Overview of Quantitative Forecasting Methods on Sales of Naphthenic oils

Transcription

1 Overview of Quantitative Forecasting Methods on Sales of Naphthenic oils ALI HADIZADEH Production Economics Master s thesis Department of Management and Engineering LIU-IEI-TEK-A-11/1237 SE

2 2 P a g e Overview of Quantitative Forecasting Methods on Sales of Naphthenic oils Ali Hadizadeh Hamun.hadizadeh@gmail.com Master Thesis Subject category: Technology Linkoping University, Institute of Technology, Department of management and engineering SE Linkoping Examiner: Mathias Henningsson Mathias.Henningsson@liu.se Supervisor: Martin Kylinger Martin.Kylinger@liu.se

3 3 P a g e Abstract An overview of mathematical forecasting methods has been presented in this research. First, the data of revenue and sales volume of 15 products is collected, cleaned, and prepared for further studies by applying data mining steps. Second, ABC analysis is applied to narrow down the domain of research to only critical products. A literature review of the most common and applicable quantitative methods of forecasting are addressed in the next phase and finally the implementation and numerical results is presented. Having considered the most well known quantitative forecasting methods, exponential smoothing and ARIMA give the best result based on MSE and ARIMA gives the best result based on MAPE, while multiple regression model with ARIMA error gives the best perspective to forecasters on finding the most effective factors in sales and revenue. Having calculated the mean of MAPE for all forecasting methods, we were interested to see if the forecasting method is a significant factor and if the difference between the average values obtained by ARIMA is statically different from other methods. To do so, we run the randomized block design method and by drawing the main effect plot we have come to this conclusion that forecasting method can be considered as a significant factor and by running Two Sample T Test in MINITAB and presenting 9% confidence interval, the ARIMA method outperforms other methods significantly. Keywords: quantitative forecasting methods, Data analysis, ABC analysis, Mean Square Error (MSE), Mean Absolute Percentage Error (MAPE)

4 4 P a g e Acknowledgement I would like to thank first and foremost my supervising tutors, Dr. Martin Kylinger and Dr. Mathias Henningson for their abundant help and productive advices. I am also grateful to my parents and friends especially Faezeh Malekian who consistently supported me during this period.

5 5 P a g e Table of Contents Chapter 1: Introduction and Motivation Introduction Aim and Scope Structure of Thesis Nynas history Nynas supply chain Nynas products Limitations Thesis outline Chapter 2: Data Cleaning and Classification Data analysis ABC analysis Chapter 3: Basics of Quantitative Forecasting Quantitative methods Accuracy measures Non-parametric trend test of product demand data Chapter 4: Research Methodology Chapter 5: Implementation and Numerical Results ABC Implementation Non-parametric trend analysis Visual analysis Output of decomposition Output of moving average Output of exponential smoothing Output of ARIMA method Output of multiple regression method Output of multiple regression method with ARIMA error Chapter 6: Comparison of Numeric Results Chapter 7: Conclusion References... 89

6 6 P a g e Table of Figures and Tables FIGURE 1.1 SUPPLY CHAIN NETWORK AT NYNAS FIGURE 2.1 THE TRANSFORMATION OF RAW DATA TO KNOWLEDGE, SOURCE: KRZYSZTOF J ET AL (27) TABLE 2.1 POLICIES ASSIGNED TO EACH CATEGORY OF PRODUCTS... 2 FIGURE 3.1 DYNAMIC DATA SERIES FIGURE 3.2 STATIC TIME SERIES FIGURE 3.3 CONSTANT SEASONAL VARIANCE FIGURE 3.4 INCREMENTAL SEASONAL VARIANCE TABLE 3.1 DIFFERENT TYPES OF EXPONENTIAL SMOOTHING FIGURE 3.5 TIME SERIES PLOT OF STATIONARY DATA TABLE 3.2 PATTERN OF ACF AND PACF FOR BASIC AR AND MA MODELS FIGURE3.8 RESIDUAL PLOT TABLE 5.1 LIST OF REVENUES IN DECREASING ORDER TABLE 5.2 CUMULATIVE DISTRIBUTION OF REVENUE FOR ALL PRODUCTS TABLE 5.3 CLASSIFICATION OF PRODUCTS BASED ON REVENUE TABLE 5.4 VOLUME AND REVENUE PROPORTION OF PRODUCTS IN DIFFERENT CLASSES FIGURE % OF THE TOTAL REVENUE IS MADE BY ONLY 17% OF THE TOTAL PRODUCTS (X AXIS INDICATES PRODUCTS) TABLE 5.5 UNIVARIATE TEST FOR THE 23 TOP RANKED PRODUCTS TABLE 5.6 UNIVARIATE TEST OF THE 5 SELECTED PRODUCTS FIGURE 5.2 TIME SERIES PLOT FOR P FIGURE 5.3 SEASONAL PLOT OF P1 FROM 24 TO FIGURE 5.4 SHIFT OF P1 SALES FROM ONE YEAR TO ANOTHER FIGURE 5.5 TIME SERIES PLOT FOR P1 IN MINITAB FIGURE 5.6 COMPONENT ANALYSIS OF DECOMPOSITION METHOD FOR P FIGURE 5.7 TIME SERIES DECOMPOSITION PLOT FOR P FIGURE 5.8 RESIDUAL PLOT... 6 TABLE 5.7 GENERATED FORECAST... 6 TABLE 5.8 MEAN SQUARE DEVIATION FOR THE 5 PRODUCTS FIGURE 5.9 FITTING PLOT OF MOVING AVERAGE WITH LENGTH TABLE 5.9 ACCURACY MEASURES BASED ON DIFFERENT LENGTH FIGURE 5.1 LINEARITY TESTS OF RESIDUALS FIGURE 5.11 RESIDUAL PLOTS OF P TABLE 5.1 FORECAST IN ADDITION TO UPPER AND LOWER BOUNDS FIGURE 5.12 FORECAST LINE WITH INTERVALS TABLE 5.11 FORECAST WITH INTERVALS TABLE 5.12 MEAN SQUARE DEVIATION FOR OTHER CRITICAL PRODUCTS TABLE 5.13 COMPARISON OF SES, HOLT, AND HOLT-WINTERS BASED ON MSD AND MAPE FIGURE 5.13 SES PLOT IN ADDITION TO THE FORECAST LINES FIGURE 5.14 RESIDUAL PLOTS FIGURE 5.15 RESIDUAL TREND PLOT TABLE 5.14 GENERATED FORECAST WITH BOUNDARIES AND MEAN SQUARE DEVIATION FIGURE 5.16 SALES PLOT OF P FIGURE 5.17 SALES PLOT FOR THE DIFFERENCED DATA SERIES TABLE 5.15 MSE COMPARISON IN DIFFERENT ARIMA METHODS TABLE 5.16 LEVEL OF SIGNIFICANCE FOR ARIMA PARAMETERS TABLE 5.17 BOX-PIERCE ANALYSIS FIGURE 5.19 RESIDUAL ANALYSIS FIGURE 5.2 RESIDUAL TESTS FIGURE 5.21 PLOT OF RESIDUALS TABLE 5.18 FORECASTS OF P1... 7

7 7 P a g e TABLE 5.19 GENERATED FORECAST FOR PRODUCT TABLE 5.2 GENERATED FORECAST FOR PRODUCT TABLE 5.21 GENERATED FORECAST FOR PRODUCT TABLE 5.22 GENERATED FORECAST FOR PRODUCT TABLE 5.23 CORRELATION AMONG SELECTED POTENTIAL VARIABLES FIGURE 5.23 SALES PLOT OF NYTRO TABLE 5.24 CORRELATION BETWEEN THE RESPONSE VARIABLE AND SEASON INDICES FIGURE 5.24 FITTED LINEAR TEST FIGURE 5.25 FITTED QUADRATIC TEST FIGURE 5.26 FITTED CUBIC TEST TABLE 5.25 REGRESSION ANALYSIS (P1 VS T & T2) TABLE 5.27 ANALYSIS OF VARIANCE AND THE REGRESSION EQUATION OF PRODUCT 1 (NYTRO) TABLE 5.28 MSE AND CRITICAL FACTORS IN REGRESSION MODEL FOR DIFFERENT PRODUCTS TABLE 5.29 MSE OF 5 CRITICAL PRODUCTS IN MULTIPLE REGRESSION WITH ARIMA MODEL FIGURE 6.1 TIME SERIES PLOT OF P1 AND P TABLE 6.1 COMPARISON OF DIFFERENT FORECASTING METHODS BASED ON MSE... 8 TABLE 6.2 COMPARISON OF DIFFERENT FORECASTING METHODS BASED ON MAPE... 8 TABLE 6.3 AVERAGE MSE FOR 5 CRITICAL PRODUCTS TABLE 6.4 AVERAGE MAPE FOR 5 CRITICAL PRODUCTS TABLE 6.5, THE RESULT OF MAPE FOR DIFFERENT PRODUCTS WITH SUM AND AVERAGE TABLE 6.6 ANALYSIS OF VARIANCE FOR FORECASTING METHOD AS THE MAIN FACTOR AND PRODUCTS AS BLOCK83 FIGURE 6.2 MAIN EFFECT PLOT FOR DIFFERENT METHODS AGAINST AVERAGE OF MAPE TABLE 6.7 TWO-SAMPLE T FOR ARIMA VS DECOMPOSITION TABLE 6.8 TWO-SAMPLE T FOR ARIMA VS MOVING AVERAGE TABLE 6.9 TWO-SAMPLE T FOR ARIMA VS EXPONENTIAL SMOOTHING... 85

8 8 P a g e Chapter 1: Introduction and Motivation

9 9 P a g e In today s business, forecasting is one of the most important tools used for operation strategies especially make to stock environments in which the main goal of forecasting is to ensure that the level of materials needed for production satisfies customer s demands without resulting any overcapacity situation and extra inventory. On the other hand, forecast should not create any shortage for the manufacturer whose main role is to fulfill customer s orders Introduction The term of forecasting is used when it is aimed to estimate the value of variables in future. It is a tool for mangers to make better plans and decisions. Forecasting can be applied for different situations as follows: 1- Inventory and production plan. [Sales, product demand, production schedule ] 2- Investment and financial information. [Interest rate, share price] 3- Economic. [Economy growth, inflation] Many case studies have revealed that inaccurate forecasts can make a catastrophic cost for companies. It causes big problems form late customer deliveries to increased inventories and higher costs. According to the research which has been made by D. R Rice Company the companies that can overcome the forecast hurdle have seen numbers such as: 1. 3% increases in on-time deliveries 2. 5% reduction in inventories 3. A staggering 8% in customer lead times 4. 2% reduction in total business costs Thus, applying the right techniques of forecasting is a big concern for supply chain managers. Generally, forecasting can be developed for different levels of product from finished goods and raw materials to components and service parts. Forecasting should not be static, rather must be reviewed by forecasters on a regular base. In this way, future information on trends, seasonality, and other external and internal elements can be extracted and employed to give a better result. There are different ways to classify forecasting problems. One method is to consider the time scale on which forecasting is applied. In other words, it depends on how far we go toward future and predict. Based on this classification, three main categories are created namely, short-term, medium-term, and long-term, each of which might have different meaning according to the situations in which forecasting is applied. For instance in energy industry, 5 to 1 years is considered short-term while in forecasting consumer demand 2 years would be a long-term forecast. Typically, there are three levels of decisions in the supply chain namely, operational, tactical, and strategic. Operational decisions encompass short-term decisions from 3-6 months such as inventory control, production planning and distribution. Tactical decisions which are appropriate for the interval between 6 months to 2 years such as decisions concern staff and facility changes. Lastly, strategic decisions covering decisions lasting for more than 2 years such

10 1 P a g e as research and development and product design change. This classification is imperative since different forecasting methods should be used in each class. For example, in the case of sales forecasting, we may be interested to forecast sales for the next 6 months or 5 years while each of them requires a suitable forecasting method. Forecasting can also be classified into other categories based on the type and genre of forecasting techniques. These classes are depicted as follows. 1- Qualitative forecast with no mathematical method and merely based on the experts experience and skills. 2- Regression models in which forecast (response) variable is linearly related to a number of other independent variables. 3- Multiple equation also known as econometrics which are a variety of dependent variables interacting with each other in number of equations. 4- Time series methods that is a single variable whose future value is related to its past and it changes over time. In this master thesis, we are motivated to introduce and analyze the abovementioned forecasting methods and apply them for the NYNAS supply chain and finally come up with the best models for this case study Aim and Scope The current thesis aims to have an overview on important quantitative forecasting methods available in literature for the products in a continuous flow production in accordance with the NYNAS case study. In this research, the general research question is which quantitative forecasting method(s) should be applied for this project and why? Nowadays, having a precise forecast plays a significant role on companies financial success. For businesses with a high level of turbulence in costs, competitors, and other dominant parameters, to have an appropriate model for forecasting is a leading character. Through the reviewed literature, we come up with appropriate methods of sales forecasting that could be practically used in the petroleum industry. In each section of this study, specific methods and techniques required for forecasting will be reviewed and some aspects of this problem are taken into consideration. This study provides us with a framework for data treatment that can be applied prior to any further analysis on the result of any research. Data analysis as one of the major phases before any process and implementation should be applied. In this paper, it is tried to describe important steps of data cleaning and especially ABC analysis. The scope of this research is defined as follows. 1- This research only considers naphthenic oils in NYNAS supply chain. 2- Among naphthenic oils, only those selected as financially critical products are studied.

11 11 P a g e 3- Among all critical products, all with full availability of data have been processed. 4- Among different types of forecasting methods, only quantitative techniques are applied Structure of Thesis The data for 15 products is extracted from NYNAS. Data is cleaned, integrated, and formatted. Most of the missing values are recovered and derived attributes are produced in access file. Pareto (ABC) analysis is made based on the revenue that each product makes and 23 critical products are selected. Data accuracy, correctness, completeness, and relevance are checked. A sample of 5 products is selected from the 25 critical products based on the data completeness. Decomposition, moving average, exponential smoothing, multiple regression, ARIMA, and regression with ARIMA error are the methods applied on the data of selected 5 products The results are recorded and the best methods based on the accuracy measures for this case study are selected. Analysis of Variance and T statistic test are run to statistically approve the significance of forecasting method factor and the difference of the mean of the best forecasting method with the mean of other methods Nynas history NYNAS business started in 192s as the first oil refinery company in nynäshmn Sweden. This company played a magnificent role during the World War II in supplies of oil substitute within the country s borders. After the world war by increasing the national demand for expanding road networks and the request for bitumen and other oil derivatives, it had a huge physical and financial growth. NYNAS policies in 196s and 197s have encountered major ups and downs. During 196 s they broadened the range of products from bitumen to fuels, lubricants, solvents, diesel etc, but in 197s when the oil crisis arrived they narrowed down their production by focusing on some special products. This decision soon urged NYNAS to be an international player in oil industry. This happened with investment in hydrogenation technology to renovate and boost the production of naphthenic. Since 199, NYNAS started to develop and enlarge the company in its specialty areas. That s how they increased their new sales companies in many other countries and simultaneously turned to one of the biggest bitumen companies in Britain. This specialization process has led NYNAS to be a world leader in the market of naphthenic specialty oils and one of the great producers of bitumen in the Europe.

12 12 P a g e 1.5. Nynas supply chain The company s supply chain is constructed on 4 layers including refineries, hubs, depots and customer areas. The crude oil is transported to the refineries by suppliers and will be processed and converted to specific raw products in refineries. These components could be shipped directly to the customers as raw materials or be blended in hubs and transported to different depots and different customers s as new raw products. The supply chain network is depicted in Fig 1.1 Mainly, the finished products are in the category of bitumen or naphthenic. In this study, the whole analysis is made on naphthenic products. Figure 1.1 Supply chain network at NYNAS 1.6. Nynas products There are two main categories of products available in Nynas namely, bitumen and naphthenic oils. Bitumen and its derivatives are much older and their history of production goes back to the time of Nynas foundation. However Naphthenic oils are much newer products with higher profit margin. Due to the higher profitability and based on the company s policy, naphthenic oils have a worldwide supply chain whereas bitumen merely meets local demands within Scandinavian, Nordic and some other European countries.

13 13 P a g e 1.7. Limitations The data and information obtained for this study is a combination of quantitative and qualitative records. An interview was arranged with a sales analyst in Nynas and the raw data has been collected over 4 months. The data had many missing values and ambiguities such as large outliers. This certainly jeopardizes the validity of this research. More importantly, due to the lack of enough interaction with the company, we could not lighten all imprecision of this research. Although, some of the missing values have been recovered by interpolation technique, we were forced to eliminate some of the products because of the huge number of lost information in the raw data. Also, the data available for this study only covers 6 years which is not enough for running a strong validity test. The analysis is only made for Naphthenic oils and the research does not consider another important product family, bitumen. Considering all these limitations, the major quantitative forecasting methods will be implemented in this research Thesis outline To do this research, all monthly data about sales volume, customer segments, sale channels and other potentially useful information at NYNAS, from 24 to 29 have been collected, cleaned and got ready to be processed. ABC analysis as a major tool for selecting, sorting and prioritizing products is accomplished. Having selected the most critical products, quantitative forecasting methods are reviewed to find a best model that answers the main question of this research which is to present the best quantitative forecasting model for the sales of naphthenic oils. Considering many criteria, the best model is suggested in the conclusion part of this study. The rest of this study is as follows. In Chapter 2, the methods of data cleaning and analysis will be explained. In Chapter 3, a theoretical review of quantitative forecasting methods is provided. Research methodology is presented in Chapter 4. In Chapter 5, the reviewed methods are applied on the real data collected from NYNAS and finally the best method based on the accuracy measures has been selected in chapter 6. Conclusion is also presented in Chapter 7

14 14 P a g e Chapter 2: Data Cleaning and Classification

15 15 P a g e Before analyzing the raw data, they should be checked and cleaned. In this study some steps of Data Mining (DM) are applied for the preparation of data. At first, a more comprehensive concept called the knowledge discovery process in which data mining is considered as the major core, will be reviewed. Having cleaned and prepared the data, ABC analysis will be implemented to narrow down the scope of this research only to those products which are financially critical for the company. At the end of this section, theoretical overview of most important quantitative forecasting method will be presented Data analysis Knowledge discovery process is defined as the nontrivial process of identifying valid, novel, potentially useful, and ultimately understandable patterns in data. Knowledge discovery concerns the entire knowledge extraction process, including how data are stored and accessed, how to use efficient and scalable algorithms to analyze massive datasets, how to interpret and visualize the results, and how to model and support the interaction between human and machine. Figure 2.1 The transformation of raw data to knowledge, Source: Krzysztof J et al (27) Typical inputs include data in various formats, such as numerical and nominal data stored in databases or flat files. The output is the generated new knowledge usually described in terms of rules, patterns, classification models, associations, trends, statistical analysis, etc. Krzysztof J et al (27) During this process, data turns into information, knowledge, and finally wisdom. In the following, we ll see how this transformation works but first, data, information and knowledge should be explained Data are any facts, numbers, or text that can be processed by a computer. The patterns, associations, or relationships among data can provide information. For example, analysis of sale transaction data at NYNAS can create information on which products to be sold and when.

16 16 P a g e Information can be turned to knowledge based on historical patterns and future trends. For example, in this study, list of information on products sales can be analyzed for fostering efforts to provide knowledge of purchasing behavior. Thus, a manufacturer could determine which items are most liable for promotional efforts. Data Mining is to make sense of large amount of mostly unsupervised data in some domain Krzysztof J et al (27). In Data Mining, data is analyzed from different views and then summarized into useful information in which the relationships are completely identified. This information could be used to increase profits and cut costs significantly. Technically it is defined as the process of discovering patterns and correlations among many areas in data base. Data mining steps are introduced in many literatures. Here The CRISP-DM methodology has been used. It was first established in the late 199s through the cooperation of four companies: Integral Solutions Ltd. (a provider of commercial data mining solutions), NCR (a database provider), DaimlerChrysler (an automobile manufacturer), and OHRA (an insurance company). The CRISP-DM consortium (2) introduces 6 steps of data mining as: 1. Business understanding 2. Data understanding 3. Data preparation 4. Modeling 5. Evaluation 6. Deployment The First four steps which have been applied for this research are described as follows: Business understanding The main part of business understanding is the determination of business objective. It could be defined as what the customers really want to be accomplished. In this step, all information about business situation should be recorded. The success criteria for the business should also be determined. For NYNAS, the objective could be defined as reaching to a best quantitative method to forecast the sales of critical products. Our success criterion is to give a useful insight into the level of demand sensitivity for A-category products to some potential factors such as prices, firm s policy, etc. For the forecasting project, we first have to find exactly where the forecaster is situated in the supply chain and how she is exploiting the flow of information from market to factory in the

17 17 P a g e forecasting process. Forecasters should determine how many products are needed from depots or hubs to customers. The important issue is the role of sellers in forecasting and how they predict customers demand. Sellers may forecast a specific number of products for a specific number of customers, but the company might produce less or more than the amount of request. They experience stock out many times and we may need to find out that this stock out or extra inventory is because of the poor forecast or is due to the impact of other potential factors. We also need to find out how is the forecast getting updated. How the feedbacks are influencing the forecasts of the next months. In discussion with the supply chain manager, it is understood that yearly budgeted volumes and consideration of Bitumen production are also taken into account in forecasting. The question is how this phenomenon impacts demand. Data understanding Data collection and verification of data quality are the major parts in this step. The quality of data plays an important role in future calculations. The high quality data is a data that users have coverage for all needed materials. High quality data is a data that has accuracy, correctness, completeness and relevance. Accuracy is the degree of closeness of measurements of a quantity to its actual value. Correctness is declared when we have a correct output for each input Data completeness is an indication showing if all the data necessary to meet the current and future information demand are available in the resource Data relevance shows how much something is connected and applicable to a specific issue After collecting data from NYNAS, all of the above cited four steps should be checked before and during data analysis. One method is to use several methods to collect and process data in order to investigate the quality of the data. Data Preparation In order to prepare the final data set and make them ready to be fed into the next phases, they should be cleaned, integrated, and formatted. Attributes (columns) and records (rows) should be selected in this step too. This is what we have done on our data. All of the missing values are recovered, and derived attributes are produced in the access file. Information is combined from multiple tables to create new values. ABC analysis as a major tool for selecting, sorting and prioritizing products is also accomplished in this phase. This analysis will be explained thoroughly in this study.

18 18 P a g e Modeling This section is the key segment of our research and the conclusion which is made at the end of the study is based on the results obtained in this phase. Different methods and techniques are chosen and applied for the same problem. Each modeling technique might have specific assumptions, (i.e. no missing value checked in the previous section could be one of these assumptions). Having considered these assumptions, we need to check the quality and validity of the selected techniques. This is called generating the test design. Error rate is one of the criteria for checking the quality of the methods. One or more years of data could also be used for testing the validity of the methods. In the upcoming segments, testing and developing of these models, will be explained but first ABC analysis is explicated ABC analysis The ABC analysis or 8/2 rule is a tool stating that a 2% of a given population stands for 8% of a particular characteristic. As mentioned earlier in this research, it is one of the steps of data preparation. ABC analysis is usually accompanied with this renowned speech: the ABC tool is used to identify the vital few from the trivial many. based on the definition above the ABC analysis classifies products or whatever under study into 3 or more levels, A, B, C. Generally, the A segment stands for almost 8% of the total spend in a group, the B segment stands for the following 15% of the total spend and the C segment represents the remaining (final 5% of total spend) EIPM (24) Before we go through the whole mechanism we have to note that ABC analysis does not lead to a straight solution. It only explores the important areas for future opportunities. In inventory management, Different types of criteria might be used for creating ABC categories. the most common criterion is the amount of produced /spent dollar for each item, it helps managers to find the few A sections that require the most special attention and this is all because of the high amount of money spent in this category. That s why small difficulties in managing this segment might lead to a large cost for the company. Categorizing products can be accomplished for many reasons. In many cases, managers need to know what products are the most critical ones to invest. The aim of ABC analysis in this study is to find the demand of the most critical products and extract their pattern and behavior over time. But the question is how do we define the concept of criticality? Today, ABC analysis is a much vaster concept; managers know that focusing merely on monetary issues like amount of dollar- usage or costs cannot present the criticality and importance of monitoring of different products. Also in some cases, products with low investment bring about the high level of risk for the company. These risks should first be determined. They can be understood differently in various areas. For example, for a production company, lead time, safety stock, and consumer sensitivity could be considered as risk factors. Having defined the risk elements, we have to identify which items (especially in C segments) are risky for the business. In this research, due to the lack of enough information about the

19 19 P a g e inventory management and production systems, these critical factors are not studied and the estimation is merely based on the amount of revenue for each product. However, a useful method with the assumption of having all available information will be suggested later in this section. Considering this method, we can have a more precise ABC analysis for the demand forecasting. The following 6-step procedure is carried out to run the ABC analysis. 1 Identify the objective and the analysis criterion 2 Collect data about the analyzed population 3 Sort out the list by decreasing impact 4 Calculate the accumulated impact and the percentage 5 Identify the classes 6 Analyze the classes and take appropriate decisions Source: EIPM (24) The above-cited steps will be thoroughly explained in the methodology section Criteria selection What we ve analyzed so far was about considering a single criterion which is the amount of dollar obtained in the sale process. However, Special attention must be paid to other factors influencing the product demand directly or indirectly. One of the first applications of ABC analysis was in inventory management methods applied in General Electric by Dickie, H.F (1951). They used a simple concept of concentration on significant few and spending less on the trivial many. Categorizing items into classes of A, B and C is generally accomplished by considering some criteria in inventory control. This criterion as already mentioned, is often the amount of dollar spent for the items. However, there are some other criteria that affect other aspects of inventory management and impress the company s financial success. For inventory managers, these criteria could be the impact of shortages, the confidence of supply, the number of obsolescent items, and so forth. Some of these criteria may even have a bigger influence than the amount of spent dollars has. Many researchers have considered these factors in their research. For example, Villarreal et al (198) use item costs, costs of subassemblies for each item, and the lead time in management of capital goods inventory as their criteria. Flores et al (1986) analyzed different non-financial criteria such as lead time, availability, sustainability, and criticality. They have found that the factor criticality is covering almost the most facets of maintenance inventory items. They define criticality as the seriousness of stock-out, the speed of purchasing process, availability of substitutes, and so on. Their main effort during their study was to see how they

20 2 P a g e can identify the degrees of criticality in a practical way. Flores, et.al (1987) explain the necessity of using multiple criteria in categorizing each product in a year later. The theoretical way of using different criteria is to have ABC categories for both the amount of spent dollars and criticality independently. However, this will make the large number of combinations for which different management policies are needed. Thus, to shorten this process, non-critical costly items and critical low cost items are located in the same category. In the first phase, managers rank the items based on the amount of spent money and assign them to A, B and C classes. In the second phase, they were asked to consider all factors concerning the criticality such as impact of an outage, ease of replacement, lead time, availability, etc and rank items accordingly. In the third phase, they are asked to see if they can combine criticality with the spent money and assign them to new categories. They gathered data from the maintenance inventory records. Critical items are assigned to category I, non-critical items are assigned to category III and those in between are categorized in class II. Many possible combinations could be made and for each combination different policies are required. However, based on what Flores et.al (1986) suggest these combinations are reduced to a manageable number. They use a simple mechanical procedure to combine different criteria and finally provide three initial categories of items: AA, BB and CC. This process is done by merging AI, AII and BI to AA, AIII, CI and BII to BB and BIII, CII and CIII to CC. A specific policy will be determined for each category. These policies are to cover four important areas: inventory record accuracy, order quantity, safety stock and the classification of the item itself. After assigning items to each class, the managers will be asked if they are eager to accept these policies shown in table 2.5 or not, for example if item #3 is assigned to class BB, the managers will be asked to see if the policies in four areas are appropriate for this item. If not, they will re-categorize items and only use the policies as a guideline. The interesting point of reclassification is that we might see a new category of items named DD which stands for don t stock items. Having reviewed the items, the managers may find some obsolete items or some items less critical even than C items, so stocking them is not a smart option. The policy of the company is to scrap or sell out all DD items in the first year; this will help to empty the warehouse spaces which lead to less money consumption and more capital generation in the future. Decision/category AA BB CC Counting frequency Monthly Every 6 month yearly Order quantity Small for costly items Medium EOQ based Large quantities Safety stock Medium for critical items Large for critical items Low or none Reclassify review Every 6 month Every 6 month yearly Source: Flores et al. (1986) Table 2.1 Policies assigned to each category of products

21 21 P a g e The order quantities are based on EOQ (Economic Order Quantity) and safety stock is derived from the criticality of the item. Due to the lack of enough information about the criticality of products this method is beyond the scope of this research. Thus, categorization of products is done only by considering the factor of income for each product in this study.

22 22 P a g e Chapter 3: Basics of Quantitative Forecasting

23 23 P a g e This study aims to present an overview of different quantitative forecasting methods for forecasting the sales of some of the critical petroleum products at NYNAS. In forecasting, there are many methods some of which are reviewed in this section and finally the best model based on the study objective is suggested. Before spelling out the different techniques of forecasting, the role and position of forecasting in the business and the factors affecting this phenomenon should be articulated. Spyros Makridakis et al (1998) describes the distinction between uncontrollable external events which originates from national economy, governments, customers and competitors and controllable internal events such as marketing or manufacturing decisions in firms. He mentions that the success of a company depends on controlling both factors. While forecasting is applied directly for the former, decision making is accomplished for the latter and planning is applied for both. Sales projection is a significant part of forecasting in each business. As if error in sales projection happens it can prompt a series of reactions on budget determination, operating costs, cash flows, inventory levels, pricing and so on. That makes forecasters try their best to select the best possible method that predicts demand precisely. Quantitative methods are accomplished when we have enough quantitative information. It is classified into two major types, time series and explanatory forecasting. Time series forecasting is based on the persistence of historical patterns such as growth in sale, while explanatory forecasting is based on understanding how different variables such as prices, firm s policy etc, are influencing sales. Similarly, Aunupindi et al (26) have classified forecasting methods into two major categories as subjective and objective methods. Subjective methods apply forecasts based on experience and judgment while the objective forecasts do so based on data analysis. The objective methods are classified into smaller groups per se. Casual models (such as explanatory forecasts) and time series analysis are considered as two basic objective methods. Casual models assume that other factors such as price, personal income, etc are effective in addition to the behavior of data, while time series analysis relies merely on past data. As Spyros Makridakis et al (1998) explain quantitative forecasting can be applied when three conditions exist: 1) Past information should be accessible 2) Past information can be quantified as numerical data 3) some aspects of past pattern keep on in future (assumption of continuity) The main question of this study is to find out which quantitative method(s) should be applied for this project. Before answering this question, a deeper understanding about these two models and their pros and cons should be obtained.

24 24 P a g e Explanatory vs. time series Explanatory forecasting demonstrates explicative relations with some independent variables. The purpose of this model is to find the form of this relationship and apply them to forecast future. Of course, these relationships are not precise, and variables in the model cannot account for all the changes in the dependant variable. So an error term should be considered to represent the randomness and unexplained behavior beyond the effective variables of the model. In contrast to explanatory forecasting, Time series forecasting does not look for potential effective factors rather, predicting future is merely based on the values of variables or/and errors in the past with the aim of finding pattern in the historical data and infer future. Makridakis et al (1998) point out 2 reasons why forecasters choose time series over other methods. First the system is not understood or even if it is understood it might be extremely hard to measure. Second, forecasters might only care about what will happen and not to know why it happens. Thus, the advantage of time series is based on the ease of use, while explanatory variables are used when policy and decision making is needed. In this project, several methods and techniques of quantitative forecasting including both explanatory and time series have been studied. Time series is a series of observation over time. In forecasting, we are eager to see how this series will continue in future. There is a variety of techniques in time series. The most important thing that helps us to find the right method is the type of data patterns and what is visualized when the data is plotted. At one glance, the data pattern can be dynamic or static. In static pattern, past data continues its behavior in future. While in dynamic pattern we cannot follow a stable behavior in past and future. In the following dynamic and static pattern are shown. 2 Time Series Plot of y 15 y Index Figure 3.1 Dynamic Data Series

25 25 P a g e 8 Time Series Plot of y y Index Figure 3.2 Static Time Series In static pattern, we might have some specific behavior as follows: 1) stationary 2) seasonal 3) cyclical 4) and trend Figure 3.2 is a static pattern that has trend and seasonality. Many data series have the combination of these behaviors at the same time and due to the large number of different patterns in a time series, the solving procedure can be very challenging Quantitative methods In this study, very popular methods of forecasting have been reviewed. Then, the candidate approaches for this case based on their applicability in forecasting will be selected. 6 different methods are used to forecast the demand of naphthenic products at NYNAS, namely, Decomposition, Moving average, Exponential smoothing, Autoregressive moving average, Multiple regression model, and Multiple regression with ARIMA error. Having analyzed the performance of these methods through different accuracy measures, one can decide which approach can be used for forecasting of a specific product. Among the aforementioned methods, the first four models are considered in the time series category, the fifth method is explanatory and the last one is the combination of explanatory and time series forecasting.

26 26 P a g e Decomposition Decomposition method is one of the oldest and at the same time most reliable techniques of time series. As mentioned above, the pattern in each data series in many instances can be decomposed into some sub-patterns so that each time series component can be specified separately. This will definitely increase the level of comprehension of the series behavior and also the forecasting accuracy. As has been said, among all time series methods, decomposition is one of the oldest methods that usually classifies pattern into two major components for describing the economic series. These two components are the trend-cycle factor and the seasonal factor. Data = pattern + error = f (trend-cycle, seasonality, error) One important assumption about decomposition method is if the parameters describing the time series are almost constant over time (static pattern), the decomposition approach will be an appropriate method to characterize the behavior of the data and forecast. In view of the fact that what type of variation pattern a time series might have, two major types of decomposition may be used. In case of increasing seasonal variation, (i.e. the variation of data series increases when the mean increases) the multiplicative decomposition method and in case of constant variation, the additive decomposition approach will be used. In the following figures, both states are depicted. Time Series Plot of y y Index Figure 3.3 Constant Seasonal Variance

27 27 P a g e 12 Time Series Plot of y y Index Figure 3.4 Incremental Seasonal Variance Multiplicative decomposition and additive decomposition methods are stated in the following formula: Multiplicative decomposition model Additive decomposition model [Makridakis et al (1998)] Where stands for the value of time series at time t depicts the trend factor, is the seasonal factor, would be the cyclical factor and demonstrates the irregular factor all at time t One important fact about decomposition method is that this approach is useful only when its forecasting components (trend, seasonality, etc) keep their pattern constant over time and so is not recommended for data series with dynamic pattern. That s why if the pattern changes, the classical decomposition method does not function very well. Furthermore, estimating the trend cycle is the most difficult process since simple functions for describing the trends such as trend line or other parametric techniques do not visualize them adequately. In this case Makridakis et al (1982) suggest that we use the Holt s method to estimate the trend of seasonally adjusted data obtained from decomposition and then add the seasonal component for the final forecast.

28 28 P a g e Moving average Moving average is a procedure of making the series of averages of different subsets of the data set so that when each new observation becomes available, the oldest observation is removed and the new average can be calculated by adding the latest observation to the equation. The result can be used as the forecast of the next period. For each averaging process, the number of data points should be fixed over time. This is shown with the value of k in the formula. Selecting a larger number of periods will produce a smoother forecasting. Moving average of order k [Makridakis et al (1998)] Although this method is widely used in industry, there are some disadvantages in applying this method. It is not an appropriate method for forecasting when the assumption of an underlying constant process is not met. In other words, when there is trend or seasonality pattern in the data series, this method is not recommended. That s how this technique is not used often as a forecasting procedure under such situations. Also, exponential smoothing generally gives more superior results than the moving average. Exponential smoothing Moving average is a method of averaging when all observations are equally weighted while exponential smoothing devotes unequal set of weights to all past observations and as these weights are exponentially decaying from the latest to the oldest observations, this method is called exponential smoothing. The procedure is that we take a weighted average of past data by using weights that decay in an exponential manner. There are different methods of exponential smoothing used in industries and especially in inventory management. In the following some of these approaches are explained:

29 29 P a g e Single exponential smoothing ) If this equation is expanded by replacing with its components, the following output will be obtained [Makridakis et al (1998)] And this proves the fact that weights are decreasing as we go toward the oldest observations. Thus, this method follows the pattern much better than the moving average approach. As indicated in the first equation, the new forecast is the sum of the last forecast and an adjustment of the forecasting error in the last prediction. This adjustment is shown by α in the formula above. When describing moving average, we mentioned that selecting larger number of periods makes a smoother forecasting. The same will happen when using a small adjustment coefficient (close to ) The value of α has a significant impact on the forecasting accuracy and we ll have different results and especially different forecast errors by using dissimilar α. obviously, by choosing a small value of (α), the primary forecasts are more dominant than when a larger (α) is selected and this could be simply understood by another indication form of single exponential smoothing as follows: In other words, the larger (α) gives a slight smoothing in forecast, whereas, a small value of (α) gives a considerable smoothing. It is better to find the optimum value for α so that the MSE or MAPE or other accuracy measures which will be described later in this chapter, get minimized. This could be done by try and error or some more sophisticated algorithms. Single exponential smoothing is useful for the pattern that has no trend, seasonality or cyclical behavior. If there is a trend in the pattern, forecast will be lagged behind the trend and also this lag will be larger for smaller α. One major advantage of this method against the moving average methods is that this technique requires a small amount of data storage and also computations. Thus, it is faster and more attractive when the number of items is large.

30 3 P a g e Single exponential smoothing with adjusted α It has the same procedure as single exponential smoothing. However, instead of α, there is α. It means this approach allows that the value of α be modified when the pattern changes and this makes the aforementioned method more attractive comparing to the single exponential smoothing. The whole formula is as follows: Where α α [Bowerman et al. (25)] stands for a smoothed approximation of the forecasting error. Similar to exponential smoothing, is calculated as a weighted average of and the last forecasting. is similar except, it is the estimate of the absolute forecast error. Even if we gain a worse forecasting result from this method than the single exponential smoothing, this approach is still more attractive since it minimizes the risk of severe errors and makes minimum administrative concerns. Especially, when there are a large number of items and there is no seasonality and trend pattern in the data series. Linear exponential smoothing (Holt s method) If there is a trend pattern in the data, the suggested method is Holt s method. This time, there are two smoothing constants as follows [Bowerman et al. (25)]

31 31 P a g e When and respectively denote the estimate of the level and slope of the series at time t. handles the forecast for the coming observations. The weights α and β can be estimated by minimizing MSE similar to what it is done in single exponential smoothing. Holt-Winters method So far, it is declared that that moving average and single exponential smoothing are suitable methods for forecasting when there are no trends or seasonality and Holt s method is also an appropriate approach when there is an increasing or decreasing trend in the pattern. However, the recommended method of exponential smoothing when there are both trend and seasonality pattern in the data series is Holt-Winters method which has been extended by Winters in 196. Despite other two methods, this method has three smoothing constants for the level, trend and seasonality. Based on the type of seasonality whether it is additive or multiplicative, there are two sorts of Holts-Winters models which are described below Holt-Winters for multiplicative seasonality [Bowerman et al. (25)] As can be seen is added to the equations and it stands for the seasonal component. Holt-Winters for additive seasonality