Determining the impact of batch sizes on the effective production capacity
of a bottleneck shared resource at case company X
by Henry Mussche
University of Groningen Faculty of Economics and Business MSc. Technology and Operations Management
March 2019
Supervisor: dr. ND van Foreest Co-assessor: dr. O.A. Kilic
2 Abstract
Purpose – Investigating the impact of batch sizes on the effective production capacity of a shared resource at case company X. Case company X uses a large fixed production batch size. This batch size is used for practical reasons and dates from a time that a limited product diversity was present. Because time-consuming changeovers are required between batches of different product families and ranges, a trade-off exists between the diversity and the total number of products that can be produced.
Methodology – First product- and machine characteristics and scheduling rules of the bottleneck shared resource at case company X are analysed. Afterwards, a model is developed, to simulate a representative production schedule for different scenarios by adjusting production batch sizes. The effective production capacity and the diversity of products produced are evaluated and compared with the overcapacity of case company X. Findings – The results of this study are in line with the expected relationships. However, for case company X, the outcomes depend on product ranges. For the two considered product ranges, batch sizes of Mid-range products do not affect the effective production capacity. For High-end products, there is a need for a changeover between every batch, and therefore significantly influences the effective production capacity.
Originality/value – Whereas the majority of studies are focused on cost optimization, this study explores the trade-off between batch sizes and the diversity of products that can be produced in a production levelling environment. Case company X can use the insights from this study to evaluate the currently used batch size and reconsider the currently used scheduling policy.
3 Contents 1. Introduction ... 4 2. Theoretical Background... 6 2.1 Product Variety ... 6 2.2 Shared Resource ... 7 2.3 Batch Sizes ... 8 2.4 Production Levelling ... 9 2.5 Conceptual Model ... 11 3. Methodology ... 12 3.1 Problem Description ... 12 3.2 Case Company X ... 13 3.3 Research Design ... 16 3.4 Data Collection ... 17
3.5 Validation and Verification ... 17
3.6 Sensitivity Analysis ... 18 4. Analysis ... 19 4.1 Product Characteristics ... 19 4.2 Resource Characteristics ... 22 4.3 Scheduling Policy ... 24 4.4 Model Development ... 26 4.5 Model Formulation ... 27 4.6 Analysis Tool ... 29 5 Experiments ... 30 5.1 Mid-range ... 30 5.2 High-end ... 31 6. Results ... 32 6.1 Mid-range ... 32 6.2 High-end ... 34 6.3 Sensitivity Analysis ... 36
7. Conclusion & Discussion ... 37
7.1 Conclusion ... 37
7.2 Discussion ... 38
7.3 Limitations & Further Research ... 39
Bibliography ... 41
Appendix I: Excel Model ... 43
Appendix II: Changeover Times ... 44
Appendix III: Production Times ... 45
Appendix IV: Experiments ... 46
4 1. Introduction
Expectations for technological consumer goods have changed during the last decade, whereby customers expect a more varied range of products. Therefore, offering a broad range of product options is important for technology companies to remain competitive. Manufacturers, should adapt and change production processes to deal with increased product variety (Benjaafar, et al., 2004). However, when a product is offered in multiple versions and the functionality remains the same, demand will increase with a small amount (Desmet & Parente, 2009). This results in a lower demand per product (Chang & Wang, 2007).
In production environments, work-in-process is often processed in fixed suitable batch sizes and end products are often transported in full containers to the next stage of the supply chain. Therefore, a conventional method used in production environments requires the batch size to be an integral multiple of a specified given batch size, which is called a batch ordering policy (Zhu et al., 2015). The aim of producing in large batches is even more important when time-consuming changeovers between batches exist, because setups influence the effective production capacity of a resource (Spence & Porteus, 1987). If multiple products are produced on the same resource, the resource is called a shared resource.
The case company involved in this research uses a batch ordering policy of 1440 units for their products. A combination of this batching policy with an increasing variating product portfolio leads to a potential misfit between demand and production. If a products have a demand smaller than the given batch size, the products will still be produced in fixed batch sizes. This results in machine occupation of a product with less priority. On the other hand, producing in smaller batch sizes increases the total changeover time. Therefore, a trade-off exists between the total number of products and the diversity of products that can be produced. Furthermore, case company X applies production smoothing, which means that on a weekly basis, the production pattern is relatively the same for all production days (Coleman & Vaghefi, 1994). Therefore, changeovers return on a daily basis.
5 In this study, effective production capacity is expressed in the total number of products that can be produced in the considered time period. This research focuses on the bottleneck shared resource because this specific resource has the largest impact on the remainder of the production environment. A model is built to analyse a representative production schedule of case company X, whereby batch sizes are the experimental variable.
The remaining part of this report will be structured as follows. First, the theoretical background is given, wherein literature is linked to this research. Then the methodology is elaborated on, whereby the design of this research is discussed. Next, the analysis and model are given, after which the experiments are discussed. In the following section, the results of this study are presented. This paper concludes with the conclusion and discussion, as well as limitations and further research.
6 2. Theoretical Background
In this section, relevant literature is linked to the topics under investigation. First, a more detailed view of product variety in production environments is given. Secondly, shared resources are explained. Next, batch sizing is elaborated on. In the fourth section, production smoothing will be discussed. This section ends with an overview of the conceptual model, whereby expected relationships are explained.
2.1 Product Variety
Due to globalisation, customers are brought into a more powerful position in terms of product variety, quality and customizability (Thull, 2003). Because of this increasing variety of products, conventional production environments with a limited amount of product diversity transform into environments with a lot of variety.
7 2.2 Shared Resource
Three types of production lines could be distinguished (Becker & Scholl, 2006). In the most simple form of production, a production line is dedicated to a certain product or product family. This is called a single model line. When multiple products or product-families are mixed on one line or resource, two variants appear. A mixed-model line produces products in an arbitrary sequence without setups. A multi-model line produces products with intervening setups. These variants are shown in figure 2.1. In this study, a multi-model line is investigated. The bottleneck of this line is considered because a bottleneck has the highest impact on the output of a production line (Hopp & Spearman, 2008). In the remainder of this study is spoken of a shared resource, because only a single stage of the multi-model production line is under investigation.
setup setup
Single-model
Mixed-model
Multi-model
Figure 2.1: Variants of production lines
The concept of shared resources is explained by Hopp & Spearman (2008). For some cases, it is economically not advantageous to replicate a resource for multiple products. This is the case when e.g. a resource has a high capacity or a high investment cost. Therefore, a resource is used for multiple products to increase utilization and/or reduce costs. An import consequence of producing multiple products on a resource is that the resource has to cope with different product characteristics and machine settings (Hopp & Spearman, 2008).
Regarding capacity, two types can be distinguished: design capacity and effective capacity. Design capacity is the theoretical capacity, depending on capacity and number of machines. The effective capacity is the capacity, whereby planned stopages (e.g. changeovers) are also considered. This means that effective capacity is always lower than the design capacity (Boydell, 2011).
8 possible output and thus the performance of a resource will be negatively influenced. Larger or more setups means either that less time is available for production processes, or that facility operating hours need to be extended.
The impact of changeovers can be influenced by sequencing rules. Trends towards shorter lead times lead to the increasing importance of scheduling and management of changeovers (Blocher, et al., 1996). Hopp & Spearman (2008) indicate the importance of focussing on bottlenecks when it comes to scheduling problems. This can break-up large scheduling problems and can be justified by the fact that a bottleneck resource dominates the behavioural of a manufacturing system.
The theory about the scheduling policy applied at case company X is discussed in section 2.4.
2.3 Batch Sizes
Regarding the type of batches, there are two distinct process batches: Sequential batches are produced after each other, whereas a simultaneous batch is determined by the number of products that can be produced together (Hopp & Spearman, 2008). This study considers sequential batches, whereby a setup is required by switching between a product range or product family.
9 Zhou, et al. (2007) addresses the importance of economies of scale in consumer packaged goods. One way to achieve this is by requiring batch orders. On the other side, in a Make-To-Stock environment, an internal batch ordering requirement can lead to overproduction and inventory, which are two of the 7 wastes of lean (Womack & Jones, 2003). Overproduction is often seen as the worst of the 7 “mudas” since overproduction causes other wastes and obscures the need for improvements (Lean Manufacturing Tools, 2017).Furthermore, when product variety increases (section 2.1) and batch sizes are large and fixed, production becomes less flexible to produce different kind of products. With respect to this research, when demand is low compared to the order size, also a risk of obsolesce is created. In this case, inventory control tools or principles need to be used or have to be developed to control inventories (Zhu et al, 2015).
Berlec, et al. (2014) discuss the advantages and disadvantages of large and small batch sizes. These are listed in table 2.1. The points in bold are closely related to this study since these are related to changeovers.
Small batch size Large batch size
Advantages - Small capital investment;
- Low storage costs;
- High flexibility if quantities change at suppliers or buyers.
- Low administrative costs;
- Few changeovers in
production.
Disadvantages - Frequent ordering costs;
- High risk of changeovers in production.
- High capital investment; - Low flexibility if quantities
change at suppliers or buyers;
- High storage costs. Table 2.1: Advantages versus disadvantages of small/large lot sizes (Berlec, et al., 2014) 2.4 Production Levelling
10 Heijunka is to equate workloads to other stages of production (Coleman & Vaghefi, 1994). This is visualized in Figure 2.2, which shows a more balanced and stabilized production pattern for a levelled production environment in comparison to a traditional production environment.
Figure 2.2: Production levelling (Heijunka).
The aim is not only to level production volume but also level diversity of products (Matzka, et al., 2012). When large setups exist, while the Heijunka scheduling method is applied, a significant amount of time is wasted on switching from one product type to another. Therefore, in a Heijunka environment setups should be small, with the intention that easily can be switched between different products (Matzka, et al., 2012). An example schedule, whereby Heijunka is applied is visualized in figure 2.3.
11 2.5 Conceptual Model
A central question to guide this research is formulated as follows:
What is the impact of batch sizes on the effective production capacity of a bottleneck shared resource in a high product variety environment?
Figure 2.4 shows the conceptual model, where the subjects previously discussed are represented to show interactions. This study investigates a production environment, where product variety is increasing. Increasing product variety has led to the decision to produce multiple products on the same resource, which leads to a so-called shared resource. The impact of producing in smaller batch sizes is investigated. Smaller batch sizes are expected to result in a fewer total number of products produced due to time-consuming changeovers. On the other hand, the diversity of products that could be produced is expected to increase because a larger batch consumes more available capacity time for one specific product. In this research, the magnitude of these relationships are investigated.
Leads to Shared resource Batch size Product variety
-Number of products produced Diversity of products produced+
12 3. Methodology
The methodology section starts with a description of the problem. Next, an overview of the production process of the case company is drawn and the scope of this research is determined. The subsequent section gives an overview of the research method, whereby the steps taken during this study are given. Afterwards, data collection, verification and validation are discussed. Finally, the sensitivity analysis is discussed.
3.1 Problem Description
Over the last years, the case company experiences changes in customer expectations; there is an increased demand for a more varied number of products. Furthermore, there is a shift from high volume-low value production towards high value-low volume production. The diversity of products is caused by colour, functionality and geographical specifications.
The case company uses a batch ordering policy, which means that production orders are rounded to a multiple of a fixed batch size. The theory behind this policy is discussed in section 2.3. Currently, for the majority of the products, the batch size is set to 1440 units. This batch size is chosen for practical reasons (e.g. transport units) and dates from the time that a limited range of products was produced in high volumes. Furthermore, changeovers exist between batches depending on product family- and range. For efficiency and practical reasons, large batch sizes are chosen.
Due to the increased variety of products with smaller demand, a potential misfit between the batch size and demand exists. The misfit between demand and the batch size is investigated by Rakhorst (2019). This study investigates the impact of fixed batch sizes on effective production capacity.
Table 3.1: Example to show the trade-off between total production and production of different products.
Batch size = 20 Batch size = 10
Product Production Changeover time Product Production Changeover time
A 20 10 A 10 10
B 20 10 B 10 10
C 10 10
Subtotal 40 20 Subtotal 30 30
13 To illustrate the problem, a simplified example is given and visualized in table 3.1 and figure 3.1.
The example in Table 3.1 shows the results in case of two different batch sizes. In this example, the assumption is made that the production time for all products is the same and that changeovers are needed for a switch between every different type of product.
This example illustrates that a smaller batch size creates the possibility to produce a higher variety of products. On the other hand, a smaller batch size results in more total changeover time, which is visualized in figure 3.1. Therefore, a trade-off exists between the variety of products that can be produced and the total number of products that can be produced. This trade-off is investigated at case company X, by applying the scheduling rules of case company X.
Figure 3.1: Example illustration of the effect of two different batch sizes
3.2 Case Company X
In this section, the production process and scope of this research is shown to give an overview of the context of this study.
Production Process
In figure 3.2, a simplified visualization of the total production process of the case company is given. 0% 20% 40% 60% 80% 100% 20 10 Capacity Bat ch si ze
Production and setups
14 Final Assembly LCC Multiple processes Reflow Moulding Raw materials Demand Forecast FIFO
APV PCBA FIFO
FIFO BBA Kanban MPS Shaving Head production MTS Products Information
Figure 3.2: Production process of the case company
At the start of the production process, raw material inventory is used as input for multiple processes, which can be divided into three distinct production processes.
The first production process starts at Reflow. At Reflow, Printed Circuit Boards (PCB’s) are assembled. The production at the Reflow stage is controlled by the Master Production Schedule (MPS). The MPS determines the weekly production schedule, based on an aggregated yearly demand forecast. Because demand is subject to seasonal influences, the production is levelled throughout the year to compensate for the capacity shortage at the end of the year. On a weekly basis, supply planners match the aggregated planning with actual demand. The actual demand orders are communicated by Late Customization Centers (LCCs), which is the next stage in the supply chain. From Reflow, products flow via the subsequent processes towards the Final Assembly.
The second production process starts at moulding. At the moulding stage, all the plastic (sub) assemblies are produced. The moulding stage consists of shared and dedicated machines. From this stage, products are delivered to eight subsequent production processes, which eventually leads to the Final Assembly. The production of this stage is controlled via a KANBAN system. This stage is already investigated by Nwanze (2016).
15 The sub-assemblies of the three distinct production processes are merged at the Final Assembly stage and shipped to the LCCs afterwards.
Scope
This research is part of a larger study at the case company. The study of Rakhorst (2019) investigates optimal batch sizes from a market perspective. On the opposite, this research investigates the impact of smaller batch sizes on the effective production capacity.
From the three previously described production stages, the FIFO line is most directly linked to the market. The KANBAN process regulates demand by cards and the MTS process is aimed at producing high quantities. Therefore, the FIFO line is considered in this research.
The focus of this study is on the bottleneck process of the FIFO line (figure 3.3) since this resource has the largest impact on the production environment. This production stage consists of two dedicated shared resources called Reflow.
Reflow 1 produces electronic parts for the high-end and mid-range products, whereas Reflow 2 produces products for the low-end products. The value and diversity of products in the Mid- and High-ranges is large in comparison to the Low-end ranges. Therefore the batch ordering policy of 1440 units is expected to have the highest impact on these ranges. This is in line with the research of Rakhorst (2019). Therefore, the scope is of this research is determined to be Reflow 1.
Figure 3.3: Scope of the research
Reflow 1
Reflow 2 Raw
materials APV ..
16 3.3 Research Design
To answer the research question, a sequence of steps are carried out (figure 3.4), which are discussed in the following paragraphs.
Since a case company is involved in this research, first the practical situation is investigated to get a good understanding of the problem. The description of the problem and an overview of the case company is given in section 3.1. Furthermore, literature is consulted to get a better understanding of the problem.
The next step is gathering data at the case company. First product characteristics are determined. Afterwards, the characteristics of the resource (Reflow machine) are gathered and analysed. The fourth step in the research design is determining the scheduling policy and rules that are important for the case company.
After the necessary data is gathered and the elements for the model are analysed, the KPI’s are set up. The objective of this study is to measure the trade-off between total possible production and the diversity of products that can be produced. Therefore, the total number of batches that could be produced is the first important KPI, to evaluate product diversity. Next, the effective use of
capacity (effective production capacity) is important. This is the output of the model, which is fed by the data and analysis executed at steps 1 till 4. To realize this output, the model is implemented in Microsoft Excel.
At the sixth and last step, the experiments are defined, whereby the experimental variable ‘batch size’ is changed for a feasible interval range. The output is compared to each other to determine the impact of the experimental variable.
Understand and define practical situation
Determine product characteristics
Determine resource characteristics
Setting up KPI s and model building Compare different scenarios Determine scheduling policy/rules 1. 2. 3. 4. 5. 6.
17 3.4 Data Collection
Robinson (2014) distinguishes three types of data (table 3.2), namely type A, B, and C data. Type A data is data that is already available and can be used straight away. Type B data is data which is not immediately available but can be collected. Type C data is data that is not available and not collectable. Obviously, type A data is the easiest type of data, whereas type B and C data are more difficult to deal with. For type C data, assumptions have to be made, because it can not be collected.
Table 3.2: Types of data (Robinson, 2014)
After the types of data have been identified, there has to be decided on the method of data collection. In this study, the methods that are used to obtain data are interviews, conversations and historical data from the ERP system. For most of the data, conversations with employees at the case company took place and after determining the need for specific data, the data could be handed over to the researcher or could be collected afterwards.
Table 3.3: Data collection of this study
3.5 Validation and Verification
To ensure that the model is sufficiently good enough for the purpose on hand, validation and verification is an important element of the methodology section of this research. Robinson (2014) defines verification as “the process of ensuring that the model design has been transformed into a computer model with sufficient accuracy” and validation as “The process of ensuring that the model is sufficiently accurate for the purpose at hand”. From these definitions, we can conclude that validation is important to ensure that the current situation
Type of data Availability
Type A Available
Type B Not available, but obtainable Type C Not available and not collectable
Data Type of data Data collection
Changeover times Type A Excel file
Production rates Type A Excel file
Capacity figures Type A ERP system
Scheduling rules Type B Interviews/ERP-system
Demand ratio Type B Assumption made based on
18 is representative of the actual situation and verification is more focused on the accuracy of the model itself.
After the model has been build and the KPIs for the purpose on hand are chosen, the model is verified. This is done by walking step by step through the model, changing parameters and checking whether the change in parameters resulted in the expected outcomes.
After the verification step has been done, the validation step is executed. For validation, the model is evaluated by the case company, which ensures that the model actually represents the situation of the case company.
3.6 Sensitivity Analysis
Because the values of parameters and assumptions are susceptible to mutations and faults, sensitivity analysis is a good way to define the usefulness of a model. A broad definition of sensitivity analysis is given by Baird (1989), who define it as “the investigation of potential changes and errors and their impacts on conclusions to be drawn from the model”.
Sensitivity analysis gives useful information about the usefulness of the model and the applicability of the conclusions that are drawn. It can give a good indication about: how robust the solutions are if parameters are changed, under which circumstances (optimal) solutions would change and what happens if circumstances would change and parameters would stay the same (Pannell, 1997).
Besides testing the robustness, sensitivity analysis also gives a better understanding of the relationships between input and output data. This makes the model more understandable by the researcher as well as the reader.
19 4. Analysis
The analysis section follows the chronological order of this study, described in the research design (3.3). Paragraphs 4.1,4.2, and 4.3 include an analysis of the necessary parts of the model and 4.4, 4.5, and 4.6 the model building process and formulation.
The model simulates a production schedule of case company X, whereby the objective is to maximise the total output. The schedule is filled with product batches of different products. Therefore, first, the product characteristics are discussed (4.1). Case company X is bounded to limited production capacity and sequence-dependent changeovers exist. Therefore, resource characteristics are discussed next (4.2). Because the setups are sequence dependent, the scheduling policy/rules influence the number of changeovers. The necessary scheduling rules of case company X are discussed in section 4.3. After these elements are analysed, the model development steps and formulation of the model is given. The analysis section concludes with an explanation of the Excel model that is used to calculate the defined KPI’s.
4.1 Product Characteristics
The structure of the products produced at the case company determines, how many different products can be produced on the shared resource. Furthermore, by explaining the product structure, the choice of dividing products into product ranges in the model can be justified. The production times determine the resource consumption of a product range, which is analysed in the second paragraph. Finally, an analysis of the demand ratio is given, to determine the ratio of the two different ranges that should be produced weekly.
Product structure
Two specific ranges are produced on the shared resource: High-end and range. The Mid-range consist of 20 product families. These 20 product families represent 223 different finished products. (figure 4.1).
Mid-range
Product families Amount: 20
Finished product Amount: 223
20 The High-end range includes 10 different product families, which in turn is eventually scattered into 143 finished products, which is visualized in Figure 4.2.
High-end
Product families Amount: 10
Finished product Amount: 143
Figure 4.2: Product structure High-end range
Altogether, the 30 different product families of both ranges result in 366 different finished products.
Production rates
The production rate is defined as the number of products that could be produced in a minute. For the shared resource under investigation, the production rate of a finished product is determined by the product family. Therefore, the Mid-range consists of 20 different production rates and the High-end has 10 different production rates.
Mid-range: μ= 19,9 M = 19,5 σ = 2,2 High-end: μ = 7,0 M = 7,5 σ = 1,7
Figure 4.3 shows the average production rates of the Mid-range and High-end product families. With an average of 19,9 products per minute and a median of 19,5, the Mid-range production rates are spread evenly over the different product families. The same holds for the High-end, whereby the average is 7 products per minute with a median of 7,5. From these figures becomes clear that High-end products have a considerable larger production time, compared to Mid-range products.
Figure 4.3: Average production rates of both ranges
21 Furthermore, the production rate of a finished product is closely related to the range of a product. Therefore, this study assumes the average production rate to be the production rate for a finished product of a specific range. An overview of all the production rates is added to Appendix III.
Demand ratio
From the previous paragraph, it became clear that High-end products consume more production time, in comparison to Mid-range products. Therefore, the demand ratio of the different ranges is determined.
Yearly weekly production schedules show that on average, 21% of the products produced in a week are High-end products and the remainder are Mid-range products. This is shown in figure 4.4. This data is added as a constraint in the model, whereby the production of High-end products should be at least 20% of the total production in a week. Since the production rate of High-end products is lower than for Mid-range products, the model will use this percentage as lower bound by itself, since the objective is to maximise total production.
Mid-range: μ= 79% M = 81% σ = 4% High-end: μ = 21% M = 19% σ = 4% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90%
Demand ratio
Mid-range High-end22 4.2 Resource Characteristics
In this section, the characteristics of the shared resource are discussed. First, the need for changeovers is considered. Afterwards, the capacity of the shared resource is discussed. Both of these characteristics are important for the model since the total changeover time increases when the batch size decreases and the capacity determines the amount of time available for production and changeovers.
Changeovers
Different types of changeovers can be distinguished for the shared resource at the case company. The types of changeovers differ in magnitude and sequence. Changeovers exist between the production of different batches. However, the impact of a changeover is dependent on the sequence of production and depends on whether there is a change between a product range or between a product family. Four types of changeovers can be distinguished. These types of changeovers are shown in table 4.5.
First, switching between two different product ranges has the highest impact and results in a changeover time of 25 minutes. Switching between High-end products always results in a changeover of 10 minutes, due to an internal changeover required for switching between a batch. For Mid-range products, the impact is smaller, because a changeover of 5 minutes is needed for switching between a product family. For a switch between the same Mid-range product family, no changeover is required. Therefore, the 5 minute changeover in figures 4.5 only applies in case of a switch between one of the 20 Mid-range product families.
Product Mid-range High-end
Mid-range 5 25
High-end 25 10
Figure 4.5: Changeover times in minutes
Figure 4.6 shows the impact of each changeover on the total weekly capacity. Each changeover decreases the available capacity. An overview of the changeovers at case company X is added to Appendix II.
Product Mid-range High-end
Mid-range 0,1% 0,4%
High-end 0,4% 0,2%
23 Capacity
The available capacity determines the total number of products that can be produced. Three different groups that consume capacity can be determined. The average weekly percentage usage of these groups is visualized in Figure 4.7.
The first group is the production time. The production time is determined by the sum of all batches and their production times.
The second group is changeover time, which depends on the sequence of production, the batch sizes of High-end products and the number of different Mid-range product families produced.
The third group is fixed in the production plan, which contains time for e.g. maintenance and R&D. The percentage each of the groups consumes on average in the current situation is shown in figure 4.7. The shared resource is available for 15 shifts a week, which translates to a total weekly capacity of 24*5 = 120 hours or 7200 minutes. Subtracting the fixed group (7200*0.85) from the total capacity results in 6120 minutes available for production and changeovers.
78% 7%
15%
Capacity consumption
Production time Changeover time Other (Maintenance/R&D/etc.)
24 Figure 4.8 shows the yearly capacity utilization of the shared resource.
Q1 μ= 86% Q2 μ= 98% Q3 μ= 95% Q4 μ= 69%
Figure 4.8: Yearly capacity utilization
Figure 4.8 shows that at the beginning and end of the year, more capacity is available compared to the remainder of a year. This has to do with an aggregated production planning, to intercept the peak demand at the end of the year. On average, 87% of capacity is filled during the year. The available capacity is a good potential for smaller batch sizes, whereby the overcapacity can be used for extra changeovers, caused by smaller batch sizes.
Especially in the 1st and 4th quarter of the year, there is room for extra changeovers. 4.3 Scheduling Policy
The production planner determines the sequence of production and therefore the number of changeovers in a week. A weekly production schedule is created Wednesday before the next production week. The production planner receives a list of products from supply planning that should be produced. The scheduling policy of the case company is closely related to production smoothing, which foundations are discussed in section 2.4. The application of this technique at case company X is first elaborated on. Next, the scheduling rules to determine the weekly production schedule are given.
Production smoothing
The shared resource delivers sub-assemblies to the subsequent stages of production. To balance the supply towards the following stages of the shared resource, production smoothing is applied. For the production schedule, this means the requirement of 2 large daily setups, to
0% 20% 40% 60% 80% 100% 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 Cap acity u tiliza tio n Weeks
Capacity Utilization
25 switch between ranges. The first part of the day is used for High-end products, whereas the remainder of the day is used for Mid-range products. Therefore, the number of large changeovers is fixed to 10 (5*2) a week.
Scheduling rules
The production planner of case company X uses the following rules, to create a production schedule.
1. If the demand for an item is larger than the batch size, the products are evenly distributed over the week in quantities of the batch size. The trigger for this rule is that products can be shipped multiple times a week to the DC’s.
2. High-end and Mid-range products are levelled over the week on a daily basis in an even ratio. This is done to deliver the products of the different ranges evenly over the week to the subsequent stages of production.
3. Every day, production starts with High-end products and ends with Mid-range products. This is due to a higher priority for High-end products due to product value and consumer expectations.
4. The products are sequenced on a daily basis to minimize changeover times.
Table 4.1 shows an example of a schedule, whereby the previously mentioned rules are applied. In this example, a weekly demand exists for five products: Two High-end products and three Mid-range products.
Production Schedule
Monday Tuesday Wednesday Thursday Friday
Product Range Qty Product Range Qty Product Range Qty Product Range Qty Product Range Qty 1 High 1440 1 High 1440 1 High 1440 1 High 1440 1 High 1440 2 High 1440 2 High 1440 2 High 1440 2 High 1440 2 High 1440
3 Mid 1440 3 Mid 1440 3 Mid 1440 3 Mid 1440 3 Mid 1440
4 Mid 1440 4 Mid 1440 4 Mid 1440 4 Mid 1440 4 Mid 1440
5 Mid 1440 5 Mid 1440 5 Mid 1440 5 Mid 1440 5 Mid 1440
26 4.4 Model Development
With the analysis of the previous sections as input, the emergence of the model is explained in three steps. Every step makes the model is made a bit more extensive.
Step 1: building a model without setups and demand
First, a model is built without setups and demand. In this step, the model will only put batches of Mid-range products into the schedule, since Mid-range products have the smallest processing time and the goal of the model is to maximise total production. The batches should fit into the total capacity. Therefore some time is left in the production schedule since a whole batch does not fit into the available time left. An example of this basic model is shown in figure 4.9.
In the example, the total number of batches that can be produced is 10 and the effective production time is 100%, if time left is included in effective production time.
Figure 4.9: Model without changeovers and demand
Step 2: Adding demand requirement to the model
In the second version of the model, the demand is also taken into consideration. The demand is implemented into the model as a minimum percentage of the total production. High-end production should be at least 20% of total production. Since High-end products have the highest process time and the total production is maximised, the model will use a number of High-end batches of close to the lower bound of 20%. An example of the second model is shown in figure 41.
27 Figure 4.10: Model without changeovers
Step 3: Adding changeover requirement to the model
In the final version of the model, the changeovers are added. In the analysis section (4.2), the types of setups are distinguished. A large setup is required when switching between the two different ranges. Case company X switches two times a day: at the beginning of the day and halfway the day. Each day, the High-end batches are scheduled first. Between each High-end batch, a setup is required. A setup for Mid-range products is only required when switching between a product family.
In the example, the total number of batches that can be produced is 5 and the effective production time is 90%, if time left is included in effective production time.
Figure 4.11: Final model
4.5 Model Formulation
28 The aim of this study is to measure the impact of batch sizes on the effective production capacity and number of different batches. The goal of using a smaller batch is elaborated on in section 3.1. To measure this impact, a model is built that maximises the total output, based on the input parameters and the constraints. 𝐵𝑟 and 𝑃𝑀 are the experimental values, which are determined after analysing the types of changeovers at the case company. In the model, ‘r’ represents the two ranges distinguished in section 4.2, whereby m = Mid-range and h = High-end.
Parameters
(1) 𝑟 = {𝑚, ℎ} , represents the two different ranges (2) 𝑃𝑟 = 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑡𝑖𝑚𝑒 𝑓𝑜𝑟 𝑟𝑎𝑛𝑔𝑒 𝑟 in minutes (3) 𝑆𝑟 = 𝑆𝑒𝑡𝑢𝑝 𝑡𝑖𝑚𝑒 𝑓𝑜𝑟 𝑟𝑎𝑛𝑔𝑒 𝑟 in minutes (4) 𝐵𝑟 = 𝐵𝑎𝑡𝑐ℎ 𝑠𝑖𝑧𝑒 𝑓𝑜𝑟 𝑟𝑎𝑛𝑔𝑒 𝑟 in minutes (4) 𝐶 = 𝑊𝑒𝑒𝑘𝑙𝑦 𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 in minutes (5) 𝑆𝑇 = 𝑆𝑒𝑡𝑢𝑝 𝑡𝑖𝑚𝑒 𝑓𝑜𝑟 𝑎 𝑠𝑤𝑖𝑡𝑐ℎ 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑟𝑎𝑛𝑔𝑒 in minutes (6) 𝐿𝑆 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑒𝑒𝑘𝑙𝑦 𝑙𝑎𝑟𝑔𝑒 𝑠𝑒𝑡𝑢𝑝𝑠 (7) 𝑃𝑀 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑀𝑖𝑑_𝑟𝑎𝑛𝑔𝑒 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑓𝑎𝑚𝑖𝑙𝑖𝑒𝑠 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑑 (8) 𝐷ℎ= 𝑃𝑜𝑟𝑡𝑖𝑜𝑛 𝐻𝑖𝑔ℎ𝑒𝑛𝑑𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠 𝑜𝑓 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑑 𝑖𝑛 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 Decision variable (1) 𝑄𝑟 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑎𝑡𝑐ℎ𝑒𝑠 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑑 𝑓𝑜𝑟 𝑟𝑎𝑛𝑔𝑒 𝑟 Objective function 𝑀𝑎𝑥𝑖𝑚𝑖𝑠𝑒 (𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑑) 𝑀𝑎𝑥𝑖𝑚𝑖𝑠𝑒 (∑ 𝑄𝑟∗ 𝐵𝑟 𝑟 𝑗=1 ) Constraints (1) (∑ 𝑄𝑟 𝑟 𝑗=1 ∗ 𝐵𝑟∗ 𝑃𝑟) + (𝑄ℎ∗ 𝑆ℎ ) + (𝑃𝑀 ∗ 𝑆𝑚) + (𝑆𝑇 ∗ 𝐿𝑆) ≤ 𝐶
Total production time + total changeover time is smaller than or equal to the total capacity (2)
𝐵ℎ∗ 𝑄ℎ ∑𝑟𝑗=1𝐵𝑟∗ 𝑄𝑟
29 Demand requirement, 𝐷ℎ is the percentage High-end production of total production. For this research, 𝐷ℎ is fixed to 0,2.
(3)
𝑄𝑟 = ℤ ,for all r
Production can be fulfilled only in full batches. Therefore, values for 𝑄𝑟 should be an integer. Assumptions
(1) There is always sufficient demand to fill the total capacity.
(2) The number of High-end products is equal to or higher than 20% of the total number of products produced.
(3) The changeover times and production times are deterministic. (4) Batch size for all products in a range is equal to 𝐵𝑟
(5) Demand for products within a range is equally distributed over the product families. KPI’s
(1) Effective production time
(2) Total number of batches produced
The capacity used for production shows the effective production capacity of the shared resource for the different experiments. The total number of batches presents the diversity of products that can be produced.
4.6 Analysis Tool
In order to evaluate different scenarios, a tool is built in excel. The model described in section 4.4 and 4.5 is implemented in Excel. The Solver in Excel is used to calculate the KPI’s, for the for scenarios whereby the total number of production is maximised.
30 5. Experiments
In section 4, an analysis is given to determine the important factors that influence the capacity of the shared resource. To determine the impact of batch sizes, a model is built, which simulates a weekly production schedule of the case company. In this section, the base case is determined and experiments for Mid-range and High-end products are discussed. An overview of all experiments is added to Appendix IV.
The base case scenario is the current situation at case company X. This will be a reference point for the remainder of the experiments. The base case is determined to be the situation that both Mid-range and High-end products are produced in batches (𝐵𝑟) of 1440 units. As discussed in section 4.4, two large changeovers for a switch between range are needed each day. The number of large changeovers is fixed in the model, and thus also for the experiments, because large changeovers are not influenced by the batch size and the case company needs this requirement for a stable supply to the subsequent stages of the shared resource.
5.1 Mid-range
Table 5.1 shows the different experiments for Mid-range products. The batch size of the base case is fixed to 1440 units because the trolleys in production have a capacity of 1440 units. In consultation with the case company, only the most feasible batch sizes are included in the experiments. Therefore, batch sizes of multiples of 60 are chosen, because the products are packed in quantities of 60 units. Therefore, the lower bound is 60 units.
31
Experiments Mid-range
Batch size (𝐵𝑟) Weekly number of different Mid-range product families (𝑃𝑀) Mid-range (𝐵𝑚) High-end (𝐵ℎ)
1440 - 60 1440 25
1440 - 60 1440 50
1440 - 60 1440 75
1440 - 60 1440 100
Table 5.1: Experiments Mid-range 5.2 High-end
From the analysis section, it became clear that a changeover is always required between a batch of high-end products. The base case explained in section 5.1, also applies to the High-end range. For the High-High-end experiments, the High-High-end batch sizes are decreased with an interval of 60. This results in a total number of 23 experiments, which are shown in table 5.2.
Experiments High-end
Batch size (𝐵𝑟) Weekly number of different Mid-range product families (𝑃𝑀) Mid-range (𝐵𝑚) High-end (𝐵ℎ)
1440 1440 - 60 25
Table 5.2: Experiments High-end
32 6. Results
In this section, the results are shown. Because the experiments are divided for the two different ranges, the results section also shows the results in two sections. First, the results of experiments for the Mid-range products are presented. Afterwards, the results for the High-end products are shown. In the last section, the sensitivity of the results is shown, by changing input variables.
6.1 Mid-range
Each switch between a Mid-range product family embodies a setup time of 5 minutes.In total, 20 product families exist in this range. Therefore, scenarios for a range of 5 till 20 product families are tested, with an interval of 5 product families. From the analysis became clear that highest possible impact of Mid-range changeovers is 20 changeovers a day, which equals 100 minutes setup time a day.
Effect on effective production capacity
When the number of Mid-range product families produced remains the same, there is no effect on total production. However, when smaller batch sizes result in a more spread demand and therefore a higher number of Mid-range product families produced on a daily basis, the batch sizes do influence the total output. The impact of producing a larger number of Mid-range product families on the production capacity is shown in figure 6.1.
33 Figure 6.1: Effective production capacity for the Mid-range experiments.
Effect on production diversity
Below, the results for production diversity are shown. In the base case situation, about 40 different Mid-range products can be produced. The number of different batches that can be produced rises exponentially with a decrease in batch size, as can be seen in figure 6.2. The number of product families that are produced have a limited impact on the number of batches that can be produced. This is in line with the results of the effective capacity, which decreases when a higher number of product families are produced. In case that all 223 Mid-range products are produced in a week, the batch size should be 240, with a 6% capacity decrease.
Figure 6.2: Number of batches for the Mid-range experiments.
82% 84% 86% 88% 90% 92% 94%
Batch size Mid-range (𝐵_𝑚)
Weekly effective production capacity
5 product families (base case) 10 product families 15 product families 20 product families
0 200 400 600 800 1000 1200 N u m b er o f b at ch es ( 𝑄 _ 𝑚 )
Batch size Mid-range (𝐵_𝑚)
Weekly number of Mid-range batches
34 6.2 High-end
From the analysis part, it became clear that changeovers for High-end products exist between equal product families and different product families (between every batch). The magnitude of a changeover between High-end products is equal for all products. A changeover between each High-end batch involves 10 minutes. In total, 10 product families exist in the High-end range. For the high-end range, the scenarios are tested for batch sizes of 1440 till 60, with an interval of 60 units.
Effect on effective production capacity
The total changeover time for the High-end products increases with every extra batch produced. Figure 6.3 shows the increase in changeover times for the High-end range. In the base case scenario (𝐵𝑟 = 1440), the High-end products count for approximately 4 % of the total weekly changeover time. Figure 6.3 shows that increasing the batch size of High-end products results in an exponential shaped increase of changeover time. Decreasing the batch size to 360 units results in a doubling of the total percentual changeover time from 4 % to 8 %. Decreasing the batch size to a lower point than 360 units results in a large increase of changeover time.
The increase in changeover time logically results in a decrease in effective production capacity. Figure 6.4 shows that, in line with the increase in changeover time, the total production numbers remain relatively stable until a batch size of 360 units. Decreasing the batch size in a batch size, smaller than 360 units results in a significant decrease of capacity. Furthermore, a
0% 5% 10% 15% 20% 25% 30% 35%
Batch size High-end (𝐵_ℎ)
Weekly changeover time High-end range
35 smaller batch size results in a lower output for the Mid-range products, since the constraint for the demand ratio of Mid-range and High-end products still remains.
Effect on production diversity
The number of batches that can be produced with a smaller batch size are shown in figure 6.5. The possibility to produce different products obviously increases. The number of batches increases in an exponential fashion. At the point of a batch size of 360 units, the number of batches increases at a large rate. All 143 products in the High-end range can be produced with a batch size of about 120.
Figure 6.5: Number of batches for the High-end experiments
60% 65% 70% 75% 80% 85% 90% 95%
Batch size High-end (𝐵_ℎ)
Weekly effective production capacity
Figure 6.4: Effective production time for the High-end experiments
0 20 40 60 80 100 120 140 160 180 200 N u m b er o f b at ch es ( 𝑄 _ ℎ )
Batch size High-end (𝐵_ℎ)
36 6.3 Sensitivity Analysis
As elaborated on in section 3.6, the demand ratio and changeover times are changed in the sensitivity analysis. From previous results, it became clear that the effective capacity is not influenced by changing the Mid-range batches. Therefore, the parameters of the High-end products are changed in the sensitivity analysis. First, the impact of changing the demand ratio is investigated. Afterwards, the magnitude of changing the changeover times is discussed. The graphs, which show the output of the sensitivity analysis can be found in Appendix V.
Demand ratio
The results of changing the demand ratio are shown in figure 6.1. The demand ratio of the High-end range is changed with a 10% increase and decrease. With the change of this value, the impact of changing the demand ratio is investigated. Because the demand ratio determines the share of High-end products in the production plan, this is expected to have a large impact.
Demand ratio Average % decrease capacity Average no. of batches
10% 2% 24
20% (base case) 4% 36
30% 6% 46
Table 6.1: Sensitivity analysis Demand ratio
The output of the sensitivity analysis shows that the number of batches and the capacity in- and decreases in an almost linear fashion.
Changeover times
The changeover times are increased and decreased by 5 minutes, to explore the impact of changing changeover times.
Changeover times Average % decrease capacity Average no. of batches
5 minutes 2% 39
10 minutes (base case) 4% 36
15 minutes 6% 34
Table 6.2: Sensitivity analysis changeover times
37 7. Conclusion & Discussion
In this section, the study is first concluded. The research question is answered and the main results are shown. Next, the research is discussed, whereby the results are compared with the expectations. Furthermore, the validity of the research design is considered. In the final section, the limitations of this research are discussed, whereby possibilities for further research are also considered (7.3).
7.1 Conclusion
At the beginning of this report, the research question was stated as follows:
What is the impact of batch sizes on the effective production capacity of a bottleneck shared resource in a high product variety environment?
With the results obtained from this study, we can infer that batch sizes indeed have a significant impact on the effective production capacity of the shared resource at case company X. However, it turns out that the magnitude of the impact depends on the product range. For Mid-range products, the batch size does not directly influence the effective production capacity and therefore does not influence the total number of products produced. The diversity of products that can be produced increases significantly with a smaller batch size. When a smaller batch size results in the production of an increasing variety of Mid-range product families, the capacity decreases with 2% for every 5 Mid-range product families produced daily.
For High-end products, the batch size does influence the effective production capacity. For every High-end batch, a changeover is required. Therefore, the capacity decreases in an exponential shaped line, shown in Figure 7.2. Decreasing the High-end batch size towards 360 units results in a capacity decrease of 5%. A batch size of 180 results in a capacity loss of 10%. The smallest tested batch size (60) results in a capacity loss of 28%.
38 a decrease of batch size is only possible for the 1st and 4th yearly quarter. This results in the necessity of a variable batch size.
Figure 7.1: Overcapacity vs capacity decrease 7.2 Discussion
The aim of this study was to investigate the impact of batch sizes on effective production capacity. In the conceptual model, discussed in section 2 of this paper, the impact of the batch sizes was expected to have a positive impact on the diversity of products that could be produced. On the other side, lower effective production capacity was expected to result in lower total production output. The results of this study are partly in line with these expectations, shown in section 7.1.
39 The validity of this research is ensured by the close involvement of Case company X by developing a representative model. During the research process, several feedback moments are scheduled, especially during the model development process.
The insights have to be placed in perspective, whereby the assumptions made should be taken into consideration. First of all, demand is only partly taken into account. However, results from Rakhorst (2019) indicate a large number of products with a small demand at the case company. Furthermore, the results of this study are only applicable to a small part of the production process of Case company X. The fact that the bottleneck is investigated, justifies the reason for this choice.
7.3 Limitations & Further Research
The limitations are discussed to indicate the restrictions of this study. Furthermore, these limitations are input for further research, which is discussed in the second paragraph.
Limitations
Due to several constraints, this research has limitations regarding reliability and generalization.
First of all, only one company is involved in this research. This makes this study less generalizable for other companies. However, companies with other characteristics could use the same approach to investigate the impact of batch sizes on effective production capacity. Only one part of the production process is taken into consideration. To make sure that the most important process is researched, the bottleneck is determined. Data from this shared resource has become input for this research.
40 Further research
The researcher made a tool in Excel and added the experiments manually to evaluate different batch sizes for the currently used production scheduling method. Therefore, this study has an exploratory nature. It turned out that the current scheduling method has a significant impact on the available capacity. In future research, a (mathematical) model could be developed to determine optimal production schedules based on production and demand requirements. This could lead to another planning method than Heijunka, which is currently used by the case company.
The impact of changing batch sizes for non-bottleneck machines could be investigated because this study only takes into account the bottleneck. Furthermore, the assumptions considered in this research could be taken into account. A combination of this study and the study of Rakhorst (2019) could lead to an optimal cost model, whereby cost and demand aspects regarding the market and production are taken into consideration. The study of Rakhorst (2019) could be used as input to determine the impact of smaller batch sizes on the weekly demand.
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43 Appendix I: Excel Model
Screenshot of Excel cells:
44 Appendix II: Changeover Times
45 Appendix III: Production Times
Family Production time (sec) Average (sec)
46 Appendix IV: Experiments
47 Appendix V: Sensitivity Analysis
Since High-end batches only influence the capacity of the shared resource, sensitivity analysis is done for the High-end experiments. Below, the changes and results of this analysis are shown.
Variable Change
Demand ratio High-end - 10% Demand ratio High-end +10% Changeovers High-end - 5 minutes Changeovers High-end + 5 minutes
Demand ratio High-end
0% 5% 10% 15% 20% 25% 30% 35% 40%
Batch size High-end
Demand ratio sensitivity (Capacity decrease)
Base case (20%) 30% 10% 0 50 100 150 200 250 N u m b er o f b at ch es
Batch size High-end
Demand ratio sensitivity (Variety increase)
48 Changeovers High-end 0% 5% 10% 15% 20% 25% 30% 35% 40% N u m b er o f b at ch es
Batch size High-end
High-end changeover sensitivity (Capacity decrease)
Base case (10 minutes) 15 minutes 5 minutes
0 50 100 150 200 250 N u m b er o f b at ch es
Batch size High-end
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