DISCUSSION QUESTIONS
1. Think of some of the leading indicators that could be used as a major input to
causal forecasts in the economy. Discuss their use.
Oil and gasoline futures. Most of the commerce in the United States depends upon
petroleum. Whether in shipping costs or the use of petroleum distillates the price of oil
affects us. New housing starts – if people have the money they will want to improve their
standard of living. Interest rates – what the Federal Reserve charges other banks for
loans affects the consumer – housing loans, credit card rates and returns on money
market and savings accounts. Durable goods – washers, dryers, refrigerators and other
items that last more than three years. As people have more money to spend they will
purchase these long-term use items. There will be others mentioned – this is just a few.
2. Which type of forecasts would most likely be used for Sales and Operations
Planning (S&OP), and why are they the most appropriate?
Quantitative and qualitative forecasts are the general types of forecasting used. The
quantitative methods that seem to be the most appropriate are the time series and causal.
These forecasts take into account "hard" data, giving a much more reliable model to
predict. All forecasting methods contain errors, quantitative data tends to be more
reliable.
3. What value does it bring to an operation if a forecasting method is used that
only forecasts for families of products?
Forecasts that look only at a type of product tend to be less accurate than a generalized
forecast (convertibles vs. all cars) that looks at a family of products. To get a good look
at particular market, looking at the family of products is more accurate.
4. Think of at least three products recently introduced that would probably use
life-cycle analogy. What products would they “copy”? Why is life-cycle
appropriate for those products?
The list here will vary. One could look at the Apple I-pod or the Sony PSP. The Sony
product could be compared to other had-held video games (Nintendo Game Boys).
Automobiles can fit here with year model changes. It seems these particular markets
turnover about every 18 months to 24 months.
2-1
5. How should a company include information for their forecast that indicates
the economy is headed for a recession? How, if at all, should that information
impact time-series forecasting information?
To include information that indicates a recession, I would use a seasonal or cyclical
adjustment to my forecast. If hard data is available from the last recession, incorporate
that data into the forecasting model. Opinion here may vary, using prime interest rates as
one mechanism to account for inflation.
6. Discuss the arguments for using a large smoothing constant for exponential
smoothing instead of a small one. Under what conditions would each be
better? Why?
The larger your smoothing constant, the more of the forecast error is accounted for. This
makes the model very responsive to market demands. However, this responsiveness can
also create havoc in the organization if the forecast changes dramatically and often. If I
want my product to be market driven, I would use the higher smoothing constant. If I
want to hold production somewhat steady then I use the lower constant. For example, if
my product has a high turnover or short shelf life - I would then use the higher constant.
7. Describe in your own words why using the MAD is better for describing the
forecast error than is the MFE. What is the major use of each? Should they
really be used together? Why or why not?
MAD measures the magnitude of the error regardless of which direction. This gives us a
good idea if our forecasts are anywhere near accurate. MFE can hide bad forecasts,
especially those that offset one another, ie a large negative and a large positive would
balance out. The MFE will tell us if we are over or under forecasting and MAD tells us
how accurate we may be. If I were to use either MAD or MFE, then I would use them
both to give a better idea of the market and my ability to predict.
EXERCISES
2-2
1. Given the following data:
Period
Demand
1
43
2
37
3
55
4
48
a. Calculate the three-period moving average for period five.
Period 5 = 46.67
b. Calculate the exponential smoothed forecast for period five using an
alpha value of 0.4. Assume the forecast for period four was the threeperiod moving average of the first three periods.
Period 5 = 46.20 (assuming forecast for period 4 = 45.00)
c. Which method appeals the most for the data? Why?
At this point, both methods yield similar results. In the long term, the exponential
smoothing may yield better results. The forecasting errors are the same at this point.
Method 1 - Moving Average:
3-Period Moving Average
Forecast for Period 5
46.67
CFE
MAD
MSE
MAPE
Method 2 - Exponential Smoothing:
3.00
3.00
9.00
6.25%

Initial Forecast
0.40
45.00
Forecast for Period 5
46.20
2-3
CFE
MAD
MSE
MAPE
3.00
3.00
9.00
6.25%
2. Given the following demand data:
Period
1
2
3
4
5
6
7
8
Demand
17
22
18
27
14
18
20
25
a.
Calculate the 4-period weighted moving average for period 9 using
weights of 0.1, 0.2, 0.3, and 0.4 where the 0.4 is the weight for the
most recent period.
Period 9 = 21.00
b.
Calculate the forecast for the period 9 using a three-month moving
average forecasting method.
Period 9 = 21.00
c.
Which method would you recommend using and why?
I would recommend using the 4-period weighted moving average. This method has
lower forecasting errors.
Method 1 - Weighted Moving Average:
4-Period Weighted Moving Average
Forecast for Period 9
21.00
CFE
MAD
MSE
MAPE
-2.30
4.33
27.58
24.75%
Method 2 - Moving Average:
3-Period Moving Average
2-4
Forecast for Period 9
21.00
CFE
MAD
MSE
MAPE
6.00
5.20
39.02
26.15%
3. Given the same data for the previous problem:
Period
1
2
3
4
5
6
7
8
Demand
17
22
18
27
14
18
20
25
a. Use Excel or some other statistical computer package to calculate the
regression equation for the data.
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
0.22
0.05
-0.11
4.55
8.00
Coefficients Standard Error
18.36
3.55
0.39
0.70
Intercept
X Variable 1
Y = 0.39 (Period) + 18.36
b. Use the regression equation to forecast the demand for period 9
Period 9 = 21.87
4. A forecasting method resulted in the following forecasts shown by the data in
the following table:
2-5
Period
Demand
Forecast
Deviation
1
132
127
5
2
141
130
11
3
137
133
4
4
159
135
24
5
146
139
7
6
162
144
18
7
166
149
17
8
175
155
20
9
194
161
33
10
181
169
12
a. Use the data to calculate the MAD.
MAD = (5+11+4+24+7+18+17+20+33+12)/10 = 151/10 = 15.1
b. Find a regression equation for the demand data
Y = 6.30 (Period) + 124.67
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
Intercept
0.94
0.88
0.86
7.56
10.00
Coefficients
Standard Error
124.67
5.16
2-6
Period
6.30
0.83
c. Use the regression equation to forecast demand for period 11
Period 11 = 193.97
d. Is the regression method preferred over the method used? Why or why
not?
The regression method is preferred in this instance to the forecasting method currently
used. The current method may be off an average of 15 while the regression method is off
an average of 7.5.
Demand
Period Line Fit Plot
250
200
150
100
50
0
Demand
y = 6.30(period) + 124.67
0
5
10
Predicted Demand
15
Linear (Demand)
Period
5. The following demand data was collected over a three year period for one
product:
Month
Demand, year 1 Demand, year 2
Demand, year 3
1
72
84
97
2
67
98
119
3
85
86
138
2-7
4
99
113
124
5
87
121
143
6
135
140
162
7
127
133
157
8
131
156
178
9
102
125
136
10
96
134
141
11
88
118
122
12
79
102
120
Use the data to develop a regression-based forecast. Be sure to note that there is
a seasonal factor to the demand.
Initial Regression Equation: y = 1.68 (month) + 85.96
Month Demand Regression
forecast
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
72
67
85
99
87
135
127
131
102
96
88
79
84
98
86
Demand/
Forecast
Seasonal Seasonally adjusted
Multipliers regression forecast
87.64
0.82
0.79
68.89
89.33
0.75
0.85
76.30
91.01
0.93
0.92
83.66
92.69
1.07
1.00
92.72
94.37
0.92
1.01
95.61
96.06
1.41
1.27
121.58
97.74
1.30
1.19
116.11
99.42
1.32
1.30
129.09
101.10
1.01
1.00
101.13
102.78
0.93
1.00
103.08
104.47
0.84
0.88
91.63
106.15
0.74
0.79
83.88
107.83
0.78
0.79
84.76
109.51
0.89
0.85
93.54
111.20
0.77
0.92
102.22
2-8
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
113
121
140
133
156
125
134
118
102
97
119
138
124
143
162
157
178
136
141
122
120
112.88
1.00
1.00
112.92
114.56
1.06
1.01
116.06
116.24
1.20
1.27
147.13
117.92
1.13
1.19
140.09
119.61
1.30
1.30
155.30
121.29
1.03
1.00
121.32
122.97
1.09
1.00
123.32
124.65
0.95
0.88
109.33
126.34
0.81
0.79
99.83
128.02
0.76
0.79
100.63
129.70
0.92
0.85
110.78
131.38
1.05
0.92
120.77
133.06
0.93
1.00
133.11
134.75
1.06
1.01
136.51
136.43
1.19
1.27
172.69
138.11
1.14
1.19
164.08
139.79
1.27
1.30
181.51
141.48
0.96
1.00
141.51
143.16
0.98
1.00
143.57
144.84
0.84
0.88
127.04
146.52
0.82
0.79
115.78
148.12
0.76
0.79
117.01
6. The following information is presented for a product:
1998
1999
Forecast
Demand
Forecast
Demand
Quarter I
212
232
222
245
Quarter II
341
318
316
351
Quarter III
157
169
160
145
Quarter IV
263
214
251
242
2-9
a)
What is the MAD for the data above?
Absolute
Forecast Demand Deviation Deviation
212
232
20
20
341
318
23
-23
157
169
12
12
263
214
49
-49
222
245
23
23
316
351
35
35
160
145
15
-15
251
242
9
-9
Year
1998 Quarter
I
1998 Quarter II
1998 Quarter III
1998 Quarter IV
1999 Quarter I
1999 Quarter II
1999 Quarter III
1999 Quarter IV
MAD =
23.25
b) Given the information above, what should the forecast be for
the first quarter of 2000 if the company switches to exponential smoothing
with an alpha value of 0.3?
220.75 (Assuming the first 3 periods average make the initial forecast of 240)
7.
The following information is presented for a product:
2001
2002
Forecast
Demand
Forecast
Demand
Quarter I
200
226
210
218
Quarter II
320
310
315
333
Quarter III
145
153
140
122
Quarter IV
230
212
240
231
a) What are the seasonal indices that should be used for each
quarter?
Forecast Demand Error
Absolute Demand /
Deviation Forecast
2-10
Seasonal Seasonally
Multipliers adjusted forecast
2001 Quarter
I
2001 Quarter II
2001 Quarter III
2001 Quarter IV
2002 Quarter I
2002 Quarter II
2002 Quarter III
2002 Quarter IV
200
320
145
230
210
315
140
240
226
310
153
212
218
333
122
231
26
10
8
18
8
18
18
9
26
-10
8
-18
8
18
-18
-9
1.13
1.08
216.81
0.97
1.01
324.14
1.06
0.96
139.68
0.92
0.94
216.69
1.04
1.08
1.01
0.96
0.94
226.80
1.06
0.87
0.96
318.15
134.40
225.60
b) What is the MAD for the data above?
MAD = 14.375
8. Consider the forecast results shown below. Calculate MAD and MFE using the
data for months January through June. Does the forecast model under- or overforecast?
Month
Actual Demand
Forecast
January
1040
1055
February
990
1052
March
980
900
April
1060
1025
May
1080
1100
June
1000
1050
Month
January
February
March
April
Actual Demand
1040
990
980
1060
Forecast
1055
1052
900
1025
2-11
Absolute
Deviation
Deviation
-15
15
-62
62
80
80
35
35
May
June
1080
1000
1100
1050
MFE = -5.33
-20
-50
-32
MAD = 43.67
This model over forecasts (MFE is a negative number - demand is lower than forecast)
2-12
20
50
262