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The role of supply seasonality in the food-processing
industry: an MRP-based inventory control system
Thesis
by
ALET SUZAN MARIA KAMPHUIS
Dual Masters in Operations Management
Faculty of Economics and Business at University of Groningen – 1906674
Newcastle University Business School at Newcastle University – 13059685
Erve Hams 11 7577 NK Oldenzaal aletkamphuis@gmail.com
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ACKNOWLEDGEMENTS
This dissertation has been written as the closing chapter of my Double Degree Master Operations Management at the University of Groningen and the Newcastle University. I am very enthusiastic to present this final result, which could not have been completed without the help and assistance of the following people.
First of all, I would like to thank Jan Riezebos for being my leading supervisor during the whole period. His thoughtful feedback, positive approach, and patience have supported me a lot. Next, I would like to thank my supervisor at Aviko, the company where this dissertation was carried out, Meindert Visser for his enthusiasm, creativity, and helpful guidance. Moreover, I would like to thank the Supply Chain department at Aviko for the pleasant stay and, in particular, Gerwin Reindsen for providing relevant data and for his support in Microsoft Excel. Also Koen Olde Scholtenhuis and Frank Scholten, my carpool buddies, contributed to the good time I have had at Aviko. Next, I would like to thank Ying Yang for being my co-assessor, reading my thesis and providing helpful feedback. At last, I would like to thank my family and friends for their support and trust.
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ABSTRACT
In organizations, almost all products and services have to cope with seasonal end products demand fluctuations, but some also have to cope with seasonality in supply – especially in the food-processing industry. However, according to literature, there is a lack of inventory approaches able to cope with various products having different supply and demand patterns. This dissertation contributes to both practical and scientific relevance by aiming to properly incorporate supply seasonality and (seasonal) demand patterns in an inventory control system, taking into account the relevant characteristics of the food-processing industry. The research will be conducted by a single case study in the potato processing industry.
The first phase includes the explorative phase, which will show that three characteristics related to supply seasonality and (seasonal) demand patterns are not (properly) taken into account in inventory control in practice and not yet treated in this combination in inventory control literature. These characteristics are: changing safety stock, changing yield due to deterioration, and price volatility.
The second phase is the numerical phase, which will show how to include the three variables in an MRP-based inventory control system. The basic and widely known MRP system will be extended with two extra types of Gross Requirement. The first one includes the changing safety stock level (to account for demand patterns) and the second extension includes the influence of changing price and yield of the raw products on the build-up plan of so-called anticipation inventory (to account for supply seasonality).
To summarize, the explorative and numerical phase of this dissertation will show that when changing safety stock, changing yield due to deterioration, and price volatility are properly incorporated in the inventory control system, cost reductions can be achieved.
4 TABLE OF CONTENTS ACKNOWLEDGEMENTS ... 2 ABSTRACT ... 3 ABBREVIATIONS ... 7 1. INTRODUCTION ... 8 2. THEORETICAL BACKGROUND ... 11
2.1 Characteristics of the food-processing industry ... 11
2.2 Demand and supply seasonality ... 12
2.3 Inventory control ... 13 2.3.1 Models... 15 2.4 Conclusion ... 17 3. RESEARCH CONTEXT ... 19 3.1 Methodology ... 19 3.2 Case company ... 19
3.2.1 Scope of the research ... 19
3.3 Data collection and analysis ... 20
3.3.1 Explorative phase ... 20
3.3.2 Numerical phase ... 21
4. EXPLORATIVE PHASE ... 22
4.1 Inventory control at the case company ... 22
4.2 Findings from the explorative phase ... 25
4.2.1 Sales forecast and inventory accumulation ... 27
4.2.2 Production planning ... 28
4.2.3 DC & DC capacity (planning) ... 29
4.2.4 Plan build-up to realized build-up anticipation inventory ... 30
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5. NUMERICAL PHASE ... 34
5.1 End products selection ... 34
5.2 Origin of the system ... 36
5.2.1 Current situation ... 37
5.3 Extension of the MRP system ... 37
5.3.1 Extension 1: Safety stock ... 38
5.3.2 Extension 1: Test on historical data ... 42
5.3.3 Extension 2: Changing yield due to deterioration and price volatility ... 43
5.3.4 Extension 2: Test on historical data ... 50
6. DISCUSSION ... 52
6.1 Results explorative phase ... 52
6.2 Results numerical phase ... 52
7. CONCLUSIONS ... 55 REFERENCES ... 57 APPENDICES ... 60 Appendix A ... 60 Appendix B ... 61 Appendix C ... 62 Appendix D ... 63 Appendix E ... 64
E) 1. Results Shapiro-Wilk test, per end product per risk period ... 64
E) 2. Normal probability (QQ-) plot per end product per risk period ... 65
E) 3. Histograms per end product per risk period ... 67
Appendix F ... 68
Appendix G ... 69
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Appendix I ... 72
Appendix J ... 73
Appendix K ... 74
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ABBREVIATIONS
SC Supply Chain
DC Distribution Centre EOQ Economic Order Quantity
MTO Make-To-Order MTS Make-To-Stock Q Order Size R Reorder level SS Safety stock RP Risk period LT Lead time r Review period
CSL Cycle Service Level
FR Fill Rate
k Service factor
MRP Material Requirement Planning GR Gross requirements
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1. INTRODUCTION
In organizations, almost all products and services have to cope with seasonal end products demand fluctuations, but some also have to cope with supply seasonality – especially in the food-processing industry. Although literature shows a huge variety of definitions on seasonality (Miron 1990), this dissertation defines seasonality as cyclical variations over time (Canova & Hansen 1995; Slack et al. 2010). Synchronizing demand and supply leads to reliability in supply chain planning and therefore high customer satisfaction. However, this synchronization is impeded by - next to fluctuating consumer demand – supply uncertainties (Angkiriwang 2014). One important supply uncertainty is supply seasonality – usually where the raw products are seasonal agricultural products – defined as fluctuations in supply that ‘may be reasonably
forecastable, but some are usually also affected by unexpected variations in the weather and by changing economic conditions’ (Slack et al. 2010: 302). Recently, to stay competitive in today’s
dynamic business environment, organizations have a growing interest in the existence of supply seasonality in food products (Foster et al. 2014).
In general, two main types of food supply chain can be distinguished. First of all, supply chains for fresh agricultural products (such as fresh vegetables, flowers, fruit) and secondly supply chains for processed food products (such as snacks, desserts, canned food products) (Van der Vorst 2000). The main difference between the two supply chains is that agricultural products are used as raw products for the production of processed food products. Where agricultural end products are fresh and therefore subject to deterioration, the processed food end products include characteristics that create extension of the shelf life of the end products (e.g. by freezing or canning the product) (Akkerman & van Donk 2007). Nevertheless, up to packaging the (intermediate) processed food products are still subject to decay. Focusing on this characteristic, the main challenge when dealing with agricultural products is to keep the availability and quality of these products at the required level (Lynn Wilkins 1996).
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inventory, used when both demand and supply fluctuations are large but highly predictable
(Slack et al. 2010). This type of inventory differs from safety stock, since safety stock is only used to allow for short-term unexpected variability in demand and supply. For example, safety stock can be used for stable demand with small fluctuations, and anticipation inventory for high fluctuations in supply availability (Angkiriwang et al. 2014; Kampen et al. 2009; Slack et al. 2010).
Also Georgiadis et al. (2005) state that when dealing with high supply seasonality and (seasonal) patterns in end products demand, it is necessary to efficiently design the storage facilities. In addition, recognizing seasonality in the supply chain can clearly contribute to minimizing operating costs while achieving high customer service (Akkerman et al. 2010; Ehrenthal et al. 2014; Thomas & Griffin 1996). Accordingly, when not properly managing seasonality in inventory this can lead to out-of-stocks and excess inventory which in turn leads to, respectively, a low customer service level and high costs (Ehrenthal et al. 2014; Van der Vorst 2000).
Nevertheless, Akkerman et al. (2010) emphasize that there is a lack of inventory approaches able to cope with multiple products having different supply and demand patterns and shelf lives, which makes it an interesting field of research. Indeed, today’s food-processing companies that deal with supply seasonality in combination with (seasonal) demand patterns in inventory control, have difficulties to achieve both high customer service and minimize inventory costs (Foster et al. 2014). Next to the general factors where every processing company has to deal with, such as production capacity, the food-processing companies also have to deal with specific characteristics such as ‘perishability of end products, variable harvest and production yields, and
the huge impact of weather conditions on consumer demand’ (Van der Vorst & Beulens 2002:
415). These characteristics of the food-processing industry might influence the general factors and make inventory control even more challenging.
10 inventory control might have a huge impact on costs and customer service (Akkerman et al. 2010; Ehrenthal et al. 2014; Thomas & Griffin 1996). This research is structured by the following main- and sub questions.
Main research question:
How to deal with supply seasonality and (seasonal) demand patterns in an inventory control system, taking into account the relevant characteristics of the food-processing industry?
Sub questions:
1. How should inventory control cope with supply seasonality and (seasonal) demand patterns according to theory?
2. Which characteristics of the food-processing industry, related to supply seasonality and (seasonal) demand patterns, should be taken into account in inventory control according to practice?
3. How can we incorporate supply seasonality and (seasonal) demand patterns in an inventory control system, taking into account the relevant characteristics of the food industry?
4. How effective is the system if tested on historical data?
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2. THEORETICAL BACKGROUND
To be able to answer the main research question, a literature review on the general characteristics of the food-processing industry and on demand and supply seasonality in the food-processing industry are valuable for this dissertation. Therefore, both will be given in the first two sections of this chapter. Then, to answer the first sub question, several strategies and models related to seasonal patterns will be discussed.
2.1 Characteristics of the food-‐processing industry
As explained in the introduction section, this paper will mainly focus on the food-processing industry. In food-processing industries, agricultural raw products are used to produce consumer products with higher added value (Van der Vorst 2000). The agricultural nature of the raw products causes that the food-processing industry includes several characteristics that distinguish this industry from other industries. The characteristics are discussed in several academic papers and will be discussed here. Namely, the food-processing industry has to deal with challenges from:
- The perishability of raw products and in some cases also perishability of semi-finished and end products (Donk et al. 2001; Akkerman et al. 2007).
- The variability or seasonality in supply and quality of raw products due to unstable yield of farmers (Donk et al. 2001). Also, Van der Vorst (2000) states that the seasonality and variability in quality and quantity of supply is one of the most important characteristics of food supply chains.
12 - Strict temperature and time requirements of raw products and processed foods in transport and storage. Food products show continuous quality changes throughout the supply chain, from raw products to final consumption. Safety, health, and quality are therefore the central consideration in food distribution. (Van der Vorst 2000; Akkerman et al. 2007; Akkerman et al. 2010)
- Several recipes that are available for an end product, since pricing; quality; and supply of raw products are uncertain. Also, food companies have a divergent product structure (mostly in the packaging stage). (Donk et al. 2001)
- The production rate within the food-processing industry, which is mainly determined by capacity (Donk et al. 2001). Also, storage capacity is often limited and has to be shared among a large amount of products (Akkerman et al. 2007).
- Processes having a variable yield and processing time. Furthermore, there are often long and sequence-dependent set-up times between different types of products. (Donk 2001) Important to note is that most of the time not all of these characteristics are present in practice (Donk 2001).
2.2 Demand and supply seasonality
Recently, there is a growing interest in both the existence of and combination of demand and supply seasonality in food supply chains (Ehrenthal et al 2014; Foster et al. 2014). Where literature shows a huge variety on definitions of seasonality (Miron 1990), this paper defines seasonality as cyclical variations over time (Slack et al. 2010).
13 incorporating seasonality by a simple distinction between weekday and weekend sales (Ehrenthal et al. 2014).
Matching demand and supply is becoming even more difficult when there is next to demand (seasonal) patterns also seasonality in the availability and quality of raw products, or supply
seasonality. The existence of supply seasonality was already recognized in 1982, in the
production of black tea (Cloughley 1982). Supply seasonality in this case denoted that the teas produced in the off-season contained 50% less caffeine than the teas produced during the peak-harvesting season and therefore induced cyclical quality variations.
Years later, Keijbets (2008) studied the existence of seasonality in the availability of potatoes in the right quality. Raw products such as potatoes are of quality when they meet an agreed standard, as decided between the supplier and the buyer (Georgiadis et al. 2005). This is crucial for e.g. potato processing companies, since the quality of potatoes gradually decreases over time after harvesting them – during the storage in barns. Concluding from this study, Keijbets (2008) state that availability of suitable cultivars, potato yield, quality in its various aspects during the growing season, and good post-harvest storage are the most important factors that influence the quality of end products and the economic success of the potato processing industry. Both Cloughley (1982) and Keijbets (2008) have focused on supply seasonality in the food and drug producing industry but their papers do not discuss the issue on how to deal with supply seasonality in inventory control.
In short, section 2.1 showed literature on the characteristics of the food-processing industry and in section 2.2 a specific literature review on demand and supply seasonality in food supply chains was given. The next section will introduce different types of strategies and models that might be relevant for this dissertation in terms of dealing with supply seasonality and (seasonal) demand patterns in inventory control, taking into account the relevant characteristics of the food-processing industry.
2.3 Inventory control
14 - How should inventory control cope with supply seasonality and (seasonal) demand
patterns according to theory?
According to Kampen et al. (2009), the following two strategies are commonly used in inventory control when dealing with demand and/or supply uncertainties in the food-processing industry: 1) safety lead time, which means adding extra time to the actual lead time to prevent problems due to order delay – and 2) safety stock, which is building up extra stock to create allowance for short-term unexpected fluctuations in demand and supply (Kampen et al. 2009). These strategies reduce inventory shortages to an acceptable level and increase responsiveness (Slack et al., 2010). Various authors have studied the use of the two strategies, and one important detail worthy to mention here is that both strategies account for short-term uncertainties in demand and supply (Angkiriwang et al. 2014; Kampen et al. 2009; Slack et al. 2010).
Next, cycle inventory is a type of inventory that is used when a production facility is not able to produce every product every week, and production of some products have to be more than their weekly demand (Slack et al. 2010; Azoury & Miyaoka 2013). This might be due to e.g. a large number of products that have to be produced on a small of number of production lines; the products produced on the production lines are associated with a wide range of demand levels, differing from very high to very low; or contamination issues, food safety standards and regulations that cause significant setup times. (Azoury & Miyaoka 2013)
Further, when dealing with relatively large and highly predictable fluctuations in supply and demand, such as in freezing or canning seasonal food, so-called anticipation inventory can be used to minimize out-of-stock and maximize customer service level (Slack et al. 2010). An example of a food-processing company that has to cope with such fluctuations is a potato processing company. To explain, potatoes (raw products) are harvested only one or two times a year and the frozen end products processed from potatoes (e.g. fries) are demanded more in summer months than in winter months. In other words, there is clearly supply and demand seasonality. (Keijbets 2008)
15 limited storage capacity, which makes inventory control a challenging aspect for the food industry in order to stay competitive (Akkerman et al. 2007; Azoury & Miyaoka 2013).
To properly manage inventory control, it is vital to include relevant factors and characteristics. Nevertheless, although several articles partly treated seasonality or uncertainty in their articles, there is no literature focusing on supply seasonality and (seasonal) demand patterns – taking into account the relevant characteristics of the food-processing industry. This dissertation will introduce an inventory control system that incorporates the relevant characteristics. This system will be based on models from literature, treated in the next sub section.
2.3.1 Models
To clarify, this section will outline three models from which the findings are summarized at the end of this section in table 2.1. The findings are used to take a look deeper into the current models from literature that already partly treat seasonality and/or uncertainties in inventory control in the food-processing industry, and might be used as insight or input for the system that will be introduced in this dissertation.
16 approach. Therefore, they follow the ‘conceptual hierarchical production planning framework
for MTO-MTS production situations as discussed in Soman et al. (2004)’ (Soman et al. 2007:
194) and conclude that this framework is very useful for companies producing perishable end products and dealing with the described MTO-MTS challenges.
Second, Azoury & Miyaoka (2013) specifically focus on the food-processing industry with
frozen end products, where inventory levels are higher than what is needed to meet demand. This
is caused by a combination of several factors. First, the production facility cannot produce every product every week and some production runs end up with larger volumes than needed. This occurs because of highly variable demand levels and because a large number of products need to be produced on a small number of production lines with limited capacity and significant setup times. Next, it is unattractive to have high fluctuations in production levels from week to week. Production smoothing is used to solve this, but might result in higher production volumes than needed. At last, due to limited storage capacity at the production facility, large volumes of frozen end products need to be transported to external distribution centres (DCs) (Azoury & Miyaoka 2013). In order to reduce the level of excess inventory, Azoury & Miyaoka (2013) introduce a non-linear optimization model. Their model incorporates limited capacity, production smoothing, lot sizing, and transportation constraints, but it neglects seasonality in the availability of quality raw products, and thus the consequences of dealing with this in inventory control. (Azoury & Miyaoka 2013)
Third, Riezebos & Zhu (2014) state that, although Material Resource Planning is one of the best known techniques in the field of inventory planning and 75% of manufacturing companies use it as their main method of material planning, it does not take into account ‘frequently encountered
situations where essential parameters such as the lead time per item are known to change during the planning horizon’ (Riezebos & Zhu 2014: 2). Changing lead times might be caused by:
17 how to extend a MRP system when dealing with parameters that change over time in a specific situation.
To summarize, the answer to the first sub question can be found in these three findings from literature – as shortly summarized in table 2.1.
Author Model To cope with...
Soman et al. 2007 A conceptual hierarchical production planning framework for MTO-MTS production situations
Limited production capacity, costly setups, multiple products, perishability, and demand uncertainties Azoury & Miyaoka
2013
A non-linear optimization model Limited production and storage capacity, multiple products production smoothing due to fluctuations in demand, lot sizing, and transportation constraints
Riezebos & Zhu 2014 Extended MRP scheme Changing lead times over time, due to several (natural) factors
Table 2.1: Existing inventory models or systems from literature
2.4 Conclusion
The end-goal of this dissertation is to incorporate supply seasonality, demand patterns and relevant characteristics of the food-processing industry in an inventory control system (based on the models and systems found in the previous section) to decide more accurately on inventory control.
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3. RESEARCH CONTEXT
3.1 Methodology
As explained in the previous section, to answer the research questions, a single case study will be conducted. The selected company should be suitable for the purposes of this research: the company should be a food manufacturer and the company has to cope with supply seasonality in combination with (seasonal) demand patterns. The next section will first elaborate on the case company and the scope of the research, and then the methodology on data collection and analysis will be explained.
3.2 Case company
Based on the criteria from the literature gap and theoretical framework, a potato-processing company in the Netherlands is chosen as the case company. The case company is one of the four largest potato processors in the world and processes 1.7 million tons per year of agricultural raw products (potatoes) into almost 1200 different – either chilled or frozen – end products with higher added value. Due to the agricultural nature of the potatoes, the availability and quality of these raw products are heavily subject to seasonal patterns (supply seasonality). To account for the large but relatively predictable fluctuations in supply, the case company holds anticipation
inventory (as defined by Slack et al. 2010). Moreover, the case company has to deal with
different types of products that all have different demand patterns. To account for the demand patterns, the case company holds safety stock.
3.2.1 Scope of the research
20 four fields that need to be taken into account: potato (supply) need; master production scheduling; distribution plan; sales forecast. Within each of the four fields, there are factors and characteristics that need to be taken into account in the midterm planning of the anticipation inventory. Those will be defined in the explorative phase, section 4. Thereafter, section 5 will incorporate the most important factors and characteristics in the inventory control system.
Figure 3.1: Scope of the research
3.3 Data collection and analysis
Data from the case company was gathered during a period of five months. To gain insight in the company, collect all relevant information, and analyse the appropriate data two subsequent phases have been completed: the explorative phase and the numerical phase.
3.3.1 Explorative phase
21 study database will be created with notes and other files, so that all gathered information could be retrieved later. At last, a chain of evidence will be maintained by feedback from and discussions with fellow students.
3.3.2 Numerical phase
The numerical phase will start with discussions with the demand & supply manager and the supply chain planner about the current situation and the challenges they experience in the midterm planning of the anticipation inventory. Next, relevant historical data of the case company in Microsoft Excel will be analysed and used to develop the inventory control system. To prevent that coincidences are analysed, and to keep data as recent and relevant as possible, as much data as available will be analysed. The case company has historical data available from 2010-2014 (five years). When going further back in time, there are too many missing data points within a data set, which makes the data not valid. Therefore, the five years of historical data are used for the analyses. Since data points will be analysed per week, almost five years of data shows approximately 230 data points. Moreover, the interesting annual points in the data are the moment of harvest, the period of keeping anticipation inventory on stock, and the period of producing/accumulating the anticipation inventory. The research model is depicted in figure 3.2 and shows the focus of both research phases.
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4. EXPLORATIVE PHASE
The explorative phase aims to answer the second sub question, defined as follows:
- Which characteristics of the food-processing industry, related to supply seasonality and
(seasonal) demand patterns, should be taken into account in inventory control according to practice?
This section will address the findings from practice; compare it with the theoretical findings from the previous section and show these in sequence of a decision-making process as realized by the case company. However, first, a more extensive description of the case company related to the aim of this dissertation will be provided.
4.1 Inventory control at the case company
As already explain, the case company is a potato-processing company in the Netherlands. This section will take a look deeper into inventory control at the case company.
23 Next to the difficulties from the supply side, there are also difficulties from the demand side. Although 70% of the end products have a stable demand pattern, the highest priority for the case company is maintaining a service level of 98,5% and therefore it is pursued to meet all customer demand, whenever the order is placed. Additionally, in summer months demand is higher than in winter months. So when the transition from summer to winter starts quite early, demand will drop drastically; and when the winter months fly by, demand will soon increase. Therefore, it can be stated that the case company has to deal with (seasonal) demand patterns (Ehrenthal et al. 2014).
To allow for the above-mentioned difficulties, the case company makes use of different strategies in terms of: safety stock, cycle inventory and grey stock inventory (bottom layers in figure 4.1 - cumulative). Safety stock and cycle inventory are both treated in literature and were already elaborated in section 2.3. The grey stock inventory for both sales and operations is a type of inventory not treated in literature but is unplanned and insurmountable inventory that arises during regular production in practice – according to interviews with the manager demand & supply, supply chain planner, and supply chain engineer. Next to these types of inventory there is one other important type of inventory: anticipation inventory, as defined by Slack et al. (2010) (top layer in figure 4.1). The reason the case company keeps anticipation inventory is because they have to cope with severe quality restrictions for a certain range of end products. To explain, since the quality of the potato slightly decreases over time due to its natural characteristic, a certain range of end products cannot be produced the whole year round. For example, after several weeks of storage the sugar formation within a potato is growing which causes that the end product will have a darker colour than the customer wants. Therefore, anticipation inventory needs to be built up in the ‘good quality weeks’ to be able to meet end products demand in the weeks (manufacturing) order release is not possible.
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Figure 4.1: Total end products inventory build-up - cumulative
Next to the elaboration of the inventory accumulation, it might be worth explaining the production planning and realization in more detail. To start, the production schedule for week X is released on the Monday morning of that week. The orders from this production schedule are completed in that week, in which a ‘week’ is defined as Monday to Sunday. Orders in this context are defined as manufacturing orders (i.e. items manufactured inside the plant) (Nicholas 1998). After the production process, the end product has to be stored for two days in freezing cells at the production location so that the temperature decreases to the desired level (minus 18 degrees). Since the production facilities run for seven days per week, and the two days of freezing are required, the maximum production time is nine days. This maximum production time is called, according to literature, the (manufacturing) lead time (LT) (Hopp & Spearman 2000). Moreover, the production schedule for week X has to be definitive already on the Tuesday in week X-1, or in other words six days before the start of the production week. These six days is called the review period (r). Both the lead time and review period together can be defined as risk period (RP), which is thus 15 days (nine days plus six days). During the risk period, it is not possible to adjust or add any orders. (Hopp & Spearman 2000)
0 10.000 20.000 30.000 40.000 50.000 60.000 1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 3 4 5 6 7 8 9 10 11 12 13 In ve nt or y le ve l Months (2012-‐2014)
Inventory accumulation -‐ Total deepfrozen products Demand plan
Safety Stock
+ Operations Grey Stock
+ Sales Grey Stock
+ Cycle Inventory
25 A review period of six days as previously described, however, only applies in the regular production weeks in which raw products are fully available in the required quality (figure 4.2).
Figure 4.2: Regular production risk period
For the weeks in which order release is not possible due to unavailability or insufficient quality of the raw products, the review period and therefore the risk period is much longer (figure 4.3). For example, some end products cannot be processed for 30 weeks per year; this means a review period of 30 weeks (210 days) plus a lead time of nine days is a risk period of 219 days. Properly managing the anticipation inventory is thus a challenging aspect for the case company.
Figure 4.3: Anticipation inventory risk period
4.2 Findings from the explorative phase
After the description of inventory control at the case company, this section will now show the
practical findings in more detail, and compare it to the theoretical findings from chapter 2. As
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27 4.2.1 Sales forecast and inventory accumulation
According to interview findings with the manager demand & supply on 8th
of August 2014 it can be stated that the case company maintains a weekly periodic review inventory approach. Weekly periodic review means that every week the inventory position of all products are reviewed, and based on these reviews the production schedule is made. Inventory position here is defined as the balance between on-hand inventory (i.e. physical inventory in stock), backorders, and replenishment orders (Nicholas 1998). When the inventory position of an end product reaches the reorder level (R), a manufacturing order is placed. The reorder level is defined as the sales forecast plus the determined level of safety stock (SS). Sales forecast here is a forecast per week for the coming year that is updated every week with the most recent data available (provided by the department ‘Demand Planning’). The timing of the manufacturing orders based on the reorder level may be irregular due to variation in demand rate, but the order size (Q) fluctuates around a constant level that can be set as the optimum economic order quantity (EOQ) (Nicholas 1998; Slack et al. 2010). At the case company, the EOQ is determined per semi-finished product, since the different end products made from one type of semi-finished product only differ in packaging. This means that several end products can be made from one semi-finished product, depending on how many end products within a semi-finished product have reached the reorder level and need to be produced in the same manufacturing order. Moreover, it is important to note that throughout this dissertation, in the context of the production process, the terms ‘semi-finished product’ and ‘end product’ are used interchangeable.
28 To give an indication of the current safety stock levels, figure 4.5 shows data from week 1 2013 until week 40 2014, with the blue line showing different service levels and the x-axis showing weeks of safety stock (based on weekly demand). This means that, for example, the lowest point in the figure shows that 2.4 weeks of safety stock resulted in a service level of 94% at some point in this period. The most crucial aspect in this figure is the red line that indicates 98.5% service level - the aim of the case company. The figure shows, however, that the service level (blue line) only crosses the required line of 98,5% at 3.4 or more weeks of safety stock and the trend line even crosses the required safety stock line at 4.3 weeks. In conclusion, the case company did not achieve its goal over the past two years.
Figure 4.5: Weeks of safety stock vs. Service level – case company
4.2.2 Production planning
29 able to satisfy customer (end product) demands. According to several interviewees, it is highly important to match available production capacity with raw material availability for all different semi-finished products. According to literature, first of all, the quality of end products and the economic success of the food-processing industry highly depend on the availability of raw material in the right quality. This, in turn, highly depends on weather conditions. Because one cannot influence the weather, it is difficult to forecast and therefore an uncertain aspect (Keijbets 2008). Second, production capacity has to be levelled over the production period, in order to set a uniform capacity level that requires the same number of staff and utilization of all production lines (Slack et al. 2010). This leads to the following statement of Donk (2001): ‘production rate
is mainly determined by capacity’ (Donk 2001: 300). In addition, Kampen et al. (2009)
emphasize that production capacity in the food-processing industry is highly utilized, which causes that production planning is not quite flexible and has to be planned properly. This strict production planning and capacity might be conflicting with the uncertain and unpredictable raw material availability.
Furthermore, the technical (im)-possibilities are important in terms of determining at which production location certain batches need to be produced. To explain, not every production location is capable to produce every product (Azoury & Miyaoka 2013; Soman et al. 2007). Since the case company has two different production locations that produce the products from the scope of this dissertation, it is an important aspect to take into account. At last the economic order quantity (EOQ), Azoury & Miyaoka (2013) demonstrate that EOQ is a significant factor when aiming to minimize costs in inventory control.
4.2.3 DC & DC capacity (planning)
After the production planning, the DC capacity and logistic plan are determined (figure 4.4). Based on findings from interviews with the supply chain engineer on the 18th of August it can be stated that, in general, the anticipation inventory products are stored further away from customer handling places than the regular make-to-stock production. Moreover, the geographical location
of the customer is taken into account in the distribution planning of the inventory among the
DCs – in order to prevent unnecessary time and costs of transhipments between DCs. Next to
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costs per DC are minimized as much as possible. To clarify, for DCs with high in/out costs it is
more profitable to store large volume of anticipation inventory instead of small volumes with relatively more in/out handling. As Azoury & Miyaoka define it as economies of scale of shipping products, they state that a properly designed distribution planning does contribute to cost minimization.
4.2.4 Plan build-‐up to realized build-‐up anticipation inventory
The plan of the build-up of anticipation inventory is based on the previous treated factors (summarized and clearly depicted in figure 4.4). Although there is a sequence in the decision making process, it is an iterative process to constantly match the relevant variables. Moreover, according to different interviews with the manager demand & supply and the supply chain planner (August, 2014), there are three more factors that are not or not properly taken into account yet. Also, there is no existing model from literature on how to include the combination of these three factors in the midterm level decision making of inventory control.
The first factor that is yet not properly taken into account in the decision making process is
safety stock. Since today’s volatile business environment requires a focus on minimizing
inventory costs while maintaining a high service level (Soman et al. 2014), it is important to accurately determine the safety stock level. To sufficient include this factor in the decision making process, it should be based on the error between the sales forecast and the realized sales, instead of only taking two or three times the weekly demand.
Second, the average yield of processing (Donk 2001, section 2.1) is 62%, which means that there are 1,6 potatoes needed to produce 1 end product. Important to note is that yield changes over time due to deterioration, or in other words due to damage, spoilage, vaporization, dryness, etc. (Bakker et al. 2012) that cause quality reduction of the potato over time. There is, however, at the case company no go/no-go point whether it is still profitable to process the potatoes into end products (e.g. at 55% yield). Indeed, these decisions are based on experience and ‘gut feeling’. At last, the case company specifically has to deal with deterioration of the potatoes in terms of:
1. Number of defects (green and black dots on the potato) – increases over time
31 3. The dry matter content - decreases over time, which leads to lower quality of the end
product.
In short, these three (deterioration) variables cause the total yield to change over time. Figure 4.6 shows a clear example – derived from the case company – of different yields resulting from the production of a semi-finished product, from week 30 (start early harvest) 2013 until week 20 (start anticipation inventory) 2014. This semi-finished product is used as example because it shows a clear declining trend over time, and peaks in the beginning of the early harvest (week 30) and in the beginning of the main harvest (week 38-44). After that, it decreases over time due to deterioration of the potato. The yield here is the output from a model used by the case company, in which the yield is measured based on three input variables (as explained above): Number of defects, roughness of the skin, and dry matter content.
Figure 4.6: An example of a product including yield changes over time
To the best of our knowledge, there is no literature taking into account this type of yield changes (due to deterioration) in inventory control in the food-processing industry.
32 flexible (according to several interviews at the case company with the manager demand & supply and the potato purchasing manager) due to the volatility of the market. The volatility of the market causes uncertainties on the one hand and opportunities on the other hand for food-processing companies. To anticipate on the opportunities and increase expected profits, managing the acquisition of (agricultural) raw products is an important aspect for inventory management (Kouvelis et al. 2009; Yang & Xia 2009). To elaborate, as Yang & Xia (2009) clearly explain: ‘Should the acquisition be made too early, the firm may incur unnecessary
holding costs and miss the opportunity for future acquisition at a cheaper price; should it be made too late, the firm may experience costly backlogging and squander the chance to acquire the raw material at an earlier cheaper price.’ (Yang & Xia 2009: 212) In short, properly
incorporating price volatility in inventory control is thus a valuable aspect for food-processing companies.
Derived from the case company figure 4.7 shows the price volatility of the potato market. In figure 4.7, the potato prices (per 100 kg) from 2010-2014 are shown. It might become clear from the figure that 2011, for example, was a so-called ‘good harvest year’ since the prices were low. In contrast, the harvest from 2012 was less successful which caused the prices to increase significantly.
Note: the harvests moments are in period 8/9 each year.
33
4.3 Conclusion
34
5. NUMERICAL PHASE
The numerical phase aims to answer the last two sub questions, defined as follows:
- How can we incorporate supply seasonality and (seasonal) demand patterns in an
inventory control system, taking into account the relevant characteristics of the food industry?
- How effective is the system if tested on historical data?
As shown in the previous section, three relevant characteristics are not yet (properly) taken into account in the inventory control at the case company and are not yet treated in this combination in literature. Therefore, this phase aims to incorporate these three in an inventory control system, defined as a quantitative model based on MRP technique, that can be used in order to support the decision making process of anticipation inventory control. The first sub section shows the selection of end products that will be analysed in the numerical phase. The second sub section will then outline the content of the inventory control system, starting with testing whether the MRP system is suitable for this case research. Then, the two extensions to the system will be introduced and tested on historical data.
5.1 End products selection
The selection of end products that will be used for the numerical analysis is based on a Pareto analysis (Nicholas 1998). In the scope of this research, the Pareto analysis can be used to determine which of the semi-finished products on anticipation inventory count for the largest share of the total anticipation inventory costs. In this case, the Pareto analysis is done with semi-finished products because (anticipation) inventory costs are determined per semi-semi-finished product and not per end product. The yearly costs (based on data from 2014) of anticipation inventory per semi-finished product can be determined by the following formula:
𝑌𝑒𝑎𝑟𝑙𝑦 𝑣𝑜𝑙𝑢𝑚𝑒 𝐴𝐼 𝑖𝑛 𝑡𝑜𝑛𝑠 𝑝𝑒𝑟 𝑆𝐹 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 × 𝐴𝐼 𝑐𝑜𝑠𝑡𝑠 𝑝𝑒𝑟 𝑡𝑜𝑛 𝑆𝐹 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 = 𝑌𝑒𝑎𝑟𝑙𝑦 𝐴𝐼 𝑐𝑜𝑠𝑡𝑠 𝑝𝑒𝑟 𝑆𝐹 𝑝𝑟𝑜𝑑𝑢𝑐𝑡
Note: the abbreviation AI means anticipation inventory, and SF semi-finished product.
The results of the Pareto analysis with the semi-finished products are shown in the table in
35 table. Namely, the first six finished products account for 17% of the total number of semi-finished products (35) and count for 82% of the total anticipation inventory costs (€72,772.56). Also figure 5.1 depicts this intersection at the sixth product (x-axis) and 82% of the cumulative costs (y-axis).
Figure 5.1: Pareto analysis
Some semi-finished products only link to one end product, while others to 15 different end products. The first six semi-finished products from the Pareto analysis are in total linked to 24 different end products. The next step is to make a selection of four interesting end products out of these 24 end products to analyze in the numerical phase. To keep the numerical phase valid, the first criterion to select the end products is that the end product should have historical data of five years. To explain, several end products are introduced only two or three years ago and are therefore not valid for this research. The second selection criterion is that the products need to differ as much as possible in demand pattern from each other, so that end products with high, medium and low variability in the demand patterns will be analyzed. At last, it might be interesting that the selected end products differ in number of weeks of anticipation inventory (e.g. a product with 9 weeks of anticipation inventory, and a product with 21 weeks of anticipation inventory), because the more weeks of anticipation inventory, the less flexibility in production.
Taking into account the criteria results in a list of end products as shown in table 5.1. Unfortunately, there were no products with high demand variability that have enough historical
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 C u m u la tive p e rce n ta g e
Number of semi-finished products
36 data to do the numerical analysis. Therefore, two products with medium demand variability and three products with low demand variability were chosen for the analysis. The four selected products differ in semi-finished products and thus in the period of anticipation inventory (table 5.1).
End product Semi-finished product
Anticipation inventory period
Type of end product Demand variability
240522 831064 21-32 French fries Low
220510 830242 11-32 Fast food fries Low
801861 833272 21-32 Fast food fries Medium
800264 830352 18-32 Wedges Low
Table 5.1. The four selected end products within the scope of the research
All in all, with the end products from table 5.1 the numerical phase will be executed, and changing safety stock, changing yield due to deterioration, and price volatility will be incorporated in a MRP system.
5.2 Origin of the system
A Material Requirements Planning (MRP) system was chosen because it is one of the best known techniques in the field of inventory planning and 75% of manufacturing companies use it as the main method for material planning (Kampen et al. 2009), and therefore good applicable in practice. The purpose of the MRP system is to determine both the quantities and timing of orders. The basic MRP technique, however, lacks support for the following:
- Situations where the parameters are known to change during the planning horizon (Riezebos & Zhu 2014)
37
Note: A more detailed explanation of the basic MRP system and the terms used in the MRP
technique can be found in appendix D. 5.2.1 Current situation
To test whether this technique is indeed applicable for the case research, the current situation (from 2010-2014) of the case company is modeled into the basic MRP system. Table 5.2 shows the findings. The projected on-hand inventory levels from reality are compared to the projected on-hand inventory levels as modeled in the MRP system. Although the values from the model and from reality are not exactly the same, this table shows that the values are relatively close to each other for the four end products. Also, the standard deviations of the errors show a relatively low value compared to the mean inventory levels. Therefore, we assume the MRP system to be suitable for our analysis.
End product
Mean inventory level (practice)
Mean inventory level (theory)
Mean error practice and theory Standard deviation error 240522 681.0 675.0 7.67 112.92 220510 469.6 470.2 -0.21 40.98 801861 831.1 837.2 -5.91 146.07 800264 325.7 325.4 -0.03 36.20
Table 5.2: Results modeling current situation case company in MRP system
5.3 Extension of the MRP system
Since the MRP technique is suitable for the case research, this section aims to extend the basic system for food-processing companies dealing with changing safety stock, changing yield due to deterioration, and price volatility. The changing factors will be modelled into the system based on the data from case company and by the following variables and parameters:
Gross requirements (1): GR 1 - weekly forecasted demand
Gross requirements (2): GR 2 - weekly (changing) level of safety stock
Gross requirements (3): GR 3 - anticipation inventory build-up based on changing potato price and yield due to deterioration
38 Scheduled receipts: SR - production orders
Net requirements: NR - production plan defined by:
𝑁R = 𝑂𝐻𝐼 + 𝑆𝑅 − 𝐺𝑅 1 + 𝐺𝑅 2 + 𝐺𝑅 3
To elaborate, there are two extra gross requirements defined. The first one, GR 2, shows the level of safety stock and the second one, GR 3, shows the build up for the anticipation inventory based on changing price and yield constraints. Moreover, an important addition in the extension of the MRP technique here is that a distinction is made between two different types of risk period – regular production risk period and anticipation inventory risk period – by adding a row in the MRP table under the week numbers. This row shows a “0” when that week is a regular production week, and a “1” when that week falls into the anticipation inventory risk period. The following sub section will elaborate how to include GR 2 and 3 into the inventory control system and will test this on historical data.
5.3.1 Extension 1: Safety stock
39 1999) The results from the tests with these different tools are shown in appendix E, and summarized in the following table (table 5.3):
End product
Demand variability (weekly)
Risk period: regular production
Risk period: anticipation inventory
240522 Low Gamma (p = 0.007) Gamma (p = 0.000)
220510 Low Normal (p = 0.112) Normal (p = 0.067)
801861 Medium Normal (p = 0.508) Normal (p = 0.151)
800264 Low Gamma (p = 0.000) Gamma (p = 0.001)
Table 5.3: Distribution of demand per risk period
As shown in the table and elaborated in appendix E, four out of eight datasets are normal distributed. The other four datasets are assumed to be gamma distributed, based on the distribution shown in the histograms in appendix E. The second step now is to take a look deeper into the formulas to calculate a level of safety stock for end products with gamma and normal demand distribution.
The first parameter needed for these formulas is the service level of the case company. According to Stadtler & Kilger (2007) various service levels are used as indicators for the delivery performance of a company – which is a performance indicator for supply chains. The two most relevant service levels (Stadtler & Kilger 2007) are introduced here. The first is the cycle service level (CSL). The cycle service level is defined as the frequency of not having inventory shortage during the replenishment cycle. The second service level is the fill rate (FR), quantity-oriented and defined as the proportion of customer demands that can be fulfilled from inventory on-hand (Chopra et al. 2004; Stadtler & Kilger 2007).
40 demand that was met from stock – which thus refers to the FR. The main difference between using either the CSL or the FR to determine safety stock is as follows: A FR of 98.5% leads to a lower customer service than a CSL of 98.5%, but allows for carrying less safety stock than with a CSL of 98.5% (Man-Yi & Xiao-Wo 2006). All in all, because the case company strives to have a CSL of 98.5%, this dissertation will determine safety stocks based on a CSL of 98.5%.
In short, the variables and parameters – that will be used in the formulas for safety stock and to test the formulas on historical data (Chopra 2003) – are introduced:
CSL: Cycle service level
k: Service factor, based on service level
SS: Safety stock
RP: Risk period, defined as review period plus (manufacturing) lead time - RP0: the regular production risk period
- RP1: the anticipation inventory risk period D!: Actual weekly demand
F!: Forecasted weekly demand t: Time (in terms of week) t!: Start week current risk period t!: Start week last risk period
t!+ RP: Last risk period (for either RP0 or RP1)
To calculate the safety stock level for week t!, the following formulas are used:
𝐷!": Sum actual weekly demand, per risk period (either RP0 or RP1)
𝐷!" = !!!!!!"𝐷!
𝐹!": Sum forecasted weekly demand, per risk period (either RP0 or RP1) 𝐹!" = !!!!"𝐹!
41 𝜀!" : Error between actual demand and forecasted demand, per risk period (either RP0 or RP1)
𝜀!" = 𝐷!"− 𝐹!"
𝜎!": Standard deviation of the error, per risk period (either RP0 or RP1) 𝜎!" = 𝑆𝑇𝐷𝐸𝑉 [𝜀!"!!! … 𝜀!"!!!!" ]
(Chopra 2003)
Important to note is that the standard deviation of the error between the actual and forecasted demand is used. The reason for this is that the case company updates demand forecast every week, and thus that there is forecast available. The accuracy of this forecast is highly important when determining the safety stock level. Moreover, the extension of the system (GR 2) is
designed so that it takes into account the historical data of the last risk period to determine safety stock level for the current risk period (for either 0 or 1). Therefore, these variables are constantly up-to-date and the level of safety stock will change per risk period. This will be modelled in the MRP system by adding a new line of GR 2.
First, the following formulas can be used to calculate the safety stock level (for t! and future)
when demand is normal distributed.
𝑆𝑆 = 𝑘 ∗ 𝜎!" with
𝑘 = 𝑁𝑂𝑅𝑀𝑆𝐼𝑁𝑉 (𝐶𝑆𝐿)
Second, when demand is gamma distributed, the safety stock level (for t! and future) can be
calculated by the following formula.
42 To include safety stock as gross requirement (2) in this research, (historical) data of the case company is used as input for the above explained formulas. Also, the CSL of 98.5% and the associated k of 2.17 are set by the case company and used in this researched. In appendix F a screenshot of the first extension of the system is depicted.
5.3.2 Extension 1: Test on historical data
The first extension of the MRP system was tested on historical data from week 1 2010 until week 40 2014, and compared to the safety stock level maintained by the case company during this period. This resulted in graphs as shown in appendix G and in a cost comparison as shown in table 5.4. This table shows that the share of safety stock costs within the total inventory would have been €397,604.22 less over the past five years for the selected four end product with the calculation from theory instead of the current determination by the case company. This in turn means that the required level of safety stock for at least three products (240522, 801861 and 800264) was significantly lower than the level the case company maintained. In other words, the share of the safety stock within the total projected on hand inventory is different than expected from the case company. This is clearly depicted in the graphs in appendix G and can be explained by the fact that the case company currently maintains the same way of calculating safety stock for each product. The new introduced way of calculating safety stock takes into account the forecast accuracy per end product (depending on demand variability), so that safety stock level for a product will be high when forecast accuracy is low, and low when forecast accuracy is high.
End product Safety stock (practice) Safety stock (theory) Difference
240522 €311,855.57 €138,321.96 €173,533.61
220510 €448,258.40 €502,191.11 - €53,932.71
801861 €475,799.45 €322,077.63 €153,721.82
800264 €433,400.60 €309,119.10 €124,281.50
+ €397,604.22
43 5.3.3 Extension 2: Changing yield due to deterioration and price volatility
This section will describe the second extension of the inventory control system (GR 3). As described in previous sections, the case company maintains anticipation inventory during an X number of weeks throughout the year to account for supply seasonality.
In the perfect (unreal) situation, taking the tactical point of view from the SC department at the case company, all anticipation inventory would be build up in the last moment of order release to keep costs of end products inventory as low as possible. However, when taking the point of view from the operations department, there are conflicting interests concerning the anticipation inventory build-up. To explain, the main interest for operations is to achieve the highest possible yield, and not the lowest inventory costs. Yield changes over time due to the expected deterioration of the potato raw products, which makes it desirable for the operations department to process potatoes as soon as possible into end products after the main harvest (around week 36). A third stakeholder in the build-up process of anticipation inventory that has conflicting interests is the supplier of the raw products (potatoes). This party aims for a constant build-up of the anticipation inventory, so that a continuous supply of raw products can be provided.
The figures below (figure 5.2) sketch the ideal anticipation inventory level from week 34 this year to week 33 next year for the three interests, assuming that the last moment of order release is week 19; the start of the risk period is week 20; demand during the anticipation inventory risk period is from week 20 to week 32; demand during the risk period is constant; and the first next possible moment of order release and therefore the end of the risk period is week 32 (Note: the regular inventory levels are disregarded in the figures).
44 Currently, the case company plans production of the anticipation inventory as late as possible, so that end products inventory costs are minimized. This planning is partly based on the smoothing factor indicated by the ERP system of the case company and is highly dependent on relevant constraints (e.g. production capacity, raw products availability – figure 4.4). In general, according to the supply chain planner, it can be assumed that when the anticipation inventory risk period is e.g. 12 weeks, this anticipation inventory will be build up in the 9 weeks (i.e. 75% of 12) before the start of the anticipation inventory RP. Concerning the planning of anticipation inventory build-up, it might be worth taking a deeper look into the impact of the costs of changing yield and raw products price volatility instead of only inventory costs.
First of all, to be able to include yield changes due to deterioration into the inventory control system, it was aimed to analyze the actual yield achieved over the past five years and compare this to the forecasted/expected yield during that period. The selected four end products for the numerical analysis are being produced at two different production locations. However, due to identical production processes and characteristics of raw products, it is assumed that the changes in yield for both locations will act in the same way. To clarify, only storage conditions and technological equipment might cause differences between the two locations, but these are negligible in this situation – according to the manager demand & supply. Therefore, for this research, the yield of only one production location will be analyzed. Moreover, due to limited available data the yield cannot be analyzed in terms of weeks, but only in terms of months. Due to the same reason, it can also be stated that there is only data available from July 2010 until November 2013. This is approximately three and a half years and includes 41 months-data points. Also, the calculations on yield changes due to deterioration can only be based on changes in dry matter content of the potatoes since there is only data available of this variable. This means that the other two variables that influence the changing yield – number of defects and roughness of the skin – cannot be taken into account in these analyses.
45 have even longer anticipation inventory RPs. For example, product 830242 even has an anticipation inventory RP of approximately four months.
Note: Appendix H shows more elaborated graphs per semi-finished product.
Figure 5.3: Yield decrease due to deterioration
Further, the linear trend lines in figure 5.3 results in the following formulas per semi-finished product. The 𝑦 value here refers to the yield, and the 𝑥 value to the months in a year, starting with the first month of the main harvest (month 8, August) as 𝑥 = 1.
831064 (blue) 𝑦 = −0,4119𝑥 + 66,744 830242 (green) 𝑦 = −0,2793𝑥 + 56,49 833272 (red) 𝑦 = −0,3703𝑥 + 60,911 830352 (lilac) 𝑦 = −0,7299𝑥 + 71,808
The next step concerning the analysis of yield changes due to deterioration is to compare the yield-forecast accuracy of the current model used by the case company and the yield-forecast
50 55 60 65 70 75 08 09 10 11 12 13 01 02 03 04 05 Yi el d Month
YIELD DECREASE DUE TO DETERIORATION AVERAGE 2011-‐2014
46 based on the above linear formulas. The yield-forecast accuracy can be determined by calculating the error, defined as the deviation of the actual yield from the forecasted yield:
𝐸𝑟𝑟𝑜𝑟 𝑦𝑖𝑒𝑙𝑑 = 𝐴𝑐𝑡𝑢𝑎𝑙 𝑦𝑖𝑒𝑙𝑑 % − 𝑌𝑖𝑒𝑙𝑑 𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡 𝑓𝑟𝑜𝑚 𝑎 𝑚𝑜𝑑𝑒𝑙 (%)
Comparing these two errors shows results (table 5.5) from which can be concluded that the linear formulas show more accurate yield forecasts for the four selected end products than the current model used by the case company. To clarify, on average the error is 7.7 times larger when using the current model of the case company instead of the linear formulas.
End product Semi-finished product Model case company – error Model case company – absolute error Inventory control system – error Inventory control system – absolute error 240522 831064 7,56 7,84 0,17 1,65 220510 830242 6,52 6,52 -0,01 0,94 801861 833272 No data No data -0,02 0,98 800264 830352 6,19 7,68 0,14 1,58
Table 5.5: The error and absolute error between actual yield achieved and two different models
Therefore, in conclusion, it can be stated that the linear formulas on changing yield due to deterioration will be used in the inventory control system in this dissertation. As it is now showed how to include changing yield in the system, the second variable within GR 3 will be explained now: price volatility.
