Question

Consider the following demand for a certain product:

Period	Demand
1	25
2	120
3	40
4	60
5	30
6	140
7	60
8	80
9	35
10	150
11	55
12	90

1. Develop a forecast for these data, using an exponential smoothing model? What is the resulting MSD?
2. Develop a forecast for these data, using an exponential smoothing with a linear trend model? What is the resulting MSD?
3. Develop a forecast for these data, using Winters method? What is the resulting MSD?
4. Which method from the methods mentioned above is “better”? How do you know that?

Answer 1

1. exponential smoothing model

Period	D=Demand	F=Forecast	Deviation	Square of Devaiation
1	25
2	120	25.00	95.00	9025.00
3	40	44.00	-4.00	16.00
4	60	43.20	16.80	282.24
5	30	46.56	-16.56	274.23
6	140	43.25	96.75	9360.95
7	60	62.60	-2.60	6.75
8	80	62.08	17.92	321.17
9	35	65.66	-30.66	940.22
10	150	59.53	90.47	8184.75
11	55	77.62	-22.62	511.86
12	90	73.10	16.90	285.63
			MSD	2655.35
F+1 = (Dxα)+((1-α)F)
α =	0.2
1-α=	0.8

2. exponential smoothing with a linear trend

Period	D=Demand	L=Level	T=Trend	F=Forecast	Deviation	Square of Devaiation
0		54.55	2.95
1	25	51.00	1.00	57.50	32.50	1056.25
2	120	65.60	5.08	52.00	-68.00	4623.38
3	40	64.55	3.24	70.69	30.69	941.75
4	60	66.23	2.78	67.79	7.79	60.74
5	30	61.21	0.43	69.01	39.01	1521.78
6	140	77.31	5.14	61.64	-78.36	6139.84
7	60	77.96	3.79	82.45	22.45	504.02
8	80	81.40	3.68	81.75	1.75	3.06
9	35	75.07	0.68	85.08	50.08	2508.40
10	150	90.60	5.13	75.75	-74.25	5513.61
11	55	87.59	2.69	95.73	40.73	1659.05
12	90	90.22	2.67	90.28	0.28	0.08
				889.68	MSD	2134.16
F+1 = (Dxα)+((1-α)F)
α =	0.2
1-α=	0.8
β =	0.3
1-β =	0.7

	Coefficients
Intercept	54.5454545
X Variable 1	2.95454545

through regression analysis

3. Winters Method

Period	D=Demand	Deseasonalized Demand	Deseasonalized Demand (After Regression)	Seasonlized Factor (No initialization)	Seasonlized Factor	L=Level	T=Trend	F=Forecast	Deviation	Square of Devaiation
0						54.88	2.94
1	25		57.82	0.43	0.43	57.85	2.95	24.94	-0.06	0.00
2	120		60.76	1.98	1.90	61.30	3.10	115.22	-4.78	22.83
3	40	61.875	63.70	0.63	0.68	63.21	2.74	44.09	4.09	16.71
4	60	65	66.64	0.90	0.97	65.09	2.48	64.17	4.17	17.40
5	30	70	69.58	0.43	0.43	67.96	2.60	29.17	-0.83	0.68
6	140	75	72.51	1.93	1.93	70.98	2.73	135.91	-4.09	16.70
7	60	78.125	75.45	0.80	0.66	77.18	3.77	48.55	-11.45	131.08
8	80	80	78.39	1.02	0.95	81.65	3.98	76.69	-3.31	10.93
9	35	80.625	81.33	0.43	0.44	84.53	3.65	37.38	2.38	5.68
10	150	81.25	84.27	1.78	1.95	85.94	2.98	171.90	21.90	479.79
11	55		87.21	0.63	0.72	86.45	2.24	63.84	8.84	78.22
12	90		90.15	1.00	0.96	89.63	2.52	85.46	-4.54	20.60
								897.34	MSD	72.78
F+1 = (Dxα)+((1-α)F)
α =	0.2
1-α=	0.8
β =	0.3
1-β =	0.7
ϒ =	0.5
p=	4

	Coefficients
Intercept	54.88095
X Variable 1	2.938988

through regression analysis

Conclusion: Out of all 3 methods, winters method is more suitable because MSD is least of all 3 .i.e 72.78 that means it has less variation & more accurate forecasting.

(Alpha, Beta & Gamma as well as P are assumed)