Master thesis
Master Business Administration – Operations & Supply Chains
University
of Groningen
Demand Forecasting for Book Sales
Gaining insights in customer demand for general books
By:
Floor ter Heijne
f.ter.heijne@student.rug.nl
Student number: 1631543
Supervisor: Prof. Dr. Roodbergen
Second assessor: Prof. Dr. Teunter
2
Preface
This paper is my final thesis for the Master Business Administration, specialization Operations and Supply Chains, at the University of Groningen. I performed my research on the Dutch general book market, developing a forecasting method to predict book sales at bookstores.
Performing this research has been a challenging experience from which a have learned a lot. However I couldn’t have done it without the help of other people. In this preface I would like to take the opportunity to thank them for their support.
First of all I would like to thank my supervisor, prof. Roodbergen, for giving me insights and feedback during my research. Secondly, my thanks goes to my second assessor, prof. Teunter, for his critical comments.
Next to my assessors, I would like to thank prof. Boter from the University of Amsterdam for providing me with a database to perform my research and brainstorming with me about the right approach. Furthermore I would like to thank my friends and family for sharing their opinions, giving feedback on my work and supporting me during this process. A special thanks goes to Sergio Sanchez Gomez, Moritz Daan and Roos ter Heijne.
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Abstract
The Dutch book market is facing challenging times. The introduction of new technologies in combination with declining sales, have led to a downfall in the number of bookstores in the past few years. To be able to cope with the challenges, bookstores have to work as efficient as possible. Efficiency can be achieved by optimizing the match between supply and demand at the stores. Currently decisions considering this match are based on knowledge and experience available at the bookstores. To get a better understanding of the customer demand and to facilitate the decision making process, in this research a forecasting method for the bookstores is developed. In order to develop a forecasting method the sales data of 24 Christian bookstores was analyzed. From this database a sample of different books was selected for further investigation. Additionally an investigation of the characteristics of the book sector and different forecasting techniques were performed. It was found that bookstores can benefit from using time series forecasting techniques to improve their decision making processes concerning customer demand. The forecasting technique that best fits the characteristics of the demand pattern and the necessities of bookstores is exponential smoothing. This technique allows for fast responses to changes in demand and is easy in use. However, bookstores should monitor the forecasts closely on two occasions. Firstly, at the occurrence of a large increase of sales in a single week. The demand pattern showed incidental sales peaks that don’t indicate a general increase of sales. Therefore, bookstores should be careful in responding to these peaks. Secondly, the first four weeks after publishing need to be monitored closely. Sales in this time period are very random, making it hard to estimate future values without extra information.
4 1. Introduction ... 5 1.1 Motivation ... 5 1.2 Problem definition ... 5 1.3 Research question ... 6 1.4 Methodology ... 6 1.5 Structure ... 8
2. The organization of the supply chain ... 9
2.1 The publishers ... 9 2.2 The distributors ... 10 2.3 The retailers ... 11 2.4 Overall ... 12 3. Theoretical background ... 14 3.1 Forecasting techniques ... 14
3.2 Selecting a forecasting method ... 18
4. Method development ... 20
4.1 Insights in the demand pattern ... 20
4.2 Selection of forecasting techniques ... 21
4.3 Research approach ... 25
5. Results ... 28
5.1 Estimation of the parameters ... 28
5.2 Influence of peaks ... 29
5.3 The first weeks ... 30
5.4 Testing the methods ... 31
5.5 Conclusion ... 32
6. Conclusion ... 33
References ... 36
Appendix I ... 40
5
1. Introduction
1.1 Motivation
This paper will investigate the supply chain of books. In this research the focus will be on books written in or translated to the Dutch language. The market of Dutch books can be divided in three different categories: general books, school books and scientific books. In this paper only the general books are discussed, including literature, non-fiction and children’s books, written or translated in Dutch.
The supply chain of books consists of three stages. At the first stage, new books are selected by publisher. Secondly, the wholesalers and distributors store books, provide logistics services and handle orders for the final players in the chain, the retailers. In the last stage, these retailers sell the books to the final customer. Retailers appear in many different types, which will be discussed later on in this paper.
In the past few years the Dutch book market faced many changes and challenges because of capricious consumer preferences and technological novelties. This led to a downfall in sales and revenues since 2007 (hbd.nl1). Since then, the number of physical bookstores has been declining as well, from 1790 in 2006 to 1710 in 2011. Declining sales, increasing costs and competition through e-commerce and new reading technologies are the main causes of this reduction (hbd.nl2; boekbond.nl3). The changes do not only occur in the last stage of the supply chain, but also affect the other players. The appearance of new printing technologies, changes in sales channels, high costs, changing consumer wishes and declining sales, resulted in cooperation’s between publishers and changes in the organization of the distribution channel (Volkskrant, 20114; Boekblad, 20115; Boekbond.nl6).
1.2 Problem definition
One of the major issues in the management of a supply chain is matching supply with demand in order to have the right amount of products at the right place on the right time (Lee et al., 2000; Simchi-Levi et al., 2008). The better the match, the more efficient the supply chain works. In an integrated supply chain, point-of-sales data can help other members of the chain to work more effectively by obtaining a better picture of actual demand (Heizer and Render, 2008). Retailers in the supply chain have the best information about actual demand because they are closest to the end-customer (Taylor and Xiao, 2010). The knowledge that the retailer has about its actual demand affects the ordering and inventory decisions it makes, which in turn affect the wholesaler or manufacturer upstream in the supply chain (Cederlund et al., 2007). Retailers that hold an accurate picture of actual demand and that are able to make good predictions of the future demand, both benefit themselves and their upstream manufacturers (Fildes et al., 2008; Williams and Waller, 2011). If done properly, sharing the demand information in the supply chain is beneficial for all its members (Lee et al., 1997; Lee et al.,
1http://www.hbd.nl/pages/13/Branches/Boekhandel.html consulted at: 30-1-2012 2
http://www.hbd.nl/pages/13/Branches/Boekhandel.html consulted at: 30-1-2012
3http://boekbond.nl/organisatie/publicaties/Actieplan 2009-2012 consulted at: 30-1-2012 4 Volkskrant 09-07-2011 p. 18-19
5
Boekblad 15-04-2011, magazine 7, p 22-23
6 2000). For the supplier it means an improvement of its demand forecasts, which enables them to create a better fit of its production to the demand and a reduction of inventories, allowing for better product management (Lee et al., 2000; Mishra et al., 2009).
In the book sector, members start to see the necessity of changing their operations because of the more challenging environment (Boekblad, April 2011). There are initiatives to collaborate in order to work more efficient (boekbond.nl7). However these initiatives cost a lot of time and effort and not everybody is willing to participate. As was stated above, accurate demand information from the retailers in the chain can already benefit the other members of the chain. Therefore, this paper will perform research at the retailers of the supply chain, the bookstores. The objective of this paper is to get insight in the customer demand at physical bookstores from the supply chain of Dutch books.
1.3 Research question
Matching supply and demand of a company can be optimized by understanding the demand pattern and using this to predict future values (Heizer and Render, 2008; Schönsleben, 2007; Simchi-Levi et al., 2008). In order to predict the future value, different forecasting techniques exist for different situations, making it important to carefully choose the right technique (Schönsleben, 2007). Forecasting is a critical tool for companies because it helps to create a better match between demand and supply, improving the management of inventory, capacity decisions and promotional planning. (Simchi-Levi et al., 2008). Good forecasts can reduce uncertainty and improve operating costs, whereas poor forecasts may result in higher costs and bad market responses because either too-much or too little stock will be available (Agrawal and Schorling, 1996; Simchi-Levi et al., 2008). Therefore the research question of this thesis is:
“What kind of forecasting method should bookstores implement in order to be able to match supply and demand?”
The following sub questions will lead to an answer of the research question:
1. What does the supply chain of books look like, who are the players and how do they make decisions?
2. What kind of forecasting techniques are discussed in literature and how can the right one(s) be selected?
3. What are characteristics of demand patterns at bookstores? 4. What type of forecasting method can best be used at bookstores?
5. How can insights on forecasting help bookstores to work more efficient?
1.4 Methodology
Data collection
This research will be conducted based on two types of research strategies; the case study and theoretical research. For the collection of data, two methods of data gathering will be used. These methods are archiving data, which entails the collection of existing data and
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7 interviewing (Welker and Broekhuis, 2010). Archiving data results in a literature review about the concept of forecasting, making use of academic search engines for scientific articles and the catalogues of the University of Groningen. The search engines that are used are: Web of science, Business source premier and Google scholar. Other data is collected by consulting newspaper and magazine articles, websites and reports of companies and associations concerning the supply chain of books. Finally, a database with sales information of 24 Christian bookstores is used, covering the sales of one year (2009). These bookstores represent traditional stores without the use of a web shop. The database holds information about the year, week and amount of a certain title, with ISBN-number, is sold by a specific bookstore. Interviews are held with representatives of: Centraal Boekhuis, Boekenbond, an educational publisher and an owner of a bookstore. The interviews are semi-structured, to give direction but leave room for the interviewee to come up with more topics and issues (Flick, 2006). The interviews are used to obtain information about the processes in the book sector.
Data analysis
To find a solution for the problem stated earlier, it’s necessary to have a clear picture of the supply chain, its structure, its members and its characteristics. Therefore an overview is presented in the first part of the research. In this part it will become clear how decisions are made and who is responsible for which tasks. This information makes it possible to make decisions between the different methods that can benefit the book sector.
In the second part of the research, a theoretical review is presented about the concept of forecasting. Accurate demand forecasting is crucial for retailers. Poor methods can lead to markdown costs due to excessive inventory of unpopular products and lost sales opportunities due to rapid sell-outs of popular products (Agrawal and Schorling, 1996; Rajaram, 2001). Besides the theoretical evidence, practical relevance for testing forecasting methods also exists. At this moment, most bookstores don’t make use of forecasting techniques, instead they rely on the knowledge and experience of employees or owners. Schönsleben (2007) states that if there are only a few items, human forecasting can be more precise, however when there are more items, forecasting techniques provide better forecasts. Bookstores have many different titles in their store, following Schönsleben’s (2007) statement it will be useful for them to develop a forecasting method.
The third part of the research contains a preliminary analysis of the bookstores and the sales data. This analysis is performed to gain insights in the sales data and to understand the necessities of the bookstores. Cooper and Schindler (2006) state that this is an important step in data analysis. It allows the researcher to see the characteristics and patterns of the data and it shows what kind of preparations are needed to perform the research. This analysis is performed making use of the forecasting literature, the characteristics of the bookstores and the available sales database. Based on this information a selection of possible forecasting techniques is made, because many techniques can already be excluded because they will not fit the bookstores. Furthermore, the third part also includes the research approach for the development of an appropriate forecasting method.
8 meaning that sales of all the different bookstores are summed for every week. This is done because the individual bookstores are very small, making it hard to get a reliable sample. In order to model and test forecasting techniques, a sample of 51 different titles is selected from the database. The size of this sample stems from the required characteristics of the dataset and the selected items. The required characteristics for the sample selection are as follows:
- The selected item should be a book - The book has to be published in 2009
- The book should be sold for more than 12 weeks in 2009. - The book should be sold more than 50 times in 2009.
In order to develop a forecasting method that is as complete as possible, the selected books have to cover the first phase after publishing and also allow for analysis in time. Since the dataset only contains sales information of one year, it is not possible to follow the development of sales for a longer time period. Furthermore, the dataset contains books that have very low sales numbers, therefore a minimum of 50 books is required to develop valid methods. Finally, the dataset contains a lot of items that are not books. These items are not relevant for this research and therefore are not selected for the sample. Before tests can be performed on the sample, two final adjustments have to be made. In order to be able to compare the different titles, the sales weeks are renumbered, naming the first week after publishing; week 0. Furthermore, weeks that are not mentioned in the data base are added and given the sales figure of zero sold items. This can be done because a book that is not sold in a week would not appear in the database.
The reliability of the developed method will be assessed as follows. Firstly, the sample is divided in two groups. The first group will be used to test and develop a forecasting method. In order to be able to compare the different techniques, the forecasting error that each technique produces is measured. In this research the mean squared error (MSE) is used to calculate the forecasting error. MSE is the average of the squared differences between the actual sales values and the forecast (Heizer and Render, 2008; Simchi-Levi et al., 2008). A drawback of the technique is that it tends to accentuate large deviations due to the squared term. But it does provide good grounds to compare different techniques for the same database (Heizer and Render, 2008). The technique that results in the lowest MSE value is chosen as optimal. Secondly, the second sample group will be used as a control group to test the forecasting techniques. To determine the applicability of the forecasting techniques they are compared with a situation in which demand is assumed to be the same as in the prior period. This situation represents the current way of forecasting at bookstores. Heizer and Render (2008) state that this simulated situation, called naïve forecasting, provides a good starting point for comparison. The comparison is performed based on the MSE outcomes all forecasting techniques produce on the control group.
1.5 Structure
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2. The organization of the supply chain
In this chapter a closer look will be taken upon the Dutch supply chain of A-books. First of all, the members of the chain are discussed individually, describing their tasks and specific characteristic. Secondly, unique attributes of the whole chain will be described since the chain has some differences in comparison with other retailing chains.
2.1 The publishers
The supply chain of books evidently starts at the writing table of the author. The written manuscript is then send to a publisher. Publishers are responsible for the selection, editing, pressing, issuing and marketing of new and existing titles. 90% of the Dutch publishers of A-books are represented by the GAU (Groep Algemene Uitgevers), the Dutch publishers association of A-books that protects the interests of its (67) members. Many of these members consist of sub-editors, representing different genres and styles (gau.nuv.nl8).
The task of a publisher begins with the selection of manuscripts from Dutch writers or English books that need to be translated. Publishers receive many manuscripts per year and they need to examine them carefully to determine if they think if it is good enough and if it will sell. Only a small percentage of manuscripts (1-2%) are considered for publishing. Even though this percentage is very low, every year about 15000 new titles appear on the market (Boekbond.nl9). After the selection the manuscript is edited, this includes re-writing and making decisions about the layout. When the final version is done, the publisher starts with the production of the books. This starts with the decision on the amount of books to be produced. The amount leads to the second decision, how and where to produce the books. The first option is to press the books, this can be done in Holland, in Europe and outside of Europe. The second option is to print the book, using a new technique called ‘printing-on-demand’, which allows for the production of small batches of books, reducing the introduction costs of a new title. This technique is still in its experimental face, but some publishers have started to use it (cb-online.com10).
When the books are produced, there are four major options for the distribution of the books. First of all, an author can decide to buy his books from the publisher and issue them by himself. For the other options, the new books have to be registered at the ISBN agency11. The book is coded with an unique ISBN number used world-wide. This coding enables the possibility to digitally store information about titles for search and ordering purposes. For the second way of distribution, the ISBN number is linked to the publisher, from where books may be ordered. Thirdly, the number is linked to a large distribution center. In Holland the two largest centers are Centraal Boekhuis (CB) and Libridis. The fourth option for the publisher is to store the books at CB from where they are send to retailers or directly to the end-customers.
The final task of a publisher is the marketing of titles. Since many new titles enter the market each year, this is an important task for the publisher. The marketing of new titles can
8
http://www.gau.nuv.nl/over-de-gau/ledenlijst-gau.1352.lynkx consulted at 02-02-2012
9 http://boekbond.nl/organisatie/publicaties/ Jaarverslag 2010 consulted at 02-02-2012
10
https://portal.boekhuis.nl/cbonline/nieuwsbericht/item/10661/uitgeverij-free-musketeers-volledig-overgestapt-op-cb-print-on-demand consulted at 02-02-2012
10 be done in many different ways, for example: Television/radio appearances of the author, book signing by the author, cooperation with selling points, review by critics, promotional material etc.
In this stage of the of the supply chain many important decision are taken about published titles, production, promotion, distribution and storage. However, little is known about the way these decisions are made. Many publishers are very traditional and rely on their own knowledge and experience to make these decisions. Furthermore, for many new titles it is very hard to predict how the market will receive them, for others extra information is available. This is the case with a sequence, a famous author or sales in other countries.
2.2 The distributors
In Holland, different distributors and wholesalers exist. The first and biggest one is Centraal Boekhuis (CB). CB is a logistics service provider in the supply chain, providing services for the entire Dutch language area. CB provides full service facilities for distribution, transportation, information, financing and administration for its clients, about 1800 Dutch and Flemish booksellers and 500 publishers. CB is a commercial company that operates in the interest of its clients both up and downstream in the supply chain. The close cooperation between the members in the supply chain can be explained by the fact that half of CB’s shares are owned by the NUV (Nederlandse Uitgevers Vereniging), the Dutch publishers association, and the other half is owned by the KBb (Koningklijke Boekverkopers bond), the Dutch association for booksellers. CB can offer a wide-variety of books, holding about 80000 different titles. Most of the books that are placed in the warehouses of CB are still the property of the publishers. They stall their books at CB and let them take care of the order handling, logistics and finances. In this way books are distributed more efficiently because publishers and bookstores don’t have to contact each other for all the different orders (portal.boekhuis.nl12).
The second large distributor is Libridis. Libridis is a wholesaler that provides innovative services to its clients, booksellers and publishers. For booksellers it provides distribution of books, advice about the assortment and promotion material. It also provides the booksellers with the opportunity to send back unsold titles. For publishers, Libridis functions as a commercial partner because of their close contact with booksellers and logistics network. In contrary to CB, Libridis does own the books they store in their warehouses, functioning as a traditional wholesaler (libridis.com13).
For the Christian bookstores a specialized Christian wholesaler exists, called CBC (Christelijke Boekencentrale). 99% of all Dutch Christian books are handled through the CBC, holding 10000 different titles. CBC, just like Libridis, functions as a traditional wholesaler and is also responsible for the distribution of other Christian articles and non-Christian books (cbcboek.nl14).
For their decision making processes, wholesalers are for a large part dependent on the decisions of the publishers, who decide on amounts and titles. On the other hand, they are
12 https://portal.boekhuis.nl/cbonline/over-ons consulted at 02-02-2012 13
http://libridis.com/nl/diensten/ consulted at 02-02-2012
11 dependent on the wishes of the booksellers, both physical stores and online sales. They try to find the best balance between both parties.
2.3 The retailers
In 2005 the law for fixed book prices was introduced. Before the introduction of this law, only assigned traditional bookstores where allowed to sell books. An implication of the law was that it allowed retailers in other industries to add books to their assortment. According to the KBb, nowadays three types of booksellers can be distinguished (boekbond.nl15).
- Bookstores (Physical and online)
The core business of this type of shops is selling books. Within this group 3 different types of shops can be distinguished.
o The traditional bookstore. This can be an independent store or a member of a large chain.
o Physical stores that have a web shop o Internet shops with only online sales. - Entertainment stores
These stores sell products that are linked to entertainment, like toys, music, electronics etc. Products are sold in the physical stores or online.
- Mass merchandisers
As the name states, this channel is a large retail store offering a wide range of product categories such as accessories and groceries.
In 2010 Holland counted 1750 physical bookstores and a total of 3500 selling points (including online stores) (gfkrt.com16). In 2011 only 1710 bookstores where left and many others had a rough year (hbd.nl17). The different categories offer a different assortment of books. The first category has the widest range, whilst the second and third categories carry much less titles. In 2010 traditional bookstores had the largest market share with, 88.6%, however e-commerce is taken up a large part of this share which is still growing (boekbond.nl18).
Three times a year, book fairs are organized. At these fairs, new titles and marketing activities are presented by the publishers. Representatives of bookstores visit the fairs to see the new titles on the market and to negotiate about purchasing and conditions. On every fair about 5000 new titles are offered from which booksellers have to make their selection. They fairs are organized by four parties: a combination of Libridis and GAU, Selexyz, Libris and the organization of Christian books. All four parties direct their fairs at their members and target group.
Important decisions about the breadth and depth of the assortment of bookstores are mainly based on the knowledge and experience of employees and owners of stores. This also includes decision making about inventories, orders and future sales expectations. Stores that are a member of any of the organizations above receive advice about the assortment and expected sales. Furthermore, these organizations set the ordering policy and provide suggestions about
15
http://boekbond.nl/organisatie/publicaties/ Jaarverslag 2010 consulted at 02-02-2012
16 http://www.gfkrt.com/benelux/diensten_producten/insights/gfk_jaargids_2010/index.nl.html Jaargids 2010
consulted at 02-02-2012
17
http://www.hbd.nl/pages/13/Branches/Boekhandel.html consulted at: 30-1-2012
12 optimal inventory levels. The representatives have more information to base their advice on, but knowledge and experience are still important factors.
2.4 Overall
The A-book market has a few characteristics that make it different from other retail markets. These features are described in this section.
First and foremost is the law for fixed book prices (Wet vaste boekprijs 2005). This law is established to protect and control the prices of books written in the Dutch language. The law states that a book must have the same selling price in each store (including e-stores). This price is determined by the publisher, which can abolish the fixed price after one year. However, in practice, editors tend to keep a fixed price for many years. The law is established to stimulate the availability of a wide range of different books and protect the cultural heritage (boekbond.nl19). Holland is not the only European country that holds a fixed price, countries like Germany and Denmark have similar laws (feb-fee.be20).
Secondly, trading margins play an important role. When booksellers order books they have two options. First of all they can order from the central depot, a legal construction in which titles are registered. Publisher can register their books in the depot so that everyone can order the titles against a fixed trading margin of 42%. CB is responsible for the distribution of books registered in the depot (galaxa.nl21). Secondly, books sellers can make arrangements with the publisher about the trading margin and conditions. This margin is normally around 39% but it usually implies placing larger orders.
Thirdly, in order to reduce inventories at bookstores the possibility of returning books exists. The conditions for the return are negotiated between the bookseller and the wholesaler, or the bookseller and the publisher. This gives bookstores the possibility to renew the titles that they have in store, but it causes higher inventories for the wholesaler and publisher.
Fourthly, collective promotion exists for the entire general-book market. The association CPNB (stichting Collectieve Propaganda van het Nederlandse Boek) organizes campaigns and promotions for the entire books market. The best known campaign the CPNB organizes is the book-week. This is a national promotion in which sales at bookstores can be tripled. CPNB is an initiative of the GAU, the KBb and the public libraries (VOB). It was founded to stimulate reading and the possession of books. The promotions are directed to genres or books in general, but not for individual titles. The GAU, KBb and VOB provide the CPNB with a budget to perform their activities, extra income is generated by revenue of sponsor contracts.
Fifthly, the sales pattern of books shows some peculiarities. On average, 80% of total sales of a title take place in the first 90 days after release. However, the total lifetime of a book can be many years (Boekblad, 201122). Obviously, it is not possible for bookstores to keep all titles in inventory. Furthermore, although many titles are offered at the bookstores, profits are made on the bestsellers. In 2010 35% of the turnover was achieved with only 500 titles, whilst the total availability consists of 82000 different titles (Boekblad 201123).
19 http://boekbond.nl/ondernemerszaken/wet-vaste-boekenprijs/ consulted at 02-02-2012 20
http://www.fep-fee.be/div_log_pass2/documents/EuropeanCountrieswithFixedBookPriceSchemes1.pdf consulted at 05-02-2012
21 http://www.galaxa.nl/cbkosten2010.pdf Centraal Boekhuis tarieven 2010 22
Boekblad 15-04-20011, magazine 7, p 22-23
13 A final characteristic of the supply chain is the existence of libraries. The public libraries provide access to information knowledge and culture (debibliotheeknederland.nl24). Members of libraries can lend all types of books, including A-books. The existence of libraries implies a reduction of the sales of bookstores. People that lend a book in the library will not buy it anymore in the bookstore.
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3. Theoretical background
In this chapter a literature review about forecasting is performed. The first part of this chapter contains an overview of the different forecasting techniques and their characteristics. In the second part methods for the selection of forecasting techniques are depicted.
3.1 Forecasting techniques
Forecasting is a widely used process to predict future values of demand. It has a great impact on decision making processes in companies, therefore this topic has received considerable attention in literature (Syntetos et al., 2009). A wide variety of different forecasting techniques exist. To create a clear overview of the techniques they are divided in three main categories: quantitative forecasting, qualitative forecasting and composite forecasting.
Quantitative forecasting techniques
Quantitative forecasting techniques make use of historical demand data to project future demand, applying of statistical methods (Schönsleben, 2007). This category can be further subdivided in time series forecasting and explanatory forecasting.
Time series forecasting, also known as extrapolation, makes use of historical values of the series that is being forecasted in order to predict its continuation (Heizer and Render, 2008; Makridakis et al., 1998; Schönsleben, 2007; Simchi-Levy et al., 2008). Because past behavior is a good predictor of future behavior, extrapolation is appealing. Furthermore it is objective, replicable and inexpensive (Armstrong, 2001a). Pure extrapolation is based only on values of the variable being forecasted but it can also be used for cross-sectional data (Armstrong, 2000). It consists of a sequence of observations over time (Makridakis et al., 1998). The use of time series techniques has been proven very successful in forecasts for a basic trend-cycle (Fildes et al., 1998; Nikolopoulos, 2010). In this subdivision multiple techniques exist that differ in complexity. The times series techniques are presented in table 1.
Forecasting technique Description Use
Naive method The most recent observation available is used as a forecast. The value of the last period is the forecasted demand for the next period.25
Simplistic, constant and stable demand
Moving average The method averages the last ‘n’ numbers of observations of a time series. The key is to select ‘n’ so that the effect of irregularities in the data is minimized26.
Simple method, demand, use of one parameter, low demand uncertainty, short time period.
Weighted moving average
An extension of the moving average, using weights to place more emphasis on more recent periods27
Constant demand, volatile demand, short time period, smoothing out sudden fluctuations
(First order) Exponential smoothing
Each forecast is a weighted average of the previous forecast and the last
Constant demand, volatile demand, short time period,
25
Makridakis et al. (1998)
26
Boylan and Johnston (2003)
27
15 demand point using a smoothing
constant28.
simple forecasting problems, smoothing out sudden fluctuations.
Autoregressive integrated moving average
(ARIMA)
An extension of the moving average capable of reflecting autocorrelations inherent in data. Also able to analyze non-stationary time series29.
Long term, seasonal influences, non-stationary but statistically clear demand data.
Table 1: Time series forecasting techniques
Explanatory forecasting takes the effect of special events, seasonality and trends into account when computing the forecast. This is an important extension, since time series do not include the timing nor the effect of special events (Nikolopoulos, 2010). Explanatory forecasting allows for the analysis of influence of different variables on demand (Nikolopoulos, 2010; Schönsleben, 2007). Time series methods can be used as a basis for explanatory forecasting by adding extra variables that explain the seasonality and trends (Holt, 2004). However, when more variables play a role, the methods get more complex and new techniques are developed to deal with it (Armstrong, 2001a; Makridakis, 1998; Nikolopoulos, 2010). For the influence of a season or trend the techniques are rather simple. Special events include shocks (events that are not expected at all, e.g. earthquakes) and expected irregular events (e.g. sales promotions) (Nikolopoulos, 2010). The different explanatory techniques are depicted in table 2.
Forecasting technique Description Use
Regression analysis Trend analysis in which values appear as a particular function of time and measure of causal relationships. The regression is done on the forecasted (dependent) variable and the explanatory (independent) variable. Simple regressions have one independent variable and multi regressions have two or more30.
Simple technique mostly used to discover patterns and interdependence in time and after special events, low forecasting accuracy, causal relationships.
Trend extrapolation forecast
Attempts to estimate a variable in the future based on the same variable known at a specific point in time using an extrapolation constant to smooth the estimates31
Simple technique to forecast demand with seasonal or trend pattern. The basic order behavior does not change. Holt’s exponentially
weighted moving averages. Second order exponential smoothing/
extension of exponential smoothing, adding trend and seasonal ratios32
Use to calculate trends and seasonal influences. Capable of capturing linear trend
Artificial neural networks (ANN)
Mathematical models inspired by the organization and functioning of biological neurons. It can
automatically approximate whatever
Non-linear demand patterns, learning patterns, abrupt changes in historical data.
28 Simchi-Levi et al. (2008) 29 Makridakis et al. (1998) 30
Makridakis et al. (1998); Simchi-Levi et al. (2008)
31
Schönsleben (2001)
32
16 functional form best characterizes the
data.33
Econometric modeling Systems of simultaneous equations to represent economic relationships. Rely on statistical procedures including historical data, domain knowledge and theory, determining a set of different variables34
Causal relationships in demand, changing causal relationships.
Table 2: Explanatory forecasting techniques
Qualitative forecasting techniques
Qualitative techniques are based upon expert opinions, judgments and customer intentions (Schönsleben, 2007). Judgmental forecasts strive to assemble the opinions of a variety of experts in a systematic way. Intuitive forecasts involve qualitative studies about customer’s behavior and intentions (Simchi-Levi et al., 2008). Qualitative forecasting is particularly useful when historical data is scarce (e.g. the introduction of new products) or when the subject under investigation is rapidly changing, making the past unable to explain (Caniato et al., 2011). Qualitative forecasting can lead to weak forecasts because of inconsistency and bias (Fildes et al., 2009). By carefully structuring information this effect is reduced (Armstrong, 2001a; Caniato et al., 2011). Nowadays, qualitative forecasting is not less accurate than quantitative forecasting and a general attitude exists that it has an important role in the accuracy of forecasting (Caniato et al., 2011; Lawrence et al., 2006; Syntetos et al., 2009). In table 3 an overview is given of the different qualitative forecasting techniques, differing in complexity and focus.
Forecasting technique Description Use
Intentions Measures of individuals’ plans, goals or expectations about what they will do in the future to forecast their actual behavior. Use of customer market research.35
When no historical data is available, introduction of new products. Ask the right questions to overcome bias. Conjoint analysis Survey based method to obtain
customer input. Measure how individuals judge trade-offs36.
Used when introducing new products or product
innovations. Panels of experts
Expert system
Agreeing upon a forecast by openly sharing information and
communicating with internal and external experts. Also occurring with 1 expert37
When historical data is scarce. Domain knowledge needed to make a forecast.
Delphi method Structured technique for reaching a consensus with a panel of experts without gathering them in a single location38. Information is gathered
Reducing bias and inconsistency when using judgmental forecasting. Takes into account external and
33 Hill et al. (1994) 34 Armstrong (2001b) 35 Morwitz (2001) 36
Wittink and Bergestuen (2001)
37
Simchi-Levi et al. (2008)
38
17 through rounds of anonymous written
interviews.39
internal variables that influence demand. When statistical methods are not consistent and reliable and expertise is needed.40
Judgmental bootstrapping Translates an expert’s rules into a quantitative model by regressing the expert’s forecast against the
information that he used.41
Lack of historical data on the variable to be forecasted. Improves the quality of experts forecast, more consistency. Most appropriate in complex situations, where judgments are unreliable.
Table 3: Quantitative forecasting techniques
Composite forecasting techniques
Composite forecasting techniques make use of both quantitative and qualitative methods. Empirical research suggests that when quantitative forecasting methods are used, they are very frequently judgmentally adjusted (Blattberg and Hoch, 1990; Caniato et al., 2011; Fildes et al., 2009; Sanders and Manrodt, 1994; Syntetos et al., 2009). The integration of both techniques has three big advantages. First of all, research shows that combining both techniques leads to more accurate forecasts (Armstrong et al., 2001; Fildes et al., 2009; Goodwin, 2002; Syntetos et al., 2009; Turner, 1990). Secondly, companies using composite forecasting techniques find that it leads to better knowledge and awareness for the whole organization, better information sharing and better control on the forecasting process (Caniato et al., 2011). Thirdly, it is very hard to implement one technique without using the other. Using statistical forecasting software, without feasible input of management can lead to large errors in the predictions of demand (Lawrence, 2006). Combining both forecasting techniques appears to be most effective when they are based on important information that is not available to statistical methods (Sanders and Ritzman, 2001). When combining the two methods, techniques will turn out more feasible and not to complex. It can be a perfect balance between statistical objectivity and expert opinions (Caniato et al., 2011). One important note that has to be made is that judgment adjustments need to be done carefully and based on reliable information. If not, the forecast can become less accurate (Fildes et al., 2009). In table 4 different composite forecasting techniques are explained.
Forecasting technique Description Use
Bayesian forecasting Family of methods combines statistical methodology with structured integration of human judgment: new evidence is used to update a statistical forecast, based on application of Bayes’ theorem. Explicit formulations of model and conditioning on known quantities.42
Highly seasonal data with short history
Rule-based forecasting Translation of forecasting expertise Use of historical data corrected 39 Schönsleben (2007) 40 Goodwin (2001) 41 Armstrong (2001b) 42
18 into a set of rules. The rules use the
managers’ domain knowledge and the characteristics of the data to produce a forecast from a combination of simple extrapolation methods.43
with expert’s knowledge. Can be added to extrapolations methods to make them more appropriate for different situations.
Expert system Use of rules to represent expert’s reasoning in solving problems. Rules are based on knowledge about methods and the problem domain, relying on various sources (research papers, interviews analyses).
Extension of rule-based forecasting44
Replace unaided judgment in cases requiring many forecasts to model complex problems with poor quality data. When experts lack an awareness of their processes.
Table 4: Composite forecasting techniques
3.2 Selecting a forecasting method
In the above section an overview is given of different forecasting techniques and their characteristics. All though, many techniques are summed up, this is only a selection of all the forecasting methods that exist. Only in economic literature over 200 forecasting methods are mentioned (Pilinkiene, 2008). The techniques above are selected because they give a good representation, covering all main categories and the most used forecasting methods. Literature suggests that in order to select and implement an appropriate forecasting technique, five steps should be taken. 1.Define the forecasting problem. 2.Gather and analyze sales data and other information. 3.Select the most appropriate forecasting technique. 4.Apply and evaluate the forecasting technique. 5.Implement the forecasting method (Armstrong, 2001a; Makridakis et al., 1998). The evaluation of the forecasting technique is very important. It allows for planners to make intuitive adjustments and to check for compatibility with the available resources and capacity (Schönsleben, 2007). Furthermore, the performance of the forecasting technique should be reexamined at certain time-intervals to confirm whether the course of the actual demand is still in line with the forecast. New data should be collected to check if the technique is still up-to-date (Heizer and Render, 2008; Schönsleben, 2007). Demand patterns can change in different stages of the product life cycle, making it important to review different forecasting techniques (Chambers et al., 1971; Simchi-Levi et al., 2008). It is important to carefully follow the different steps in creating a forecasting method and regularly evaluate its functioning because, different methods have their advantages and disadvantages, depending on the situation (Pilinkiene, 2008).
For the selection of the right method, different factors should be taken into account that determine the applicability of the forecasting method for the market demand (Makridakis et al., 1998; Pilinkiene, 2008). These factors are depicted below:
- The forecast objective: Is the objective to better understand the factors that influence the variable that is to be forecasted (Explaining) or is it a prediction about future value (Forecasting) (Makridakis et al., 1998).
- Type of data: The time period over which data is collected and the level of aggregation. This can explain trends, seasonality and randomness. In general
43
Armstrong (2001a)
44
19 randomness diminishes as the level of aggregation increases (Makridakis et al., 1998).
- Characteristics of time series: the magnitude of randomness and the behavior of the trend cycle. On average larger randomness calls for simpler forecasting methods (Makridakis et al., 1998).
- Amount of initial data: The availability of historical data (Pilinkiene, 2008).
- Forecast accuracy degree: The impact of errors in the forecast. Is the forecast used as a guideline or are actual numbers needed (Pilinkiene, 2008; Wacker and Sprague, 1995).
- Number and frequency of forecasts: The amount of forecasts per time period that are needed (Makridakis et al., 1998).
- The costs of the forecast: Different techniques cost more. How much can be spend? (Pilinkiene, 2008)
20
4. Method development
In this chapter characteristics of the bookstores and the demand pattern of books are analyzed. The features of the bookstores and the sales data form the conditions of the selection of possible forecasting techniques. Additionally, this chapter presents a research approach to test the selected forecasting techniques.
4.1 Insights in the demand pattern
Insights in the demand pattern are obtained by performing a preliminary analysis on the sales data. In appendix I the sales patterns of the individual titles from the selected sample are presented. At first, the sales patterns of the different titles seem very different. The main reason for this diversity is the fact that not all books cover the same time period nor have sold the same amount of items. Having a closer look upon the figures, commonalties and characteristics can be depicted. First of all, the majority of the titles have most of their total sales in the first months after publishing despite the time of year it is published in. This time period covers about three months. This is in accordance with the average turnover of general books, where 80% of total sales take place in the first three months after publishing (Boekblad, 2011). Secondly, the mid-term sales pattern (5-12 weeks) of most of the titles is relatively stable. Thirdly, the sales patterns show increases in sales for single weeks. The majority of these increases is caused by incidental sales at a single store and don’t imply an overall sales increase. For example, they could indicate that a book signing session was organized in a store or that a store sold a large order of books to a library or another organization. The exact cause of the peaks is not known, however it is clear that the sales increase only lasts one week. Since these sales peaks drive up total sales and result in a disturbed demand pattern it is suggested to react carefully when they occur. In figure 1, two examples of such incidental sales increases are presented.
Figure 1: Example of the weekly sales pattern of two individual titles with large sales peaks
21 A final characteristic of the sales data is that it seems that the first month after publishing is more random than the rest of the sales period. Increases in one week alternate strong decreases in the next week. As with the sales peaks, it is not clear what caused these fluctuations. For example, it could be that the low sales numbers are caused by insufficient inventory. The peaks in the first weeks could be caused by recovered sales of the week before or they could indicate publicity campaign in certain weeks. Unfortunately, the exact cause of the volatility is unknown however it is clear that the first couple of weeks should be treated with care. An example of the alternations is presented in figure 2.
Figure 2: Example of the weekly sales pattern of two individual titles with random demand in the first weeks
Item 3216 starts off with seven sold items in the first week, declining in the next week to two items. The third week a peak of 26 items is reached, declining to nine again in the fourth week. Item 12910 is unstable as well, with a large sales peak of 65 sold items in the second week, followed by declining sales in the following two weeks. Both figure 1 and 2, show the volatile characteristics of the data and also demonstrate that the mid-term of the sales pattern is relatively stable.
4.2 Selection of forecasting techniques
The characteristics of the sales data, the necessities of the bookstore and the information available are important factors in selecting an appropriate forecasting technique. All forecasting techniques have different requirements and features, which implies that there are limitations in the selection of forecasting techniques that are appropriate to use at bookstores. In chapter three the different forecasting techniques where presented that are considered for use at the bookstores.
Quantitative forecasting techniques
Quantitative forecasting techniques use historical demand data to project future demand and make use of statistical methods (Schönsleben, 2007). For this research, historical demand data is available. Therefore these techniques can be considered to develop a forecasting method for the bookstores. In chapter three, two types of quantitative techniques where described, these are time series forecasting and explanatory forecasting.
22 2008). The objective of the bookstores is to forecast future demand using in-expensive methods that can be made on a weekly base. Time series techniques fulfill this objective since the techniques aren’t costly, can be performed quickly and most of the techniques only require simple spread sheet programs to make the calculations. The naïve forecasting technique will be used to test the functionality of the developed forecasting method and is therefore not tested as a forecasting technique for the bookstores. The moving average, weighted moving average and exponential smoothing are simple forecasting methods that only need little historical data and require one parameter to perform calculations. The moving average is most useful if market demand is fairly stable, whereas exponential smoothing and weighted moving average can react more quickly to demand changes (Heizer and Render, 2008). The moving average and weighted average are effective in smoothing out sudden fluctuations in the data (Heizer and Render, 2008). The ARIMA method is less appropriate since it is calculated over the long-term data, taking into account seasonal influences (Makridakis et al., 1998). The database that is available for this research does not have sufficient time-span to test this method.
Explanatory forecasting techniques calculate the effect of special events, seasonality and trends in the sales pattern (Nikolopoulos, 2010; Schönsleben, 2007). The effect of promotional activities and other special events on the sales in bookstores would be very interesting to investigate. In the book sector, promotional activities can be organized by the CPNB, publishers, authors, wholesaler and by the bookstores themselves. By performing a regression analysis, the effects of these activities can be measured. Furthermore it can give insights in ways to create incentives, increasing sales in a particular store and on specific products. However, the available database does not allow for testing of special events since no information about past events is available. The sales data was recorded in 2009 and the exact dates of promotional activities or other events in that year are not known. A new sales database, containing extra information about activities should be recorded to calculate these effects.
Seasonal fluctuations in the demand pattern are caused by factors such as weather, holidays and vacation periods. Seasonality is of great influence for retailers, however to test for it, the demand patterns of multiple years should be compared (Schönsleben, 2007). In the retail sector, seasonal influences have a lot of impact. The last month of the year, December, is an important month for retailers in the Netherlands, with very high sales figures (Gfk45). Bookstores should be very aware of the seasonal influences, to not miss out on the increasing demand. However, for this research only one year of sales data is available, which doesn’t allow for the testing of seasonal influences. Furthermore, the sale of individual titles is more dependent on the publishing date than on the time of year. As was stated above, titles have the majority of their sales in the first three months after publishing. This can also be seen from the sales patterns of the selected sample in appendix I, where most titles have high numbers at the beginning of their lifecycle. Seasonal influences will probably have more impact on the total sales at bookstores than on the sales of individual titles.
A trend is a general upward or downward movement of a variable over time (Schönsleben, 2007). Regression analysis, trend extrapolation and second order exponential smoothing are
23 forecasting techniques that are able to take trends in demand into account. Trends in sales data can be recognized by simply looking at the pattern of the sales data. When there is doubt about the pattern, a trend line can be fitted through the data. When there is still doubt, a regression analysis can be performed to calculate the strength of the trend line in the sales pattern. The demand follows a clear trend when there is a perfect relationship between the trend line and the sales data, resulting in . When it means that the sales data does not follow any trend (Keller and Warrack, 2003; Schönsleben, 2007). In figure 3 the combined amount of sold items per week of the titles in the sample are presented. From the figures it is hard to see a trend however it seems that the sales amounts slowly decline in time. To confirm this idea two types of trend lines are fitted through the data, a linear trend line and a polynomial trend line. The linear trend line is a straight line that minimizes the sum of the squared difference between the points and the line. The polynomial trend line is used to detect non-linear trends, fitting the best line through the data detecting any possible trend (Keller and Warrack, 2003). The left figure holds all the sales data of the sample. As can be seen, it contains many outliers that weaken the trend line. To get a better image of the sales pattern, the outliers are removed for further determination of the trend line. The right image presents the new scatter plot. The regression analysis is performed on the values in the new scatterplot and is calculated for the linear and the polynomial trend line. The linear trend line in the figure seems to signal a negative trend in the sales pattern, however the . This indicates a very weak relationship with the trend line, meaning that the sales data does not follow a linear trend. The polynomial trend line signals a slowly declining trend as well. But again the regression analysis indicates otherwise, with meaning that the sales data also doesn’t follow a polynomial trend line. According to these tests, the sales data of the titles in the sample do not follow any trend. Therefore the forecasting techniques that take trend into account will not be tested in this research.
Figure 3: Left: Scatter plot of the combined sales titles per week of 51. Right: Scatter plot on a smaller scale of the combined sales per week of 51 titles. The linear and a polynomial trend-line are drawn in the data without
24
Qualitative forecasting techniques
Qualitative forecasting techniques do not predict future demand with historical data, but with knowledge of experts, customer opinions and judgments (Schönsleben, 2007; Simchi-Levi et al., 2008). The advantage of qualitative forecasting is that they can incorporate a great deal of information that can be difficult to structure quantitatively (Makridakis et al., 1998). Since qualitative forecasting is not less accurate than quantitative methods and are very useful in situations with little historical data (Caniato et al., 2011; Lawrence et al., 2006; Syntetos et al., 2009), it seems like a good option for the bookstores. However, making well-structured qualitative forecasts for each title is very time-consuming and costly due to the large amount of titles available. Furthermore, bookstores already make their forecasting decisions based on expert opinions and judgments. This research is performed because the idea exists that the current way of working can be improved, making use of simpler techniques that can help bookstores in making their forecasts, therefore qualitative forecasting techniques will not be tested in this research.
Composite forecasting techniques
Composite forecasting techniques combine qualitative and quantitative forecasting methods. Prior research showed that combining the two techniques results in more accurate forecasts than the single inputs (Blattberg and Hoch, 1990). Furthermore, in practice many quantitative forecasting models are judgmentally adjusted because more features can be taken into account (Blattberg and Hoch, 1990; Caniato et al., 2011). For bookstores, combining the two techniques is viable for three reasons. First of all, employees of the bookstores will actively check whether qualitative methods are reasonable and adjust for the extra information they possess, resulting in more accurate forecasts. Secondly, bookstores will probably find it easier to accept new methods because their input is still highly valued. Thirdly, the sale of books is dependent on many factors that can change from store to store. It is hard to integrate these factors in one forecasting method. Combining forecasting techniques will make it possible to include all factors. Although composite forecasting can fit the bookstores, they cannot be tested in this research. The available sales data does not allow for the appreciation of expert inputs since only historical data is recorded. To measure its effectiveness, data should be collected of bookstores applying composite methods and different decision rules of experts.
Conclusion
25
4.3 Research approach
In order to develop a forecasting method for the bookstores, four steps need to be taken. First of all, the parameters of the forecasting techniques need to be estimated. The formulas for the three selected forecasting techniques are as follows:
1. ∑
2. ∑ ∑
3. Where: = number of periods in weeks
= new forecast
= previous period’s forecast = previous period’s actual demand = smoothing constant (
26 be used in this research and allow for comparison of the different methods. However, in new situations the values of the parameters should be reexamined to determine the best fit with the data.
Secondly, the influence of the peaks that were depicted in figure 1 has to be determined. Since sales peaks disturb the demand pattern, they can influence the accuracy of the demand forecast. Before the influence of the peaks can be determined a definition of a peak needs to be established. The peak definition will be expressed as the percentage at which sales increase between two consecutive weeks. Besides this percentage, the flattening level needs to be determined. This flattening level decreases the value of the peak, making it less influential. To calculate these elements different values for both factors are tested by calculating the MSE value for each combination. The tests are performed using exponential smoothing, moving average and weighted moving average. The combination of values that results in the lowest MSE value will be chosen as the optimal value. The data table function of Excel is used to execute these calculations. When the peaks are defined, their influence can be determined. This is done by comparing the MSE outcomes of the three selected forecasting techniques on the actual sales data and the smoothed sales data.
Thirdly, a closer look will be taken upon the first four weeks of sales. As was described earlier, demand in the first weeks seems more volatile than in the rest of the sales periods. To check whether this is true, the forecasting error of the first four weeks will be compared with the forecasting error of the other time periods. A withdrawal of this test is that a higher forecasting error can also be caused by the smaller amount of historical data available. Less data can make the forecast less accurate, which can make the data look more volatile. However this test will give an indication of the differences per period. The forecasting technique that is used to make the comparison is exponential smoothing because this technique allows for forecasting in the first weeks of sales. Furthermore, the relationship between the values in the first four weeks is tested. The objective is to test whether an increase/decrease in one week leads to an increase/decrease in the following week. To determine this relationship, the difference in percentage between two consecutive weeks is calculated. The correlation between the different weeks is calculated using spearman’s rank correlation. This is a nonparametric technique that can be used when data is not normally distributed. The test statistic is Spearman’s rho ( ) and lies between -1 and 1. -1 indicates a perfect negative correlation, 1 indicates a perfect positive correlation and 0 indicates that there is no correlation between the variables (Keller and Warrack, 2003). If the correlation between the first weeks is low, it will be hard to predict future values of demand. If the correlation is high, predictions will be much more accurate when making use of forecasting techniques that depend on historical information.
27 forecasting method is considered successful when its forecasting error is significantly lower than the forecasting error of naïve forecasting. This will indicate that the developed forecasting method improves demand forecasting at bookstores.
28
5. Results
In this chapter the selected forecasting techniques are tested and a forecasting method for the bookstores is developed. First the parameters are defined. Secondly, the influence of peaks is determined. Thirdly, a closer look is taken upon the first four weeks after sales. Fourthly, the developed method is tested to check whether it is applicable for the bookstores. Finally, the applicability of the techniques is explained for the bookstores.
5.1 Estimation of the parameters
The moving average
As stated in the prior chapter, the moving average requires a determination of the optimal amount of time periods. In order to compare the effectiveness of the different time periods in the moving average, the forecasting error needs to be calculated over the same amount of time periods. The largest amount of periods over which the average is calculated is eight. Therefore, the forecasting error for all values of n is calculated, starting from week eight. Table 5, presents the forecasting error of the different time periods. From the table it shows that a 3-period moving average results in the lowest forecasting error. Therefore this value is chosen for further testing of the moving average.
n 2 3 4 5 6 7 8
MSE 208.09 191.95 197.83 214.15 217.91 225.62 232.12
Table 5: MSE outcomes calculated starting from period 8 for different values of n periods applying moving average
The weighted moving average
For the weighted moving average the optimal amount of periods has to be chosen, as well as the weights assigned in each period. The decision about the weights chosen for each period was explained in the prior chapter. The highest weights are assigned the to the most recent time period, equivalent to the value of n. The highest value of n that is tested is eight. In table 6 the MSE outcomes for all the forecasting periods with their weights are presented. The forecasting error for all values is calculated starting from week eight. The four-period weighted moving average has the lowest forecasting error. For further calculations with the weighted moving average, this value will be used.
n 2 3 4 5 6 7 8
weight
MSE 219.39 197.77 192.08 194.34 196.52 200.02 203.72
Table 6: MSE outcomes calculated starting from period 8 for different values of n periods applying weighted moving average, where the assigned weight for the most recent period is equal to the value of n.
Exponential smoothing
29 MSE outcomes for different values of alpha. The values of alpha that are tested in this table round at 0.05. The data table is presented in table 7. From the table it shows that 0.4 results in the lowest forecasting error. This is in accordance with the value that was produced by the solver. Furthermore, it shows that the forecasting error for an alpha of 0.05 is much higher than the other forecasting values. This high value is caused by a few large errors that where magnified by squaring the outcomes and does not indicate a duplication of the actual error. For further calculations an alpha of 0.4 will be used, to avoid rounding problems.
α MSE α MSE α MSE α MSE
0.05 602.83 0.3 316.90 0.55 319.46 0.8 357.09 0.1 426.57 0.35 313.20 0.6 324.59 0.85 368.36 0.15 366.73 0.4 312.16 0.65 330.92 0.9 381.06 0.2 339.05 0.45 313.08 0.7 338.43 0.95 395.32 0.25 324.60 0.5 315.58 0.75 347.13
Table 7: MSE outcomes for different values of alpha applying exponential smoothing.
5.2 Influence of peaks
To determine the influence of the sales peak on the forecasting accuracy, the peak and flattening level need to be calculated first. In appendix II the data tables with the forecasting errors for different values of the peak and flattening level are presented. From the appendix it can be seen that for all three methods the peak determination factor is 0.3. This means that if sales in a consecutive week increases with 30%, this will be considered a peak. For the moving average and the weighted moving average, the optimal flattening level is 0.5. Exponential smoothing presents a flattening level of 0.6. These levels indicate that if a peak is found, it should be flattened with a factor 0.5 or 0.6. To establish the influence of the sales peaks, the forecasting errors of all three techniques are calculated over the corrected data and over the actual sales data. To be able to compare the outcomes, the forecasting error is calculated starting from period four. Table 8 presents the results.
Moving Average (3-period) Weighted Moving Average (4-period) Exponential Smoothing (0.4) No correction 275.26 262.57 255.39 Peak 0.3/ Flattening 0.5 232.48 229.19 231.53 Peak 0.3/ Flattening 0.6 234.78 230.09 231.30
Table 8: MSE outcomes of three forecasting techniques comparing two different flattening levels with a situation where no corrections are made, calculated starting from period 4.
