Question

You are not sure that the forecasting technique that your company is using is correct for two items that you manage. At this time you want to consider several new options and pick the one that reduces the amount of forecast error. To accomplish this task you will use the data listed below. Month 1 Month 2 Month 3 Month 4 Month 5 Month 6 Month 7 Month 8 Month 9 Month 10 Month 11 Month 12 stereo system 22 29 32 33 25 20 30 32 32 37 35 26 cameras 55 64 69 71 68 71 69 76 71 83 80 77 Step 1. Use the first 8 months of data (Month 1-8) to develop a forecast for Month 9 using 1 month moving average, 3 month moving average, Exponential Smoothing (alpha=.2), Exponential Smoothing (alpha=.4), and linear regression. For Exponential Smoothing you can use the forecasted value of 70 for month 8 for backup cameras and 30 for speakers. Please note that in this step you are pretending like you do not have the information for months 9-12 because you are holding this information aside to test what would have happened using your forecasting techniques. 2. Make forecasts for months 9-12 and calculate MSE, MAD, and MAPE for each of the forecasting techniques. 3. Based on your analysis, make a recommendation to the Operations Manager for which forecasting technique you should use for each of the two items and state why. You should include graphics to support your recommendation.

Answer 1

In the moving average method we average the n periods and forecast for n+1 period.

In case of exponential smoothing we use the formula F2 = alpha*A1 + (1 – alpha)*F1

In case of linear regression we consider the period as the x variable and the data to be y variable.

1 month moving average

3 month moving average

ES 0.2

ES 0.4

Linear regression

The table below summarizes the MAD, MSE, and MAPE for each of the products and the product line.

		1MA	3MA	ES 0.2	ES 0.4	LR
MAD	stereo system	4.00	5.08	4.37	4.12	4.73
	cameras	5.75	4.08	5.17	4.26	4.46
MSE	stereo system	27.50	32.69	23.61	25.62	25.08
	cameras	46.75	33.53	46.71	35.19	24.19
MAPE	stereo system	13.46	16.76	13.98	13.65	14.56
	cameras	7.29	5.03	6.37	5.26	5.86

The graph below shows the comparison. Looking at the graph we can see that for Stereo systems, 1 month moving average seems to be the best option as it has lowest value when MAD, MSE, MAPE are considered. Similarly for cameras, 3 months moving average yields the best result.