Signed, sealed, delivered; it is broken
A quantitative analysis on the costs of dead-on-arrival productsT.V. van Swieten
Masterthesis Econometrics, Operation Research and Actuarial Studies Specialisation: Operation Research - Inventory Control
Signed, sealed, delivered; it is broken
A quantitative analysis on the costs of dead-on-arrival products
T.V. van Swieten
August 27, 2013
Abstract
Within this paper, case study research is conducted in three high-tech, original equipment manu-facturing (OEM), companies on the causes and cost impact of dead-on-arrival (DOA) spare-parts; parts that arrive in non-functional state at the customers’ site. Material and transport costs are quantified by the use of empirical data, while the impact on inventory control is evaluated through the theoretical analysis of a single item, (S −1, S) ordering policy with compound Poisson demand rates and exponential lead-times for replenishment. From this research we are able to conclude that the financial impact of DOAs comes down to approximately four percent of total revenues.
Preface
Within this paper the reader will find a result of four months of research on the subject of dead-on-arrival spare-parts. Prefore the start of this research, I was to a high extend unacquainted with the field of spare-part management and the phenomenon of dead-on-arrival products. It was a great experience on both an educational as personal level to be able to research three prominent companies in the field of high-technology, which enriched my knowledge on both after-sale services as well as the pitfalls and issues that occur in practical applications of field services as well as on the management level.
Evenly important, within this research I was able to use my knowledge and tools gained in the past four years of studying in the field of Econometrics, Operation Research and Actuarial Sci-ences. Especially within my Masters program I feel that I have been pushed to the limit, dived into unknown subjects and extended my ways of thinking. I cannot express enough gratitude towards the professors of the Master program, who have enthused and inspired me throughout the entire year. My special thanks go out to Professor Ruud Teunter, who took a prominent role in creating a valuable thesis. He granted me the freedom to explore my own way of researching, whilst supporting me substantially in the content of the subject. He is an inspiring professor with extensive mathemat-ical expertise, but above that a researcher with great talent for questioning the practmathemat-ical implication and application of the subject at hand.
Furthermore I wish to thank the Faes Group, and in particular Johan Faes en Bart van Dijk, for providing financial support, assistance in the introduction at various companies and the facilitation of a valuable discussion forum on DOA issues. I also would like to acknowledge the contribution of the three anonymous case study companies, which not only provided relevant data, but also assisted in the creation of a complete view on the DOA phenomenon by interviews and questionnaires. In particular, my thanks go out to Ruud, Walter and Paul.
Also, I would like to thank my family and friends for their support throughout the entire year, in which most of them did not see me too often due to my study related workload. Lastly, I am most grateful to my parents, who made my study and thesis writing possible in the first place.
CONTENTS
Contents
1 Introduction 7 2 Research methodology 11 2.1 Research method . . . 11 2.2 Case selection . . . 11 2.3 Terminology. . . 12 3 Definition of DOAs 13 4 DOA occurrence & causes 15 5 Cost components 19 5.1 Part damage . . . 195.2 Transportation . . . 22
6 Inventory Control 25 6.1 Setting. . . 26
6.2 Steady state distributions . . . 28
6.3 Numerical study of exponential lead-times . . . 31
6.4 Inventory cost per case study . . . 36
7 Results on cost mapping 38
8 Concluding remarks 40
LIST OF TABLES
List of Figures
1 Service Response Time process . . . 9
2 Logistical routes of spare-parts . . . 13
3 Interaction between root causes and severity levels of DOAs . . . 15
4 Reduction of logistical DOAs (case I). . . 18
5 Cost components of DOAs . . . 20
6 Average cost price of DOAs, ACPdoa at company II, (2007 − 2013) . . . 20
7 Logistical routes of DOAs . . . 21
8 Flow diagram of IL states (no DOAs) . . . 28
9 Flow diagram of IL states including DOAs with probability p for (S − 1, S) policy . 29 10 Optimal S levels and corresponding cost increase due to DOAs . . . 33
11 Holding and backorder cost at different levels of S levels for b = 99 and h = 1 . . . . 33
12 Optimal S for different DOA percentages (λ = 1, µ = 12, b = 99 , h = 1) . . . 34
13 Costs of DOA parts expressed as a percentage of its average part value. . . 38
List of Tables
1 Terminology and abbreviations repeatedly used in text . . . 122 Main (registered) DOA issues . . . 14
3 DOA frequencies per case study(2012) . . . 15
4 DOA registration lay-out per case (2012) . . . 17
5 Statistics of cost prices of DOA parts per case in Euros (2012) . . . 19
6 Repair ratios of DOAs . . . 21
7 Additional FSE cost due to installation DOA as percentage of average cost price (ACPdoa) . . . 22
8 Part damage cost as a fraction of the average DOA cost price (ACPdoa) . . . 22
9 Transportation costs . . . 23
10 Transportation costs as a percentage of average cost price (ACPdoa) . . . 23
11 Mathematical notations of inventory concepts . . . 26
12 Percentage increase in inventory costs due to DOAs for h = 1, µ = 12 and λ = 1 under optimal S . . . 32
13 Increase in inventory costs for service level constraints (the corresponding fill rates are denoted between brackets) . . . 35
14 The cost impact of DOAs on inventory cost for the three case study companies Euros (2012) for holding cost λ = 1, µ = 12, h = 1 . . . 36
15 Inventory costs in Euros (2012) . . . 37
1 INTRODUCTION
1
Introduction
After-sales services have been subject to accelerating attention over the past decade. Nowadays, the production industry widely acknowledges the revenues and profit that can be gained from superior post-product management. The service market is estimated to be at least four times larger than the market of the corresponding products itself [7]. Additionally it is shown that not only revenues, but also profits tend to be significantly higher than in regular production markets [14]. This holds in particular in the production industry. After-sales services account for approximately 25 percent of revenues across manufacturers and represent even 40 − 50 percent of their profits [28].
In the high-technology industry consistent numbers are found. Cohen [8] investigated 9 high-tech companies in the computer industry, where he found that, on average, over 40 percent of total oper-ating costs are assigned to logistics, such as transportation and inventory. This business makes up for a substantial part of revenues, due to the fact that a lot of parts exist out of scarce materials and are in many cases expensive to transport and store.
In recent years, especially in the high-tech industry, we have seen that Original Equipment Manu-facturer (OEM) companies have been subject to increasing pressure in the field of after-sale services from both internal and external factors. Internally, the introduction of continuously improving elec-tronics has increased the complexity of production, inventory and maintenance [40]. Additionally, life time cycles of electronics have decreased from 10 − 25 years to 2 − 5 years [25], which caused frequency and variety of demand to increase. This fast moving character of products complicates after-sale services such as maintenance and inventory management due to lack of predictability. Externally, worldwide internet access and usage caused a decrease in customer loyalty and increased competition between firms [27]. As a result, customers have become more demanding with respect to product reliability and service levels [8]. Companies that perform well in this branch will have a significant competitive advantage. Therefore, after-sales management is an important qualifier for the survival of a company [8] and can be used as a competitive tool [26].
One particular phenomenon that spoils efforts to manage after-sale services to maintain customer satisfaction is the occurrence of dead-on-arrivals (DOAs). An item is dead-on-arrival when it is received in a non-functional state, also referred to as a ‘zero-hours failure’. In practice, this is a very distressing event for customers. In most cases the ordered item is a critical spare-part needed for the functioning of some equipment or machine. The machine needs to be restored on short notice to avoid major down-times. The failure of the spare-part that caused machine-downtime in the first place, followed by the arrival of a broken service-part, leads to annoyance and dissatisfaction. DOAs might arise due to logistical deficiencies, such as incorrect handling during transportation or incorrect stocking of products (in moist places for example). Especially in the high-tech industry the designer not always anticipates the conditions a product is subject to in the distribution chan-nel [35]. Another issue that causes DOAs, is the occurrence of inspection errors. Especially in the high-tech industry, in which products are of high complexity, errors are not always detected. In case of critical spare-parts, causing serious hazard or high costs in case of failure, the false acceptance of non-functional parts (referred to as Type II errors) is much more expensive than the false rejection of functional parts (Type I error)[10]. This phenomenon has been studied thoroughly [34], [11], [10], although the focus is mainly on optimization of test rounds, assuming that the costs of type II errors are known. None of the studies remarked on the importance of finding the actual costs of sending broken parts into the field.
1 INTRODUCTION
[25] is, to the best of our knowledge, the only researcher that describes the phenomenon of DOAs and aims at quantifying its costs. He claims that the required value of inventory of spare-parts is approximately ten percent of yearly revenues in order to provide proper service to customers. There-fore, if DOAs occur in 1.5 percent of the cases, the company loses about 0.15 percent of its revenue value to DOAs. He calls this the ‘DOA reduction dollar opportunity’ and stresses that 0.15 percent of revenues is a significant profit enhancement opportunity. However, it is remarkable that only the cost of material is taken into account.
Logically, costs related to DOAs are more substantial than only the cost of material loss. In fact, these types of reverse logistics are a burden on the complete supply chain. This is measurable through the increase in spare-parts inventories, additional costs of engineering work and the material costs of the spare-part [40].
Especially for OEM companies, the delivery and stocking of spare-parts is costly. Many OEM companies work on an iterative level with their customers, meaning that most products are send to the customers’ plant in a conceptual state. The product is then finalized by adding customer-specific parts at a later moment in time. Hence, these types of companies need to stock large amounts of service-parts. As Cohen et al. [8] also point out, since most firms operate on a global level, service parts are dispersed on a wide geographical scale, which increases the complexity of transport and inventory control even further.
Not only does spare-part management encompass huge costs, it is also an important element for the quality of after-sale services. In the high-tech industry, in which the failure of parts can have huge implications on the production process, companies need to offer high availability of spare-parts and rapid repairs [19]. Homburg and Rudolph [20] found through interviews that customers put most weight on complaint handling, with a special focus on replacement guarantees, when rating service satisfaction.
1 INTRODUCTION
unrealistic one.
The logistical process of spare-parts, from demand until installation, is illustrated in Figure 1 in a simplified manner. Normally, the Field Service Engineer (FSE) orders a spare-part directly after the request for a spare-part arrives. The FSE schedules the repair at the customer site at some point in time after the planned arrival date of the spare-part. In case the part is critical and therefore needed urgently, the FSE might schedule the repair directly after the part arrives.
In most cases, the engineer does not discover that the item is DOA until it is installed. After installation, when the machine does not work properly, the FSE realises that the item is DOA. Con-sequently, a new item is ordered. This new part might have to be shipped from a central warehouse or even from an external supplier. Hence, on average the lead-time of the same service part might be considerably longer in case a DOA occurred (referred to as lead-time II in Fig1) than the initial lead-time (referred to as lead-time I). Then, the item needs to be installed a second time. As Figure 1 shows, this can cause a significant increase in both the length of the Inventory Response Time (IRT) and the Service Response Time (SRT).
Figure 1: Service Response Time process
1 INTRODUCTION
Overall, it seems that DOAs influence material costs, engineering hours, general labour time, in-ventory costs and possibly also contractual service costs. The purpose of this paper is to provide a first analysis of the direct and indirect cost components related to DOAs. Additionally, the mag-nitude of the different costs will be researched and a total effect on revenues and profits will be estimated. Since DOAs influence the complete supply chain, and therefore have a multidisciplinary character, reducing DOAs can be difficult. The cost of DOA reduction policies can therefore be quite substantial and should be compared to the profits of lowering DOA occurrences. This trade-off can only be conducted if the costs due to DOAs are known, which is the aim of this paper.
This research is conducted by combining existing knowledge on supply chain costs with raw data of three OEM companies. All three companies are stock-listed firms, operating in the high-tech industry. The use of case studies is of crucial importance, since DOAs are a practical problem. The hypothesis is that costs are often excessively high due to emergency handling, the average cost prices of DOAs and additional inventory costs. Without studying actual data, reliable cost mapping will be extremely difficult.
Although researching the financial impact of DOAs is the ultimate goal, an analysis of the main causes of DOAs is useful in order to determine the exact characteristics of the phenomenon and how DOAs are currently handled. This will indirectly provide insight in the cost factors.
Hence, the contribution of this paper is four-fold. First of all, the phenomenon of DOAs is re-searched in a broad sense, by analysing the definition, causes and damage severity. Then, a mapping of the different cost components is given, where after an exploratory analysis on the quantitative magnitude of these cost is conducted. Lastly, a deep-dive analysis will be dedicated to inventory control costs. A theoretical approach is used to lay out the effect of DOAs on the cost and optimality of ordering policies.
2 RESEARCH METHODOLOGY
2
Research methodology
2.1 Research method
In order to evaluate the costs concerning DOAs, three cases are studied. Case study research is par-ticularly suitable for research topics that are in their early stages, in which formatting of the subject is still in order [37]. Furthermore, practice based problems, and especially in case the context of different actions is crucial, case study analysis is a convenient research method [6]. This environ-ment of research applies to the nature of the DOA phenomenon. Little research has been performed in this field, hence the topic is still in a pre-mature stage. Also, the phenomenon of DOAs is an issue that arose from practice and so main findings should be based on observations from actual data. The aim of the study within this paper is a combination of exploratory, descriptive and explanatory research. First of all, since little research on the phenomenon of DOAs has been conducted in the past, key issues and variables concerned with DOAs have to be put in a conceptual framework. Exploratory research provides the flexibility to generate problem definitions and hypotheses. The second method used is descriptive research, based on the exploration done by interviews and data collection. A description of the phenomenon at hand is needed in order to delimit the subjects of research. Explanatory research is conducted by studying the collection of data of three companies. Both within-case analysis and cross-case analysis is carried out in order to provide the first relations between environmental settings and DOA occurrence. These analyses will furthermore establish fundamental insights in the main cost drivers of DOAs.
After-sale services are significantly more substantial in some businesses than in others. In the high-tech industry, spare-part management and maintenance services are a significant part of business [8] which makes it a suitable industry for investigating the effect of DOAs. Furthermore, since DOAs influence the complete supply chain, OEM companies are most convenient for data collection. In case we would look at a distributor of spare-parts, there is a risk of missing important cost aspects. The variety and intensity of the data related to DOAs differs widely among the three case stud-ies. In the appendix an overview is given of the data used in the analyses, the sources and the corresponding years in which the data was collected.
2.2 Case selection
All three OEM companies are stock market listed and producers of high technology products that operate on an international level. Although the three companies function in the same industry, com-pany characteristics are different due to branch and product variety. This is reflected in cost prices, revenues and profits. The fact that the companies differ in the majority of characteristics creates the opportunity to control for environmental variation. In order to extend results to general cases, or to define the limits of generalization, sample variation is crucial [12], [17].
2 RESEARCH METHODOLOGY
portfolio of 19, 000 different types of parts. The majority of the sold items, over 85 percent, were bought externally, although all items were distributed to customers and local warehouses directly from the factories. Revenues in 2012 came down to 0.68 billion Euros with an operating margin of 16.99 percent. The average part costs of DOAs in 2012 equals 4, 434 Euros, reaching its maximum of 427, 975 Euros per broken part.
The last case, case III, is a company that develops semi-conductor equipment, such as electronic chips and lithographic devices. It sold over 40, 000 parts in 2012, while the portfolio only exists of 380 different service parts. Revenues in 2012 were 4.31 billion Euros with a profit (EBITA) margin equal to 21.84 percent. Of the DOA cases the average costs came down to 15, 164 Euros per part, with a maximum cost price of 665, 024 Euros.
2.3 Terminology
Table6gives an overview of the terminology and abbreviations that are used in this paper. We aimed at selecting terminology in accordance with international standards. However, some researchers and companies might apply different references to these concepts.
Terminology Description
Cost price The cost required to produce a spare-part
Average cost price Average cost price of the spare-parts within the portfolio of a company After-sales service All actions undertaken after the part is sold
Reliability The quality performance of product over time Customer The end-user of the product/part
Manufacturer The OEM company, hence not necessarily the producer of the product Supplier The party that supplies parts to the OEM company
Service-part A part that is used in the after-sales process
Dependability The collective performance of reliability, availability of products and maintenance Non-functional Not of use to the customer
Abbreviation Description
ACPpart Average cost price of all spare-parts
ACPdoa Average cost price of the DOAs within the portfolio of a company
DOA Dead-on-arrival
DEFOA Defect-on-arrival
FRU Field Replaceable Unit
FSE Field Service Engineer
HUB Central transhipment base
NFF No Fault Found
OEM Original Equipment Manufacturer
3 DEFINITION OF DOAS
3
Definition of DOAs
As already mentioned in the introductory section, up to this point little is researched or written related to the subject of DOAs. International consensus on the definition of the DOA phenomenon does not exist yet. It is therefore crucial to delimit the concept of a DOA before researching the effects of it.
The definition of a DOA does not only differ widely among firms, but also within firms it is not always clearly specified when we are dealing with an actual DOA. The intention of outlining the precise term of a DOA is solely to make sure fair comparisons between case studies are made within this paper; not to create a definition for DOAs that would be suitable for every department, company and branch. This would be in no way convenient, since semi-conductor chips might not be rejected on their cosmetically appearance, while a computer display will.
The most general definition of a DOA would be to say that an item is DOA when it arrives in a ‘non-functional’ state. Within this generic definition many different interpretations are possible. The process of ‘arriving’ implies the existence of a sender and a receiver. Most OEM companies use external suppliers and deliver to Field Service Engineers (FSE). The most common logistical paths are presented in Figure2. Some companies do only take into account the DOAs that are sent by the supplier (so paths 1, 2, 5), while others also take into account the items send by the OEM company itself (paths 3 and 6). The fact that companies register these cases differently is mainly due to financial purposes. DOAs from external suppliers can be financially claimed, while DOAs from the producer itself need to be fixed on own account. Some companies prefer to separate these two financial issues completely.
Additionally, the receiving party may differ as well. Some companies do not see any use in analysing DOAs that do not have any customer impact. Hence, if a DOA is replaceable before it gets to the client, the defect is often not registered as a DOA. Other companies do register DOAs that arrive at the FSE, since they see the need in analysing such deficiencies.
In this paper all possible routes are included except for intercompany DOAs and DOAs that are supplied by an external supplier to the OEM company (path 2). This is due to the fact that two out of the three case studies do not register these cases, which makes analysis hard to verify and compare.
Figure 2: Logistical routes of spare-parts
3 DEFINITION OF DOAS
1.Completely dead 2.Cosmetically unacceptable 3.Delivery issues
Software Partly broken (Late delivery)
Hardware Scratched (Wrong customer)
Packaging Wrong product
Not clean Missing parts
Table 2: Main (registered) DOA issues
First of all, the item might be completely dead on arrival. This can be either due to software or hardware issues. This item will not function at all; not at the customer and not at the factory. This is the most severe state for DOAs, since the item might not be repairable and if it is, it might come with great costs and effort.
The second level includes all DOAs that are cosmetically unacceptable. This includes items that still function, but are subject to hardware damage such as scratches, indentations or unacceptable packaging. In general costs are a lot lower for these types of DOAs, especially when it only concerns the wrapping box. This area is not defined as a DOA in every company (one out of three case companies does not register cosmetically unacceptable items as DOAs), though it will be taken into account in this research since the procedure for handling these types of items is similar to the first category.
The third area concerns items that are non-functional to the customer due to delivery faults. This level is even less commonly registered as DOA. Late deliveries or wrong deliveries are often fixed without any registration and are seen as logistical issues. One could reason that in case parts are missing, the product is entirely useless to the customer, hence it is a DOA. An item that does not arrive at all, for instance in case it is delivered at a wrong address, cannot arrive ‘dead’. An item that is delivered late is also hard to quantify as a DOA, since we would need to specify the definition and range of ‘lateness’. An item that arrives a month after the deadline might be registered as non-functional, although an item that arrives five minutes overdue will not cause any serious problems. For these reasons we will leave out ‘late delivery’ and ‘wrong customer’ of the scope of DOAs. Hence, the definition of a DOA as used in this paper is as follows:
4 DOA OCCURRENCE & CAUSES
4
DOA occurrence & causes
In order to evaluate the costs of DOAs for OEM companies in the high-tech industry we start by evaluating the frequency and registered causes of DOAs. The cause of a DOA might influence the severity of damage and therefore also the costs. The companies researched in this paper all register DOAs very differently; while one company asks a written description from a FSE, the other only wishes the FSE to tick the checkbox ‘DOA’. The fact that these registrations differ provides us a wider scope of DOA issues to analyse, although comparison of environments is more difficult. Before analysing different causes and severity levels of DOAs, overall DOA frequency rates should be discussed. Table3presents the frequency statistics for the three case studies, based on the definition of DOAs as described in section 3. As the table shows, case I contains the lowest percentage of DOAs in 2012. This is partly due to the fact that case I recently went through a process of change, with a duration of three years, to reduce DOA occurrences. By simplifying logistical handling and packag-ing methods the ratio of DOAs decreased from 1.3 percent to 0.9 percent. In general it seems that we may well assume that the DOA occurrence ranges approximately between one and two percent of total sold service parts.
Case Total parts DOA parts % I 1, 187, 000 10, 595 0.9
II 71, 258 1337 1.9
III 42, 051 728 1.7
Table 3: DOA frequencies per case study(2012)
Figure3 represents the root causes of DOAs and is based on a combination of interviewing experts on DOAs within each company and descriptions of FSEs, registered when a DOA was found.
4 DOA OCCURRENCE & CAUSES
As Figure 3 shows, three areas are described as root causes of DOAs; logistics, part quality and service quality. Within these three areas the most common sub-causes are described. Lastly, a re-lation is presented between the different root causes and the levels of damage severity, as described in section 3. Below, each root cause is described individually, in order to provide more context on DOA concerning issues.
• Logistics
Within logistics, DOAs occur due to three main causes, namely transportation, (re)packaging and stocking. Some items need to be distributed worldwide and it is not uncommon that items are redistributed three or four times to other destinations. During transport, which can refer to shipment overseas, air cargo or road transportation, packages are subject to different weather conditions and are often handled roughly. This can cause items to break or to become cosmetically unacceptable.
Packaging is another obstacle in the process of delivering packages. The quality of the package obviously contributes significantly to the probability of DOAs, since a cardboard package that gets easily dented will cause damage on the items more easily than, for example, metal cases. Besides the package itself, the handling during (re)packaging can cause serious damage. Espe-cially in the high-tech industry, many parts are sensitive to light, touch or even air. Vacuum or electrical charged items are not uncommon. In case personnel are instructed insufficiently, items can break down easily by a single touch or the use of a wrong package.
The process of stocking influences DOA frequency rates in two ways. First of all, items might leave the warehouse in a defect state. This might be due to obsolescence, inattentive handling or stocking of parts in humid or moist places. The second issue is the processing of demands within the warehouse. Labelling outgoing parts will determine the destination and content of the package. Hence, incorrect labelling and processing causes delivery of faulty products or packages to be send to incorrect addresses.
All these factors drive DOA frequencies and influence all three registered levels of damage severity, as described in section 3, namely ‘dead items (1)’, ‘cosmetically unacceptable items (2)’ and ‘delivery issues (3)’.
• Service quality
Service quality refers to the capabilities, knowledge and tooling of the FSE. In case pack-ages are wrongly opened, products incorrectly handled or installed, DOAs might occur. The FSE might break the product by simply dropping it by accident, but might also have no knowl-edge on how to install a particular item, so that trial and error causes the spare-part to break. This might also happen when no FSE is involved and the customer is unaware of the handling descriptions that come along with the product. A part that arrives in perfect shape can there-fore become a registered DOA.
4 DOA OCCURRENCE & CAUSES
Service quality will only influence the registration of ‘dead items (1)’ and ‘cosmetically un-acceptable items (2)’, by damaging or breaking the product.
• Part quality
Part quality is another issue that raises the occurrence of DOAs. DOA frequency is influ-enced by part quality in several ways. First of all, in case spare-parts are fragile, this can be either due to software or hardware issues, the probability of a DOA is higher. Fragility can be reduced by using more robust material or better design. Some items are designed with little consideration concerning packaging or transportation.
A second issue that has been studied extensively [10], [11], [34], is the occurrence of errors in quality inspections. Before leaving the factory, most products are screened on defects and accepted if none are found. If an item is accepted while it is actually defect (Type II error), the product will be already DOA by the time it leaves the factory.
Insufficient part quality will only raise the level of registered ‘dead items (1)’, as described in section 3. In a very few cases the item can be cosmetically unacceptable due to the quality of the part, although scratches do not occur due to the quality of material in most cases, but rather due to incorrect handling.
Table3 presents the registered DOAs per company in percentage of the total DOA amount. As can be seen, case I registers DOA based on their level of severity, while case III registers root causes as described above. Case II unfortunately does not register causes or severity levels at all and only distinguishes between damaged/defect products and delivery related parts.
Case Issue %
I Broken/Defect Hardware 54
Software 24
Cosmetically unacceptable 11
Delivery issue Wrong product 9 Missing parts 2
II DOA 87
Delivery issue Wrong product 11 Missing parts 2
III Logistics Stock 3
Packaging 12 Transport 6 Part quality 26 Service Tooling 4 Instructions 5 Fault FSE 22 Unknown 22
Table 4: DOA registration lay-out per case (2012)
4 DOA OCCURRENCE & CAUSES
wrong deliveries will not be subject to expensive repair, while hardware defects might be scrapped in many cases for a full hundred percent.
As we can see from Table3, the majority of the DOAs are subject to severe damage (approximately eighty percent), while only a little more than ten percent is DOA due to cosmetic deficiencies. The other ten percent of DOA parts are due to delivery issues. This is also confirmed by the second case, in which delivery faults are also a little more than ten percent.
Case III provides insight in the possible root causes of DOAs. Case company III performs in-depth analyses, for each DOAs that occurs, to verify the (visual) analysis performed by the FSE. This results in reliable data on root causes, although even extensive analysis might not identify the exact reason for the failure of a spare-part. Logistical processes are often complex and multiple redistributions and repackaging are not uncommon. In case no testing has been performed during the distribution process, DOAs might even have left the factory, warehouse or one of its many dis-tributers in a defected state. Root causes are hard to identify in those cases.
As is shown in Table 3, 21% of the DOAs are due to logistical faults, another twenty-six percent are due to part quality issues. Service quality defects are mainly due to the handling of the FSE (twenty-two percent), with a total contribution of thirty-one percent. The other twenty-two percent are DOAs whereby the FSE and in-depth analysis was unable to construct a root cause. This is in line with the above statement that due to the complexity of logistics and multidisciplinary character of a DOA, root causes are hard to find.
Qualitative research related to the summarized data in Table 3 indicated that DOAs due to lo-gistical deficiencies is often underestimated. DOAs that arrive in packages of good shape are often assigned to part quality issues while the handling of the package might still be the cause of breakage. Logistical issues can be solved by improving the packaging process. Case study company I re-duced the number of packaging types by a significant amount (from approximately 600 to 25) and additionally increased information accessibility for logistical parties. In five years time the company was able to reduce (registered) logistical DOAs from 0.46 to 0.22 percent of total parts sold. This trend is shown in Figure4.
5 COST COMPONENTS
5
Cost components
Within this section the aim is to give an overview of the financial impact of DOA incidences by analysing different cost components in the supply chain. Unnecessary reverse logistics such as DOAs (and NFF) can be costly throughout the entire supply chain, which can be measured through in-creased inventory volumes, additional response times and additional manpower [40]. The focus within this cost analysis will be mainly on logistics, such as maintenance (repairs), transport and inventory, since this encompasses approximately forty percent of total operating costs in the high-tech industry [40].
The cost found within this research will be expressed in terms of the average cost price of the DOA parts in each case study. The reason for this research in the first place is due to the hypothesis that DOAs cause more cost than solely their cost price. Hence, by expressing the total financial loss in term of the cost price, we obtain a clear answer to the stated hypothesis.
Figure5shows the general set-up of the cost structure analysed in this section. Costs are driven for a significant part by three components, namely part damage, transportation and inventory control. The cost drivers have been categorized into direct and indirect cost. The indirect cost will not be discussed within this research, which should not imply that its relevance is questioned. In-depth analysis is required in order to construct any hypotheses on the cost magnitude of the indirect cost. The direct cost of the first two factors will be individually described and analysed in subsequent paragraphs within this section. The cost component inventory control will be discussed in the suc-ceeding section, since some technical evaluation of inventory policies are needed to sketch a realistic cost impact figure.
Another aspect that is influenced by DOAs is the magnitude of financial claims that result from violations of contractual service levels. In case the service customer degree is not met, customers are in most cases authorized to file a financial claim. These claims can vary from fixed payments to a certain amount of dollars per second downtime of machines. Although this is an important subject, none of the three case studies had any registration of financial claims in the past years. Moreover, the backorder costs of spare-part shortage is taken into account in section 6 and can be seen as a financial punishment of violating the obligation to serve customers within a certain time-frame. 5.1 Part damage
The direct costs of part damage are the cost of production, material of the spare-part and a small profit margin, referred to as the new buy value, the repair cost and the lost time of the FSE, as shown in Figure5.
The cost price of spare-parts, which include the costs of material and production, differ widely among the three case studies. Additionally, within each firm the cost prices of spare-parts are also subject to high variation, which is shown in Table5.
Average Maximum Variance Case I 710 112, 813 3, 449 Case II 4434 427, 975 16, 997 Case III 15164 665, 024 76, 435
5 COST COMPONENTS
Figure 5: Cost components of DOAs
Due to the high variation of cost prices among spare-parts, the financial loss that is incurred by the presence of DOAs might vary greatly, since it highly depends on whether the defect spare-part is expensive or not. Case II was able to provide cost prices of DOAs over the past five years, which are presented in Figure 6. It shows that the average cost price of spare-parts that become DOA is considerably stable over the years. The variation between the different years is only five percent. The average cost price per case study company will therefore be used in the calculations concerning the cost of part damage.
Figure 6: Average cost price of DOAs, ACPdoa at company II, (2007 − 2013)
5 COST COMPONENTS
scrapped (route 3) influences the total cost of part damage. It should be noted that not every OEM company will have their repair center at one of the factories, though for the sake of simplicity we present it as such.
Figure 7: Logistical routes of DOAs
Unfortunately, not all companies register the repair ratios of incoming DOAs. Of the three compa-nies analysed in this research, case II is the only company that could provide information on these procedures, although fifty percent of their cases received a status ‘unknown’. The company regis-tered over 30, 000 DOAs in the past decade, which gives us a little more than 15, 000 cases to rely on, which will be assumed to be sufficient for robust analysis.
The reparability statistics of case II are given in Table 6. As is shown, fifty-one percent of the DOAs are completely scrapped. Despite the fact that these parts are scrapped, the average repair costs and time are quite high. This is due to the fact that ninety-six percent of the DOAs that have been scrapped, preceding went to repair. Hence, the ratio of failed repairs is remarkably high. Another forty-four percent consist of (succesfully) repaired parts and the remaining five percent have been sent back to the warehouse to be stocked. This last procedure does come with some repair costs, probably due to small repairs at the warehouse or local distributor.
Treatment % of total Av. repair costs Av. repair time (hrs) Av. cost price
Repair 45 3, 139 4.4 4, 288
Scrap 51 801 4.4 4, 444
Return to stock 5 141 5.8 3, 323
5 COST COMPONENTS
Assuming 100 Euros per hour repair time, we can calculate the cost of part damage on average, by adding cost of ‘repair’, ‘scrap’ and ‘return to stock’ using the given ratios. We find that the average costs of part damage come down to 4, 510 Euros. Surprisingly, this amount is 2 percent higher than the average cost price of the DOAs, which equals 4, 434 Euros. Hence, scrapping all DOAs directly would imply less costs than using the repair process that is currently in place. Interviews revealed that the process of repair is mainly driven by customer requests for root cause analysis and feedback. Although no other case could provide reparability ratios, all agree that the process of repair might not be profitable at all times, but is of importance in the process of solving deficiencies and improving the percentage of unnecessary part failure.
Overall it seems that the financial loss of ‘part damage’ due to DOAs is reasonably quantified by using the complete scrap value, or equivalently the cost price, of the spare-part. This is in line with the rough assumption made by Jones [25] in his paper on customer satisfaction.
Another aspect to take into account are the lost hours of the FSE. These costs are often direct cost for the OEM company, since FSEs work on an hourly basis. On average FSE hours seem to fluctuate between three to five for installation of defect products. FSEs are paid around hundred Euros an hour, which means that we could add at least three-hundred Euros for lost hours to the FSE.
ACPdoa FSE hours % of ACPdoa
Case I 710 300 42.3
Case II 4, 434 300 6.8
Case III 15, 164 300 2.0
Table 7: Additional FSE cost due to installation DOA as percentage of average cost price (ACPdoa)
For all three cases this fixed cost has a different impact as can be seen in Table7, ranging from two to forty-eight percent of the average cost price. It should be noted that the hours of installation do not differ per company and do not increase with part costs. This is due to the fact that there is no data available on FSE hours in the remaining two case studies and there is no reason to assume more expensive parts come with additional installation hours.
The overall part damage cost are the sum of the scrap value and the FSE cost, which are both presented above. The total cost of part damage, expressed as a fraction of the average cost price of DOAs, denoted as ACPdoa is shown in Table 8.
ACPdoa Scrap value FSE hours % of ACPdoa
Case I 710 710 300 142.3
Case II 4434 4434 300 106.8
Case III 15164 15164 300 102.0
Table 8: Part damage cost as a fraction of the average DOA cost price (ACPdoa)
5.2 Transportation
5 COST COMPONENTS
Over the past decade distribution channels have been outsourced more and more, which is often referred to as third part logistics. This is due to the fact that most companies produce and deliver their parts in different continents. A coordinated distributor can gain from combining different de-liveries in certain areas, while the producer cannot. This shift lowered costs for OEM companies, although insights in transportation costs got partly lost.
All three companies use 150 Euros as the business case amount for average transportation. Ex-press services equal approximately eight times this amount, hence about 1200 Euros. Especially in the situation in which DOAs occur, it is reasonable to assume that emergency transport is used more often than in the case of standard maintenance procedures. Only one company, case III registers the ratio emergency transport used in their logistical process.
We use this information to calculate the average cost of transportation for both DOAs and reg-ular spare-parts. The formula used is straightforward, given by:
Total cost = Emergency cost × Emergency rate + Regular cost ×(1−Emergency rate) Table9shows that DOAs are in the field of transportation subject to approximately 1.5 the costs of normal spare-parts due to a significantly higher ratio of emergency transportation. This is due to the fact that DOAs cause a higher ratio of stock outs, especially in case spare-parts have low failure rates.
Return Regular cost Emergency cost Emergency % Total cost
DOA parts 150 1, 200 14 298.9
Normal parts 150 1, 200 4 191.9
Table 9: Transportation costs
All three companies work with lateral shipments between local warehouses and replenish from the central warehouses. Since costs for transport are not significantly different and all three seem to have similar logistical systems, we take the conclusions in table9 to be true in general.
Next to the fact that the ratio of emergency transport is significantly higher in case of DOAs, we also need to take into account the transport to the repair center from the local depot. Assuming this to be done by ‘normal’ transportation, hence assuming a four percent emergency transportation, and adding this to the cost of replacement of the DOA at the customers’ site, we obtain the total additional cost of transportation due to DOAs.
Transport cost =DOA transport cost + Normal transport cost = 298.9 + 191.9 = 490.7 This value is 2.5 higher than the cost of transportation in case the spare-part would have arrived in an acceptable condition. This implies an increase of 69, 11 and 3 percent of average cost price respectively for case I , II and III as can be seen in table10.
ACPdoa Transport cost % ACPdoa
Case I 710 490.7 69.1
Case II 4, 434 490.7 11.1
Case III 15, 164 490.7 3.2
5 COST COMPONENTS
On top of the bare costs of transportation there are also overhead costs that come with the admin-istration and analysis of DOAs. A sequence of cost components contain the process of packaging and package material, design improvement teams to reduce DOAs, managers to analyse DOAs and outbound personnel that inform customers properly.
6 INVENTORY CONTROL
6
Inventory Control
Within this section the additional cost of inventory in case of DOAs will be evaluated. We will review the impact of DOAs on inventory costs within the setting of single-echelon, continuous review and (s, S) ordering policies. This policy entails an order level s, at which an order is triggered. The order amount is such that the inventory position is replenished up to S. Since inventory can be reviewed continuously, the amount needed to increase the inventory level up to S is known. Under general conditions this policy is optimal for single-echelon systems [2].
We choose to evaluate a specific, (s, S) ordering policy, by setting s = S − 1. This is also known as a one-for-one replenishment policy, which means that the exact number of items that are demanded by the customer are directly reordered. This policy indirectly implies that ordering costs are insignifi-cant compared to the holding costs, and are therefore disregarded [3].
Since we are dealing with expensive spare-parts that have low demand rates, ordering cost will not drive the cost minimization process. Furthermore, the cost of additional transportation due to DOAs, which can be seen as ordering cost, is already evaluated in the previous section. Hence, the one-for-one replenishment policy is convenient and pragmatic for the purpose of our analysis. The inventory cost will therefore only include holding and backorder cost.
The inventory cost are controlled by forecasting demand, so that the inventory levels are main-tained at the lowest possible level while the waiting time for customers is restrained. Hence, the cost of inventory highly depends on the precision of demand forecasting. In case of spare-parts, failure rates are often of low intensity and can therefore be conveniently predicted by a pure Poisson process, which implies stationary and independent increments and demand size equal to one with probability one. If the mean and variance of demand can be deduced from historical data, forecasting demand in order to optimize stock levels becomes straightforward.
Many factors may cause demand to become more difficult to model. Preventive maintenance pro-cedures, for instance, cause demand for spare-parts to transform into a ‘lumpy’ process [43]. A ‘lumpy’ demand process is subject to sudden peaks in the quantity demanded by the customer. This complicates the ordering of (fixed) batches and minimization of inventory costs. Even if the time between the arrival of demands is known, the expected quantity is not, which is extremely variable in the case of stuttering Poisson processes [24]. In case of critical and expensive spare-parts, lumpy demand influences performance and economic return on capital significantly [36].
Despite the fact that inventory management becomes more complicated due to non-regularities in demand quantity, the arrivals of demand can still be predictable to a certain level. Due to preventive maintenance, forecasting the inter-event distribution of demand becomes even more accurate. In the case DOAs occur, demand does not only transform into a lumpy process, the arrivals become highly unpredictable as well. Forecasting parameters therefore encompass high variation, which increase either average holding costs or decrease customer service levels [44].
Such unpredictable demand is often modelled by a stuttering Poisson process; the occurrence of demand is modelled by a pure Poisson process and the size of demand is subject to a delayed ge-ometric distribution. This process will describe DOA occurrences in quite a precise manner for positive inventory levels. At the moment a demand comes in, the probability that another demand is created, by the occurrence of a DOA, is geometrically distributed.
6 INVENTORY CONTROL
process from the moment inventory hits the inventory level −1. Due to the non-uniformity of the different inventory levels, we are not able to evaluate inventory cost under fixed lead-times, which is a common assumption in inventory research. In order to model such a complicated process, we will assume exponentially distributed lead-times in order to be able to evaluate the different states of the inventory level and their complementary probabilities.
The next subsection will go into the details of the inventory setting used for evaluating the cost of DOAs. Then, the cost function for both the process without DOAs and the process including DOAs will be constructed through steady state distributions. Subsection 6.3 will present a numeri-cal study, based on the findings in subsection 6.2. The last subsection will provide the actual impact of DOAs on the inventory cost for the three case study companies.
The definitions and abbreviations used within this section are explained in table 11. The math-ematical notations are mainly based on the literature provided by Axs¨ater on inventory control [2] and are commonly used and widely known in inventory related research.
C Cost function
D(t) Demand in time-interval t fj probability of demand size j
fjk probability that k demand occurrences equals total size j IL Inventory level = stock on hand − backorders
IL+ Positive inventory level = max{IL, 0} IL− Negative inventory level = min{IL, 0}
IP Inventory position = stock on hand + outstanding orders − backorders p Probability of a DOA occurrence
S Order up-to level s Re-order level
S2 Fill rate = fraction of demand, satisfied immediately from stock on hand
S3 Ready rate = Pr(IL > 0) = fraction of time with positive stock on hand
λ Demand intensity rate µ Replenishment arrival rate Πi Probability of state IL = i
ρ λ/µ (< 1 in order to obtain an irreducible Markov chain)
Table 11: Mathematical notations of inventory concepts
6.1 Setting
A compound Poisson process models demand as a stochastic process with stationary and mutually independent increments [2]. The compounding distribution determines the size of each demand. In case the demand size and the probability of its occurrence are negatively related, the geometric Poisson process, also referred to as the ‘stuttering’ Poisson process, is a convenient way of modelling demand. Here, demand sizes are modelled by a delayed geometric distribution. This implies that the probability of demand size j is given by: fj = (1 − p)pj−1.
6 INVENTORY CONTROL fjk= j−1 X i=k−1 fik−1fj−1 (1)
Now, combining the Poisson demand process for demand arrivals with a geometric compound distri-bution for demand sizes, provides a total demand probability distridistri-bution. The probability of total demand j in time interval t is given by:
Pr(D(t) = j) = ∞ X k=0 λtk k! e λtfk j (2)
Linking this to the situation researched in this paper, we can describe p as the probability that a DOA occurs, in case a spare-part is demanded. In case no DOAs occur, p is equal to zero and hence fj = 1. Then, fjk = 1 for k = 1 and 0 otherwise. The demand process then transforms to a pure
Poisson process, defined by:
Pr(D(t) = j) = ∞ X k=0 λtk k! e λt (3)
As already mentioned in the introductory notes of this section, the stuttering Poisson process does not accurately describe the DOA process from the moment inventory levels become non-positive. The idea behind the dependences between demand arrivals and DOAs is as follows. At the time a demand comes in, a spare-part is sent to the customer. This spare-part may appear DOA, which causes an additional demand. A new spare-part will be sent to the customer, which also has a posi-tive probability of arriving DOA. In case the inventory level is zero DOAs do not occur any longer, since no spare-parts can be send to the customers’ site.
Hence, we are compelled to evaluate the different states of the inventory level separately, due to the lack of uniformity. If lead-times are assumed to be fixed, which is one of the most common as-sumptions in inventory control research, we are unable to evaluate the states of the inventory levels. We therefore assume the lead-time of replenishment to be identically and independently exponen-tially distributed, with arrival rate µ. This is a convenient assumption due to the fact that arrivals of replenishments are in that case memoryless and arrive independently, which makes the process easily tractable [33].
The assumption of exponential replenishment arrivals furthermore implies that the lead-time does not depend on the order quantity. This is a reasonable assumption, since obtaining a certain number of spare-parts from stock or production often covers only a small part of the total lead-time [33]. Next to the assumption concerning the demand process and the lead-time distribution, we need to make some additional assumptions to complete the setting. In the situation that demand cannot be satisfied, items are backordered. This implies that customers will not walk away in case a spare-part is not available, but instead wait for its arrival. Hence, no sales are lost due to a zero stock level. This is a fair assumption in spare-part management, since most parts cannot be obtained easily from another vendor.
6 INVENTORY CONTROL
The total cost will hence exists of shortage and holding costs. The total cost function is expressed as:
C = bE(IL−) + hE(IL+) = −bE (IL) + (h + b)E(IL+) (4) The expected inventory level will be evaluated through the probabilities of the steady states of the inventory level. These probabilities are evaluated in the next subsection, section 6.3. Using these probabilities we are able to calculate the cost function of inventory. Some numerical scenarios are evaluated in section 6.4. Within that subsection, we will also evaluate a so-called service level con-straint optimization scenario.
6.2 Steady state distributions
We start by evaluating the cost function of inventory for exponential lead-times. The relative in-crease in costs due to a pre-specified DOA probability p will be evaluated afterwards. As described in the previous subsection, we need to find expressions for both E(IL+) and E(IL).
We evaluate the stochastic behaviour of all the inventory level states, from −∞ up to S. This process is influenced by both the demand process and the replenishment distribution. Excluding any DOA possibilities, the flows and their corresponding probabilities from one state to another are presented in Figure8.
Figure 8: Flow diagram of IL states (no DOAs)
As shown in Figure8, the probability to shift from one state to another is defined by the probability of demand, equal to λ, and the probability of supply, equal to iµ. The reasoning behind the replen-ishment probability is as follows. Since we are dealing with an (S − 1, S) policy, an order of quantity i is placed at the moment demand of size i comes in. This puts us in state S − i with an outstanding order of quantity i. Hence, the probability to get into state S − i + 1 from state S − i is iµ, since this is the probability of the arrival of 1 part out of the i ordered parts.
These types of processes, in many different settings, are discussed in a numerous amount of papers, such as [4],[13] and [15], and textbooks [1], in which detailed proofs can be found of the derivations in this section. In order to find the steady state probability we look at the following set of equations:
6 INVENTORY CONTROL
for i ≤ S − 1. We focus on the steady state distribution, since it is of more importance to know the overall level of inventory in a given time-period than the inter-event distribution of the demand arrivals [24]. Due to the memoryless property of both the demand process and the lead-time distri-bution, the inventory level can be expressed as a continuous-time Markov chain with a state space ranging from S to −∞ [31]. Furthermore, we are dealing with an irreducible, positive recurrent Markov chain, which implies that the steady state exist, in case µ > λ. For a detailed proof we refer to a paper written by Liu and Yang [31]. However, many text books on queuing theory provide similar proofs.
In steady state, as ∆t → ∞, we have that Πi(t + ∆t) → Πi(t). By equating the inflows and
outflows of each state it is possible to find that:
ΠS = (1 − λ)ΠS+ µΠS−1 =⇒ ΠS−1=
λ µΠS Πi = (1 − λ − (S − i)µ)Πi+ λΠi+1+ (S − i − 1)µΠi−1 =⇒ Πi−1=
λ
(S − i − 1)µΠi for i ≤ S −1. Now, using thatPS
i=−∞Πi = 1 and defining parameter ρ = µλ−1 ⇒ λ((S −i−1)µ)−1=
ρ(S − i − 1)−1, we recursively solve the above equations and obtain:
Πi−1 = ρ S − i − 1Πi =⇒ Πi= ρi i!ΠS ΠS = 1 ρΠS−1 =⇒ ΠS = S−1 X i=−∞ ρi i! + 1 !−1
These explicit expressions are used to construct the cost function for the demand process in which the probability level of DOAs is set to zero. The next step is to find the steady state probabilities of the inventory level states for a process that does include DOAs. Then we are able to compare the cost differences.
Figure 9: Flow diagram of IL states including DOAs with probability p for (S − 1, S) policy
6 INVENTORY CONTROL
be seen in Figure9, the expected inventory level (IL) becomes considerably more complicated when DOAs are included. For positive inventory levels the demand process is influenced by DOAs. In practice, the negative inventory level is influenced by DOAs through the replenishments. In case the inventory level is positive, replenishments are placed in stock, hence DOAs will not be discovered until the customer receives the spare-part. For negative inventory levels, spare-parts are often sent directly to the customer to satisfy the backorder within the shortest time frame possible. Although we recognize the influence of DOAs on backorders, we disregard this factor in the analysis. We choose to do so, due to the fact that DOAs mostly occur due to deficiencies in storage, repack-aging and plural redistribution. In case a spare-part is sent directly to the customer from a supplier, the spare-part is to a less extend subject to logistical errors. Furthermore, in case we do take the DOA occurrences into account, a one-for-one replenishment policy might not be optimal any longer, since we would most probably anticipate on the possible occurrence of DOAs by ordering slightly more than the demand size.
As can be seen in Figure 9, the outflow from states S,..,1 is a finite sum to all other states with the lowerbound state to be −1. This sum of outflow probabilities for state Πi is defined
byPi−1
k=0λ(1 − p)pk+ λpi. This is equivalent to a geometric series and hence we simplify this to:
i−1 X k=0 λ(1 − p)pk+ λpi = λ(1 − p)1 − p i 1 − p + λp i = λ (5)
6 INVENTORY CONTROL • for i = S + 2 : ΠS−i = (λ + (i − 1)µ) ΠS−i+1− S X k=0 λpkΠk iµ • for S + 3 ≤ i : ΠS−i = λΠS−i+1 iµ
Now, using the fact that PS
i=−∞Πi = 1 we can solve the equations recursively and calculate the
optimal S level numerically. Then, the E(IL) and E(IL+) can be calculated. Since we do not have an explicit expression for both E(IL) and E(IL+), the evaluation of the cost impact of DOAs will be conducted by a numerical study. This is presented in the following subsection.
6.3 Numerical study of exponential lead-times
Within this subsection the inventory cost increase due to the presence of DOAs will be evaluated. In order to do so, realistic holding costs h, backorder costs b, demand rate λ and lead-time rate µ need to be determined.
The demand rates and lead-times will differ highly among different types of spare-parts. Lead-times depend on the availability of the spare-part at the central warehouse and additionally whether supply is internal or external. Within the high-tech industry, and in particular within the companies studied in this research, the failure-rate of parts is low on average. Cohen [8] finds in his study on fourteen firms within the computer industry a 0.87 turnover per year on average. We aspire a realistic base case, and therefore set the demand rate close to this number, at λ = 1, which corresponds to an expected demand of one spare-part per year. The lead-time will be taken to be one month, hence µ = 12. For items that are demanded only once a year, this seems to be a realistic replenishment rate. Furthermore, we need to determine the holding and backorder cost of inventory, which is some-what difficult. Holding cost depend on many factors, such as warehouse location, personnel salary, administration costs and risk of obsolescence. Companies register this in their own way and com-parison of these costs can be difficult.
The backorder costs are even more difficult to quantify, since stock-out can cause machine downtime, lower customer satisfaction and image infliction. Those factors mostly do not have an actual price tag attached. Oral et al. [32] find a relationship between gross profits and shortage costs, which is tested on approximately sixty distributors. However, no distinction is made between spare-part distributors and distributors of consumer products. Since we focus solely on spare-parts, this rela-tionship between profits and shortage cost might be highly underestimated, since machine-downtime is more costly than a customer waiting on a new television set.
6 INVENTORY CONTROL
field of inventory management, two very commonly used service level measures, are the so-called ‘fill rate’, which we denote by S2, and the ‘ready rate’ denoted by S3. These service levels are defined
as follows for a compound Poisson process [2]:
S2 = The fraction of demand immediately satisfied from stock on hand
= ∞ X k=1 ∞ X j=1 min j, kfkPr(IL = j) ∞ X k=1 kfk
S3 = The fraction of time that the inventory level is positive
= Pr(IL > 0)
The fill rate and the ready rate may differ in case the demand process is not pure Poisson. However, in case the probability of high demand sizes is small, the levels are approximately equal. The backorder cost and holding cost are related to the ready rate for compound Poisson processes (and fill rate in case of pure Poisson distributed demand) in the following manner, for the optimal order-up-to level S, denoted by S∗.
S3(S∗) ≤
b
h + b ≤ S3(S
∗+ 1). (6)
It should be noted that the above equation, (6), holds for compound Poisson processes, although not for the demand process that include a given DOA probability. However, it is still convenient to choose the cost parameters accordingly, since it still provides indication of a certain service level. Let us denote this ratio, b/(b + h), by dF R, which stands for the ‘approximate fill rate’. Within this numerical study we chose such a composition of backorder and holding costs such that dF R varies between 98.7 to 99.9 percent. These levels might seem high at first sight, but most high-tech companies do aim for service levels that are close to hundred percent for critical parts. This is mainly due to the fact that a machine contains a great amount of parts, which implicates that the service level for each part needs to be substantially high in order to maintain an acceptable service level overall.
Furthermore, the optimal S∗ level is always below dF R, as shown by (6). Hence, this might cause the actual fill rate for an optimal S to be significantly lower than implied by dF R. In case backorder probabilities are considerably sensitive to the order-up-to level S, the cost function can be steeply curved between S∗ and (S∗+ 1).
b = 75 99 125 200 350 1000
d
F R = 98.7 99.0 99.2 99.5 99.7 99.9 (Actual Fill Rates)
S∗ = 1 1 1 1 2 2 S = 1 S = 2
% DOA 1.0 2.35 3.10 3.65 4.95 0.57 1.75 (91.13) (99.55) 1.5 3.54 4.69 5.51 7.46 0.89 2.71 (90.70) (99.48) 2.0 4.73 6.26 7.36 9.96 1.23 3.75 (90.27) (99.41)
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Table 12 gives an overview of the increase in inventory costs due to different DOA probabilities. The impact of inventory causes a cost range from 2.35 percent per average DOA value up to ap-proximately 9.96 percent. Furthermore, the relative cost increase does not necessarily increase with backorder cost. This is due to the fact that for both the DOA demand process and the demand process without DOAs, an additional spare-part is placed in stock. This effect is most clearly shown in Figure10.
Figure 10: Optimal S levels and corresponding cost increase due to DOAs
Additionally shown in Table 12 are the actual fill rates with respect to the optimal S level for dif-ferent DOA percentages. As already mentioned previously in this section, the actual fill rate can be substantially lower than dF R, which is the case in this setting. For S∗ = 2 the levels do get close to the approximate fraction, however for S∗ = 1 the fill rates are remarkably low.
To see why this is, we need to look at the composition of the inventory cost. The backorder cost and holding cost both react differently to a change in S. This relation is shown in Figure11. As can be seen in the Figure, the inventory cost drops rapidly due to the behaviour of the backorder cost, which decreases with an exponential rate. Due to the fact that the spare-parts are slow-moving, one additional spare-part in stock implies the probability of backorders to fall immediately to a insignificant level.
Figure 11: Holding and backorder cost at different levels of S levels for b = 99 and h = 1
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Figure 12: Optimal S for different DOA percentages (λ = 1, µ = 12, b = 99 , h = 1)
Figure12presents the costs for different stock levels for one demand per year (on the left) and three demands per year (on the right). The left figure shows that only in case the DOA percentage is above twenty-five percent the costs for having an additional spare-part in stock (S = 2) gets lower than maintaining the level of one part (S = 1). This level is extremely high; no spare-parts in any of the three cases reached such a rate in 2012.
In the right figure, the case in which a rate of three demands per year is assumed, the costs of the order-up-to levels S = 2 and S = 3 are compared. The cost of level S = 1 is left out, since this would be an unusual choice for three demands per year and causes extremely high (backorder) costs. We see that the break-even point occurs at a lower DOA percentage than in the case of a demand rate equal to one part per year. The DOA rate should be above approximately thirteen percent in order to make additional spare-part stocking profitable. Hence, the frequency of demand influences the decision of adding parts to stock significantly.
It should be mentioned that cases may exists in which an additional part in stock is profitable, for more realistic DOA rates. In case of fast moving parts with a very low mean lead-time (implying µ < λ) inventory levels are much more sensitive to small DOA percentages. Additionally, the fill rates are subject to jumps when the DOA probability is varied. Hence, the service levels do not remain constant in Figure12. In case the inventory control is managed by service level constraints, stock levels are required to increase even for small DOA percentages. This will be shown later on within this subsection.
Concluding, increasing inventory to reduce the cost effect of DOAs is only profitable for (unreal-istically) high DOA ratios as presented in Figure 12. In some very specific cases, in which demand rates are high and lead-times are low, additional inventory might provide a more profitable scenario. However, in most cases, a quick evaluation of costs will provide negative advice for the increase of safety stock.
Instead of using backorder cost, the level of S can also be optimized by constraining the service level. In this situation companies do not have the option of placing additional spare-parts in the warehouses, but are obliged to do so in order to maintain a minimum service level. This type of inventory control is used often in practice and is therefore relevant for analysis.
6 INVENTORY CONTROL
cost rate. We can simply minimize the holding cost, which is a common approach in service level constraint modelling [9]. Service level constraints encompass some problems of its own, such as the difficulty of its shape. They are mostly non-linear by nature [18] and cause jumps in the cost of inventory. This is caused by the fact that an additional spare-part needs to be stocked in case the service level constraint is violated. This creates a non-smooth cost function.
Furthermore, this approach does not take into account that high costs can be avoided by plac-ing additional stock of cheaper, fast movplac-ing, spare-parts that increase the average service level, since we evaluate single-item systems in this research.
In order to get an overview of the magnitude of the cost impact, we will evaluate different val-ues of λ, so that the order-up-to level S varies. For simplicity, we set the holding cost, h, equal to one. We evaluate service level constraints by using the fill rate, which we set consecutively at 99.0, 99.3, 99.6 and 99.9 percent. We use the fill rate, since this is a practical service level, whereas the ready rate is somewhat misleading in case of compound Poisson processes. [2].
S2= 99.0% λ S for 0% DOAs (and fill rate) S for 1% DOA (and fill rate) % cost increase
0.1 1(99.17) 2(99.99) 100.5
1 2(99.67) 2(99.55) −
5 3(99.11) 4(99.89) 34.26
10 5(99.83) 5(99.78) −
S2= 99.3% λ S for 0% DOAs S for 1% DOA % cost increase
0.1 2(100.00) 2(99.99) −
1 2(99.67) 2(99.55) −
5 4(99.91) 4(99.89) −
10 5(99.83) 5(99.78) −
S2= 99.6% λ S for 0% DOAs S for 1% DOA % cost increase
0.1 2(100.00) 2(99.99) −
1 2(99.67) 3(99.98) 51.42
5 4(99.91) 4(99.89) −
10 5(99.83) 5(99.78) −
S2= 99.9% λ S for 0% DOAs S for 1% DOA % cost increase
0.1 2(100.00) 2(99.99) −
1 3(99.99) 3(99.98) −
5 4(99.91) 5(99.99) 27.55
10 6(99.98) 6(99.97) −
Table 13: Increase in inventory costs for service level constraints (the corresponding fill rates are denoted between brackets)
As can be seen in Table13the cost impact heavily depends on the situation at hand. In most cases, the inventory cost stay unchanged. Only for some specific scenarios the optimal levels of S differ in the two scenarios. In case the level S∗ differs, the additional costs are significantly large; varying from twenty-seven percent up to over a hundred percent. Hence, this analysis shows the importance of knowing the actual cost of certain service level constraints, since the slightest adjustment might reduce costs substantially.
