AWERProcedia Information Technology & Computer Science

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1 AWERProcedia Information Technology & Computer Science Vol 03 (2013) rd World Conference on Information Technology (WCIT-2012) Automatically Forecasting Magazine Demands and Modeling Seasonality Abdullah Aktel, Department of International Logistics, Okan University, Akfırat-Tuzla, Istanbul 34959, Turkey. Erkam Guresen*, Department of Industrial and Systems Engineering, Turkish Military Academy, Ankara 06654, Turkey. Suggested Citation: Aktel, A., & Guresen, E. Automatically Forecasting Magazine Demands and Modeling Seasonality, AWERProcedia Information Technology & Computer Science. [Online]. 2013, 3, pp Available from: Proceedings of 3 rd World Conference on Information Technology (WCIT-2012), November 2012, University of Barcelon, Barcelona, Spain. Received 7 April, 2013; revised 12 May, 2013; accepted 2 August, Selection and peer review under responsibility of Prof. Dr. Hafize Keser Academic World Education & Research Center. All rights reserved. Abstract Finding the optimum quantity of the circulation of magazines is a difficult task due to the effects of promotions, special issues and seasonality. The accuracy of magazine forecasting is very important to prevent oversupply or undersupply because each magazine issue can be thought as a different product due the change of magazines cover, contents and promotions from issue to issue. Another important point that oversupplying sales points cause worthless stock or an additional disposal cost after a new magazine issue is released. This paper aims to find a sensible way to model the seasonality and forecast the demand of magazines automatically. For this reason, a youth magazine and a computer magazine from Turkey were studied for about sales points respectively. Each sales point has both past sent and past sales data for 58 months from January 2003 to August Data clarifications are applied due to missing data and unknown actual possible sales for undersupplied sales points. To forecast magazine sales automatically two classical methods and two machine learning methods are compared. Simple Exponential Smoothing and combination of Simple Exponential Smoothing and No Trend Holt-Winters Methods are used as classical methods where multi-layer perceptron and radial basis function networks are used as popular machine learning methods. Four methods are evaluated with respect to Mean Absolute Deviation (MAD). Best performing model suggested as automatically forecasting tool. Keywords: Magazine sales forecasting, modling seasonality, simple exponential smoothing, no-trend holtwinters, multi-layer perceptron, radial basis function networks; * ADDRESS FOR CORRESPONDENCE: Erkam Guresen, Department of Industrial and Systems Engineering, Turkish Military Academy, Ankara 06654, Turkey, address: erkamguresen@gmail.com / Tel.:

2 1. Introduction Magazines have some characteristic features which are different from other perishable products. Each magazine issue can be thought as a different product because the magazines cover, contents and promotions change from issue to issue. Due to the effects of promotions, special issues and seasonality the magazine demand is not stationary. It is widely accepted that magazine demand has mostly impulsive characteristic, because the demand is created by the available copies at the endpoint. The supply-demand balance is difficult to obtain. The accuracy of magazine sales forecasting is very important to prevent oversupply or undersupply because each magazine issue can be thought as a different product due the change of magazines cover, contents and promotions from issue to issue. Another important point that oversupplying sales points cause worthless stock or an additional disposal cost after a new magazine issue is released. As customers usually decide to buy a magazine after seeing the cover, having a look at the articles inside, considering the promotions of the magazines thus the demand has mostly impulsive characteristics. The sales show variation from magazine to magazine, from city to city and from month to month. Because of the fact that demand is not stationary and many stock-outs are observed, each issue should be thought as coming from a new demand distribution and only one observation per distribution is available. Therefore, it is impossible to fit a distribution to the sales data and test the assumptions about the demand distribution. Thus in this study machine learning methods are evaluated as well as classical time series methods, instead of just using demand and sales simulation based on assumed demand distributions. This study aims to find a sensible way to model the seasonality and forecast the demand of magazines automatically. For this reason a youth magazine and a computer magazine from Turkey were studied for about sales points. The rest of the paper is organized as follows. Next section provides a review of the magazine distribution planning and magazine demand forecasting. Section 3 describes the methodology (i.e., data, prediction model types and the evaluation methods used in the study) followed by Section 4 which provides the prediction and analysis results. Finally, Section 5 summarizes the study, discusses the findings, and identifies the limitations and future research directions. 2. Literature Review In the magazine planning literature, the main concern is the distribution planning of magazines. In Bell (1978) a distribution procedure for periodicals is investigated. In Artto and Pylkkänen (1999) an effective and practically applicable supply decision procedure for magazine single copy distribution is developed. Özgün (2006) explained magazine distribution planning system by using Turkish magazine sale data and uses simple exponential smoothing as a forecasting method of magazine distribution planning system. However, forecasting the magazine demand accurately is an important part of the magazine planning procedure. So it is natural to ask if more sophisticated forecasting methods can improve the planning process. In Hyndman et al. (2002) a new approach to automatic forecasting based on an extended range of exponential smoothing methods is developed. Dekker et al. (2004) presents alternative forecasting methods that are based on using demand information from a higher aggregation level and on combining forecasts. A good automatic forecasting method is also required in using best initialization methods and optimal smoothing parameters. Taylor (1981) examines initialization procedures proposed in the literature, analyzes their weighting of initial predictions and available historical data, and proposes a new initialization procedure. Gardner (1985) discusses class of exponential smoothing methods and explains the initialization methods of the each model. 371

3 3. Research Method In this study different approaches are tried to model seasonality and forecast the demand accurately. Then a combined approach which compares different classical forecasting models errors and selects the model for forecasting that gives minimum error is developed. For organizing and forecasting with Simple Exponential Smoothing and combination of Simple Exponential Smoothing and No Trend Holt-Winters Methods, a free programming language and statistical package R is used. For multi-layer perceptron and radial basis functions network, SPSS Clementine software is used Data description and preprocessing Data from a magazine distribution planning company in Turkey is used in this study. A youth magazine and a computer magazine were studied for about sales points. Each sales point has both past distribution and past sales data for 58 months from January 2003 to August To forecast the future magazine demand using past delivery and sales amount as a source of data is not enough. If the past sales data are directly used to forecast the demand of a future issue, the forecast will be biased low because we only know a lower bound for the actual demand. The real demand is censored, when all the copies sent to an endpoint are sold. This bias will be larger for endpoints having frequent stock-outs. Therefore, the sales data should be adjusted that they reflect the expected demand without bias. Bell (2000) adjusts the demand by replacing the sales figure with the conditional expectation if a sellout occurred. Denoting the endpoint j s demand for issue i by d ij and the number of copies delivered by y ij, and if the demand distribution is discrete then, the expected demand in case of sellout is calculated as: d ij dij yij xf x) dx/ f ( x dx E ( ) (1) y ij y ij where f(x) is the density of the demand distribution of the endpoints for issue i. Adjustment, given above [8], is adopted for this study and sale points with zero sales are ignored. Corrected and cleared data is used for forecasting magazine demand Modeling and methods Simple Exponential Smoothing Method is a well-known method for time series forecasting. Simple exponential smoothing can be described by following equation St Yt (1 ) St 1 (2) where S t is an unbiased estimator of the forecast for any period ahead. Here α is a smoothing constant between zero and one. The value assigned to α is an important factor that effects forecasting. If it is desired that predictions are stable and random variations smoothed, a small value of α is required. If a rapid response to a real change in the pattern of observations is desired, a larger value of α is appropriate. There are two special α values which are α = 0, and α = 1. α = 0 means that the forecasted value equals to the first smoothed value. So, α = 1 means that the forecasted value equals to the last observation. Estimation of α is an iterative procedure that minimizes the mean squared error (MSE). Also an initial forecast (S 0 ) is required to start up an exponential smoothing forecasting system. The first observation or the mean of the observations can be used as an initial forecast (S 0 ). In this study mean of first six observations are used as S

4 Holt-Winters Method has two types: additive and multiplicative. The additive Holt-Winters method is used for time series with constant (additive) seasonal variation, whereas the multiplicative Holt- Winters method is used for time series with increasing (multiplicative) seasonal variation. Since the magazines demands show increasing or decreasing seasonal variation according to their level, the multiplicative model will be used for forecasting in this study. Multiplicative Holt-Winters method can be described by following equations: St ( Yt / It p) (1 )( St 1 Tt 1) (3) Tt ( St St 1) (1 ) Tt 1 (4) It ( Yt / St ) (1 ) It p (5) Yˆ t ( m ) ( St mtt ) It p m (6) where S t-1 denote the estimate of the level in time t-1, and T t-1 denote the estimate of the growth rate in time t-1. Then, suppose that we observe a new time series value Y t in time period t, and let I t-p denote the most recent estimate of the seasonal factor for the season corresponding to time period t. Here p denotes the number of seasons in a year (p = 12 for monthly data), and thus t-p denotes the time period occurring one year prior to time period t. Furthermore, the subscript t-p of I t-p denotes the fact that the time series value in time period t-p was the most recent time series value observed in the season being analyzed and thus the most recent time series value used to help find I t-p. For applying multiplicative Holt Winters method to our magazine data we had to add a fixed value, ten, which can be a different positive number, to all endpoints demands because if an endpoint demand is zero then that endpoint future demand cannot be calculated by using multiplicative Holt- Winters method. Therefore, a fixed value was added before the forecasting, and this added value was subtracted after the forecasting phase. After some analysis it was seen that the magazine data mostly fit to Simple Exponential Smoothing Method and No Trend Multiplicative Holt-Winters Method Multi-Layer Perceptrons (MLPs) are one of the most popular artificial neural networks (ANNs) used as machine learning tools. In this study MLPs used with back-propagation learning algorithm to forecast sales from past sales data. Similarly, Radial Basis Functions (RBFs) are powerful ANN architectures which operate by organizing each training data from other. This gives RBFs an advantage especially for classification problems. Generally, ANNs have been utilized to model highly-nonlinear relationships among the predictor variables and the dependent variable (Mitchell, 1997). ANNs are highly sophisticated analytic techniques capable of learning from existing data (Haykin, 1999). In this study new sales demand is forecasted (on specific variables) from previous sales of each sales point. 4. Results Since all forecasting situations involve some degree of uncertainty, some error in forecasting must be expected. Denoting the actual value of the variable of interest at time t as y t, the predicted value as y ˆt and subtracting the predicted value of y ˆt from the actual value y t we can obtain the mean absolute deviation (MAD) forecast error as: n MAD 1 / n y t yˆ (7) t 1 t All adjusted data, due to stock out, are rounded and a constant value (ten) is added to the all values to prevent zero forecasts for multiplicative Holt-Winters method. After results are produced constant value is subtracted from all values to obtain actual results. For machine learning methods, MLP and RBFN, a constant lag of twelve is used for one ahead forecasting. First 48 months are used to prepare models and train them and months from 49 to 58 are used for only testing and never used for training or building models. Results of this study are given in Table

5 Table 1. MAD values of each method for each magazine from 49 th month to 58 th month Magazine Simple Exponential Smoothing Combined Method Multilayer Perceptron Radial Basis Function Network Youth Magazine Computer Magazine As seen in Table 1, machine learning methods MLP and RBFN outperformed classical forecasting methods simple exponential smoothing and combination of simple exponential smoothing and multiplicative Holt-Winters method. Clearly RBFN gives lower MAD results for youth magazine and MLP for computer magazine. 5. Discussion and Conclusions The objective of this study was to develop an automatic forecasting system to increase the effectiveness of magazine distribution systems. Classical smoothing methods and several alternative forecasting methods were analyzed. Simple exponential smoothing was adopted as a benchmark method. As we wanted to model the seasonality in the magazine demand, we first tried Holt-Winters for all endpoints. However, Holt-Winters performed very poorly. Therefore, in this study a combined method is used to model seasonality. The combined method compares the historic errors of exponential smoothing and Holt-winters to select the best method for each endpoint. We also used the best initialization methods and optimal smoothing parameters to get better forecasts. Results showed that RBFN was superior to other methods. When considering that twelve months forecast for about ten thousand end sales points, even a small difference (0.037) will mean a huge decrease in disposal, distribution and opportunity costs. Thus, RBFN model was proposed for youth magazine and MLP model was proposed for computer magazine as an automatically sales forecasting method. References *1+ Artto, K. A., & Pylkkänen, E. (1999). An effective procedure for distribution of magazines. International Transactions in Operation Research, 6, [2] Bell, P. C. (1978). A new procedure for distribution of periodicals. Journal of the Operational Research Society, 29(5), [3] Bell, P. C. (2000). Forecasting demand variation when there are stockouts. Journal of the Operational Research Society, 51(5), [4] Dekker, M., Donselaar, K. V. & Ouwehand, P. (2004). How to use aggregation and combined forecasting to improve seasonal demand forecasts. International Journal of Production Economics, 90, [5] Gardner, E. S. Jr. (1985). Exponential smoothing: The state of the art. Journal of Forecasting, 4, [6] Haykin, S. (1999). Neural Networks: A Comprehensive Foundation. New York: Prentice Hall. [7] Hyndman, R. J., Koehler, A. B., Snyder, R. D., & Grose, S. (2002). A state space framework for automatic forecasting using exponential smoothing methods. International Journal of Forecasting, 18, *8+ Özgün, O. (2006). Distribution planning of magazines. Master s Thesis, Boğaziçi University. [9] Mitchell, T. (1997). Machine learning. McGraw-Hill [10] Taylor, S. G. (1981). Initialization of exponential smoothing forecasts. Journal of Forecasting, 13,