# Forecast

1. Develop a forecasting method for Brother’s and forecast total demand for 2001
In order to develop a forecasting model, forecast demand was found for every month of the given 5 years under forecasting methods such as, simple average, moving average, weighted average, exponential smoothing, trend analysis, multiplicative and additive forecasting. MAD and BIAS was calculated to find the level of forecasting error in each method and the one with the lowest error was the selected model.
| Naive | SimpleAverage | 2-months moving average | 3- months moving average | 4-months moving average | Weighted average | 3- months weighted average | 4-months weighted average |
MAD   | 4.58 | 4.66 | 4.24 | 4.69 | 4.80 | 4.41 | 4.32 | 4.45 |
BIAS | - 0.27 | - 2.51 | - 0.43 | - 0.58 | - 0.57 | - 1.58 | - 0.49 | - 0.44 |

| Exponential SmoothingAlpha= 0.2 | Exponential SmoothingAlpha= 0.5 | Exponential SmoothingAlpha= 0.8 | Trend analysis | Multiplicative forecast | Additive forecast |
MAD   | 4.43 | 4.26 | 4.31 | 4.18 | 2.65 | 2.56 |
BIAS | -1.75 | - 0.48 | - 0.32 | - 0.001 | 0.09 | 0.00 |
Forecasting error is the smallest for additive method of forecasting, and this justifies that there is a seasonal pattern evident in the given data set. Also, if we see the sales distribution graph below for the first 12 months, sales have a sudden rise from August (month 8) to December (month 12). In month-13(January’97) the sales dropped from 1800 to 800. This cycle is seen to repeat every year where sales seem to peak in the winter seasons and then drop during the summer. Thus there is a seasonal pattern present in the sales behavior.

Therefore, the most correct method of forecasting would be the additive method; however the multiplicative method also captures the nature of seasonality with an acceptable level of forecasting error. Forecasted sales for the year 2001 are thus found by using both methods, although Mr. A.M.Khan is advised to follow the additive...