develop hybrid forecasting models in order to obtain the most accurate model for predicting the uncertain demand

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4. Methodology

ARIMA model is composed of moving average (MA) and Autoregressive (AR) as equation (1)

1 ( ) 1 1 1 1 t q i i t i d p i i ϕ i L L X θ L ε ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − ∑ ∑ = = (1)

Where

iL is Lag operator

ϕi is a parameter of autoregressive part

θ i is a parameter of moving average part

ARIMA model used in this paper that is appropriately selected by AIC (Akaike’s Information Criteria), which gives the lowest value. When updated data are realized, the data will be used to forecast for the following information and this procedure will be repeated.

Holt–Winters model or triple exponential smoothing is a mathematical formula that is the combination of the smoothed values of the constant part for time, the sequence of best estimates of the linear trend and the sequence of seasonal correction factor as equation (2). The additive Holt-Winters model is

0 0 s = x ( ) ( )( ) t = t − t−L + 1− t−1 + bt−1 s α x c α s ( ) ( ) t = t − t−1 + 1− bt−1 b β s s β ( ) ( ) t t t t L c x s c = − + − − γ 1 γ ( ) t m t t t L ( ) ( )( ) m L F s mb c + = + − + −1 mod (2)

Where 0 x is beginning value at time t = 0 t

s is the smoothed value of the constant part for time

bt is the sequence of best estimates of the linear trend

t c is the sequence of seasonal correction factor

Ft+m is the forecasting value of m ahead

Holt-Winters method used in this study, the fitted model is decided using Sum Squared Error (SSE). In the model, we use the present data to predict the future data. The updated data will also be used for forecasting the next data repeatedly.

SVM model is machine learning as supervised learning model to find fitted coefficient to set up a line to classify dataset in training process. Not only SVM model can formulate linear model but also SVM model can formulate nonlinear model to classify the nonlinear dataset. In this research, we slot 10

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