11
FORECASTING CHAPTER MODELS
SOLUTIONS TO DISCUSSION QUESTIONS
11-1. The steps that are used to develop any forecasting system are:
1. Determine the use of the forecast.
2. Select the items or quantities that are to be forecasted.
3. Determine the time horizon of the forecast.
4. Select the forecasting model.
5. Gather the necessary data.
6. Validate the forecasting model.
7. Make the forecast.
8. Implement the results.
11-2. A time-series forecasting model uses historical data to predict future trends.
11-3. The only difference between causal models and time-series models is that causal models take into
account any factors that may influence the quantity being forecasted. Causal models use historical data as
well. Time-series models use only historical data.
11-4. Qualitative models incorporate subjective factors into the forecasting model. Judgmental models are
useful when subjective factors are important. When quantitative data are difficult to obtain, qualitative
models are appropriate.
11-5. Least squares refers to holding the sum of the square of the difference between the observed values
and the regression line to a minimum.
11-6. The disadvantages of the moving average forecasting model are that the averages always stay within
past levels, and the moving averages require extensive record keeping of past data.
11-7. When the smoothing value, , is high, more weight is given to recent data. When is low, more
weight is given to past data.
11-8. The Delphi technique involves analyzing the predictions that a group of experts have made, and
then allowing the experts to review the data again. This process may be repeated several times. After the
final analysis, the forecast is developed. The group of experts may be geographically dispersed.
11-9. MAPE is a measure for determining the accuracy of a forecasting model by taking the average of
the absolute percent errors. MAPE is important because it can be used to help increase forecasting
accuracy.
11-10. We can draw line plots of the actual and forecast values for each observation (or time period).
Such line plots are automatically drawn by most forecasting software including ExcelModules. The line
plots can be used to show whether there are sizable errors in the forecast. In addition, they can be used to
detect whether the forecasting model does a good job of replicating the pattern of actual values over the
past few time periods. For the model to be valid, there should be no consistent under- or over-forecast
seen, and forecast errors must be randomly distributed.
11-11. The correlation coefficient is a measure of the strength of the linear relationship between two
variables. That is, it measures how one variables value is linearly related to changes in the value of the
other variable. It is usually denoted by r and can be any number between and including -1 and +1. A value
of +1 indicates the two variables are perfectly correlated in a positive manner (i.e., if either variable
increases in value, the other one follows suit). A value of -1 indicates the two variables are perfectly
correlated in a negative manner. Finally, a value of 0 indicates the two variables are not linearly
correlated.
11-12. In order to use Solver to determine the optimal weights in the weighted moving average model, we
set the weights as the decision variables (or Changing Cells). The objective (or Target Cell) is the
measure of forecast error, such as MAD, MSE, or MAPE, which we wish to minimize. If we want to
specify that the weights must add up to 1, we must include it as a constraint in the model. The only other
constraint is the non-negativity constraint on the decision variables (weights). The Assume Linear Model
option should not be checked in solving this problem since the formula for the objective function is
nonlinear.
SOLUTIONS TO PROBLEMS
11-13.
(a, b, and c) See file P11-13.XLS, sheets 2-MA, 3-MA, 4-MA, 3-WMA, and Exp Sm.
Period Actual Value 2-per MA 3-per MA 4-per MA 3-per WMA Exp Sm (0.3)
Year 1
4
5.000
Year 2
6
4.700
Year 3
4
5.000
5.090
Year 4
5
5.000
4.667
4.500
4.763
Year 5
10
4.500
5.000
4.750
5.000
4.834
Year 6
8
7.500
6.333
6.250
7.250
6.384
Year 7
7
9.000
7.667
6.750
7.750
6.869
Year 8
9
7.500
8.333
7.500
8.000
6.908
Year 9
12
8.000
8.000
8.500
8.250
7.536
Year 10
14
10.500
9.333
9.000
10.000
8.875
Year 11
15
13.000
11.667
10.500
12.250
10.412
Year 12
14.500
13.667
12.500
14.000
11.789
(d) MAPE2-MA= 22.57%, MAPE3-MA= 22.92%, MAPE4-MA= 27.07%, MAPE3-WMA= 21.17%, MAPEExp Sm =
25.50%. The three-year weighted moving average should be selected because it has the lowest MAPE.
11-14.
(a and b) See file P11-14.XLS, sheets 3-MA and Exp Sm.
Period Actual Value 3-per MA Exp Sm (0.3)
Sem 1
2.2
2.200
Sem 2
2.7
2.200
Sem 3
2.5
2.350
Sem 4
2.4
2.467
2.395
Sem 5
3.0
2.533
2.397
Sem 6
Sem 7
Sem 8
Sem 9
Sem 10
MAPE
2.7
2.5
3.6
3.2
2.633
2.700
2.733
2.933
3.100
10.20%
2.578
2.614
2.580
2.886
2.980
11.51%
(c) The three-period moving average should be selected, as it has the lowest MAPE.
(d) See file P11-14.XLS, sheet 3-WMA.
Period Actual Value 3-per WMA
Sem 1
2.2
Sem 2
2.7
Sem 3
2.5
Sem 4
2.4
2.320
Sem 5
3.0
2.580
Sem 6
2.7
2.700
Sem 7
2.5
2.520
Sem 8
3.6
2.800
Sem 9
3.2
3.060
Sem 10
2.780
MAPE
7.46%
Optimal weights (found using Goal Seek) for WMA are 1.794, 0, and 1.196, respectively, for periods 1
(earliest) to 3 (latest). This is an improvement over the prior methods.
11-15. See file P11-15.XLS, sheets 2-MA, 3-MA, and 4-MA.
Period Actual Value 2-per MA 3-per MA
Day 1
522
Day 2
318
Day 3
508
420.000
Day 4
652
413.000 449.333
Day 5
488
580.000 492.667
Day 6
556
570.000 549.333
Day 7
589
522.000 565.333
Day 8
575
572.500 544.333
Day 9
606
582.000 573.333
Day 10
625
590.500 590.000
Day 11
615.500 602.000
4-per MA
500.000
491.500
551.000
571.250
552.000
581.500
598.750
11-16.
(a and b) See file P11-16.XLS, sheets Exp Sm and LTA. The optimal weight for the exponential
smoothing model is 0.27 (found using Solver). The linear trend equation is [438.667 + 19.133 Day].
Period Actual Value
Day 1
522
Day 2
318
Day 3
508
Exp Sm
522.000
522.000
466.659
LTA
457.800
476.933
496.067
Day 4
Day 5
Day 6
Day 7
Day 8
Day 9
Day 10
Day 11
652
488
556
589
575
606
625
477.874
525.111
515.043
526.154
543.203
551.829
566.524
582.387
515.200
534.333
553.467
572.600
591.733
610.867
630.000
649.133
(c) The method with the lowest MAPE should be selected. In this case, it is the 4-period moving average
model, with MAPE = 6.17%.
11-17. See file P11-17.XLS, sheets 2-MA, 3-MA, and 4-MA.
Period Actual Value 2-per MA 3-per MA
Week 1
17
Week 2
22
Week 3
25
19.500
Week 4
16
23.500
21.333
Week 5
28
20.500
21.000
Week 6
23
22.000
23.000
Week 7
19
25.500
22.333
Week 8
20
21.000
23.333
Week 9
17
19.500
20.667
Week 10
25
18.500
18.667
Week 11
33
21.000
20.667
Week 12
32
29.000
25.000
Week 13
32.500
30.000
4-per MA
20.000
22.750
23.000
21.500
22.500
19.750
20.250
23.750
26.750
11-18.
(a and b) See file P11-18.XLS, sheets 3-WMA and Exp Sm. Optimal weights (found using Solver; Set sum
of weights to 1) for WMA are 0, 0.417, and 0.583, respectively, for periods 1 (earliest) to 3 (latest). The
optimal weight for the exponential smoothing model (also found using Solver) is 0.14.
Period Actual Value 3-per WMA
Week 1
17
Week 2
22
Week 3
25
Week 4
16
23.750
Week 5
28
19.750
Week 6
23
23.000
Week 7
19
25.083
Week 8
20
20.667
Week 9
17
19.583
Week 10
25
18.250
Week 11
33
21.667
Week 12
32
29.667
Week 13
32.417
Exp Sm
17.000
17.000
17.702
18.727
18.344
19.700
20.163
20.000
20.000
19.579
20.340
22.118
23.506
(c) Exponential smoothing should be selected because it has the lower MAPE (although both models are
close).
11-19.
(a, b, and c) See file P11-19.XLS, sheets Exp Sm 0.3, Exp Sm 0.6, Exp Sm 0.9, 3-MA, and LTA. The linear
trend equation is [421.2 + 33.6 Year]. Of the three exponential smoothing constants, = 0.9 gives the
forecast with the lowest MAPE (7.05%).
Period Actual Value Exp Sm (0.3) Exp Sm (0.6) Exp Sm (0.9)
Year 1
450
410.000
410.000
410.000
Year 2
495
422.000
434.000
446.000
Year 3
518
443.900
470.600
490.100
Year 4
563
466.130
499.040
515.210
Year 5
584
495.191
537.416
558.221
Year 6
521.834
565.366
581.422
3-per MA
487.667
525.333
555.000
LTA
454.800
488.400
522.000
555.600
589.200
622.800
(d) Of all the models, linear trend analysis is preferred because it has the lower overall MAPE (1.08%).
11-20.
(a, b, and c) See file P11-20.XLS, sheets 3-WMA, Exp Sm, and LTA. The linear trend equation is [20.121
+ 0.622 Week].
Period Actual Value 3-per WMA
Week 1
20
Week 2
24
Week 3
21
Week 4
25
21.714
Week 5
19
23.714
Week 6
23
21.000
Week 7
26
22.143
Week 8
24
24.143
Week 9
27
24.429
Week 10
27
26.000
Week 11
25
26.571
Week 12
29
25.857
Week 13
27.571
Exp Sm
20.000
20.000
21.600
21.360
22.816
21.290
21.974
23.584
23.751
25.050
25.830
25.498
26.899
LTA
20.744
21.366
21.988
22.611
23.233
23.855
24.478
25.100
25.723
26.345
26.967
27.590
28.212
(d) Linear trend analysis should be used because it has the lowest MAPE (7.11%).
11-21.
(a) See file P11-21.XLS, sheet Scatterplot for the graph. The observations do not form a perfect straight
line but seem to approach linearity over the range shown.
(b and c) See file P11-21.XLS, sheet Regress. The linear regression equation is Average Demand = 1.0 +
1.0 TV Appearances. If Green Shades performed 9 times last month, the forecast is for an average
demand of 10 brass drums this month.
11-22.
(a and b) See file P11-22.XLS, sheets 3-MA and 3-WMA.
Month Actual Value 3-per MA 3-per WMA
Jan
11
Feb
14
Mar
16
Apr
10
13.667
14.500
May
15
13.333
12.667
Jun
17
13.667
13.500
Jul
11
14.000
15.167
Aug
14
14.333
13.667
Sep
17
14.000
13.500
Oct
12
14.000
15.000
Nov
14
14.333
14.000
Dec
16
14.333
13.833
Jan
11
14.000
14.667
Feb
13.667
13.167
(c) MAPE for 3-per MA is 17.14% while MAPE for 3-per WMA is 21.37. Choose the 3-per MA model.
11-23.
(a) See file P11-23.XLS, sheets Exp Sm 0.1, Exp Sm 0.6, and Exp Sm 0.9.
Period Actual Value Exp Sm (0.1) Exp Sm (0.6) Exp Sm (0.9)
Week 1
50
50.000
50.000
50.000
Week 2
35
50.000
50.000
50.000
Week 3
25
48.500
41.000
36.500
Week 4
40
46.150
31.400
26.150
Week 5
45
45.535
36.560
38.615
Week 6
35
45.482
41.624
44.362
Week 7
20
44.433
37.650
35.936
Week 8
30
41.990
27.060
21.594
Week 9
35
40.791
28.824
29.159
Week 10
20
40.212
32.530
34.416
Week 11
15
38.191
25.012
21.442
Week 12
40
35.872
19.005
15.644
Week 13
55
36.284
31.602
37.564
Week 14
35
38.156
45.641
53.256
Week 15
25
37.840
39.256
36.826
Week 16
55
36.556
30.703
26.183
Week 17
55
38.401
45.281
52.118
Week 18
40
40.061
51.112
54.712
Week 19
35
40.055
44.445
41.471
Week 20
60
39.549
38.778
35.647
Week 21
75
41.594
51.511
57.565
Week 22
50
44.935
65.604
73.256
Week 23
40
45.441
56.242
52.326
Week 24
Week 25
65
44.897
46.907
46.497
57.599
41.233
62.623
(b) Students should note how stable the smoothed values are for = 0.1. When compared to actual week
25 calls of 85, the = 0.6 model appears to do a better job. On the basis of the forecast error also, the =
0.6 model is better. However, other smoothing constants need to be examined. For example, using Solver
we find that the smoothing constant that minimizes MAPE is 0.279. The MAPE in this case is 35.06%.
11-24.
(a) See file P11-24.XLS, sheets Exp Sm 0.2, Exp Sm 0.5, and Exp Sm 0.9.
Period Actual Value Exp Sm (0.2) Exp Sm (0.5) Exp Sm (0.9)
Week 1
17
17.000
17.000
17.000
Week 2
21
17.000
17.000
17.000
Week 3
19
17.800
19.000
20.600
Week 4
23
18.040
19.000
19.160
Week 5
18
19.032
21.000
22.616
Week 6
16
18.826
19.500
18.462
Week 7
20
18.260
17.750
16.246
Week 8
18
18.608
18.875
19.625
Week 9
22
18.487
18.438
18.162
Week 10
20
19.189
20.219
21.616
Week 11
15
19.351
20.109
20.162
Week 12
22
18.481
17.555
15.516
Week 13
19.185
19.777
21.352
(b) If = 0.2, MAPE = 13.40%. If = 0.5, MAPE = 14.79%. If = 0.9, MAPE = 18.40%. The forecast
with = 0.2 has the lowest MAPE, and should therefore be used.
11-25.
(a) See file P11-25.XLS, sheets Exp Sm 0.1 and Exp Sm 0.3.
Month Actual Value Exp Sm (0.1) Exp Sm (0.3)
Jan
70.0
65.0
65.000
Feb
68.5
65.5
66.500
Mar
64.8
65.8
67.100
Apr
71.7
65.7
66.410
May
71.3
66.3
67.997
Jun
72.8
66.8
68.988
Jul
70.0
65.0
65.000
Aug
67.4
70.132
(b) If = 0.1, MAPE = 5.91%. If = 0.3, MAPE = 4.74%. The forecast with = 0.3 has the lowest
MAPE, and should therefore be used.
(c) See file P11-25.XLS, sheet Exp Sm Opt. The optimal value for (found using Solver) is 0.7, which
results in a MAPE of 3.65%.
11-26.
(a) See file P11-26.XLS, sheets (a) Exp Sm, (a) LTA, and (a) Regr. Comparing the MAPE values for the
three models, we see that MAPE Exp Sm = 20.89%. MAPELTA = 1019.32%, and MAPERegr = 707.88%. The
exponential model smoothing seems to be the clear choice for the best model.
(b) We can easily make a case for excluding older data. If we do so, the conclusions may change. For
example, if we include the data for just the last 16 years (1989 onwards), the revised MAPE values are
MAPEExp Sm = 17.05%, MAPELTA = 14.83%, and MAPEReg = 28.20%. See file P11-26.XLS, sheets (b) Exp
Sm, (b) LTA, and (b) Regr.
11-27.
(a) See file P11-27.XLS, sheet LTA. The trend equation is Average Ridership = 11.288 + 1.738 Year. The
forecasted riderships for years 13, 14, and 15 are 33.879, 35.617, and 37.354, respectively. The MAPE is
26%, indicating that the LTA model may not be very effective.
(b) See file P11-27.XLS, sheet Scatterplot. It appears from the graph that the points scatter around a
straight line.
(c) The linear equation is Average Ridership = 5.060 + 1.593 Tourists.
(d) Expected ridership for 10 million tourists is 2,099,000 riders.
11-28. See file P11-28.XLS.
The trend equation is Average Patients = 29.733 + 3.285 Year. For years 11, 12 and 13, the forecasted
patients are 65.867, 69.152, and 72.436 respectively. Comparing the trend line with the actual
observations, we see that the model is reasonably accurate (albeit not exceptionally accurate). The MAPE
is 7.01%.
11-29.
(a) See file P11-29.XLS, sheet Scatterplot. It appears from the graph that the points scatter around a
straight line.
(b) Average Patients = 1.229 + 0.545 Crime Rate
(c) If crime rate = 131.2, average patients = 72.7.
(d) If crime rate = 131.2, average patients = 50.6.
11-30. See file P11-30.XLS.
The seasonal indices are 0.90 for fall, 1.30 for winter, 0.63 for spring, and 1.17 for summer. Seasonalized
demand in year 3 for these four seasons is forecast to be 270, 390, 189, and 351 radials, respectively.
11-31. See file P11-31.XLS.
Seasonalized sales forecast = Trend forecast x seasonal index.
Hence the seasonalized forecasts for quarters I to IV are $130,000, $108,000, $98,000, and $176,000
respectively.
11-32. See file P11-32.XLS.
(a) Average Dividends = -0.101 + 0.351 EPS
(b) The R2 value for this model is 0.69. Hence, earnings per share (EPS) explains 69% of the variance in
dividends per share (DPS).
(c) When EPS = $0.33, average DPS = $0.015.
11-33. See file P11-33.XLS.
(a) Average GPA = 1.028 + 0.003 SAT. As an indication of the usefulness of this relationship, we can
calculate the correlation coefficient r = 0.692 and r2 = 0.479. A correlation coefficient of 0.692 is not
particularly high. The coefficient of determination indicates that the model explains only 47.9% of the
overall variation. Therefore, while the model does provide an estimate of GPA, there is considerable
variation in GPA, which is as yet unexplained.
(b) If SAT = 450, the average GPA is 2.38
(c) If SAT = 450, the average GPA is 3.77. However, SAT of 800 is outside the range of independent
variable values for which this regression model was developed. It may therefore not be appropriate to use
this model to predict Sarahs score.
11-34. See file P11-34.XLS.
(a) Average Market Value = 17,227.294 - 0.096 Mileage
(b) R2 = 0.722, which implies 72.2% of the variation in market value is explained by mileage.
(c) At 45,700 miles, the market value is predicted to be $12,861.75. To build a 95% confidence interval,
we compute 12,861.75 2.26 standard error. This results in an interval from $10,341.19 to $15,382.32.
11-35. See file P11-35.XLS.
(a) The prediction equation is: Average Mileage = 16,699.519 - 0.039 Mileage - 507.303 Age
(b) R2 = 0.739, which implies 73.9% of the variation in market value is explained by mileage and age.
(c) The revised interval is from $9,754.76 to $14,979.50. Because more variance has been accounted for,
the interval changes slightly.
11-36. See file P11-36.XLS.
(a) Average GPA = 2.094 + 0.002 GMAT
(b) R2 = 0.439, which implies 43.9% of the variation in GPA is explained by GMAT scores.
(c) 3.22 to 3.96
11-37. See file P11-37.XLS.
(a) Average GPA = 1.378 + 0.002 GMAT + 0.034 Age
(b) R2 = 0.695, which implies 69.5% of the variation in GPA is explained by the combination of GMAT
scores and age.
(c) 3.223 to 3.801. The added predictive power of age changes the size of the confidence interval.
11-38. See file P11-38.XLS.
(a) Average Demand = 13.937 +0.005 Advertising dollars
(b) R2 = 0.454, which implies 45.4% of the variation in demand is explained by advertising dollars spent.
(c) The predicted demand for an advertising budget of $3,600 is 33.244 units.
11-39. See file P11-39.XLS.
(a) Average Demand = 13.249 + 0.004 Advertising dollars + 0.104 Snowfall
(b) R2 = 0.461, which implies 46.1% of the variation in demand is explained by advertising dollars spent
and annual snowfall.
(c) The predicted demand for an advertising budget of $3,600 and expected snowfall of 360 inches is
34.030 units.
11-40. See file P11-40.XLS for the calculations using centered moving averages. We have data for 48
periods with 12 seasons (months) per year. The MAPE is 4.58% indicating that the multiplicative
decomposition model does a reasonable job of predicting quarterly sales. This is also indicated by the
error graph, which shows that the forecasted and actual values are very close to each other. Seasonalized
forecasts for the 12 months of 2005 are 56,483.303, 66,054.361, 23,927.390, 28,619.656, 27,562.990,
16,483.092, 17,497.696, 19,545.717, 20,013.797, 62,135.426, 93,005.609, and 83,282.348 respectively.
11-41. See file P11-41.XLS for the calculations using centered moving averages. We have data for 16
periods, with 4 seasons (quarters) per year. The MAPE is just 1.06% indicating that the multiplicative
decomposition model does a very good job of predicting quarterly sales. This is also indicated by the error
graph, which shows that the forecasted and actual values are nearly identical. Seasonalized forecasts for
the 4 quarters of 2005 are 59.451, 66.134, 72.848, and 98.331 respectively.
11-42.
(a) See file P11-42.XLS, sheet Exp Sm. The optimal value of (found using Solver) is 1. MAPE = 1.09%.
(b) See file P11-42.XLS, sheet LTA. The linear trend equation is Average GNP = 8550.825 + 112.476
Time period. MAPE = 0.76%. Forecast for first quarter of 2005 is 10,462.925.
(c) See file P11-42.XLS, sheet 4-MA. MAPE = 2.79%. Forecast for first quarter of 2005 is 10,104.
(d) Linear trend analysis should be selected because it has the lowest MAPE.
11-43. See file P11-43.XLS for the calculations using centered moving averages. We have data for 16
periods, with 4 seasons (quarters) per year. The MAPE for this model is 0.76%. Seasonalized forecasts for
the 4 quarters of 2005 are 10,473.877, 10,580.211, 10,657.009, and 10,818.609 respectively.
11-44.
(a) See file P11-44.XLS, sheet Exp Sm. The gasoline price for January of Year 4 is $1.24.
(b) See file P11-44.XLS, sheet Exp Sm. The linear trend equation is Average Gas Price = 1.156 + 0.012
Period. The gasoline price for January of Year 4 is $1.598.
(c) Exponential smoothing is more accurate with a MAPE of 5.66%.
11-45. See file P11-45.XLS. We have data for 36 periods with 12 seasons (months) per year. The MAPE
for this model is 8.71%. Seasonalized forecasts for the 12 months of Year 4 are 1.490, 1.535, 1.613,
1.658, 1.752, 1.786, 1.696, 1.681, 1.720, 1.690, 1.667, and 1.638 respectively.
11-46.
(a) See file P11-46.XLS, sheet 4-MA. Forecast for first quarter of Year 5 is 359.250. MAPE = 8.75%.
(b) See file P11-46.XLS, sheet LTA. The linear trend equation is Average Sales = 335.775 + 2.696
Quarter. Forecast for first quarter of Year 5 is 381.6. MAPE = 8.67%.
(c) The linear trend model is slightly more accurate as it has a lower MAPE.
11-47.
(a) See file P11-47.XLS, sheet Mult. Seasonalized forecasts for the 4 quarters of Year 5 are 335.740,
348.626, 372.056, and 426.170 respectively. MAPE = 4.41%.
(a) See file P11-47.XLS, sheet Add. Seasonalized forecasts for the 4 quarters of Year 5 are 335.258,
347.784, 371.059, and 423.335 respectively. MAPE = 4.34%.
(c) The additive decomposition model has a slightly lower MAPE.
11-48.
(a) See file P11-48.XLS, sheet 4-MA. Forecast for first quarter of year 5 is 448.25. MAPE = 23.31%.
(b) See file P11-48.XLS, sheet Exp Sm. Forecast for first quarter of year 5 is 470.606. MAPE = 24.20%
(c) The four-period moving average is slightly more accurate as it has a lower MAPE.
11-49. See file P11-49.XLS.
(a) See file P11-49.XLS, sheet Mult. Seasonalized forecasts for the 4 quarters of Year 5 are 397.769,
588.836, 587.768, and 446.333 respectively. MAPE = 11.48%.
(a) See file P11-49.XLS, sheet Add. Seasonalized forecasts for the 4 quarters of Year 5 are 405.142,
567.794, 564.197, and 452.391 respectively. MAPE = 10.82%.
(c) The additive decomposition model has a slightly lower MAPE.
Case: North-South Airline
See file P11-Airline.XLS. Utilizing ExcelModules, we can develop the following regression equations for
the variables of interest. Each regression is shown on a separate worksheet.
Northern Airline -- Airframe maintenance cost:
Cost = 36.097 + 0.0026 x Airframe age. R2 = 0.769. Coefficient of correlation = 0.877.
Northern Airline -- Engine maintenance cost:
Cost = 20.571 + 0.0026 x Airframe age. R2 = 0.612. Coefficient of correlation = 0.783.
Southeast Airline -- Airframe maintenance cost:
Cost = 4.597 + 0.0032 x Airframe age. R2 = 0.390. Coefficient of correlation = 0.625.
Southeast Airline -- Engine maintenance cost:
Cost = 0.671 + 0.0041 x Airframe age. R2 = 0.460. Coefficient of correlation = 0.678.
Northern Airline: There seem to be modest correlations between maintenance costs and airframe age for
Northern Airline. There is certainly reason to conclude, however, that airframe age is not the only
important factor.
Southeast Airline: The relationships between maintenance costs and airframe age for Southeast Airline
are much less well defined. It is even more obvious that airframe age is not the only important factor -perhaps not even the most important factor.
Overall, it would seem that:
Northern Airline has the smallest variance in maintenance costs, indicating that the day-to-day
management of maintenance is working pretty well.
Maintenance costs seem to be more a function of airline than of airframe age.
The airframe and engine maintenance costs for Southeast Airline are not only lower but also more
nearly similar than those for Northern Airline, but from the graphs at least, appear to be rising
slightly more sharply with age.
From an overall perspective, it appears that Southeast Airline may perform more efficiently on
sporadic or emergency repairs, and Northern Airline may place more emphasis on preventive
maintenance.
Ms. Youngs report should conclude that:
There is evidence to suggest that maintenance costs could be made to be a function of airframe
age by implementing more effective management practices.
The difference between maintenance procedures of the two airlines should be investigated.
The data with which she is presently working do not provide conclusive results.
Case: Southwestern University
(1) Since homecoming and the crafts festival occur during the same games each year, we could think of it
as there being a seasonal effect on attendance each year. We can therefore develop a multiplicative
decomposition model for SWU. We have data for 30 past periods (games), with 5 seasons each year. The
calculations using centered moving average are shown in file P11-SWU.XLS. The MAPE is only 3.63%
indicating that the multiplicative decomposition model does a reasonable job of predicting football
attendance. This is also indicated by the error graph, which shows that the forecasted and actual values
are very close to each other.
Attendance in the 5 games of 2005 (i.e., games 31 to 35) is 48098, 55055, 51451, 36116, and 49559
respectively. Attendance in the 5 games of 2006 (i.e., games 36 to 40) is 50520, 57799, 53990, 37880,
and 51957 respectively.
(2) With a ticket price of $20, revenues in 2005 (i.e., games 31 to 35) are expected to be $961,968,
$1,101,106, $1,029,023, $722,312, and $991,177 respectively. With a ticket price of $21 (5% increase),
revenues in 2006 (i.e., games 36 to 40) are expected to be $1,060,915, $1,213,784, $1,133,793, $795,488,
and $1,091,100 respectively.
(3) It appears that the school will run out of space for the homecoming game in 2006. It may be time for
Dr. Starr to start to a fund raising campaign for a stadium expansion project. Of course, they could run out
of space even earlier if SWU does get the number-one ranking next year. Alternatively, attendance could
drop off sharply if Pitterno does not achieve what is expected of him.