CHAPTER 13
FORECASTING
9. a. F5 = (700 + 600 + 400)/3 = 567
b. F4 = F3 + (A3 – F3) = 350 + .20(600 – 350) = 400
F5 = F4 + (A4 – F4) = 400 + .20(700 – 400) = 460
11. a-c. For the exponential smoothing forecast we need a beginning forecast for March and an
. For the beginning forecast use the average of the first three periods and select  = .30.
Other choices will produce different answers.
3-Mo. Absolute Exponential Absolute
Month Demand MA Deviation Smoothing Deviation
January
110
February
130
March
150
130.00
April
170
130
40
136.00
34.00
May
160
150
10
146.20
13.80
June
180
160
20
150.34
29.66
July
140
170
30
159.24
19.24
August
130
160
30
153.47
23.47
September
140
150
10
146.43
6.43
MAD
23.3
21.1
Based upon MAD, the exponential smoothing model appears to be the best.
16. a. FSeptember = (170 + 180 + 140)/3 = 163.3
b. FSeptember = .50(170) + .30(180) + .20(140) = 167.0
a. FJuly = FJune + (AJune – FJune) = 130 + .3(140 - 130) = 133.00
FAugust = FJuly + (AJuly – FJuly) = 133.00 + .3(180 – 133.00) = 147.10
FSeptember = FAugust + (AAugust – FAugust) = 147.10 + .3(170 – 147.10) = 153.97
17. a. FOctober = (75 + 80 + 60 + 75)/4 = 72.5
b. FOctober = FSeptember + (ASeptember – FSeptember) = 65 + .2(75 – 65) = 67.0
c.
148
Forecasting
y = 405/6 = 67.5
x = 21/6 = 3.5
 xy  n x y
b=
x
2
 nx
2

1485  6(3.5)67.5
= 3.86
91  6(3.5) 2
a = y  b x = 67.5 – 3.86(3.5) = 54.00
Y = a + bx = 54.0 + 3.86x
d. FOctober = 54.00 + 3.86(7) = 81.01
149
Chapter 13
18.
Quarter
Last year
This year
I
23,000
19,000
II
27,000
24,000
III
18,000
15,000
IV
9,000
Each strategy is used to predict the third quarter of this year. Then, the best one is used to
predict the fourth quarter of this year.
Strategy A: Whatever we sold in the past three months is what we will probably sell in the
next three months. Therefore, our forecast is 24,000. Actual was 15,000. 24,000/15,000 =
160%.
Strategy B: What we sold in the same three-month period last year, we will probably sell in
that three-month period this year. Therefore, our forecast is 18,000. Actual was 15,000.
18,000/15,000 = 120%.
Strategy C: We will probably sell 10 percent more in the next three months than we sold in
the past three months. Our forecast is 1.10(24,000) = 26,400. Actual was 15,000.
26,400/15,000 = 176%.
Strategy D: We will probably sell 50 percent more over the next three months than we did for
the same three months of last year. The forecast would be 1.50(18,000) = 27,000. Actual
was 15,000. 27,000/15,000 = 180%.
Strategy E: Whatever percentage change we had for the past three months this year compared
to the same three months last year will probably be the same percentage change that we will
have for the next three months of this year. The forecast would be (24,000/27,000)18,000 =
16,000. Actual was 15,000. 16,000/15,000 = 107%.
The best method is E. Apply it to the fourth quarter of this year.
(15,000/18,000)9,000 = 7,500
150
Forecasting
19.
Absolute Sum of Absolute
Period Forecast Actual Deviation RSFE deviation
deviations
1
1500
1550
50
50
50
50
2
1400
1500
100
150
100
150
3
1700
1600
-100
50
100
250
4
1750
1650
-100
-50
100
350
5
1800
1700
-100
-150
100
450
MAD TS
50.0 1.00
75.0 2.00
83.3 0.60
87.5 -0.57
90.0 -1.67
3
TS
2
1
0
-1
1
2
3
4
5
-2
Period
a.
For period 5, the MAD = 90.00, and the TS = -1.67
b.
The model seems acceptable since the tracking signal is 1.67 off the mean and is reasonable. However, the downward trend in the graph does present a concern.
151
Chapter 13
20.
Month
3-mo.
(t) Demand MA
1
62
2
65
3
67
4
68
64.67
5
71
66.67
6
73
68.67
7
76
70.67
8
78
73.33
9
78
75.67
10
80
77.33
11
84
78.67
12
85
80.67
Absolute 3-mo Absolute
deviation WMA deviation
3.33
4.33
4.33
5.33
4.67
2.33
2.67
5.33
4.33
MAD
65.40
67.10
69.30
71.40
74.10
76.40
77.60
79.00
81.60
4.07
2.60
3.90
3.70
4.60
3.90
1.60
2.40
5.00
3.40
Ft
61.00
61.30
62.41
63.79
65.05
66.84
68.68
70.88
73.02
74.51
76.16
78.51
3.46
Absolute
deviation
4.21
5.95
6.16
7.32
7.12
4.98
5.49
7.84
6.49
Tt
1.80
1.82
1.94
2.03
2.00
2.07
2.11
2.22
2.28
2.11
1.99
2.08
Ft
60.00
61.86
64.07
66.31
68.23
70.46
72.67
75.14
77.55
79.28
80.98
83.27
6.17
Absolute
FITt deviation
61.80
63.68
66.01
68.33 0.33
70.23 0.77
72.53 0.47
74.78 1.22
77.36 0.64
79.83 1.83
81.39 1.39
82.96 1.04
85.35 0.35
0.89
Based upon MAD, the exponential smoothing with trend component appears to be the best method.
21.
x
1
2
3
4
5
6
7
8
36
Total
y
205
140
375
575
475
275
685
965
3695
y =
461.88
x=
4.50
b=
a=
 xy
x
d
2
 n x yd
 nx
y d  bx =
2
=
Average
from same
quarterly
period
340.0
207.5
530.0
770.0
55.78
210.87
152
Seasonal
factor
0.736
0.449
1.147
1.667
0.736
0.449
1.147
1.667
Deseasonalized demand
278.48
311.63
326.80
344.91
645.27
612.12
596.95
578.84
3695.00
x2
1
4
9
16
25
36
49
64
204
x*deseasonalized
demand
278.48
623.25
980.40
1379.63
3226.33
3672.74
4178.66
4630.75
18970.24
Forecasting
Period (x)
9
Summer ’06
10
11
12
Yd
712.88
768.66
824.44
880.22
Forecast
Seasonal (Yd*seaso
factor nal factor)
0.736
525
0.449
345
1.147
946
1.667
1467
22.
Quarter
2004
2005
I
1,125
1,000
II
1,310
1,175
III
1,075
975
IV
1,550
Each strategy is used to predict the third quarter of this year. Then, the best one is used to
predict the fourth quarter of this year.
Strategy A: Whatever we sold in the past three months is what we will probably sell in the
next three months. Therefore, our forecast is 1,175. Actual was 975. 1,175/975 = 121%.
Strategy B: What we sold in the same three-month period last year, we will probably sell in
that three-month period this year. Therefore, our forecast is 1,075. Actual was 975.
1,075/975 = 110%.
Strategy C: We will probably sell 10 percent more in the next three months than we sold in
the past three months. Our forecast is 1.10(1,175) = 1,292.5. Actual was 975. 1,292.5/975 =
133%.
Strategy D: We will probably sell 50 percent more over the next three months than we did for
the same three months of last year. The forecast would be 1.50(1,075) = 1,612.5. Actual was
975. 1612.5/975 = 165%.
Strategy E: Whatever percentage change we had for the past three months this year compared
to the same three months last year will probably be the same percentage change that we will
have for the next three months of this year. The forecast would be (1,175/1,310)1,075 = 964.
Actual was 975. 964/975 = 99%.
If only the first three are used, the best method is B. Therefore, the forecast for the fourth
quarter is 1,550.
If all five methods listed in the Text are used, then the best method is E. Applying it to the
fourth quarter of this yea produces a forecast of
(975/1,075) 1,550 = 1,406.
153
Chapter 13
23.
a. F (this month) = (325 + 350 + 400)/3 = 358
b. F (next month) = (300 + 325 + 350)/3 = 325
c. F (two months ago) = 450 + .20(400 – 450) = 440
F (one month ago) = 440 + .20(350 – 440) = 422
F (this month) = 422 + .20(325 – 422) = 403
24.
Month
Forecast Actual Deviation RSFE
May
450
500
50
50
June
500
550
50
100
July
550
400
-150
-50
August
600
500
-100
-150
September
650
675
25
-125
October
700
600
-100
-225
Absolute
deviation
50
50
150
100
25
100
Sum of
absolute
deviations
50
100
250
350
375
475
MAD
50.00
50.00
83.33
87.50
75.00
79.17
TS
1.00
2.00
-0.60
-1.71
-1.67
-2.84
4
TS
2
0
-2
1
2
3
4
5
6
-4
Period
The TS itself is acceptable. However, you would like to see the TS going back and forth
between positive and negative. It currently is headed down (4 consecutive point in a row
downward). If this trend continues, the forecasts will be unacceptable. This forecast
should be closely monitored to see if the downward trend continues, or if this occurred by
random chance.
154
Forecasting
25.
a.
Company A
Period
2002-I
II
III
IV
2003-I
II
III
IV
2004-I
II
III
IV
2005-I
II
III
EPS
1.67
2.35
1.11
1.15
1.56
2.04
1.14
0.38
0.29
-0.18
-0.97
0.20
-1.54
0.38
MAD
Forecast Absolute
 = 0.10 deviation
1.67
1.67
0.68
1.74
0.63
1.68
0.53
1.62
0.06
1.62
0.42
1.66
0.52
1.61
1.23
1.48
1.19
1.36
1.54
1.21
2.18
0.99
0.79
0.91
2.45
0.67
0.29
0.64
Forecast Absolute
 = 0.30 deviation
1.67
1.67
0.68
1.87
0.76
1.64
0.48
1.50
0.06
1.52
0.52
1.67
0.53
1.51
1.13
1.17
0.88
0.91
1.09
0.58
1.55
0.12
0.08
0.14
1.68
-0.36
0.74
-0.14
0.96
0.79
Company B
Period Demand
2002-I
0.17
II
0.24
III
0.26
IV
0.34
2003-I
0.25
II
0.37
III
0.36
IV
0.44
2004-I
0.33
II
0.40
III
0.41
IV
0.47
2005-I
0.30
II
0.47
III
MAD
. AbsoForecast lute devi- Forecast
 = 0.10 ation
 = 0.30
0.17
0.17
0.17
0.07
0.17
0.18
0.08
0.19
0.19
0.15
0.21
0.20
0.05
0.25
0.21
0.16
0.25
0.22
0.14
0.29
0.24
0.20
0.31
0.26
0.07
0.35
0.26
0.14
0.34
0.28
0.13
0.36
0.29
0.18
0.37
0.31
0.01
0.40
0.31
0.16
0.37
0.32
0.40
0.12
155
Absolute
deviation
0.07
0.07
0.13
0.00
0.12
0.07
0.13
0.02
0.06
0.05
0.10
0.10
0.10
0.08
Chapter 13
MAD
Goodyear Tire
Cooper Tire
.96
.79
.12
.08
 = 0.10
 = 0.30
b. Based upon MAD, an  of .30 performs better than .10.
c.
Company A
x
y
1 1.67
2 2.35
3 1.11
4 1.15
5 1.56
6 2.04
7 1.14
8 0.38
9 0.29
10 -0.18
11 -0.97
12 0.20
13 -1.54
14 0.38
Total
105
9.58
y =
0.684
x=
7.5
b=
a=
 xy
x
d
2
 n x yd
 nx
y d  bx =
2
=
Average
from same
quarter
0.495
1.148
0.427
0.577
x*
Seasonal Deseasonalized
deseasonalized
factor
demand
x2
demand
0.723
2.309
1
2.309
1.677
1.401
4
2.803
0.624
1.780
9
5.341
0.843
1.365
16
5.458
0.723
2.157
25
10.783
1.677
1.217
36
7.299
0.624
1.828
49
12.798
0.843
0.451
64
3.607
0.723
0.401
81
3.608
1.677
-0.107
100
-1.073
0.624
-1.556
121
-17.113
0.843
0.237
144
2.848
0.723
-2.129
169
-27.676
1.677
0.227
196
3.172
9.580
-0.254
2.5867
156
1015
14.165
Forecasting
Period (x)
15
16
17
18
19
20
Yd
-1.217
-1.470
-1.725
-1.978
-2.232
-2.485
Forecast
Seasonal (Yd*seasonal
factor
factor)
0.624
-0.76
0.843
-1.24
0.723
-1.25
1.677
-3.32
0.624
-1.39
0.843
-2.09
Company B
Total
x
1
2
3
4
5
6
7
8
9
10
11
12
13
14
y
0.17
0.24
0.26
0.34
0.25
0.37
0.36
0.44
0.33
0.40
0.41
0.47
0.30
0.47
105
4.81
y =
0.344
x=
7.5
b=
a=
 xy
x
d
2
 n x yd
 nx
y d  bx =
2
=
Average
from same Seasonal Deseasonalized
quarter
factor
demand
0.263
0.764
0.223
0.370
1.077
0.223
0.343
0.999
0.260
0.417
1.213
0.280
0.764
0.327
1.077
0.344
0.999
0.360
1.213
0.363
0.764
0.432
1.077
0.371
0.999
0.410
1.213
0.388
0.764
0.393
1.077
0.436
4.810
0.016
0.225
157
x2
1
4
9
16
25
36
49
64
81
100
121
144
169
196
x*
deseasonalized
demand
0.223
0.446
0.781
1.121
1.636
2.061
2.522
2.902
3.887
3.714
4.513
4.651
5.104
6.110
1015
39.672
Chapter 13
Period (x)
15
16
17
18
19
20
d.
Forecast
(Yd*seasonal
factor)
0.46
0.58
0.38
0.55
0.53
0.66
Seasonal
factor
0.999
1.213
0.764
1.077
0.999
1.213
Yd
0.462
0.478
0.494
0.510
0.525
0.541
The results indicate that Goodyear Tire’s EPS is on a downward trend, while Cooper
Tire’s EPS is growing.
26. Since we our interested in forecasting the next four years, many of the procedures presented
in the Text will not work. For example, moving average and exponential smoothing will only project one period into the future. Therefore, of the methods presented in the Text, regression appears to be the logical approach.
Revenue
6000
5500
5000
4500
4000
1
2
3
4
5
6
7
8
9
10
11
Year
Examination of the graph of revenue over time suggest that there maybe a slight upward
trend. Additionally, there may be a cyclical component, possibly 6 or 7 years. With the
limited data, it is very difficult to determine the cycle. Consequently, simple regression
appears to be the available choice for the forecast.
158
Forecasting
y
4865.9
5067.4
5515.6
5728.8
5497.7
5197.7
5094.4
5108.8
5550.6
5738.9
5860.0
xy
4865.9
10134.8
16546.8
22915.2
27488.5
31186.2
35660.8
40870.4
49955.4
57389.0
64460.0
x2
1
4
9
16
25
36
49
64
81
100
121
y2
23676982.8
25678542.8
30421843.4
32819149.4
30224705.3
27016085.3
25952911.4
26099837.4
30809160.4
32934973.2
34339600.0
Total 66 59225.8
361473.0
506
319973791.0
x
1
2
3
4
5
6
7
8
9
10
11
6
x=
y =
b=
5384.164
 xy  n x y =
 x  nx
2
2
a = y  bx =
55.62
5050.444
LINEST:
b
a
55.62
5050.444
Period
12
13
14
15
Forecast
5718
5774
5829
5885
159
Chapter 13
27.
a. Answers using LINEST function in Microsoft Excel.
Sales
Price
Advertising
Fitted Values
400
280
600
451.72
700
215
835
977.21
900
211
1100
1090.98
1300
210
1400
1195.40
1150
215
1200
1095.85
1200
200
1300
1231.99
900
225
900
929.25
1100
207
1100
1118.62
980
220
700
898.79
1234
211
900
1025.98
925
227
700
850.42
800
245
690
722.80
Constant
Price
Advertising
2191.3374
-6.9094
0.3250
y  a  b1x1  b2 x2  2191.3374  6.9094x1  .3250x2
Where
a = y intercept
x1 = price
b1 = slope of price
x2 = advertising
b2 = slope of advertising
b. Price has a large effect on sales because it slope value is much higher (-6.9094 versus
.3250). Price actually has a negative effect since raising price decreases sales.
c.
Sales = 2191.3374 - 6.9094 (300) + .3250 (900)
Sales = 411.04
160
Forecasting
28.
Ft  300
Tt  8
  .30
  .40
At  288
FITt  Ft  Tt  300  8  308
Ft 1  FITt   ( At  FITt )  308  .3(288  308)  308  6  302
Tt 1  Tt   ( Ft 1  FITt )  8  .4(302  308)  8  2.4  5.6
FITt 1  Ft 1  Tt 1  302  5.6  307.6
161