12 Forecasting

Answers to Questions
12-1. Production planning, such as scheduling, inventory, process, facility layout and design, work force, and
material purchasing, financial planning, including the development of budgets and capital expenditures;
and various marketing functions are dependent on forecasting demand.
12-2. Qualitative forecasting methods are subjective estimates based on judgment, opinion, past experience,
and so on, whereas quantitative methods are mathematical, based on formulas.
12-3. Short-range forecasts typically encompass the immediate future, in other words, several months, and are
concerned with daily operations; medium-range forecasts encompass anywhere from several months up
to several years and are used for annual budgets and production plans or the development of a project or
program; long-range forecasts usually are for periods longer than one or two years and are used for strate -
gic planning, such as new product development or new programs.
12-4. All the elements of the supply chain including purchasing, inventory, production, scheduling, facility lo-
cation, transportation and distribution are affected by forecasting. An inaccurate forecast can result in ex -
cessive costly inventories or frequent stockouts and late deliveries.
12-5. Continuous replenishment requires that suppliers replenish a company’s inventory levels as products are
demanded. The primary benefit of a continuous replenishment system is minimal inventory. Thus, it re -
quires very accurate forecasts by suppliers to always be able to meet customer demand on very short no -
tice. Without accurate inventories, suppliers must maintain high inventory levels themselves.
12-6. Quality customer service means having products or services available when customers demand them,
and, being able to deliver products and services on time. Without accurate forecasting of customer de -
mand them is difficult to keep the appropriate amount of inventory on hand to meet demand in a timely
manner without excessive costs.
12-7. Qualitative methods are most often used for long-range strategic planning. Often called, “the jury of ex -
ecutive opinion” it uses judgment, expertise and opinion of knowledgeable people in a company. Other
methods include consumer research, the Delphi method and consulting firms.
12-8. The Delphi method uses the informed opinions, expertise and judgments of knowledgeable individuals
and experts. A questionnaire is used to develop a consensus forecast of future trends and events. It’s es -
pecially useful for predicting technological advances.
12-9. A trend is a gradual, long-term, up or down movement of demand; a cycle is an undulating up-and-down
movement that repeats itself over a lengthy time span; a seasonal pattern is an oscillating movement in
demand that occurs periodically and is repetitive.
12-10. Exponential smoothing is a moving average that weights the most recent past data more strongly than
more distant past data.
12-11. Other ways used to obtain initial forecasts include taking an average of demand in preceding periods or
making a subjective estimate. If forecasting has been a continual process, then preceding forecasts might
be used.
12-12. The higher the smoothing constant, the more sensitive the forecast will be to changes in recent demand.
12-13. Adjusted exponential smoothing is the simple exponential smoothing forecast with a trend adjustment
factor added to it.
12-14. It is a judgmental choice, but in general, a high smoothing constant reflects trend changes more than a
lower 
12-15. In a linear trend line equation, the independent variable, x, is always time.
12-16. This question requires an opinion of the student, but in general, the appropriate model is determined pri -
marily by the extent of any trend pattern.
12-17. A linear trend model will not adjust to a change in trend as the adjusted exponential smoothing model
will, thus limiting the trend line method to a shorter time frame.
12-18. By summing the differences between the actual forecast and demand; a large positive value indicates the
forecast is probably consistently low, whereas a large negative value implies the forecast is consistently
high.
12-19. The movement of a tracking signal is compared to control limits, as long as the tracking signal is within
the control limits, the forecast is in control and not biased.
12-20. This question requires a subjective estimate on the part of the student. A particular method might be
viewed as being superior because it is easier to use (compared to the other methods), it is easier to inter -
pret, it makes more sense, it can be used alone rather than in comparison, or it seems to fit the data bet -
ter.
12-21. Linear regression relates demand to one other independent variable, whereas multiple regression reflects
the relationship between a dependent variable and two or more independent variables.
12-22. y is the dependent variable, x is the independent variable, a is the intercept, and b is the slope of the line.
12-23. The Delphi method might be an appropriate method to use to forecast technological advances in video
equipment, whereas market/consumer research could be used to forecast consumer demand. Various indi-
viduals in-house might also be able to assist in developing a forecast.

Solutions to Problems

12-1. a., b.

3-Month 5-Month
Moving Moving
Month Sales Average Average
January 9.00 — —
February 7.00 — —
March 10.00 — —
April 8.00 8.67 —
May 7.00 8.33 —
June 12.00 8.33 8.20
July 10.00 9.00 8.80
August 11.00 9.67 9.40
September 12.00 11.00 9.60
October 10.00 11.00 10.40
November 14.00 11.00 11.00
December 16.00 12.00 11.40
January — 13.33 12.60

c. 3-month 5-month The dealer should use the 3-month forecast for January
because the smaller MAD indicates a more accurate forecast.
12-2. a., b.

Weighted
3-Month 3-Month
Moving Moving
Month Sales Average Average
1 5 — —
2 10 — —
3 6 — —
4 8 7.00 17.20
5 14 8.00 7.58
6 10 9.33 11.06
7 9 10.67 11.08
8 12 11.00 9.93
9 — 10.33 10.77
c. 3-month weighted 3-month The 3-month moving average forecast ap-
pears to be slightly more accurate.

12-3. a., b., and c.

3-Quarter Weighted
Moving 5-Quarter 3-Quarter
Average Moving Moving
Quarter Demand Forecast Error Average Error Average Error
1 105.00 — — — — — —
2 150.00 — — — — — —
3 93.00 — — — — — —
4 121.00 116.00 5.00 — — 113.95 7.15
5 140.00 121.33 18.67 — — 116.69 23.31
6 170.00 118.00 52.00 121.80 48.20 125.74 44.26
7 105.00 143.67 –38.67 134.80 –29.80 151.77 –46.77
8 150.00 138.33 11.67 125.80 24.20 132.40 17.60
9 150.00 141.67 8.33 137.20 12.80 138.55 11.45
10 170.00 135.00 35.00 143.00 27.00 142.35 27.65
11 110.00 156.67 –46.67 149.00 –39.00 160.00 –50.00
12 130.00 143.33 –13.33 137.00 –7.00 136.69 –6.60
13 — 136.67 — 142.00 — 130.20 —

d. Cumulative errors are:

3-quarter moving average,
5-quarter moving average,
Weighted 3-quarter moving average,
The weighted 3-quarter forecast appears to be the most accurate. All the forecasts exhibit a low bias.
There appears to be a slight upward trend in the demand data and a pronounced seasonal pattern with a
peak increase during the second quarter each year, followed by a substantial decrease in the third quar -
ter.
12-4.

12-5. a., b.

3-Semester Exponentially
Moving Smoothed
Semester Enrollment Average Forecast
1 270 — —
2 310 — 270.00
3 250 — 278.00
4 290 276.67 272.40
5 370 283.33 275.92
6 410 303.33 294.74
7 400 356.67 317.79
8 450 393.33 334.23
9 — 420.00 357.38
c. 3-semester exponentially smoothed 3-semester moving average appears to
be slightly more accurate.
12-6. a., b.

Adjusted
Exponentially
Exponentially Smoothed
Smoothed Forecast
Forecast (
Month Demand ( ) )
October 800 800.00 —
November 725 800.00 800.00
December 630 777.50 773.00
January 500 733.25 720.70
February 645 663.27 639.23
March 690 657.79 637.46
April 730 667.45 653.18
May 810 686.21 678.55
June 1200 723.35 724.64
July 980 866.34 895.98
August — 900.44 930.96
c. Exponentially smoothed MAPD = 1282.86/6910 = 18.6%
 Adjusted forecast MAPD = 1264.59/6910 = 18.3%
Both forecasts appear to be approximately equally accurate.

12-7.
Adjusted
Exponentially Linear
Exponen- Smoothed Trend
tially
Smoothed Forecast Line
Forecast (
Month Price ( ) )
1 62.70 62.70 — 64.15
2 63.90 62.70 62.70 64.75
3 68.00 63.18 63.32 65.36
4 66.40 65.10 65.78 65.97
5 67.20 65.62 66.25 66.57
6 65.80 66.25 66.88 67.18
7 68.20 66.07 66.46 67.79
8 69.30 66.92 67.45 68.39
9 67.20 67.87 68.53 69.01
10 70.10 67.60 67.98 69.61
11 — 68.60 69.17 70.22

Adjusted
Exponentially Exponentially Linear
Smoothed Smoothed Trend
Cumulative
Error 14.75 10.73 —
MAD 1.89 1.72 1.09
The linear trend line forecast appears to be the most accurate.
12-8.
Adjusted
Exponentially Linear
Exponentially Smoothed Trend
Smoothed Forecast Line
Occupancy Forecast (
Year Rate ( ) )
1 .75 .75 — .71
2 .70 .75 .75 .73
3 .72 .74 .74 .76
4 .77 .74 .73 .78
5 .83 .74 .74 .80
6 .81 .76 .76 .83
7 .86 .77 .77 .85
8 .91 .79 .80 .88
9 .87 .81 .82 .90
10 — .82 .83 .92

Exponentially
Smoothed Adjusted Linear Trend
Forecast Forecast Trend Forecast
.046 .044 —
MAD .064 .061 0.026
The linear trend line forecast appears to be the most accurate.

12-9. a. 3-month moving average forecast for month

b. 3-month weighted moving average forecast for month

c. Exponentially smoothed forecast for month

MAD = 2.99
d. The lowest MAD values are with both the weighted 3-month moving average forecast and the expo -
nentially smoothed forecast.

12-10. Group data into 3-month periods to forecast periods 19, 20 and 21.
Possible models include the following:

Exponential smoothing forecasts

Linear trend line forecasts

12-11.

Adjusted
Exponentially
Exponentially Smoothed
Ice Smoothed Forecast
Cream Forecast (
Quarter Sales ( ) ) Error
1 350 350.00 — —
2 510 350.00 350.00 160.00
3 750 430.00 470.00 280.00
4 420 590.00 690.00 –270.00
5 370 505.00 512.50 –142.50
6 480 437.50 407.50 72.50
7 860 458.75 454.37 405.62
8 500 659.37 757.50 –257.50
9 450 579.69 588.91 –138.91
10 550 514.84 487.03 62.97
11 820 532.42 527.30 292.69
12 570 676.21 745.55 –175.55
13 — 623.11 631.22 —

The forecast seems to be biased low.

12-12. Seasonal factors: Quarter 1:
Quarter 2:
Quarter 3:
Quarter 4:
Forecast for 2005:
Seasonally adjusted forecasts:

Quarter 1:

Quarter 2:

Quarter 3:

Quarter 4:

The seasonal factor seems to provide a more accurate forecast.

12-13. Seasonal factors: Quarter 1:
Quarter 2:
Quarter 3:
Quarter 4:
Forecast year 4:
 Seasonally adjusted forecasts:

Quarter 1:

Quarter 2:

Quarter 3:

Quarter 4:

12-14.
Day Daily Demand
1 212
2 182
3 215
4 201
5 158
6 176
7 212
8 188

Linear trend forecast for day 9:

12-15.
Adjusted
Exponentially Linear
Exponentially Smoothed Trend
Smoothed Forecast Line
Forecast (
Year Sales ( ) )
1 4,260.00 — — 4,478.33
2 4,510.00 4,260.00 4,260.00 4,266.67
3 4,050.00 4,335.00 4,350.00 4,055.00
4 3,720.00 4,249.50 4,244.40 3,843.33
5 3,900.00 4,090.65 4,054.80 3,631.67
6 3,470.00 4,033.45 3,993.34 3,420.00
7 2,890.00 3,864.42 3,798.52 3,208.33
8 3,100.00 3,572.09 3,460.91 2,996.67
9 — — 3,313.19 2,785.00

Adjusted
Exponentially
Smoothed Linear Trend
Forecast Line
MAD 431.71 166.25
E –2.522
The linear trend line forecast appears to be the most accurate.

12-16. a. Seasonally adjusted forecast

Linear trend line forecast for 2011:

January–March forecast for 2011:

April–June forecast for 2005:

 July–September forecast for 2005:

October–December forecast for 2005:

b. Linear trend line forecast for January–March 2005:

Linear trend line forecast for April–June 2005:

Linear trend line forecast for July–September 2005:

Linear trend line forecast for October–December 2005:

c.
Linear
Seasonally Trend
Adjusted Line
Year/Quarter Orders Forecast Forecast
2006 Jan–Mar 18.6 18.58 0.02 17.98 0.62
Apr–June 23.5 23.74 0.24 23.54 0.04
Jul–Sep 20.4 19.61 0.79 19.50 0.90
Oct–Dec 41.9 41.29 0.61 42.20 0.30
2007 Jan–Mar 18.1 19.82 1.72 19.67 1.57
Apr–June 24.7 25.32 0.62 25.33 0.63
Jul–Sep 19.5 20.92 1.42 20.65 1.15
Oct–Dec 46.3 44.04 2.26 44.46 1.84
2008 Jan–Mar 22.4 21.06 1.34 21.36 1.04
Apr–June 28.8 26.91 1.89 27.12 1.68
Jul–Sep 21.0 22.23 1.23 21.80 0.80
Oct–Dec 45.5 46.80 1.30 46.72 1.22
2009 Jan–Mar 23.2 22.30 0.90 23.05 0.15
Apr–June 27.6 28.49 0.89 28.91 1.31
July–Sep 24.4 23.54 0.86 22.95 1.45
Oct–Dec 47.1 49.56 2.50 48.98 1.88
2010 Jan–Mar 24.5 23.54 0.96 24.74 0.24
Apr–June 31.0 30.08 0.92 30.70 0.30
July–Sep 23.7 24.85 1.15 24.10 0.40
Oct–Dec 52.8 52.31 0.49 51.24 1.56

Seasonally adjusted forecast

Linear trend forecast for seasons

Although both forecasts seem to be relatively accurate, the linear trend line forecast for each season is slightly
more accurate according to MAD.
12-17.

Forecasts for 2005:

Fall:
Winter:
Spring:
Summer:

Yes, there does appear to be a seasonal pattern.

12-18.

Year
Time 1 2 3 4 5 6 Total
7:00 AM 56 64 66 60 72 65 383
8:00 31 41 37 44 52 46 251
9:00 15 22 24 30 19 26 136
10:00 34 35 38 31 28 33 199
11:00 45 52 55 49 57 50 308
Noon 63 71 57 65 75 70 401
1:00 PM 35 30 41 42 33 45 226
2:00 24 28 32 30 35 33 182
3:00 27 19 24 23 25 27 145
6:00 31 47 36 45 40 46 245
7:00 25 35 41 43 39 45 228
8:00 14 20 18 17 23 27 119
9:00 10 8 16 14 15 18 81
Total 410 472 485 493 513 531 2904

Linear Trend Line:

a= 410.40
b= 21.03
Linear trend line forecast for year 7 = 557.6

Year 7 Forecasts:
 SF1 (7:00)= 73.54
SF2 (8:00)= 48.19
SF3 (9:00)= 26.11
SF4 (10:00)= 38.21
SF5 (11:00)= 59.14
SF6 (noon)= 77.00
SF7 (1:00)= 43.39
SF8 (2:00)= 34.95
SF9 (3:00)= 27.84
SF10 (6:00)= 47.04
SF11 (7:00)= 43.78
SF12 (8:00)= 22.85
SF13 (9:00) = 15.55

12-19.

Exponentially Adjusted
Pool Smoothed Smoothed
Year Attendance Forecast Error Trend Forecast Error
1 410 410.00
2 472 410.00 62.00 0.0000 410.00 62.00
3 485 428.60 56.40 3.7200 432.32 52.68
4 493 445.52 47.48 6.3600 451.88 41.12
5 513 459.76 53.24 7.9368 467.70 45.30
6 531 475.73 55.27 9.5436 485.28 45.72
9 492.31 10.951 503.27
MAD = 49.364

12-20.
Patients per Period
Week-
Week Weekend days Total
1 105 73 178
2 119 85 204
3 122 89 211
4 128 83 211
5 117 96 213
6 136 78 214
7 141 91 232
8 126 100 226
9 143 83 226
10 140 101 241
Total 1277 879 2156

Linear Trend Line:

a = 186.93
b = 5.21
 Linear trend line forecast for Week 11 = 244.27

SF1 (weekend) = 144.68

SF2 (weekdays) = 99.59

12-21.

Linear trend line forecast for week 11:

Weekend forecast:
Weekday forecast:

Actual Forecast Running Cumulative Tracking

Month Demand Demand Error MAD Error Signal
1 160 170 –10 10 10.00 –10 –1.00
2 150 165 –15 15 12.50 –25 –2.00
3 175 157 18 18 14.33 –7 –0.49
4 200 166 34 34 19.25 27 1.40
5 190 183 7 7 16.80 34 2.02
6 220 186 34 34 19.67 68 3.46
7 205 203 2 2 17.14 70 4.08
8 210 204 6 6 15.75 76 4.83
9 200 207 –7 7 14.78 69 4.67
10 220 203 17 17 15.00 86 5.73
86 150

Cumulative error 86.00

Bias 8.60
MAD 15.00
MAPD 0.08
There is really no way to determine if this is an accurate forecast method unless it is compared with some
other method.

12-22. See Problem 12-21 solution for tracking signal values.

 The forecast appears to be biased low (i.e., actual demand exceeds the forecast).
12-23. There does not seem to be any high or low bias in the forecast.

12-24.

Cumulative Running Tracking

Year Error Error MAD Signal
1 — — —
2 250 250 250.00 1.00
3 –300 –50 275.00 –0.18
4 –524.4 –574.4 358.13 –1.60
5 –154.8 –729.4 307.30 –2.37
6 –523.34 –1,252.54 350.51 –3.57
7 –908.52 –2,161.06 443.51 –4.87
8 –360.91 –2,521.97 431.71 –5.84
 The control chart suggests the forecast is not performing accurately and is consistently biased high (i.e.,
the actual demand is consistently lower than the forecast).
12-26.
a.
Running Cumulative Tracking
Month Demand Fore- Error MAD Error Signal
cast
March 120 — — — — — —
April 110 120.0 –10.00 10.00 10.00 –10.0 –1.00
May 150 116.0 34.00 34.00 22.00 24.0 1.09
June 130 129.6 0.40 0.40 14.80 24.4 1.65
July 160 129.7 30.30 30.30 18.67 54.7 2.93
August 165 141.8 23.20 23.20 19.58 77.9 3.98
September 140 151.1 –11.10 11.10 18.17 66.8 3.67
October 155 146.7 8.30 8.30 16.76 75.1 4.48
November 150.0 75.10 117.30

Bias 10.73
MAD 16.76
MAPD 0.1038
Cumulative error 75.10
b.
3-Month
Moving
Month Demand Average Error
March 120 — — —
April 110 — — —
May 150 — — —
June 130 126.67 3.33 3.33
July 160 130.00 30.00 30.00
 3-Month
Moving
Month Demand Average Error
August 165 146.67 18.33 18.33
September 140 151.67 –11.67 11.67
October 155 155.00 0.00 0.00
November 153.33 39.99 63.33
Bias 8.00
MAD 12.67
MAPD 0.08
MSE 276.64
Cumulative error 39.99
The 3-month moving average seems to provide a better forecast.
c. The tracking signal moves beyond the 3 MAD control limit for July and continues increasing indicat -
ing the forecast is consistently biased low.

12-26. The 3-month moving average forecast appears to be more accurate.

Month De- Forecast Month Demand Forecast

mand
January 9 9.00 — August 11 9.27 1.73
Febru- 7 9.00 2.00 September 12 9.62 2.38
ary
March 10 8.60 1.40 October 10 10.09 0.09
April 8 8.88 0.88 November 14 10.07 3.92
May 7 8.70 1.70 December 16 10.86 5.14
June 12 8.36 3.64 January — 11.88 —
July 10 9.09 0.91

Moving Average Exponentially Smoothed

Forecast (Prob. 12-1a) (Prob. 12-20)
Mad 1.89 2.16

12.27.

According to these measures, the forecast appears to be fairly accurate.

Running Cumulative Tracking

Year Demand Forecast Error MAD Error Signal
1 16.8 16.8 0 — — —
2 14.1 16.8 2.70
3 15.3 15.7 1.55
4 12.7 15.5 1.97
5 11.9 14.4 2.10
6 12.3 13.4 1.90
7 11.5 12.9 1.82
8 10.4 12.4 1.79
 The tracking signal goes outside of the control limits beginning in year 4, indicating a forecast that is bi -
ased high.

Linear trend model:

Year Demand Forecast

1 16.80 15.87
2 14.10 15.10
3 15.30 14.33
4 12.70 13.56
5 11.90 12.79
6 12.30 12.02
7 11.50 11.24
8 10.80 10.47
9 — 9.70

The linear trend line forecast appears to be more accurate for MAD.

12-28. where rate and

Forecast if the Blue Sox win 85 games: occupancy rate.

yes;

12-29. a. where and

Forecast if 25 permits are filed:

b. The correlation coefficient is .914 indicating a strong causal relationship.

12-30. a. where of ice cream and Forecast for temperature

of

b. The correlation coefficient is 0.833, indicating a strong causal relationship.

12-31. Coefficient of indicating that 69.4% of the variation of ice cream sales
can be attributed to the temperature.
12-32. a. where and

If tuition is $10,000 forecast is applications.

If tuition is $7,000, forecast is applications.

b. The correlation coefficient is indicating a fairly strong linear relationship between tuition costs
and number of applicants.
c. Number of class sections, number of dormitory rooms, number of persons per class, plus numerous
budgeting decisions.
12-33.
 There seems to be a relatively strong relationship between production time and defects.
Forecast for “normal” production time of 23 minutes:

defects

12-34.
which indicates a fairly strong relationship between hits and orders

which means 55.3% of the variation in orders can be attributed to the number of web site hits.

At 60,000 hits/month, =10.4 or 10,400 orders

12-35.

Linear Trend
Year Application Line Forecast
1 6,010 6,069.72
2 5,560 5,886.12
3 6,100 5,702.51
4 5,330 5,518.91
5 4,980 5,335.30
6 5,870 5,151.69
7 5,120 4,968.09
8 4,750 4,784.78
9 4,615 4,600.88
10 4,100 4,417.27
11 — 4,233.66

Correlation
a. The linear regression forecast (from Problem 12-30) has a MAD value of 310 whereas the MAD value
for the linear trend line forecast in this problem is 256, indicating that the linear trend line forecast is
somewhat better.
b. The correlation coefficient is indicating a strong relationship between applications and time.

12-36. The slope, indicates the rate of change, that is, the number of gallons sold for each degree in-
crease in temperature.
12-37. a.

b.

c. MAD for the linear trend line forecast in a. equals 85.69 while MAD for the linear regression forecast
in b. equals 45.20. In addition, the correlation coefficient for the linear trend is whereas the
correlation coefficient for the linear regression is This evidence seems to indicate the fore-
cast model in b is best.
12-38.

Year Demand Forecast

1 381 —
2 579 381.00
3 312 440.40
4 501 401.88
5 296 431.62
6 415 390.93
7 535 398.85
8 592 439.21
9 607 485.04
10 473 521.63
11 507.04

The exponential smoothing forecast appears to be less accurate than the linear regression
forecast developed in 12-35a.

12-39. a. Seasonally adjusted forecast.

Quarter 1:

Quarter 2:

Quarter 3:

Quarter 4:
 Linear trend line forecast for year 6: ; ;

b. Quarter 1:

=60.64
Quarter 2:

Quarter 3:

Quarter 4:

c. This is an intuitive assessment, which managers must do on occasion. In general, the linear regression
forecast provides a more conservative estimate.

12-40. The adjusted exponentially smoothed forecast has a first quarter forecast for year 6 of
75.68 percent seat occupancy. It has a (bias) value of 1.08 and a MAD value of 8.6, which seem low.
Thus, this may be the best overall forecast model compared to the one developed in 12-37a.

12-41. The following table shows several different forecast models developed using Excel and selected mea -
sures of forecast accuracy.
 Year 25
Forecast Method Forecast MAD (bias)
Moving average 5.89 1.58 .127
Linear trend line 8.22 1.86 0.000
Exponential smoothing
6.64 1.59
Exponential smoothing
6.13 1.29 .031
Exponential smoothing
6.24 1.33
Exponential smoothing
5.94 1.22 0.003

Although this selection of forecast models is not exhaustive, it does seem to indicate the exponential
smoothing models are the most accurate, especially the adjusted model with ( and ).
12-42.

12-43. (a) Forecast of applicants:

Forecast of % acceptances:

(b) Forecast of % offers:

(c) If the forecast of % acceptances is accurate then the number of applicants is not relevant; 12,634 offers
will yield 5,000 acceptances.

12-44. (a)

(b)

There appears to be a very strong linear relationship

12-45. (a)

(b)

The club should use the linear regression model. The correlation coefficient shows that town population is
a good predictor of the growth in the number of club players plus it provides a more favorable forecast for
the club.

12-46. (a)

(b)

Very little difference between the two forecasts. Annual budget appears to replicate endowment.

12-47. where and expenditures.

Correlation
The correlation coefficient indicates a weak linear relationship between sales and promotion, thus a linear
regression model should not be used.
12-48. We tested 3 forecasting methods, as follows.

Adjusted
Exponentially
Linear Smoothing
Trend 3-Month Forecast
Line Moving (
Month Demand Forecast Average )
1 8.20 8.24 — 18.20
2 7.50 8.42 — 8.20
3 8.10 8.59 — 7.99
4 9.30 8.77 7.93 8.02
5 9.10 8.95 8.30 8.40
6 9.50 9.13 8.83 8.61
7 10.40 9.31 9.30 8.88
8 9.70 9.49 9.67 9.34
9 10.20 9.67 9.87 9.44
10 10.60 9.84 10.10 9.67
11 8.20 10.02 10.17 9.95
12 9.90 10.20 9.67 9.42
13 10.30 10.38 9.57 9.57
15 11.70 10.74 10.23 10.00
16 9.80 10.92 10.83 10.51
17 10.80 11.09 10.67 10.30
14 10.50 10.56 9.47 9.79
18 11.30 11.27 10.77 10.45
19 12.60 11.45 10.63 10.70
20 11.50 11.63 11.57 11.27
21 10.80 11.81 11.80 11.34
22 11.70 11.99 11.63 11.18
23 12.50 12.17 11.33 11.33
24 12.80 12.34 11.67 11.68
25 — 12.52 12.33 12.29

Forecasting Alternatives MAD E

Linear trend line 0.546 —
3-month moving average 0.825 9.2
Adjusted exponential smoothing 0.817 9.47
All three methods we chose to evaluate appear to be relatively accurate. The student might select another
method that will be more accurate.

12-49. a.

b.

c.
12-50. a. y = 144.67 + 0.371X1 – 0.307X2

b.

c. = 144.67 + 0.371(1500)-0.307(300) = 608.50

12-51. a.

b.

c.

12-52. Selected forecast models 5-day moving average forecasts for day 21:

Exponentially smoothed forecasts for day 21:

Linear trend line forecasts for day 21:

The “best” forecast model depends on what models are selected for comparison. For the models tested
above, they all seem to be relatively close, although the linear trend model consistently had the highest
next period forecast and a slightly lower MAD value.

12-53. a.

where

b.
Approximately 70% of the amount of variation in SOL scores can be attributed to teacher salaries and
tenure. This is a moderately strong relationship indicating the superintendent is at least partially right.

c.

No, the SOL score would only increase to 76.66.

CASE 12.1: Forecasting at State University
Forecasting would be appropriate in a number of different areas. The university needs to be able to forecast future
applications and enrollments both in the short and long term. A forecast of the college age population that will ap -
ply to State is very important for planning purposes. A multiple regression model that related applications to vari -
ables such as population, tuition levels, and entrance requirements would probably be most appropriate for this
purpose.
Internal forecasts for classroom space, facilities, dormitory space, dining, etc., would enhance the planning
process. Times series methods would probably be sufficient for this type of forecasting.
The university might consider using a forecasting model to determine future funding from the state. Several
models, such as a multiple regression and perhaps a qualitative technique like the Delphi method might be com -
bined. Forecasts for other sources of funding such as endowments and tuition increases could be forecast using
more conventional methods such as regression or time series.
The university’s TQM approach requires a forecast of what customers perceive educational quality to be in the
future—that is, a definition of quality according to students, parents, and legislators. In-house forecasting using
key administrators, faculty, and students might be appropriate. Surveys and market research techniques of alumni,
students, and parents might be useful in determining what quality factors will be important in the future.

CASE 12.2: The University Bookstore Student Computer Purchase Program

The following table shows several different forecast models developed using POM for Windows and selected
measures of forecast accuracy.

Year 25
Forecast Method Forecast MAD (bias)
Moving average 1,004.66 96.96 66.00
Linear trend line 1,020.07 73.24 0.00
Exponential smoothing
941.53 126.88 108.59
Exponential smoothing
1,003.70 104.95 74.72
Exponential smoothing
983.22 109.58 62.19
Exponential smoothing
1,031.09 105.13 61.31

Although this selection of different models is not exhaustive, it does seem to indicate that the linear trend line
model is the best.
Other forecast models that the bookstore might consider include forecasts of student enrollment and entering
freshmen. Also for longer term forecasts the bookstore could investigate which different majors and classes might
be moving to more extensive computer usage in the future, thus driving up long run student demand. Additionally
forecasts for other products would help the bookstore plan their inventory, warehouse usage and distribution bet -
ter.
CASE 12.3: Cascades Swim Club
Attendance

Week
Day 1 2 3 4 5 6 7 8 9 10 11 12 13 Total
M 139 198 341 287 303 242 194 197 275 246 224 258 235 3,139
T 273 310 291 247 223 177 207 273 241 177 239 130 218 3,006
W 172 347 380 356 315 245 215 213 190 161 274 195 271 3,334
Th 275 393 367 322 258 390 304 303 243 308 205 238 259 3,865
F 337 421 359 419 193 284 331 262 277 256 361 224 232 3,956
Sa 402 595 463 516 378 417 407 447 241 391 411 368 317 5,353
Su 487 497 578 478 461 474 399 399 384 400 419 541 369 5,886
Total 2,085 2,761 2,779 2,625 2,131 2,229 2,057 2,094 1,851 1,939 2,133 1,954 1,901 28,539
 The seasonal factors for each weekday are as follows:

The linear trend line equation computed from the 13 weekly totals is,

Using this forecast model to forecast weekly demand for each of the 13 weeks for the next summer and multi -
plying each weekly forecast by the daily seasonal factors will give the daily forecast for the next summer. For ex -
ample, the daily forecast for week 1 is computed as,

Week 1 Forecasts

The remaining 12 weeks of daily forecasts would be developed similarly.

If the board of directors perceived that the pattern of weekly attendance totals would be closely followed next
summer—i.e., low demand in the first week followed by high demand in weeks 2, 3 and 4 followed by gradually
declining demand for the remaining 9 weeks—then a seasonally adjusted forecast could be used. That is, seasonal
factors could be developed for all 13 weeks, and, weekly forecasts could be computed by multiplying these
weekly seasonal factors by the projected summer total attendance, rather than using the linear trend like forecast
to compute forecasted weekly attendance.
CASE 12.4 – FORECASTING ARIPORT PASSENGER ARRIVALS

Seasonal factors:

6-8 am 111,000/677,200 = .164

8-10 am 116,100/677,200 = .171
10- Noon 65,200/677,200 = .096
Noon – 2 pm 80,700/677/200 = .119
2-4 pm 85,300/677,200 = .126
4-6 pm 74,800/677,200 = .110
6-8pm 34,600/677,200 = .051
8-10pm 10,600/677,200 = .016

(A) Linear trend line forecast for year 4 developed by averaging 10 sample days for each
year, creating 3 data point:
y = 11,413.3 + 5580 x
y (4) = 33,733.3

(B) Linear trend line forecast for year 4 developed using all 30 sample data points:
y = 14,893 + 503.62 x
y (31) = 30,505.2
 Seasonally Adjusted Forecast (A) Seasonally Adjusted Forecast (B)

6-8 am 5529.24 5000.12

8-10 am 5783.28 5229.85
10- Noon 3247.80 2937.01
Noon – 2 pm 4019.91 3635.22
2-4 pm 4249.05 3842.43
4-6 pm 3726.01 3369.45
6-8pm 1723.53 1558.60
8-10pm 528.02 477.59