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 forecast.
| 2001 Demand forecast |
Months | Multiplicative | Additive |
January | 1,603 | 1,761 |
February | 1,621 | 1,801 |
March | 2,014 | 2,081 |
April | 2,144 | 2,161 |
May | 1,954 | 2,021 |
June | 2,139 | 2,201 |
July | 2,405 | 2,421 |
August | 2,981 | 2,841 |
September | 2,918 | 2,781 |
October | 3,609 | 3,321 |
November | 2,868 | 2,721 |
December | 2,407 | 2,441 |
Total | 28,661 | 28,551 |

2. How might Mr. A. M. Khan improve the accuracy of the forecast

In general, it is easier to measure forecast accuracy, if all the customers are same and their requirements are alike; but, like in this case, it gets complex when dealing with different customers with different requirements, lead time etc.

However, some general improvements can be made to whichever forecasting method is used by Mr. A. M. Khan. These are:

* Using alpha values with reduced differences (for example calculating with alpha=0.1, 0.15, 0.2, 0.25 and so on) for the exponential smoothing method. This will allow the forecaster to come up with a more accurate alpha value and hence a more accurate forecast.

* Reduce months in moving average method. For example if we calculate 2 months moving average instead of 3, we will be more accurate. Also this will take into consideration seasonal effects, thus November??™s 2-month moving average (which uses data of September and October) will have two winter month??™s input.

* Go back further into the past and use those older data to obtain a more accurate trend line.

* Use several methods as with changing conditions the best method to use also changes. Also match the method to the situation to ensure changing factors are always incorporated and the method traditionally used not become stagnated. The selection tree for forecasting methods can be used to narrow down choices. (see fig 1 in the appendix)

* Breakdown the problem into pieces, solve the pieces and put them back together. For example, for sales forecasting we can break it down according to level, trend, seasonality etc. the more pieces we break it into, the greater the accuracy we can ensure.

* The power of averaging should not be underestimated. Combine past forecasts by continuously averaging them until no change occurs to the result anymore. Also combine the results from up to five different forecasting methods. This too reduces error as each method takes into consideration a different aspect of forecasting and hence the combined result will have it all.

3. Should Mr. Khan??™s experience with the market be factored into the forecast If so, how
Yes. Mr. Khan has been working in this industry for more than 20 years and has undoubtedly picked up on fads and trends of the industry. As most forecasts just allow one to narrow down the possible future demand being forecasted, an element of judgment is often an improvement upon the quantitative method of forecasting used.
What Mr. Khan can do is use the quantitative method of forecasting and use the results obtained as a range, rather than a point.
For example, the 28661 boxes for 2001 suggested by the Multiplicative method and the 28551 boxes for 2001 suggested by the Additive method can be combined by him to provide a range between 27,462 ??“ 27,556 boxes to be produced for 2001.
Mr. Khan can then use his own expert judgment and decide on a number within this range based on qualitative factors such as market and industry change, style change etc.
Mr. Khan can alternatively assign weights to his experience to include it in the forecasting, and the rest of the weight would be assigned to the forecasting technique used.
Weight can be determined by examining his previous records on what Mr. Khan predicted for past forecasts, and then we can compare them with the actual results to calculate how much error there was in his forecasts. The less his percentage error, the more he will be weighted on his experience, and vice versa. Once the percentage weight has been determined, forecast can be done by the following formula:
Net Forecast value = (% weight of Mr. Khan??™s Experience X Mr. Khan??™s Forecast value) + (% weight of forecast technique X Technique Forecast Value)