Qa
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16.8865 + 0.3485t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
17.24 17.58 17.93 18.28 18.63 18.98 19.33 19.67 20.02 20.37 20.72 21.07 21.42 21.77 22.11 22.46 22.81 23.16 23.51 23.86 24.21 24.55 24.9 25.25 25.6 25.95 26.3 26.64 26.99 27.34
0.35
Problem 3 A customer comment phone line is staffed from 8:00 a.m. to 4:30 p.m. five days a week. Records are available that show the number of calls received every day for the last five weeks. a. Use the information to calculate a seasonal index. Week Day t Y : Number 1 Mon 1 28 Tue 2 12 Wed 3 16 Thu 4 15 Fri 5 23 2 Mon 6 29 Tue 7 10 Wed 8 14 Thu 9 14 Fri 10 26 3 Mon 11 32 Tue 12 15 Wed 13 15 Thu 14 18 Fri 15 27 4 Mon 16 35 Tue 17 17 Wed 18 16 Thu 19 20 Fri 20 29 5 Mon 21 37 Tue 22 19 Wed 23 18 Thu 24 21 Fri 25 28 325 534
tY
t²
28.00 24.00 48.00 60.00 115.00 174.00 70.00 112.00 126.00 260.00 352.00 180.00 195.00 252.00 405.00 560.00 289.00 288.00 380.00 580.00 777.00 418.00 414.00 504.00 700.00 7,311.00
สมการแนวโน้ม
Yt = a + bt
โดยท่ี
= [ 7,311 - (325*534)/25 ] / [ 5,525 - 325²/25]
b
1.00 4.00 9.00 16.00 25.00 36.00 49.00 64.00 81.00 100.00 121.00 144.00 169.00 196.00 225.00 256.00 289.00 324.00 361.00 400.00 441.00 484.00 529.00 576.00 625.00 5,525.00
= 0.2838 a
= Yt -bt = 534/25 - 325/25 * 0.2838 = 13.6738
ดังนัน ้ สมการคือ 13.6738 + 0.2838t Week
Day 1 Mon Tue Wed Thu
t 1 2 3 4
Y : Number 28 12 16 15
13.96 14.24 14.53 14.81
2.01 0.84 1.10 1.01
Fri 2 Mon Tue Wed Thu Fri 3 Mon Tue Wed Thu Fri 4 Mon Tue Wed Thu Fri 5 Mon Tue Wed Thu Fri
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Day Mon Tue Wed Thu Fri
23 29 10 14 14 26 32 15 15 18 27 35 17 16 20 29 37 19 18 21 28
15.09 15.38 15.66 15.94 16.23 16.51 16.80 17.08 17.36 17.65 17.93 18.21 18.50 18.78 19.07 19.35 19.63 19.92 20.20 20.49 20.77
Seasonal Irregular Component 2.01 , 1.89 , 1.90 , 1.92 ,1.88 0.84 , 0.64 , 0.88 , 0.92 , 0.95 1.10 , 0.88 , 0.86 , 0.85 , 0.89 1.01 , 0.86 , 1.02 , 1.05 , 1.02 1.52 , 1.57 , 1.51 , 1.50 ,1.35
1.52 1.89 0.64 0.88 0.86 1.57 1.90 0.88 0.86 1.02 1.51 1.92 0.92 0.85 1.05 1.50 1.88 0.95 0.89 1.02 1.35 Seasonal Factor 1.92 0.85 0.92 0.99 1.49 6.17
1.56 0.69 0.74 0.81 1.20 5.00
b. Deseasonalize the data. Week
Day 1 Mon Tue Wed Thu Fri 2 Mon Tue Wed Thu Fri 3 Mon Tue Wed Thu Fri 4 Mon Tue Wed Thu
t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Y : Number Deseasonalized 28 17.95 12 17.39 16 21.62 15 18.52 23 19.17 29 18.59 10 14.49 14 18.92 14 17.28 26 21.67 32 20.51 15 21.74 15 20.27 18 22.22 27 22.50 35 22.44 17 24.64 16 21.62 20 24.69
tY
t² 17.95 34.78 64.86 74.07 95.83 111.54 101.45 151.35 155.56 216.67 225.64 260.87 263.51 311.11 337.50 358.97 418.84 389.19 469.14
1.00 4.00 9.00 16.00 25.00 36.00 49.00 64.00 81.00 100.00 121.00 144.00 169.00 196.00 225.00 256.00 289.00 324.00 361.00
Fri 5 Mon Tue Wed Thu Fri
20 21 22 23 24 25 325
29 37 19 18 21 28
24.17 23.72 27.54 24.32 25.93 23.33 535.23
สมการแนวโน้ม
Yt = a + bt
โดยท่ี
= [ 7,411.06 - (325*535.23)/25 ] / [ 5,525 - 325²/25]
b
483.33 498.08 605.80 559.46 622.22 583.33 7,411.06
= 0.3485 a
= Yt -bt = 535.23/25 - 325/25 * 0.3479 = 16.8865
ดังนัน ้ สมการคือ 16.8865 + 0.3485t c. Find the trend line. Yt = 16.8865 + 0.3485t
Number of Call received 25
Yt
20 15 10
Column B
5 0 R R R RR R R R RR R R R R RR R R R RR R R R R o o o oo o o o oo o o o o oo o o o oo o o o o w w w ww w w w ww w w w w ww w w w ww w w w w t
d. Assume there is no cyclical component and forecast the calls for a week
Day M
t 26
Trend Forecast (T=16.8865 Number of Calls per + 0.3485t) Seasonal Factor Day Forecast 25.95 1.5600 40
400.00 441.00 484.00 529.00 576.00 625.00 5,525.00
T W TH F
27 28 29 30
26.3 26.64 26.99 27.34
0.6900 0.7400 0.8100 1.2000
18 20 22 33
cords are available
13.67
0.28
17.24 17.58 17.93 18.28 18.63 18.98 19.33 19.67 20.02 20.37 20.72 21.07 21.42 21.77 22.11 22.46 22.81 23.16 23.51 23.86 24.21 24.55 24.9 25.25 25.6 25.95 26.3 26.64 26.99 27.34
0.35
Problem 3 A customer comment phone line is staffed from 8:00 a.m. to 4:30 p.m. five days a week. Records are available that show the number of calls received every day for the last five weeks. a. Use the information to calculate a seasonal index. Week Day t Y : Number 1 Mon 1 28 Tue 2 12 Wed 3 16 Thu 4 15 Fri 5 23 2 Mon 6 29 Tue 7 10 Wed 8 14 Thu 9 14 Fri 10 26 3 Mon 11 32 Tue 12 15 Wed 13 15 Thu 14 18 Fri 15 27 4 Mon 16 35 Tue 17 17 Wed 18 16 Thu 19 20 Fri 20 29 5 Mon 21 37 Tue 22 19 Wed 23 18 Thu 24 21 Fri 25 28 325 534
tY
t²
28.00 24.00 48.00 60.00 115.00 174.00 70.00 112.00 126.00 260.00 352.00 180.00 195.00 252.00 405.00 560.00 289.00 288.00 380.00 580.00 777.00 418.00 414.00 504.00 700.00 7,311.00
สมการแนวโน้ม
Yt = a + bt
โดยท่ี
= [ 7,311 - (325*534)/25 ] / [ 5,525 - 325²/25]
b
1.00 4.00 9.00 16.00 25.00 36.00 49.00 64.00 81.00 100.00 121.00 144.00 169.00 196.00 225.00 256.00 289.00 324.00 361.00 400.00 441.00 484.00 529.00 576.00 625.00 5,525.00
= 0.2838 a
= Yt -bt = 534/25 - 325/25 * 0.2838 = 13.6738
ดังนัน ้ สมการคือ 13.6738 + 0.2838t Week
Day 1 Mon Tue Wed Thu
t 1 2 3 4
Y : Number 28 12 16 15
13.96 14.24 14.53 14.81
2.01 0.84 1.10 1.01
Fri 2 Mon Tue Wed Thu Fri 3 Mon Tue Wed Thu Fri 4 Mon Tue Wed Thu Fri 5 Mon Tue Wed Thu Fri
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Day Mon Tue Wed Thu Fri
23 29 10 14 14 26 32 15 15 18 27 35 17 16 20 29 37 19 18 21 28
15.09 15.38 15.66 15.94 16.23 16.51 16.80 17.08 17.36 17.65 17.93 18.21 18.50 18.78 19.07 19.35 19.63 19.92 20.20 20.49 20.77
Seasonal Irregular Component 2.01 , 1.89 , 1.90 , 1.92 ,1.88 0.84 , 0.64 , 0.88 , 0.92 , 0.95 1.10 , 0.88 , 0.86 , 0.85 , 0.89 1.01 , 0.86 , 1.02 , 1.05 , 1.02 1.52 , 1.57 , 1.51 , 1.50 ,1.35
1.52 1.89 0.64 0.88 0.86 1.57 1.90 0.88 0.86 1.02 1.51 1.92 0.92 0.85 1.05 1.50 1.88 0.95 0.89 1.02 1.35 Seasonal Factor 1.92 0.85 0.92 0.99 1.49 6.17
1.56 0.69 0.74 0.81 1.20 5.00
b. Deseasonalize the data. Week
Day 1 Mon Tue Wed Thu Fri 2 Mon Tue Wed Thu Fri 3 Mon Tue Wed Thu Fri 4 Mon Tue Wed Thu
t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Y : Number Deseasonalized 28 17.95 12 17.39 16 21.62 15 18.52 23 19.17 29 18.59 10 14.49 14 18.92 14 17.28 26 21.67 32 20.51 15 21.74 15 20.27 18 22.22 27 22.50 35 22.44 17 24.64 16 21.62 20 24.69
tY
t² 17.95 34.78 64.86 74.07 95.83 111.54 101.45 151.35 155.56 216.67 225.64 260.87 263.51 311.11 337.50 358.97 418.84 389.19 469.14
1.00 4.00 9.00 16.00 25.00 36.00 49.00 64.00 81.00 100.00 121.00 144.00 169.00 196.00 225.00 256.00 289.00 324.00 361.00
Fri 5 Mon Tue Wed Thu Fri
20 21 22 23 24 25 325
29 37 19 18 21 28
24.17 23.72 27.54 24.32 25.93 23.33 535.23
สมการแนวโน้ม
Yt = a + bt
โดยท่ี
= [ 7,411.06 - (325*535.23)/25 ] / [ 5,525 - 325²/25]
b
483.33 498.08 605.80 559.46 622.22 583.33 7,411.06
= 0.3485 a
= Yt -bt = 535.23/25 - 325/25 * 0.3479 = 16.8865
ดังนัน ้ สมการคือ 16.8865 + 0.3485t c. Find the trend line. Yt = 16.8865 + 0.3485t
Number of Call received 25
Yt
20 15 10
Column B
5 0 R R R RR R R R RR R R R R RR R R R RR R R R R o o o oo o o o oo o o o o oo o o o oo o o o o w w w ww w w w ww w w w w ww w w w ww w w w w t
d. Assume there is no cyclical component and forecast the calls for a week
Day M
t 26
Trend Forecast (T=16.8865 Number of Calls per + 0.3485t) Seasonal Factor Day Forecast 25.95 1.5600 40
400.00 441.00 484.00 529.00 576.00 625.00 5,525.00
T W TH F
27 28 29 30
26.3 26.64 26.99 27.34
0.6900 0.7400 0.8100 1.2000
18 20 22 33
cords are available
13.67
0.28
