Question

The income for Saxbys Cafe at Temple University income for the period January - June, 2020 is as follows:

Month	Income (In thousands $)
January	70.0
February	68.5
March	64.8
April	71.7
May	71.3
June	72.8

(a) Use exponential smoothing with α =0.1 and α =0.3 to forecast July income. Assume that the initial forecast for February 2020 is $65,000.

Show Work please

(b) Based on MAD, which smoothing constant provide a better forecast? Justify your answer.

Answer 1

a.Exponential smoothing forecast

Alpha = 0.1

Month	Income (In thousands $)	Exponential smoothing Forecast alpha = 0.1 (In thousands)	Forecast in thousands
January	70
February	68.5	65	65
March	64.8	(68.5*0.1)+(65*0.9)	65.350
April	71.7	(64.8*0.1)+(65.35*0.9)	65.295
May	71.3	(71.7*0.1)+(65.295*0.9)	65.936
June	72.8	(71.3*0.1)+(65.936*0.9)	66.472
July		(72.8*0.1)+(66.472*0.9)	67.105

Alpha = 0.3

Month	Income (In thousands $)	Exponential smoothing Forecast alpha = 0.3 (In thousands)	Forecast (In thousands)
January	70
February	68.5	65	65
March	64.8	(68.5*0.3)+(65*0.7)	66.050
April	71.7	(64.8*0.3)+(65.050*0.7)	65.675
May	71.3	(71.7*0.3)+(65.675*0.7)	67.483
June	72.8	(71.3*0.3)+(67.483*0.7)	68.628
July		(72.8*0.3)+(68.628*0.7)	69.879

b. MAD

Month	Income (In thousands $)	Exponential smoothing Forecast alpha = 0.1 (In thousands)	Forecast in thousands	Error	Absolute deviation
January	70
February	68.5	65	65	3.5	3.5
March	64.8	(68.5*0.1)+(65*0.9)	65.350	-0.55	0.55
April	71.7	(64.8*0.1)+(65.35*0.9)	65.295	6.405	6.405
May	71.3	(71.7*0.1)+(65.295*0.9)	65.936	5.3645	5.3645
June	72.8	(71.3*0.1)+(65.936*0.9)	66.472	6.32805	6.32805
July		(72.8*0.1)+(66.472*0.9)	67.105	Sum	22.14755
				MAD	4.42951

Month	Income (In thousands $)	Exponential smoothing Forecast alpha = 0.3 (In thousands)	Forecast (In thousands)	Error	Absolute deviation
January	70
February	68.5	65	65	3.5	3.5
March	64.8	(68.5*0.3)+(65*0.7)	66.050	-1.25	1.25
April	71.7	(64.8*0.3)+(65.050*0.7)	65.675	6.025	6.025
May	71.3	(71.7*0.3)+(65.675*0.7)	67.483	3.8175	3.8175
June	72.8	(71.3*0.3)+(67.483*0.7)	68.628	4.17225	4.17225
July		(72.8*0.3)+(68.628*0.7)	69.879	Sum	18.76475
				MAD	3.75295

The better forecast is exponential smoothing with alpha = 0.3 because the Mean Absolute deviation value is lesser.