 1998;
Matzka, Di Mascolo, & Furmans, 2012). Creating run sizes with production levelling increases
the amount of work-in-progress (WIP) (Hussain & Drake, 2011). Therefore, it is important to find an optimal trade-off between the production levelling strategies and the amount of WIP.
Manufacturers have to select the right production control strategy that is in line with the external environment in order to meet customer demand and achieve best production performances (Gunasekaran, Patel, & Mcgaughey, 2004). Most manufacturers use pull production strategies that were introduced around the 1970s. Pull production strategies use the principle of pulling products through their supply chain, which means that orders are produced only when capacity is available and there is customer demand.
One of the commonly used pull production planning methods is Kanban (Stevenson, Hendry, & Kingsmany, 2005). Kanban is an inventory control system which was developed in the 1970s by Toyota (Sugimori, Kusunoki, Cho, & Uchikawa, 1977). Kanban systems work with physical cards. These cards are the triggers to start a production run and visualize the current WIP level. All cards represent a production order and the cards contain the product name, the quantity (batch size based on run length), the required workstation, and the preceding workstation. The cards are placed on a Kanban board when the product needs to be produced.(Sugimori et al., 1977). Using this Kanban board, operators can easily select which product should be produced first in a shared resource, because products with the highest number of Kanban cards (perceptual) are selected (Shingo, 1989). Kanban systems are easy to understand for operators, due to the visualization method. Furthermore, dispatching rules are not required due to decentralization of decision authority and because of the easiness to implement Kanban (Al-Baik & Miller, 2014). Many companies, therefore, want to preserve the Kanban system due to its simplicity.
The interaction between shared resources and Kanban control systems is complex, because Kanban systems show limitations in high variety environments where shared resources are used (Jonsson & Mattsson, 2003). One of the most important limitations is the overflow of WIP, because more product variety on shared resources forces manufacturers to use production levelling techniques, which only provide an indication of lead time if the calculation is combined with the Kanban calculation. Shared resources with time consuming changeovers force manufacturers to extend run sizes. Furthermore, a pull strategy requires minimal inventory levels which increase if more products are produced. By extending production run lengths, the amount of WIP and the number of Kanban cards (if the cards remain the same batch size) will increase. More cards can result in an overflow of WIP and prioritization for operators becomes
more difficult. The reason is that production levelling is planned centrally while the Kanban decisions are made in a decentralized fashion, which can cause incompatibilities in planning, since Kanban does not visualize the real demand and this can mean that decentralized decisions (Kanban) are different from centralized decisions (production levelling) (Roser, 2016). For instance, operators can prioritize product B (highest number of Kanban cards on the board), while product A is needed first by an internal customer according to the planning and production sequence of production levelling. Therefore, it is challenging for companies within a high variety environment to use Kanban (Jonsson & Mattsson, 2003). According to Jonsson and Mattson (2003), other planning methods for pull production, such as material requirements planning (MRP) or order based planning, are more applicable within high variety environments, but these control methods are more complicated and harder to maintain (Jonsson & Mattsson, 2003). The applicability of a Kanban system in high variety environments in combination with shared resources is still under examined and little research has been done on the topic (Lage Junior & Godinho Filho, 2010). Therefore, it is interesting to investigate the effects of shared resources on the applicability of a Kanban control system in high variety environments. The applicability of a Kanban system is based on the service level (successfully delivered orders).
The throughput should be as high as possible while the WIP should be as low as possible (Moeeni, Sanchez, & Vakha Ria, 1997). The applicability of a Kanban system has been tested by performing a simulation study which was based on a company situation. The study analyses the relationship between the most important performance criteria (service level, throughput, WIP) for Kanban systems. The research question of this study is as follows:
What are the effects of shared resources on the applicability of Kanban control systems in high variety environments?
The next chapter describes the theory used in this research and determines relationships between production levelling and Kanban. It enables this research to develop a conceptual model. Based on the conceptual model, experimental settings for the simulation could be determined. The third chapter describes how the research was undertaken. To give a better understanding of the simulation, a case description is outlined in chapter 4. The results are described in chapter 5, and this is followed by the conclusion and discussion. Additionally, detailed information concerning specific setups is presented in the appendices.
2. Theoretical background
The theoretical framework provides more insight on the theory used for this study. The first section describes the definition of a high variety environment and its characteristics. One of the characteristics is that manufacturers are compelled to work with shared resources. The second section describes the characteristics of shared resources. Shared resources must cope with changeovers and this forces manufacturers to use production levelling to calculate an optimal balance between the number of changeovers and the amount of WIP. The theory behind production levelling is described in the third section. Once the optimal levels are calculated, operational control systems are required to produce the products. One of the commonly used control systems is Kanban. The fourth section explains how Kanban works and what the advantages and disadvantages are. The fifth section explains the relationship between production levelling and Kanban, and this is followed by a conceptual model presented in the final section of this chapter.
2.1 High variety environments
Due to globalization, customers have greater opportunities to buy a product from a range of many different organizations, which has increased the power of the customer causing higher expectations for products and services (Thull, 2003). Research has shown that customers expect more product variety, higher quality standards and prefer customizability (Thull, 2003).
Globalization presents challenges for companies, because most companies respond to customers in order to attain market share and sales. As a result, the number of similar products and competition between manufacturers has increased (Ramdas, 2003).
In order to react quickly to market changes, manufacturers are forced to change their production strategies from repetitive production strategies to make-to-order production strategies (Ramdas, 2003). Repetitive production strategies can be characterized as standardized production with often large batches and less setup times (Toni et al., 1993). Make-to-order production (MTO) is only triggered when a product is ordered by a customer and when production capacity is available in the whole supply chain. This prevents the supply chain from becoming overcrowded with production orders (Stevenson et al., 2005). The result is flexible production, which enables manufacturers to react faster to market changes and gives them the ability to increase the number of products produced. Make-to-order production is characterized by alternating products in low volume and a lot of changeovers (White & Prybutok, 2001).
When manufacturers increase the number of products in production, this does not automatically lead to more demand, because the total demand is spread over the products with the same functionality, which causes a high variety of products and low demand per product type (Desmet & Parente, 2009). The low volumes and increased variety result in more uncertainty for manufacturers, because the chance of higher fluctuations between the demands for products is increased. When manufacturers use dedicated resources, highly fluctuating demands are undesirable, because the risk of low machine utilization is likely (Hopp & Roof, 1998). To reduce the risk of low machine utilization, manufacturers switch to shared resources.
Shared resources enable manufacturers to smooth out the fluctuations from different product types which can lead to a more stabilized demand for the machine (Becker & Stern, 2016; Van Donk & Van der Vaart, 2005).
2.2 Shared resources
Shared resources are machines which can produce multiple products. An important characteristic of shared resources is that the machines must cope with changeovers, because most products have their own characteristics and require different machine settings (Hopp &
Spearman, 2008). These changeovers can affect the total available time if changeovers are time consuming (Hopp & Spearman, 2008). Changeovers do not always lead to capacity problems, because it depends on the occupation level of the shared resource. When the occupation level of a shared resource is below 85%, changeovers will not affect the performance, because the available slack time can deal with unexpected demand or unexpected changeovers (Hopp &
Spearman, 2008). Hence, there is no fixed rule concerning when changeovers may become a problem, but manufacturers must always prevent changeovers from taking up too large a part of the total available time (Hopp & Spearman, 2010).
All shared resources must cope with changeovers, but a changeover does not always require time. Changeovers only influence the performance of the shared resource when changeovers require time. The performance is negatively influenced by the duration of the changeover (Velez, Dong, & Maravelias, 2017). If a shared resource does not have changeover times, the changeover is not important to consider for planning, because this changeover does not affect the availability of the system. Hence, when shared resources have to cope with changeover times and the occupation of the machine is above 85%, changeovers should be taken into account for planning (Hopp & Spearman, 2008). Production levelling is a method to incorporate changeover time into planning and this method tries to find the optimal trade-off between the number of changeovers and the amount of WIP (Hopp & Roof, 1998; Matzka et al., 2012).
Furthermore, production levelling can stabilize the demand pattern for the machine while the real demand is highly fluctuating.
2.3 Production levelling
There are a range of different methods that manufacturers can choose from to optimise production. Fluctuation creates uncertainty and can be very costly, because demand fluctuations can result in undelivered orders, and unexpected maintenance can stack up the production (Roser, 2016). Therefore, production levelling has the purpose of balancing production by incorporating most of the fluctuation aspects of a production line (Roser, 2016). In principle, production levelling calculates a production interval which considers the amount of WIP and the number of changeovers. Production levelling assumes that products are produced in a sequence, such as ABC. The production interval is the length of one sequence. For instance, a production interval of one week means that the products A, B, and C are produced in a weekly sequence and will repeat every week.
The most commonly used method for calculating production intervals or patterns is the Every-Part-Every-Interval method (EPEI) (Guild, 1990; Matzka et al., 2012). In EPEI, a certain demand is produced in a fixed period which is determined by an EPEI calculation. This method uses a repeating sequence which is fixed and based on time and not on quantity. It splits up a total demand of a certain fixed period into pieces based on a time frame and delineates smaller cycles within that period (Furmans, 2005). For example, if manufacturers have demand information for the whole month they could decide to produce all the demanded products in one single run which results in a long cycle. With EPEI, optimal interval times can be calculated by checking the required changeover time in comparison to the total available time. This can result in an interval of, for example, one week (smaller cycle). This means that every week a quarter of the total demand for the fixed period chosen is produced. This results in a lower inventory on hand and will stabilize production. However, there can be disadvantages if an EPEI is used, if changeovers are required and need to be taken into consideration, when the interval can become very long (Matzka et al., 2012). If manufacturers want fewer changeovers, long EPEI intervals are desired.
There are two ways for EPEI, Non-levelled initial state creates large batches of products and reduces the number of changeovers. This method is interesting when a shared resource must cope with a lot of different products with relatively long changeover times (Velez et al., 2017).
The other method is fixed daily repeating sequence. With this method, an optimal number of
products in a day is being produced. The weekly batch is divided over the available days. If manufacturers want to lower their amount of inventory this can be an interesting method to use, although this method causes a lot more changeovers than the non-levelled initial state method.
Figure 1 shows the production pattern of a non-levelled initial state and figure 2 the fixed repeating daily sequence.
The demand and number of products for the fixed period (one week) is the same in both figures. In figure 1 the interval equals the fixed period and requires seven changeovers. The average WIP is half of the weekly demand. Figure 2 produces the average daily demand of all products and this results in a lower WIP (1/10 of the weekly demand), but creates a lot more changeovers. The number of changeovers is five per day when using a daily interval. As a result, the daily interval results in 50% less WIP, but increases the number of changeovers approximately by 3.5 times.
Figure 1 Non-levelled initial state
Figure 2 fixed repeating daily sequence
To calculate the optimal interval (non-levelled or fixed repeating), the formula for the EPEI below can be used and is shown in figure 3. The optimal interval means the best trade-off between the number of changeovers and WIP. The formula only calculates the length of the interval of the sequence (Guild, 1990). Once the length of the interval is clear, the number of products can be calculated within that production interval.
Calculating EPEI can be very useful, as mentioned above. However, researchers have contradictory opinions concerning the usability and effectiveness of production levelling in general. Some researchers state that production levelling is essential and helpful to achieve a superior performance (Bohnen, Maschek, & Deuse, 2011; Matzka et al., 2012), while other researchers find that production levelling makes production systems more complex, because in normal operations manufacturers have to deal with inconsistencies, such as lack of material or machine failure (Roser, 2016). If a machine failure occurs, the EPEI should be recalculated which will cost a lot of time. Furthermore, EPEI is not able to deal with demand changes within the fixed period, because the intervals are calculated for a fixed period to level out the total demand. Demand changes can result in totally different interval levels. As a result, the chance of backorders is increased when demand patterns are subjected to considerable fluctuation. Due to all these constraints, an operational planning strategy is helpful (Bohnen et al., 2011; Zhu, Hu, Koren, Marin, & Huang, 2007).
𝐸𝑃𝐸𝐼 𝑖𝑛 𝑑𝑎𝑦𝑠 = ∑ 𝐶𝑂
(T ∗ A) − ∑(𝐷 ∗ 𝑃) 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝑝𝑒𝑟 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙 = D ∗ EPEI in days
CO = Changeover time per part in hours T = Daily time available in hours (Total time in a day) A = Availability time of the machine (Availability rate of machine) D = Daily demand for each product (Demand in period/available days in period)
P = Production time for each product (Time to produce one product)
Figure 3 Formula EPEI calculation
2.4 Kanban
Production control systems are production strategies which enable manufacturers to produce according to a specific method. To achieve the best performance, a production control system should fit within the external environment (Gunasekaran et al., 2004, Jonsson &
Mattsson, 2003). Before the 1970s, most companies produced products by using a push production control system. Push production is designed to produce as much as possible to achieve high machine use and often has a constant production rate which is based on expected demand (González-R, Framinan, & Pierreval, 2012; Gstettner & Kuhn, 1996). Around the 1970s, more and more companies changed their production strategy to a pull production system, because pull production control is better able to perform in high variety environments (Spearman & Zazanis, 1992). In principle, a pull production control system pulls new production orders only when capacity is available through the factory. Pull production control systems are based on the lean manufacturing philosophy. The lean manufacturing philosophy tries to eliminate the seven wastes (transport, inventory, motion, waiting, over-processing, overproduction, and defects). In order to eliminate these wastes, lean manufacturing works as much as possible with visual aspects to expose the wastes (Sugimori et al., 1977).
To control the pull production strategies, a planning method is needed. One of the commonly used pull production planning methods is Kanban (Stevenson et al., 2005). Kanban was the first pull production control system developed for Toyota in the late 1970s (Sugimori et al., 1977). Kanban control equates to the stock system of a grocery store. When products are out of stock, a signal is given to produce new products. Kanban control systems work with physical cards which makes production easier to understand and to control. The cards are the triggers to start a production run and represent the WIP. All production cards include the product name, the amount or quantity that needs to be produced, the required workstation and the preceding workstations (Sugimori et al., 1977).
A great advantage of visualizing is that companies can discover the seven wastes. The substantial difference of Kanban from traditional planning is the control method. Kanban systems are decentralized and manually controlled, while MRP systems are centralized and work automatically. The decentralization of the Kanban control system creates more flexibility for operators to select the production sequence on their own initiative (Akturk & Erhun, 1999;
Bard & Golany, 1991). Furthermore, traditional Kanban systems do not need dispatching rules, because the sequence is determined by the number of cards on the Kanban board. The physical
cards circulate through the production system in loops to control the level of WIP (Sugimori et al., 1977).
There are two types of Kanban control systems: single-card Kanban systems and dual-card Kanban systems. A single-card Kanban system makes use of one card; this card is a production order card which starts the production. This Kanban card is attached to the production order, which means that the card follows the production order. When the production order arrives at the next workstation, the Kanban card goes back to the preceding workstation. A single-card Kanban system is only suitable if the sequenced workstations are physically near to one another, as the replenishment time is short (Karmarkar & Kekre, 1989).
A dual-card Kanban production system uses two types of Kanban cards and is more complex than the single-card system. It consists of one production order card, and one withdrawal card.
The withdrawal card is the transportation card. This second card triggers the logistics department to transport the order to the next workstation in the process. The withdrawal card can only be used if the production order card is completed. Dual Kanban systems are usually applied if the preceding or next workstations have a great physical distance between them, as the replenishment time can be long (Karmarkar & Kekre, 1989).
To calculate the required number of cards, Sugimori (1977) developed a formula which is derived from Little’s Law. The number of cards in the system has a compelling effect on the performance of the system. The formula is shown in figure 4.
The formula shows that lead time is a key factor for calculating the number of required cards. The lead time is the total amount of time required to deliver the product to the (internal)
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐾𝑎𝑛𝑏𝑎𝑛 𝑐𝑎𝑟𝑑𝑠 = 𝐷𝐿(1 + 𝐴) 𝐵 Y = the total number of cards.
D = the demand in time L = Total lead time of one container
A = the container capacity B = Safety factor in percentages
Figure 4 Formula Kanban calculation
customer. This includes replenishment time, waiting time and production time (Kumar &
Panneerselvam, 2007). For a dedicated resource, it is easy to calculate the lead time of a product, because one product is produced and no changeovers need to be considered. Using Kanban on shared resources can make the calculation more complex, because it is hard to measure how the Kanban system will behave in a real situation. This makes it difficult to calculate the lead time of the products. Therefore, another solution might be to calculate a production interval. The production interval represents the lead time of the products. Figure 5 provides a better understanding of the lead time calculation with EPEI. The figure shows a production interval wherein three types of products are produced. The lines below indicate the interval for the product individually. Hence, the lead time of products corresponds with the EPEI. Thereafter, Kanban card calculation can be performed because lead time is known.
A B B C C A B B C C
Second interval First interval
Leadtime product A
Leadtime product B
Leadtime product C
Figure 5 Interval and lead time
To verify if a Kanban system performs well and is applicable in the environment, performance criteria need to be defined. Earlier research has demonstrated that a Kanban control system performs well if the amount of cards is minimized, the throughput is maximized and the WIP is minimized (Onyeocha, 2015). Furthermore, throughput rate and flow-time of Kanban cards are other significant performance indicators (Kumar & Panneerselvam, 2007).
2.5 Relationship between Kanban, high variety and shared resources
When focusing on the differences between production levelling and Kanban calculation, interesting variations can be noticed. When shared resources have changeovers and produce multiple products, production levelling is essential, while a Kanban system does not use any type of decision rules. Production levelling techniques can reduce the number of changeovers, but a lower number of changeovers will lead to longer production runs. Longer production runs lead to more WIP, because the time between the production of different types is increased.
Production levelling can work beneficially when repetitive products are produced, because
stable demand patterns do not result in significant interval changes which makes the system easy to maintain. Calculations of EPEI are less reliable in high variety environments with large fluctuations, because EPEI needs a fixed period for the calculation. If this fixed period is subject to uncertain demand patterns, the calculations are less reliable (Bohnen et al., 2011; Roser, 2016). The less reliable calculations increase the chance of backorders (not delivered to customers) or high amounts of WIP of products. Furthermore, production levelling can work counterproductively in high variety environments with low demands (Bohnen et al., 2011;
Roser, 2016).
Sequencing rules (that is, which product should be produced first) for shared resources can be important, although studies show contradictory outcomes in combination with Kanban. A simulation study shows that priority rules have a small impact on the throughput rate and WIP (Yang, 2000), while other research demonstrates that sequencing methods show a significant effect on the Kanban performance (Berkley, 1993; Berkley & Kiran, 1991). Due to these contradictory outcomes, it is useful to test how a Kanban system can work with shared resources and the associated EPEI calculations and sequencing rules, because EPEI calculates fixed sequences of production.
The combination of an increased number of card loops and higher changeover times results in an increase of the WIP (Germs & Riezebos, 2010). A high inventory level can jam the production line due to a lack of space. Furthermore, shared resources require production levelling to produce on a sustainable level, but production levelling creates a sequence while Kanban does not use a sequence. This results in extra WIP, but the effects of the relationship between Kanban and high variety environments have not previously been investigated. This study develops a simulation model to test the effects of shared resources on the applicability of a Kanban system in high variety environments. Production levelling methods and Kanban methods are incorporated in the model to show the effects. The reason for testing a Kanban control system is because this system is most accessible for the manufacturing industry due to its simplicity (Al-Baik & Miller, 2014).
2.6 Conceptual model
To create a better insight into the relationships between concepts in theory, a conceptual model was developed. The conceptual model is shown in figure 6. The model shows that in high variety environments where manufacturers are forced to use shared resources, production levelling techniques are necessary to calculate the optimal number of changeovers and
availability, but theory is not univocal about the effectivity of production levelling. The combination of production levelling and Kanban card calculation results in a negative performance, but Kanban card calculations are required to use a Kanban board.
The conceptual model shows the direct effect of shared resources on performance and the two moderating effects of Kanban and production levelling. The moderating effects were tested independently in relation to the performance of a shared resource. Furthermore, the moderators, Kanban and production levelling, were tested together to assess the interaction effect. All the relationships were tested by performing a simulation study.
High variety environment
Kanban
Production Levelling Shared resources
Leads to Performance
Figure 6 Conceptual model
3. Case description
The case description provides information about the simulated case. This chapter begins with a description of the production area and concludes with an outline of the machine that was the subject of the research. The public version is less substantive about the processes due to confidential information.
3.1 Production department
The company produces products (confidential) which all are made from raw material (confidential). Most of the sub-parts are produced at the production department. The production department is one of the first steps in the internal production process.
In total, the department has to produce high numbers different products and delivers to multiple internal customers, each with their own demand pattern. This results in high fluctuations in demand. To serve all customers, sufficient production machines are available to produce the requested parts. To simplify the structure and the planning process, the company assigned all parts to a fixed production machine. Currently 31 machines are shared resources and produce multiple products and 29 production machines are dedicated and produce one product. The number of machines producing multiple parts has grown substantially in the last year. Three years ago, only ten machines were a shared resource. In the future, more products will be introduced and more machines will become a shared resource.
3.2 Production control system
As previously mentioned, every product uses a fixed production machine, but a lot of products have multiple customers. If the order must be planned beforehand, it will be time consuming. Therefore, the production department uses Kanban due to the simplicity of the system and its minimal maintenance time. Every machine has its own Kanban board. Operators can decide which product should be produced and in which sequence. Figure 7 shows a schematic overview of the production control system at the company. The numbers correspond with the section titles below.
Inventory
Internal customer
Kanban board Retrieval board
Production process Card/Product Product
Card Card
Card
1 4
2 3 5
Figure 7 Schematic overview Kanban
3.2.1 Kanban board (1)
The Kanban board is the basis of the production control system. Figure 8 shows a picture of the Kanban board for one machine. This machine produces nine products. The board is divided in nine vertical areas, separated by a small white line and represents the Kanban for a product. Horizontally, three different areas can be distinguished: green, yellow and red. Those areas represent the release and priority of products. Retrieval cards are always placed in the green area of the specific product. When the green area of a product is occupied, then cards are placed in the yellow area or in the red area if yellow is also occupied. Production decisions are made the other way around which means that products in the red area get priority above yellow and green.
The coloured areas represent a part of the inventory and are priority indicators for operators.
The number of places per area depends on the expected demand for the current month. The expected demand per product is available in the enterprise resource planning system (ERP), but this only provides a rough estimate. The real demand from internal customers can vary somewhat in comparison to the ERP system. The company has designed their own calculating method for determining the number of Kanban cards per area and this differs from the method described in the theoretical background
Before calculations can be made, lead time for products must be determined. The company calculates the lead time by using an EPEI-based calculation method. The calculations are simplified using fixed interval levels of 40, 60, 80 or 120 hours. The company calculates the required time for every interval and uses a strict procedure. The procedure is shown in figure 9.
This sequence is undertaken for all the fixed interval levels. Thereafter, an EPEI level is selected which has a minimum of 10 hours free time to deal with unexpected failures.
Figure 8 Kanban board
Confidential
Interval demand Formula
Monthly demand/(480/
EPEI) Calculation
Product A: 10/(480/80) = 5 Product B: 20/(480/80) = 10 Legend
Available hours in month: 480 hours Selected EPEI: 80 hours
Demand product A: 30 Demand product B: 60 Changeover time (CO): 2 hours Process time: 5 hours
Calculate production time Formula
(Interval demand * process time) + CO time Calculation
Product A: 5 * 5 + 2 = 27 hours Product B: 10 * 5 +2 = 52 hours Total time = 79 hours
Freetime = 1 hour
Figure 9 EPEI calculations case company (fixed interval)
Once the lead time is known, the total number of cards is calculated. The green zone represents the average demand of the interval (lead time) or a minimal run length (described below). The yellow area is only a trigger and is one or two cards. The red area represents the safety stock. Besides this, the company has added an extra rule that a minimal run should take four production cards. This is done in order to lower the number of changeovers. For example, if the calculation of the green area is two cards, the company will change it to three cards.
Furthermore, if the green area requires three cards, then the yellow area gets one card. This gives a total four which represents the minimal run length. The formulas for each area are displayed in figure 10.
Furthermore, operators use a sequencing rule for selecting a product from the Kanban board.
Operators work from the left to the right side of the Kanban board, because this is the way in which the products are aligned, based on the shortest changeover time during colour changes.
Operators always start at the parts which were previously produced on the shared resource. For example, if the last produced product was product C, then the sequence will be: C-D-E-F-G-H- I-A-B. If the last produced product was F, then the sequence will be: F-G-H-I-A-B-C-D-E. They work as follows: first, check if cards are in the red area. If no cards are in the red area, the cards are checked in the same sequence for the yellow area. The cards are recalculated on a monthly basis. If the upcoming month requires more cards, extra cards are placed on the board. If the upcoming month requires less cards, the cards are phased out once the product is removed from the inventory.
𝐺𝑟𝑒𝑒𝑛 𝑎𝑟𝑒𝑎 (𝑚𝑖𝑛𝑖𝑚𝑎𝑙 3 𝑐𝑎𝑟𝑑𝑠) = 𝑀𝑜𝑛𝑡ℎ𝑙𝑦 𝑑𝑒𝑚𝑎𝑛𝑑
𝐼𝑛𝑡𝑒𝑟𝑣𝑎𝑙 (ℎ𝑜𝑢𝑟𝑠) ∗ 𝑇𝑜𝑡𝑎𝑙 (ℎ𝑜𝑢𝑟𝑠) 𝑚𝑜𝑛𝑡ℎ 𝑌𝑒𝑙𝑙𝑜𝑤 𝑎𝑟𝑒𝑎 = 𝐼𝑓 𝐺𝑟𝑒𝑒𝑛 𝑖𝑠 > 3 𝑡ℎ𝑎𝑛 2, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 1
𝑅𝑒𝑑 𝑎𝑟𝑒𝑎 = 𝐺𝑟𝑒𝑒𝑛 𝑎𝑟𝑒𝑎 − 𝑌𝑒𝑙𝑙𝑜𝑤 𝑎𝑟𝑒𝑎
Figure 10 Calculation method case company
3.2.2 Production process (2)
Once the operators have selected a product, all the cards of a product on the Kanban board (green, yellow and red areas) are taken into production. One card represents 1,440 products which perfectly fit on one trolley. This can result in different run lengths based on the number of cards available on the Kanban board. Changeover time differs per machine.
3.2.3 Inventory, retrieval board and internal customer (3, 4, 5)
After production, all parts are placed on trolleys. Every trolley represents one card. Once an internal customer picks up a trolley, the card is sent to the retrieval board. The retrieval board is manually checked every two hours and the operator brings the cards back to the Kanban board.
3.3 Production machine
This study simulated the most complex machine of the production department. This shared resource produces nine different kinds of products. The demand for the nine products fluctuates most in comparison to the other machines. Furthermore, this shared machine resource must deal with different internal customers. One of the customers also uses a Kanban system to retrieve orders which results in high fluctuation in demand. The machine is available for 88% of the time and has a Mean time to repair (MTTR) of 30 minutes. The machine information is derived through unstructured interviews with maintenance engineers.
3.4 Problem description
The production department copes with several problems. First, due to the increased variation, the Kanban board becomes so big that making decisions becomes harder. Secondly, the company uses its own created calculation method to calculate the number of Kanban cards for the system which has resulted in high WIP levels and space problems caused by inventory.
Third, the sequencing rule to work from left to right makes the Kanban a complex system.
The additional rules have resulted in a complex control mechanism for the company and are not sustainable for the long term. Soon, the number of products will increase and probably cause stacked and overcrowded production which makes the production selection more difficult for the operators. Furthermore, the company wants to use a sustainable control mechanism for their production department and acknowledges that the Kanban system has limitations.
3.5 Differences with theory
The company uses different methods in comparison to the theory. The company sets fixed intervals to calculate the EPEI, while Guild (1990) develops a formula to calculate an optimal interval in terms of time. The company uses fixed intervals, because all other departments use the same intervals and this ought to provide more stability in demand for the whole supply chain. Furthermore, the Kanban method in use at the company is totally different from the usual Kanban calculation. The green area calculation is based on the average demand, but is increased if the level is too low. Furthermore, the yellow area calculation is particularly strange, because this does not represent inventory but is used as a trigger. Finally, the red area uses a different method, because theoretical models use percentages for safety stock. The safety stock is calculated by taking the standard deviation of demand pattern. It is interesting to note that the company used a different Kanban calculation method a few months ago. This method calculated the safety stock by taking 15% of the average daily demand. The calculation was changed because the previous method caused a lot of backorders.
4. Methodology
This chapter describes the research design, the research method, the experimental settings, the simulation model and the approach used for analysis of the results. Furthermore, a pre- analysis is undertaken to check if the statistical tests can be plausibly used in this research.
4.1 Research design
To discover the effects of shared resources on the applicability of a Kanban system at the production department of the company, a simulation model was used. The combination of shared resources and Kanban was a complex situation. Therefore, a simulation study provided most of the necessary information and could check the effects and interconnectedness between variables of different experimental settings. Simulation models can check the effects of multiple methods and can result in a rich amount of data (Terzi & Cavalieri, 2004). This study was quantitative and conclusions were based on numbers and significance levels. Previous research has demonstrated that logistical problems are often effectively addressed through simulation due to their complexity (Khouja & Goyal, 2008).This study used the framework of Robinson (2008) to build the simulation model.
The simulation model was built in Siemens Tecnomatix Plant Simulation 12. This is a discrete event simulation technique which uses Simtalk as a programming language and syntax.
The programming language can be compared with the VBA syntax of Microsoft Office. The reason for the choice of this software package was the license availability, the possibilities for programming and prior knowledge gained during a simulation course.
4.2 Experimental design
This stimulation model was a bilateral design and tested the effects of changes in product variety and the interval and Kanban calculation. The simulation was based on the company’s production department, but theoretical calculations for production interval and card calculations were also included. The reason is that the method at the company differed from theory which made it harder to generalize the results.
The model tested nine levels of product variety. The model simulated a dedicated machine with from one product to nine products which is a shared resource. This enabled the study to find grounded conclusions about the effects of shared resources on the applicability of a Kanban system.
The simulation tested two methods in order to calculate a production interval. The first one was the current method of the company and the second method was the EPEI calculations from Guild (1990). The Kanban card calculation was tested with three levels. Those levels included the method of the case company, theoretical Kanban calculation (Sugimori et al., 1977), and the standard deviation method which is an extension of the Sugimori Kanban card calculation.
Finally, the “sequence rule” was tested, based on the method of the case company (shortest changeover time) and the highest demand. In total, 108 experiments were simulated to test what the influence was of shared resources on the applicability of a Kanban system. Table 1 shows the experimental settings. All those settings were tested with the different product variety levels between one product and nine products.
Table 1 Experimental design
Factors/Levels Level 1 Level 2 Level 3
Production interval Fixed interval (Company) EPEI (theory)
Kanban calculation Case company calculation Standard deviation (theory) Kanban (theory)
Sequencing Shortest changeover (company)
Highest demand
Product variety 1 product
2 products
3 products
4 products
5 products
6 products
7 products
8 products
9 products
4.3 Data collection
This research followed a solid design in order to collect the required data. Robinson has distinguished three types of data: contextual data, model data and validation data. Contextual data are necessary to understand problem definition. Model data are data required to build the simulation model. Validation data are data to validate the simulation model.
The contextual data was attained by analysing a thesis by another student who had undertaken a literature research related to the Kanban system of the case company. This thesis was very helpful for gaining a good general overview of the department in a small amount of time (Nwanze, 2017). Furthermore, interviews were held with logistics engineers, the supply chain project manager, operators, maintenance engineers and team leads. Also, a tour through the department gave a good impression of the company. Additionally, standard-operating- procedure (SOP) documents were made available to check procedures. Further research was mainly undertaken by using available data. Robinson has distinguished three sorts of data in
terms of A, B and C. Type A data are available data and can be found easily, type B data are not available because they are not measured but this type of data can be collected by using other variables. Type C data are not available and are not collectable. Almost all processes were documented at the company and machine performance was available in the ERP system. During the contextual and model data gathering some type B was used to gain better insight into the processes and to build the model. The type B data was verified by performing interviews. The data for the simulation model is discussed in section 4.5 below and the data for validating the model can be found in section 4.6. Appendix A shows the conceptual model of the simulation model.
4.4 Data analysis
It was important to analyse the demand patterns of the nine products independently as input for the simulation model. Two types of data were available in the ERP-system: data concerning produced parts at the production department and data concerning assembled. The data concerning produced parts was not useful for analysis, because the production behaviour depended on the chosen production intervals and which type of Kanban calculations were used.
During the simulation, different interval calculations and Kanban calculations were made. The data concerning assembled products gave a good insight into the demand pattern of the customers. To analyse the demand for each product independently several steps were followed, which are described in the next paragraph.
The first step for analysing the demand pattern was to determine which parts were used for which end-products. The next step was to collect all the booking moments from SAP at end- product level. The demand was backwards calculated by checking the bill of material lists. The third step calculated the time between two booking moments at the assembly line. Those differences in time represented the inter-arrival times between products and were aligned with the pickup times from inventory.
A statistical tool DATAFIT was used for determining the inter-arrival distribution per part.
This tool is integrated in Tecnomatix Plant Simulation 12. The tool uses three types of statistical methods to test the validity of the model. The chi-square test, Kolmogorov-Smirnov and Anderson-Darling test are performed to check if a distribution fits within the statistical boundaries. In the analysis phase the focus was to get a statistical fit with chi-square statistics, and the other two statistical tests were used as second choice. The calculation of the distributions
can be found in appendix B and the validation of the distributions can also be found in appendix B.
The simulation included different product variety levels, but to compare the effects of the factors in the simulation model, the total demand needed to be the same. Therefore, additional calculations were conducted. For all products, the mean (inter-arrival time) and standard deviation (fluctuation in inter-arrival time) was calculated, but lowering the product variety resulted in other means and standard deviations for the distributions. The method is described in appendix B. A validation showed that the simulated demand in all product variety environments was almost the same.
4.5 Assumptions
A few assumptions were made to simplify the model due to time constraints. These assumptions did not affect the output of the simulation and the focus of this research.
• Unlimited space availability: The simulation consciously ignored the space availability for inventory, because this disturbs the relationship analysis between the chosen methods and amount of WIP.
• Operators are not simulated: The simulation assumed that operators are always available.
• The card retrieval time was 2 hours, but this was not simulated in the model, because the production time was 2.3 hours per card.
• Only production order cards were incorporated in the model. Dual-card Kanban does not affect the outcome of the simulation.
• Setup time between two parts was fixed with a normal distribution of two hours with a standard deviation of 0.5 hour. The first idea was to simulate real changeover times between parts by using a setup-matrix, but due to a lack of data this was not possible.
By interviewing maintenance engineers, we concluded that the average time was 2 hours with a standard deviation of 0.5 hours.
• One new product on the machine was not simulated. Due to lack of data it was not possible to develop a valid distribution.
• The demand of excluded products for lowering demand variety was equally distributed over the residual products.
4.6 Simulation model
The simulation model is complicated and can be difficult to understand. For this reason, a introduction is given here on how the system worked. The model simulated one year and generated different demand for each month to make the model more realistic. A flowchart is provided to explain the behaviour of the simulation model.
Figure 11 shows the general overview of the simulation model. The simulation model only simulated the Kanban cards and not the products. Entities in the model represented a Kanban card. The first step of the model calculated the monthly forecast based on the calculated distributions. Once the forecast was known, the production interval was calculated and the number of Kanban cards could be calculated. This method sent information to the Kanban board about the number of green, yellow, and red areas on the Kanban board. Furthermore, the Kanban calculation method triggered the “card creation” method to create the required number of cards which was based on the expected number of cards (“Kanban calculation”) and the real number of Kanban cards in the system. The “Production” was the production step of the simulation and took 2.3 hours. The availability rate was 88% and the changeover time was two hours with a standard deviation of 30 minutes. Thereafter, products were placed in the inventory. The customer triggered the inventory with the calculated distributions. When a product was picked up by an internal customer, a trigger was given to the “card creation” method. This method checked if the number of cards in the systems equalled the expected number of cards. If this number was below the expected number, new cards were created and if the number of cards was too high, the system phased out the cards until the expected level was reached (see case description for more information). All blocks have an underlying flowchart and description which can be found in appendix C.
Forecast calculation
Interval calculation
Kanban
calculation Card creation
Kanbanboard
Card release Production Inventory
Information - Threshold levels
Customer trigger Information
-Number of cards -Threshold levels
Distribution
Customer Trigger method
Trigger every month
Number of cards Trigger
Figure 11 General overview simulation
Figure 12 displays a screenshot of the simulation. The methods (indicated with an “M”
pictogram) on the left side calculated the forecast, intervals and created the cards. The red area represents the Kanban board. The green area is the production machine and the blue zone the inventory. The model is developed from top to bottom.
Figure 12 Screenshot simulation model
4.7 Model validity
Before the simulation was developed, a domain expert (employee of the case company) checked if all elements were included in the flowchart model to test the internal validity.
Furthermore, the demand patterns were analysed and checked as described in the previous section. The construct validity was grounded by using the framework developed by Robinson (2008). The theoretical background and case description provided a comparison between the systems in use at the case company and the theoretical system to calculate and use production interval, Kanban and sequencing rules. The system at the case company and the theoretical models were included in this study which enabled this study to discuss the results from the theoretical and the case company perspective.
The black-box validation of the model ensured that the model represented the real situation (Robinson, 2014). This black-box validation is conducted by performing a historical data analysis. To check the black-box validity, the average throughput, average inventory and average number of empty lanes were compared with the outcome of the model. The simulation showed similar results when using the same methods as used at the case company.
The white-box validation checked if the internal structure of the model was valid and that methods were well coded. The model was checked by testing the methods individually on
correctness and the supervisor of this study checked the simulation model together with the author of this study. Therefore, the output of the simulation model could be assessed as valid, enabling this research to use the data for further analysis.
4.8 Experimental Setting
After starting the simulation model, the first data were normally not valid, because the starting positions of the entities were unrealistic. Data of a simulation were valid once the simulation model had ended up in the steady state (Robinson, 2003). The steady state means that the entities in the models were stabilized. To measure the steady state for this study, the occupation rate of the product inventories was used to calculate the steady state. The Welch method was used for the analysis. This method calculated the moving average and graphically showed the steady state. This method did not calculate the exact warmup time (required time when the simulation was in steady state), but only calculated a rough estimation by a graphical method. Therefore, the runtime estimation was rounded up. Furthermore, the warmup period for each product was calculated individually, because products with a higher forecast have a shorter warmup period. The warmup period with the highest value was used for the simulation.
The runtime was set on 1,200 hours and 20 replications were performed to ensure a valid runtime could be selected. All the graphs per product can be found in appendix D. Product G needed the longest warmup time. Therefore, the warmup time was set on 480 hours which corresponded with one month of production.
The run length of the simulation was one year and weekends were excluded. Because production takes place 24 hours a day on business days. The run size was one year, because monthly changes in demand needed to be simulated in this study. Furthermore, Robinson has stated that the run length should be at least ten times the warmup time (2008). Therefore, this simulation satisfied the minimal run length.
To determine the number of replications, the confidence interval method of Robinson was used (2008). The mean lifespan per part was used as an input variable for the calculations. The confidence interval method tests how many replications after the standard deviation were within the significance level, and data are valid for further analysis. For every part, 60 replications were conducted, because all products had different demand patterns. The product which required the highest replication rate was used as the replication rate for the whole simulation.
Appendix E shows the outcome per product and plots the confidence levels. The table below shows the minimal replication rate per product. The table makes clear that for product ‘A’ a
minimum of 35 runs needed to be done. The simulation conducted 40 replications per experiment to be sure that all the output data was within the confidence interval. Table 2 shows the experimental setting of the simulation model.
Table 2 Simulation model
Subject Number
Warm up time 1 month (20 days)
Run time 1 year (240 days)
Simulation time (run time + warmup time) 1 year + 1 month (260 days)
Replications/Observations 40
4.9 Output analysis
The performance of a Kanban system was tested using five performance indicators: the throughput rate, the number of backorders (not delivered customers), total number of changeovers and the WIP level. The output results were statistically analysed to ground the conclusions of this research. The simulation used an independent random stream which enabled this study to analyse the results with an MANOVA or ANOVA test.
To test the interaction effects of the experimental settings, a multivariate test (MANOVA) was conducted in SPSS. This method was selected due to the high number of dependent values and independent values. Multiple ANOVA tests might have been an alternative, but they increase the chance of a Type-1 error (French, Macedo, Poulsen, Waterson, & Yu, 2002). The MANOVA compared all the experimental levels to the performance criteria. This method is commonly used to check the significance levels of interactions (French et al., 2002). Before the method could be used some assumptions needed to be clarified. First, a normality check was conducted and showed no normality. But due to the great amount of output and equal number of experiments it could be assumed that the data were valid according to the central limit theorem (Stein, 1972). Second, the linearity was tested by performing a Durbin-Watson test.
The Durbin-Watson test showed an output of 1,924. This meant that the output data showed a linear distribution in comparison with the throughput, because the Durbin-Watson was between 1 and 3 (French et al., 2002). The output is shown in table 3.
Table 3 Durbin-Watson test
R R square Adjusted R square Error of the estimate Durbin-Watson
.240a .058 .057 60.001 1.924
a. Predictors: (constant), WIP, changeovers, backorders b. Dependent variable: throughput
Finally, the homogeneity needed to be equal between all the experiments. This meant that all the experiments were independent and every group equalled the same number of observations (runs). The Levene’s tests showed that the equality of variances was significant, p
< 0.00, for all dependent variables. This meant that the values were not equally distributed. But the simulation was designed to simulate equal number of experiments with independence and an equal number of observations. Therefore, all assumptions were acceptable which enabled this study to conform to the statistical test. The results of the MANOVA are described in the next chapter.
