Question

(24 points) The manager of a travel agency has been using seasonally adjusted forecast to predict demand for packaged tours. The demand and the forecast for the last 14 weeks are given below: 4. Demand 113 129 191 175 139 151 227 211 163 189 269 245 191 211 Predicted 95 123 203 181 123 153 251 221 151 187 281 259 173 209 (12 points) Compute MAD for the sixth period, then update it period by period using exponential smoothing with a 0.3. Compute a tracking signal for periods 6 through 14 using the initial and updated MADs. If limits of t 4 are used, what can you conclude? (12 points) Compute MSE and s using the first six quarters. Construct a control chart with 2s control limits. What can you conclude? a. b.

Answer 1

Answer:

The given data alongwith calculations for MAD, Mean Absolute Deviation = Sum of Absolute deviations/ Number of observations,    as follows:

Period	Demand	Predicted	Deviation	Absolute deviation
1	129	117	12	12
2	194	200	-6	6
3	164	150	14	14
4	91	100	-9	9
5	84	80	4	4
6	132	142	-10	10
7	126	128	-2	2
8	133	124	9	9
9	95	102	-7	7
10	149	150	-1	1
11	109	94	15	15
12	85	82	3	3
13	129	140	-11	11
14	134	128	6	6
			Total =	109
			MAD =	7.7857143

Formula for Tracking Signal = Sum of the deviations / MAD

Formula for forecasting using exponential smoothing is NF = OF + α(AD-OF)

Using the above formula New forecasts with new MADt is as follows:

Period	Demand	Predicted	Deviation	Absolute deviation
1	129	117	12	12
2	194	200	-6	6
3	164	150	14	14
4	91	100	-9	9
5	84	80	4	4
6	132	142	-10	10
7	126	128	-2	2
8	133	124	9	9
9	95	102	-7	7
10	149	150	-1	1
11	109	94	15	15
12	85	82	3	3
13	129	140	-11	11
14	134	128	6	6
		Total =	17	109
			MAD =	7.7857143
			TS =	2.1834862
Period	AD	OF	AD-OF	NF	Deviation	Absolute deviation
1	129	129	0	129	0.000	0
2	194	129	65	135.5	-58.500	58.5
3	164	135.5	28.5	138.35	-25.650	25.65
4	91	138.35	-47.35	133.615	42.615	42.615
5	84	133.615	-49.615	128.654	44.654	44.654
6	132	128.654	3.346	128.988	-3.012	3.012
7	126	128.988	-2.988	128.689	2.689	2.689
8	133	128.689	4.311	129.120	-3.880	3.88
9	95	129.120	-34.120	125.708	30.708	30.708
10	149	125.708	23.292	128.038	-20.962	20.962
11	109	128.038	-19.038	126.134	17.134	17.134
12	85	126.134	-41.134	122.020	37.020	37.02
13	129	122.020	6.980	122.718	-6.282	6.282
14	134	122.718	11.282	123.847	-10.153	10.153
				Total =	46.381	303.259
				MAD =	21.661357
				TS =	2.1412009