Exponential smoothing models

The starting point for the computation of the exponential smoothing model with trend and seasonal effects is the additive component model ... 

We now illustrate the role of another classic demand-forecasting model—the exponential smoothing model. The exponential smoothing model works as follows Given a demand forecast from previous periods and an observation this period, and a parameter a, the exponential smoothing model is that... 

We now illustrate the role of the exponential smoothing model in a supply chain. The model will... 

Z Retailer updates demand forecast based on observed demand. This forecast follows an exponential smoothing model with parameter a. 

In this chapter we have provided a quick review of four possible approaches to forecast demand and its use in planning. The constant demand model allows for a quick analysis of the effect of ordering costs in a system. The models of demand as a distribution permit details of lead time and demand uncertainty to be included. The modeling of demands as a mixture of distributions enables us to consider the role of information acquired over time. Finally, the exponential smoothing model shows how demand forecast updating can create large swings upstream in a supply chain. 

Winter s three-parameter linear and seasonal exponential smoothing model is an extension of Holt s method to cover seasonal variation. This method uses a seasonal index to estimate seasonality. 

Regular exponential smoothing model estimates the constant level (L) to forecast future demands. Holt s model improves it by estimating both the level (L) and trend factor (T). It adjusts both the level and trend factor using exponential smoothing. Holt s method is also known as double exponential smoothing or trend adjusted exponential smoothing method. 

The technique of seasonal decomposition uses the same additive and multiplicative models as in exponential smoothing, but without the smoothing procedure. 

The moving average is a process similar to exponential smoothing. The exponential smoothing method (see also Section 6.4.2) has exponentially decreasing coefficients of the recent values. In a MA model the single coefficients b1 b2,. .., b were calculated by minimization of the sum of squared errors. 

So, with such a degree of randomness, the approximation of the demand in a certain period according to the demand in the previous period is a bad alternative. In fact, the model tends to select moving averages of a large number of periods. In the same vein, the model determines that the best solutions with exponential smoothing are offered by very low parameters, in order to minimize the effect of the latest demands in the forecast. 

To develop the tool, we have considered only simple forecasting methods, such as moving averages and exponential smoothing, so that each level of the chain uses the best one that suits the demand it should deal with. With them, it is possible to achieve great results in reducing Bullwhip Effect. Even so, we have also shown that the inclusion of more advanced forecasting methods (ARIMA models) allows an even better system performance. 

Yu Zhifeng Xie Zhengwen. 2007. Improved grey model by exponential smoothing for settlement predication and its application. Central South Highway Engineering (T) 12Q-122. 

No other analytic solution to the master equation for a weak collision system over the whole range of pressures has yet been found. A solution is known, at the low pressure limit only for a rather limited exponential probability model of a unimolecular reaction [77.T2 80.F1], and Troe has developed empirical schemes for determining the pressure range over which the fall-off exhibits curvature and for joining smoothly the high and low pressure limiting solutions [77.Q 79.T2]. 

The decision-making model uses a trend-adjusted exponential smoothing algorithm [11]. It uses two smoothing parameters, 0 < a < 1 and 0 < < 1, as... 

Univariate Forecasts of a given variable demand are based on a model fitted only to present and past observations of a given time series. There are several different univariate models, like Extrapolation of Trend Curves, Simple Exponential Smoothing, Holt Method, Holt-Winters Method, Box-Jenkins Procedure, and Stepwise Auto-regression, which can be regarded as a subset of the Box-Jenkins Procedure. 

Forecast is generated consider either quantitative models (e.g.. Trend analysis. Exponential Smooth technique and Looks Like artalysis, etc.) or qualitative models (e.g., Sales Force Composite, Assumptirm Based Model, etc.). 

Interested readers can refer to the original paper by Croston (1972). Willemain et al. (1994) did a comparative evaluation of Croston s method in forecasting intermittent demand in manufacturing using industrial data. They concluded that Croston s method was superior to the exponential smoothing method and was robust even under situations when Croston s model assumptions were violated. 

Fig. 5.13. Temporal evolution of the NeNePo signal of silver clusters Agn taken with A = 400 nm. (a) n = 9, (b) n = 5, (c) n = 3. The solid lines were given by a simple exponential decay model which was convoluted with the system response time in (a) and (b), and a smooth interpolation in (c). The fine structure around At = 0 arises from the interference between the pump and the probe pulse (taken from [424])...

Exponential smoothing is similar to the moving average methods but it eliminates some of the calculations. The model uses a smoothing factor (less than 1) for forecasting the next period activity. The mathematical formula is... 

Forecast models can be used to prepare a statistical demand forecast. It is based on previous consumption or future demand trends of an reference number. A simple, powerful, forecast model is the "first-order exponential smoothing". 

The probability of occurrence of an accident P E has to be estimated during the setting of the model, and kept constant in further observation. The historical value of / ( ) during the year t, called P(E can be estimated as ratio between the number of accidents happened during one year and the number of total worked hours. The actual value of P E can be estimated by applying exponential smoothing to the historical values. In the analysed case, the historical values of the last three years have been used these values are reported in Table 2. Exponential smoothing (Equation 8) has been applied to the historical values P E) reported in Table 2. 

TREND-CORRECTED EXPONENTIAL SMOOTHING (HOLT S MODEL) The trend-corrected exponential smoothing (Holt s model) method is appropriate when demand is assumed to have a level and a trend in the systematic component, but no seasonality. In this case, we have... 

TREND-AND SEASONALITY-CORRECTED EXPONENTIAL SMOOTHING (WINTER S MODEL) This method is appropriate when the systematic component of d and has a level, a trend, and a seasonal factor. In this case we have... 

Trend-Corrected Exponential Smoothing (Holt s Model)... 

Forecast quarterly demand for year 5 using simple exponential smoothing with a = 0.1 as well as Holt s model with a = 0.1 and / = 0.1. Which of the two methods do you prefer Why ... 

Consider monthly demand for the ABC Coiporation as shown in Table 7-3. Forecast the monthly demand for Year 6 using moving average, simple exponential smoothing, Holt s model, and Winter s model. In each case, evaluate the bias, TS, MAD, MAPE, and MSE. Which forecasting method do you prefer Why ... 

Estimate demand for the next two weeks using simple exponential smoothing with a = 0.3 and Holt s model with... 

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