APPLICATION OF TIME-SERIES DEMAND FORECASTING MODELS WITH SEASONALITY AND TREND COMPONENTS FOR INDUSTRIAL PRODUCTS

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1 International Journal of Mechanical Engineering and Technology (IJMET) Volume 8, Issue 7, July 2017, pp , Article ID: IJMET_08_07_176 Available online at ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed APPLICATION OF TIME-SERIES DEMAND FORECASTING MODELS WITH SEASONALITY AND TREND COMPONENTS FOR INDUSTRIAL PRODUCTS Harpreet Singh Assistant Professor, Department of Mechanical and Industrial Engineering, Lovely Professional University, Phagwara, PB, India. Ankur Bahl Assistant Professor, Department of Mechanical and Industrial Engineering, Lovely Professional University, Phagwara, PB, India. Anil Kumar Assistant Professor, Department of Mechanical and Industrial Engineering, Lovely Professional University, Phagwara, PB, India. ABSTRACT The demand forecasting is used when there is a need to predict a numerical parameter for which past results are good indicators of future behavior. Three forecasting techniques were evaluated using the provided data (past time periods data) of nine products of the industry. The three forecasting techniques evaluated are: the Exponential Smoothing Forecasting Model; the Exponential Smoothing with a linear trend Forecasting Model (Holt s- Double) and Winters - Triple Seasonality forecasting model. The Visual Basic for Applications (VBA) 6.0 version language was used to implement the functionality of these three above mentioned models for the creation of GUI and into Microsoft Excel for this study. Additionally, VBA was used to compute the Mean Absolute Error, which was used to compare each of the models. Overall, the exponential smoothing with a linear trend (Holt s- Double) forecasting model is the best forecasting model for the examined business units. The exponential smoothing with a linear trend model (Holt s- Double) should be used in the most cases where the coefficient of variance of the demand data is small. Winters - Triple Seasonality model should be used in most cases where the coefficient of variance is of the demand data is large. The exponential smoothing with a linear trend forecasting model was the best forecasting model which resulted in the least absolute forecasting error of 0.29.Winters model was the better model after Holt s- Double and resulted in the least forecasting error of editor@iaeme.com

2 Application of Time-Series Demand Forecasting Models with Seasonality and Trend Components for Industrial Products Key words: Demand forecasting; Time-series; Error calculation; Smoothing constants; Visual basic for applications; Graphical User Interface (GUI) Cite this Article: Harpreet Singh, Ankur Bahl and Anil Kumar Application of Time- Series Demand Forecasting Models with Seasonality and Trend Components for Industrial Products. International Journal of Mechanical Engineering and Technology, 8(7), 2017, pp INTRODUCTION The purpose of present study of time series of demand forecasting within this application is to predict the future product sales for each of nine products for different two industrial plants of futuristic financial year that were provided by Starlit-Shiva group in order to evaluate each of the forecasting methods based upon their accuracy in predicting the product sales. The Visual Basic for Applications (VBA) is a computer programming language which is used to control Microsoft Excel functionality by means of macros. Taylor (2010) also recommended for the framing of GUI for predicting of electricity demands. For this purpose, an optimization process plan has been developed to calculate Running Sum Forecasting Error (RSFE); Mean Squared Error (MSE); Mean Absolute Deviation (MAD); Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE). An assumption of τ with the periods away from the time period has been taken, i.e., [τ =1, for the period of availability of actual demand At and τ = 1,2,3,..12, for the period of unavailability of actual demand At]. Furthermore, it is required to identify the areas of interest such as calculation of smaller forecast error for large groups of products with large total volume (Rahimzadeh et al., 2012) and concoction of the products into BUs and de-seasoning from coefficient of variance. 2. LITERATURE REVIEW Marao and Bargelis (2006) adopted and considered the Rule-Based Forecasting (RBF) approach for the demand forecast in a mechanical products industry. A methodology used to evaluate the weight between the Linear Trend and Exponential Smoothing in order to achieve the final forecasted value of the product. It is together to the RBF were analyzed another two possibilities to evaluate the weight between the forecasting methods in order to achieve the final value of forecast. A value of α allow determine the amount of data of the forecast will be new. On the other hand, the value of β chosen allows the trend estimate to react to changes in the rate of growth of the series. Therefore, the methods analyzed are four used at the Rule- Based Forecasting (RBF). The techniques used are Random Walk, Linear Regression, Exponential Smoothing (Holt s) and Linear Exponential Smoothing (Brown s). It refers to its trend estimate as the basic trend; Holt s linear exponential smoothing captures information about short-range trends and we call this the recent trend and Brown's linear exponential smoothing with trend also measures the short-range trend. Gato et al. (2007) proposed a methodology that frames the model depends on the postulate that total water use is made up of base use and seasonal use evaluated by Winters seasonal equations. The issue addresses is the forecasting residential water demand with respect to water- supply distribution zone level. The total water use is made up of base use Wb and seasonal use Ws, where base use is characterized by the water use during winter months and seasonal use on seasonal, climatic, and persistence components. Using the daily data collected by Yarra Valley Water for East Doncaster water supply distribution zone and the corresponding rainfall and temperature data from the Bureau of Meteorology from 1990 to The variation in seasonal use is expected to be influenced by prevailing weather editor@iaeme.com

3 Harpreet Singh, Ankur Bahl and Anil Kumar conditions such as air temperature, evaporation, and rainfall. The results and discussions drawn a resemblance of the evaluation begins with an estimation of base use. Model performances are evaluated according to two criteria: Standard Error (SE) and the coefficient of determination, R². A favorable model is the one with high R², but low residual standard error. Gamberini et al. (2010) analyzed the forecasting of sporadic demand patterns with seasonality and trend patterns. The demand time series with seasonality and trend components is the aim of the present paper in order to establish some useful guidelines for practitioners. The methodology applied consists of testing several (S) ARIMA models and then choosing the best model only in terms of forecasting performances, which is subsequently compared with the Holt s-winters method. In particular, in the case of seasonality without a consistent trend component, the best (S) ARIMA model found and the Holt s-winters exponential smoothing model give similar results in terms of MAD/A. These results are enforced by the evaluation of MSE/A. Hence, when the sporadic demand data series structure becomes more complex because of the relevant presence of both seasonal and consistent trend components, the (S) ARIMA model, which is more adaptive than the Holt s-winters method, is also more effective. Rahimzadeh et al. (2012) adopted bullwhip effect and is measured in a simple three-stage supply chain consisting of a retailer, a manufacturer, and a supplier. It has been identified five main causes of bullwhip effect, including demand forecasting, lead time, batch ordering, shortages and price fluctuations. In the first place, manufacturer observes more variations in exponential smoothing method when using alpha more than 0.6. This point depends on L and T. In the second place, supplier observes more demand variation in comparison to moving average, unless the smoothing parameter is low. The exponential smoothing method results better, when smoothing parameter is low and less than The useful amount of for selecting exponential method, depends on L+T and L'+T'. The purpose of the current study is the determination of forecasting parameters and related factors affecting bullwhip effect in a supply chain where it is developed to the third stage. 3. RESEARCH METHODOLOGY In this paper, it is first proposed a general framework for computation of present and future state forecasts and errors in relation to their comparisons that are considering smoothing variables. Section 3.1 addresses empirical relations for calculation of trend of period, length of seasonality, multiplicative seasonality factor based on past time periods data and smoothing variables. Section 3.2 gives the estimation part of the trend and seasonal smoothing aspects for application of Winters method to control γ value. Furthermore, Section 3.3 refers to the methodology for implementation of prediction intervals with depiction of algorithm of dynamic structure of optimization modeling. 3.1 Time-Series Models The approach of time series analysis here is to identify and measure the influences of time related factors on time-series values: actual demand At, ft and F(t+τ). Makridakis (2012) and Bedi (2012) recommended the calculations of forecasting parameters f(t), FIT and Ft+τ of adopted three techniques are exponential smoothing, Holt s-double linear trend and Winters - seasonality models and of first two are given below: Forecast of period t, f t = α A t + (f t-1 + T t-1) (1) Trend of period t, T t = β (f t f t-1) + (1-β) T (t-1) (2) editor@iaeme.com

4 Application of Time-Series Demand Forecasting Models with Seasonality and Trend Components for Industrial Products Makridakis et al. (2012) used the calculations of the smoothed estimate; smoothed trend; multiplicative seasonality factor and the forecast for Winters method for seasonality are given below: T = (3) ct = ;ct = ; ct = ; ct = and ct = (4) F = f + T τc (5) where, N = Length of Seasonality (e.g., No. of months and quarters in a year), ct = Seasonality component or multiplicative-seasonality factor and α, β and γ are smoothing constants for exponential smoothing (neither trend nor seasonality), trend only and trend and seasonality both respectively. Figure 1 System Architecture Algorithm Depicting MAPE Computation Process Flow Diagram 3.2 Smoothing Parameters or Weights Trend-adjusted exponential smoothing requires two parameters: α value used by exponential smoothing, β and γ values used to control how the trend and seasonality components enter the model respectively. Table 1 is depicting the trend and seasonal smoothing aspects for application of Winters method to inventory demand for product TC/15 with seasonal coefficient of γ = Procedure for Implementation of Time-Series Forecasting Model Figure 1 is showing the flow process parameters of α, β and γ for MAPE error estimations with respect to MS access database and dynamic modeling of GUI for forecast in terms of F(t+τ).Bermudez et al., 2007 suggested optimization based approach to estimate the initial and smoothing values. The strategy for evaluating the forecasting methodology is as follows: editor@iaeme.com

5 Harpreet Singh, Ankur Bahl and Anil Kumar Step 1: Estimating the optimal smoothing parameters. Step 2: Estimating the initial values for trend. Step 3: Estimating and normalizing the initial values for seasonality. Step 4: Optimization modeling and dynamic modeling. Step 5: Data error (s) computations and MAPE estimations. Step 6: Parametric considerations of system modules for GUI creation Table 1 Application of Winters method for seasonality technique to inventory demand for product TC/15 with seasonal coefficient of γ = 0.3 Year Mont h (t) Month Name Actual Demand A t Smoothing Estimate f t Trend Multiplicative Tt Seasonality Factor c t 1 April May June July Winters' Forecast F t+τ 5 Aug Sep Oct Nov Dec Jan Feb March RESULTS Using the methodology described in Section 3, this section summarizes with respect to analysis of proposed system takes required information such as actual demand, product code, smoothing constants values. Thereafter, system processes the determination of forecasting indices of actual demand. System also uses various databases such as actual demand, MS database of eighteen products, MAPE database and mathematical relations for the determination of forecasting indices. 4.1 Optimization of Smoothing Parameter (s) and Forecasting Errors Bermudez et al. (2006) recommended optimization based approach to estimate the initial smoothing, trend and seasonality values. The application of absolute percent error and its optimization process is that the curve of forecasted demand ft tracing the actual demand curve At closely by the gap of the lowest absolute percent error value of 5.04 at smoothing constant α equal to 0.9 among of different nine value of optimized variables as shown in Figure Measurement of Forecasting Error and Analysis of Forecasting Based upon Modern Prospective of GUI Figure 3addresses the graph depicting the result by means of the curve for Holt s- Double linear trend model of forecasted demand ft tracing the actual demand curve At by the gap of the lowest of absolute percent error value of around Also, Figure 4 is sharing a part of seasonal and trend database in MS Access for Product TC/ editor@iaeme.com

6 Application of Time-Series Demand Forecasting Models with Seasonality and Trend Components for Industrial Products Forecasted Demand APRIL MAY JUNE JULY AUG. SEP. OCT. NOV. DEC. JAN. FEB. MARCH Months ACTUAL DEMAND (D) ESF (α=0.1) ESF (α=0.2) ESF (α=0.3) ESF (α=0.4) ESF (α=0.5) ESF (α=0.6) ESF (α=0.7) ESF (α=0.8) ESF (α=0.9) Figure 2 Forecasts f t with α = 0.1 to 0.9 ( ) Forecasted Demand APRIL MAY JUNE JULY AUG. SEP. OCT. NOV. DEC. JAN. FEB. MARCH ACTUAL DEMAND (UNITS)=D EXPONENTIAL SMOOTHING MODEL HOLT'S- DOUBLE LINEAR TREND MODEL WINTERS'- TRIPLE SEASONALITY MODEL Months Figure 3 Comparison of Forecasted Values f t of Time- Series Models with respect to Actual Demand A t Figure 4 Winters - Seasonal Model Database in MS Access for Product TC/015 with Seasonal Value editor@iaeme.com

7 Harpreet Singh, Ankur Bahl and Anil Kumar 5. DISCUSSION-VALIDATION OF DYNAMIC MODEL Holt s- Double linear trend, exponential trend and Winters models have the error variability of maximum of 0.82, 8.81 and 17.4 respectively and the mean absolute percent error variability have 0.29, 5.04 and 9.31 respectively as shown in Figure 5. Also, Figure 5 is showing an input dialog window of GUI of Winters - Seasonal Model for a Product RB-66. Absolute Percent Errors APRIL MAY JUNE JULY AUG. SEP. OCT. NOV. DEC. JAN. FEB. MARCH Months Figure 5 Analysis of Various Values of APE with Input Dialog Window of GUI of Winters - Seasonal Model for a Product RB CONCLUSIONS A computer aided system created for the determination of forecasting, measurement and optimization of forecasting errors has been presented in this work. The forecasting indices used in this work are past data; product name and code; smoothing parameters; multiplicative seasonality factor and sustainability indicators of dynamic model. The sustainability indices determined by the system are close to that calculated on the basis of actual measurements of process parameters. This shows that the proposed system is valid and could be used for determination of forecasting indices from process plan of the system. For the future work, the cross- sectioning of the methods and pairing of products from same model can be proposed with respect to four sets of factors influence time- series as trend, seasonal variations, cyclical fluctuations and irregular or random movements. REFERENCES [1] Bedi, K., (2012), Production and Operations Management, 2 nd Edition, Oxford University Press, New Delhi, India. [2] Bermudez, J. D. (2006). Improving Demand Forecasting Accuracy Using Nonlinear Programming Software. Journal of the Operational Research Society, 57(1), [3] Gamberini, R. (2010). Forecasting of Sporadic Demand Patterns with Seasonality and Trend Components: An Empirical Comparison between Holt s-winters and (S) ARIMA Methods. Hindawi Publishing Corporation, 23(3),1-14. [4] Gato, S. (2007). Forecasting Residential Water Demand: Case Study. Journal of Water Resources Planning and Management, 133(4), [5] Kahn, K. B. (2003). How to Measure the Impact of a Forecast Error on an Enterprise? Journal of Business Forecasting Methods and Systems, 22(1), [6] Makridakis, S. (2012), Forecasting: Methods and Applications, 3 rd Edition, Wiley India (P.) Ltd., New Delhi, India editor@iaeme.com

8 Application of Time-Series Demand Forecasting Models with Seasonality and Trend Components for Industrial Products [7] Marao, J. L. (2006). Demand Forecasting of Mechanical Products in Batch and Mass Production. Proceedings of 11 th International Conference, Mechanika, [8] Rahimzadeh, A. (2012). Stabilizing a Three- Stage Supply Chain with Exponential Smoothing Forecasting Method. African Journal of Business Management, 26(29), [9] Taylor, J. W. (2010). Triple Seasonal Methods for Short-Term Electricity Demand Forecasting. European Journal of Operational Research, 204(2), [10] Denny Nugroho Sugianto, Muhammad Zainuri, Alfin Darari, Suripin, Suseno Darsono and Nur Yuwono Wave Height Forecasting Using, Measurement Wind Speed Distribution Equation In Java Sea, Indonesia. International Journal of Civil Engineering and Technology, 8(5), 2017, pp [11] Dr. E. Priyadarshini, Analysis Of The Performance Of Artificial Neural Network Technique For Forecasting Mutual Fund Net Asset Values, International Journal of Management (IJM), 4(6), 2013, pp editor@iaeme.com