4-2 Exponential Smoothing with Trend Adjustment (Holt) Forecast including trend (FIT t ) = exponentially smoothed forecast (F t ) + exponentially smoothed trend (T t )
4-3 F t = Forecast with Trend last period + (Last periods actual – last periods Forecast with Trend F t = FIT t-1 + (A t-1 – FIT t-1 ) or T t = Trend estimate last period + (Forecast this period - Forecast with Trend last period) T t = T t-1 + (F t - FIT t-1 ) or Exponential Smoothing with Trend Adjustment (Holt)
4-4 F t = exponentially smoothed forecast of the data series in period t T t = exponentially smoothed trend in period t A t = actual demand in period t = smoothing constant for the average = smoothing constant for the trend Exponential Smoothing with Trend Adjustment (Holt)
4-5 Comparing Actual and Forecasts
4-6 Exponential Smoothing with Trend - Example With the following data, calculate the Holt forecast for each period. Assume that the initial forecast for month 1 was 11 units and the trend for that period was 2 units.
4-7 Seasonality Repeating up and down movements in data Related to recurring events Christmas sales of toys Lawnmower sales When seasonality exists in data must incorporate into forecasting model
4-8 Model with Seasonality 1.Find average historical demand for each season by summing the demand for that season in each year, and dividing by the number of years for which you have data. 2.Compute the average demand over all seasons by dividing the total average annual demand by the number of seasons. 3.Compute a seasonal index by dividing that seasons historical demand (from step 1) by the average demand over all seasons. 4.Estimate next years total demand 5.Divide this estimate of total demand by the number of seasons, then multiply it by the seasonal index for that season. This provides the seasonal forecast.
4-9 Sales DemandAverage Demand Month MonthlySeasonal Index Jan Feb7085 Mar Apr May Jun Jul Aug Sept Oct Nov Dec Monthly Sales of Laptop Computers
4-10 Monthly Sales of Laptop Computers Sales DemandAverage Demand Month MonthlySeasonal Index Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec
4-11 Over the past year Meredith and Smunt Manufacturing had annual sales of 10,000 portable water pumps. The average quarterly sales for the past 5 years have averaged: spring 4,000, summer 3,000, fall 2,000 and winter 1,000. Compute the quarterly index. If annual sales for next year are 11,000, forecast quarterly sales. Example 2 - Seasonality
4-12 Mean Absolute Deviation (MAD) Mean Absolute Percent Error (MAPE) Forecast Error Equations