Question

1. Evaluate the forecasting model using 3 month moving average, and 3 month moving weighted average, and exponential. The weights are .5 for the most recent demand, .25 for the other months. Alpha = .3. Use the weighted moving average for January Forecast.

	Actual Demand
Oct	300
Nov	360
Dec	425
Jan	405
Feb	430
March	505
April	550
May	490

2. Calculate MAD and MAPE for each and compare. Which method is a better forecast and why?

Answer 1

Formulae to be used:

Absolute deviation= |Forecast - Actual|

Percent error= (absolute deviation/actual sales) * 100

MAD= mean absolute deviation= sum of absolute deviation/no. of periods

MAPE = mean absolute percent error = sum of percent error / no. of periods

· the formula to be used in Simple Exponential smoothing is

Ft+1= alpha*At + (1-alpha) Ft

At means Actual demand of t'th period, if you want to find out the Forecast through exponential smoothing= forecast of 3rd period = alpha*actual demand of 2nd period +(1-alpha) *forecast demand of 2nd period

· remember forecast of 1st period is 300, alpha= 0.3

• Forecast of a period with n period moving average = average of last n periods demand
• Weighted Forecast of july period = (0.5*sales of most recent period + 0.25*sales of next most recent period+ 0.25*sales of third recent period)

Period, t	Actual , At	3 period moving average forecast,	Absolute deviation= |Forecast - Actual|	Percent error= (absolute deviation/actual sales) * 100	Forecast weighted moving average(wts 0.5, 0.25, 0.25)	Absolute deviation= |Forecast - Actual|	Percent error= (absolute deviation/actual sales) * 100
Oct	300
Nov	360
Dec	425
Jan	405	361.67	43.33	10.70%	377.50	27.50	6.79%
Feb	430	396.67	33.33	7.75%	398.75	31.25	7.27%
Mar	505	420.00	85.00	16.83%	422.50	82.50	16.34%
Apr	550	446.67	103.33	18.79%	461.25	88.75	16.14%
May	490	495.00	5.00	1.02%	508.75	18.75	3.83%
			54.00	11.02%		49.75	10.1%
			MAD	MAPE		MAD	MAPE

Period, t	Actual , At	Ft, Exponential Forecast	Absolute deviation= |Forecast - Actual|	Percent error= (absolute deviation/actual sales) * 100
Oct	300	300.0
Nov	360	300.0
Dec	425	318.0
Jan	405	350.1	54.90	13.6%
Feb	430	366.6	63.43	14.8%
Mar	505	385.6	119.40	23.6%
Apr	550	421.4	128.58	23.4%
May	490	460.0	30.01	6.1%
			79.26	16.29%
			MAD	MAPE

Forecast weighted moving average(wts 0.5, 0.25, 0.25) is best because it has lower MAD and MAPE values.