Exponential smoothing, forecasting

Continuing with this example, if the actual demand in week 5 was 140 the exponential smoothing forecast for week 6 is calculated as ... 

Chen, F., J.K. Ryan, D. Simchi-Levi. 2000. The impact of exponential smoothing forecasts on the bullwhip effect. Naval Research Logistics 47, 269-286. 

Step 3 Select any time series forecasting method. For illustration, we will use the exponential smoothing forecasting method with a = 0.2.For the initial forecast for Quarter 1 of year 2008, we will use 600. 

To illustrate, consider Example 2.2 where we forecasted the demand for month 7 as 316 based on the last 6 months of demand, using Exponential Smoothing. Forecasts beyond month 7 are given by... 

Exponential smoothing is intended for calculation of one step ahead forecasts. All further forecasts x t+2), a(/+3),. .. relate to the recent forecasted value x(t+ ), x t+2),. .. and also, in dependence on the value of the smoothing parameter, to more recent, real values ... 

Because these are forecasted limits, the same exponential smoothing can be applied ... 

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... 

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. 

ES Agent, finally, determines forecasts according to the simple exponential smoothing method, which estimates the demand in any period as the weighted average of the last period demand and the forecast of demand in that period. It can be expressed... 

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. 

Zhu Qingming Hao Zhang. 2012. Study on the application of cubic exponential smoothing method in coal mine accidents forecasting. Joural of Safety Science and Technology (4) 105-107. 

Harrison, R, 1967. Exponential smoothing and short-term sales forecasting. Management Science, 13(11), 821-842. 

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. 

Statistical forecast methods (e.g.. Exponential Smoothing, Box-Jenkins, Holt and Holt-Winters) are used to plan business volume for short term period (1 week to 4 months). Combined forecast methods are also used to improve forecast accuracy. 

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.). 

This simplified version of the exponential smoothing equation is often faster to compute on a calculator and is easier to understand intuitively. This equation states that the forecast for the next period (F +i) is equal to the forecast for this period (F ) plus a weight (a) times the error in this period s forecast (d—F). 

Mean absolute deviation (MAD)—The average of the absolute values of the deviations of observed values from some expected value. MAD can be calculated based on observations and the arithmetic mean of those observations. An alternative is to calculate absolute deviations of actual sales data minus forecast data. These data can be averaged in the usual arithmetic way or with exponential smoothing. 

Lawrence [68] uses a forecasting based approach for estimating flow times. In particular, he focuses on approximating the flow time estimation error distribution (which is assumed to be stationary, and denoted by G) by using the method of moments [111]. He uses six methods for forecasting flow times. NUL sets flow times to zero, such that G becomes an estimator for the flow time. ESF uses exponential smoothing, such that the flow time estimate after the completion of k jobs is fk = otFk + (1 — oc)fk-i- The other four rules... 

Using the sample data given in Table 2.1, determine the forecast for month 7 using the Exponential Smoothing method. 

Step 4 Apply the exponential smoothing method on the deseasonalized demand to get deseasonalized forecast as shown in Table 2.3. For example, deseasonalized forecast for Quarter 1 (2011) is given by... 

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