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Problem 18-4
Here are the data for the past 21 months for actual sales of a particular product:
LAST YEAR
THIS YEAR
January
365
300
February
455
375
March
400
375
April
430
455
May
432
440
June
505
380
July
400
385
August
320
305
September
395
365
October
500
November
590
December
490
Develop a forecast for the fourth quarter using a three-quarter, weighted moving average. Weight the most recent quarter 0.50, the second most recent 0.25, and the third 0.25. Do the problem using quarters, as opposed to forecasting separate months. (Round your answer to 2 decimal places.)
Forecast for the fourth quarter
Explanation:
Third most recent quarter 300 + 375 + 375 = 1,050
Second most recent quarter 455 + 440 + 380 = 1,275
Most recent quarter 385 + 305 + 365 = 1,055
WMA = (0.25 × 1,050) + (0.25 × 1,275) + (0.50 × 1,055) = 1,108.75
References
WorksheetDifficulty: Challenge
Problem 18-4Learning Objective: 18-02 Evaluate demand using quantitative forecasting models.
Problem 18-7
The following table contains the demand from the last 10 months:
MONTH
ACTUAL DEMAND
1
32
2
35
3
36
4
38
5
41
6
39
7
39
8
41
9
44
10
40
a.
Calculate the single exponential smoothing forecast for these data using an α of 0.30 and an initial forecast (F1) of 32. (Round your answers to 2 decimal places.)
Month
Exponential Smoothing
1
2
3
4
5
6
7
8
9
10
b.
Calculate the exponential smoothing with trend forecast for these data using an α of 0.30, a δ of 0.20, an initial trend forecast (T1) of 1.00, and an initial exponentially smoothed forecast (F1) of 31. (Round your answers to 2 decimal places.)
Month
FITt
1
2
3
4
5
6
7
8
9
10
c-1.
Calculate the mean absolute deviation (MAD) for the last nine months of forecasts. (Round your answers to 2 decimal places.)
MAD
Single exponential smoothing forecast
Exponential smoothing with trend forecast
c-2.
Which is best?
Exponential smoothing with trend forecast
Single exponential smoothing forecast
Explanation:
a. to c.
Month
Demand
Exponential Smoothing
Absolute Deviation
Tt
Ft
FITt
Absolute Deviation
1
32
32.00
1.00
31.00
32.00
2
35
32.00
3.00
1.00
32.00
33.00
2.00
3
36
32.90
3.10
1.12
33.60
34.72
1.28
4
38
33.83
4.17
1.20
35.10
36.30
1.70
5
41
35.08
5.92
1.30
36.81
38.11
2.89
6
39
36.86
2.14
1.47
38.98
40.45
1.45
7
39
37.50
1.50
1.38
40.02
41.40
2.40
8
41
37.95
3.05
1.24
40.68
41.92
0.92
9
44
38.87
5.13
1.18
41.64
42.82
1.18
10
40
40.41
0.41
1.25
43.17
44.42
4.42
MAD
3.16
2.03
Based upon the MAD of each forecast, the exponential smoothing with trend is the better forecasting model.
References
WorksheetDifficulty: Challenge
Problem 18-7Learning Objective: 18-02 Evaluate demand using quantitative forecasting models.
Problem 18-10
The number of cases of merlot wine sold by the Connor Owen winery in an eight-year period is as follows:
YEAR
CASES OF MERLOT WINE
2005
291
2006
377
2007
419
2008
477
2009
379
2010
521
2011
431
2012
397
Using an exponential smoothing model with an alpha value of 0.40, estimate the smoothed value calculated as of the end of 2012. Use the average demand for 2005 through 2007 as your initial forecast for 2008, and then smooth the forecast forward to 2012. (Round your intermediate calculations and final answer to the nearest whole number.)
Forecast for 2012
Explanation:
Year
Demand
F(t)
2005
291
2006
377
2007
419
2008
477
362
2009
379
408
2010
521
396
2011
431
446
2012
397
440
References
WorksheetDifficulty: Challenge
Problem 18-10Learning Objective: 18-02 Evaluate demand using quantitative forecasting models.
Problem 18-15
Historical demand for a product is
DEMAND
January
16
February
14
March
18
April
16
May
19
June
18
a.
Using a weighted moving average with weights of 0.50 (June), 0.20 (May), and 0.30 (April), find the July forecast. (Round your answer to 1 decimal place.)
July forecast
b.
Using a simple three-month moving average, find the July forecast. (Round your answer to 1 decimal place.)
July forecast
c.
Using single exponential smoothing with α = 0.20 and a June forecast = 12, find the July forecast. (Round your answer to 1 decimal place.)
July forecast
d.
Using simple linear regression analysis, calculate the regression equation for the preceding demand data. (Do not round intermediate calculations. Round your intercept value to 1 decimal place and slope value to 2 decimal places.)
Y = + t
e.
Using the regression equation in d, calculate the forecast for July. (Do not round intermediate calculations. Round your answer to 1 decimal place.)
July forecast
Explanation:
a.
FJuly = 0.50(18) + 0.20(19) + 0.30(16) = 17.6
b.
FJuly = (18 + 19 + 16)/3 = 17.7
c.
FJuly = FJune + α(AJune – FJune) = 12 + 0.20(18 − 12) = 13.2
d.
t
y
ty
t2
January
1
16
16
1
February
2
14
28
4
March
3
18
54
9
April
4
16
64
16
May
5
19
95
25
June
6
18
108
36
Total
21
101
365
91
Average
3.5
16.8
= 3.5
= 16.833
Y = a + bt = 14.5 + 0.66t
e.
FJuly, where July is the 7th month.
Y = a + bt = 14.5 + 0.66(7) = 19.1
References
WorksheetDifficulty: Challenge
Problem 18-15Learning Objective: 18-02 Evaluate demand using quantitative forecasting models.
Problem 18-22
Your manager is trying to determine what forecasting method to use. Based upon the following historical data, calculate the following forecast and specify what procedure you would utilize.
MONTH
ACTUAL DEMAND
1
61
2
64
3
67
4
66
5
71
6
70
7
73
8
74
9
74
10
83
11
84
12
86
a.
Calculate the simple three-month moving average forecast for periods 4–12. (Round your answers to 3 decimal places.)
Month
Three-Month Moving Average
4
5
6
7
8
9
10
11
12
b.
Calculate the weighted three-month moving average for periods 4–12 using weights of 0.40 (for the period t−1); 0.40 (for the period t−2), and 0.20 (for the period t−3). (Do not round intermediate calculations. Round your answers to 1 decimal place.)
Month
Three-Month Weighted Moving Average
4
5
6
7
8
9
10
11
12
c.
Calculate the single exponential smoothing forecast for periods 2–12 using an initial forecast (F1) of 66 and an α of 0.30. (Do not round intermediate calculations. Round your answers to 3 decimal places.)
Month
Single Exponential Smoothing Forecast
2
3
4
5
6
7
8
9
10
11
12
d.
Calculate the exponential smoothing with trend component forecast for periods 2–12 using an initial trend forecast (T1) of 1.70, an initial exponential smoothing forecast (F1) of 65, an α of 0.30, and a δ of 0.20. (Do not round intermediate calculations. Round your answers to 3 decimal places.)
Month
Exponential Smoothing with Trend
2
3
4
5
6
7
8
9
10
11
12
e-1.
Calculate the mean absolute deviation (MAD) for the forecasts made by each technique in periods 4–12. (Do not round intermediate calculations. Round your answers to 3 decimal places.)
Mean Absolute Deviation
Three-month moving average
Three-month weighted moving average
Single exponential smoothing forecast
Exponential smoothing with trend
e-2.
Which forecasting method do you prefer?
Three-month moving average
Three-month weighted moving average
Single exponential smoothing forecast
Exponential smoothing with trend forecast
*******Explanation: see second page for chart
a. to e.
Single Exponential Smoothing
Exponential Smoothing with Trend
Month (t)
Demand
Three-Month Moving Average
Absolute Deviation
Three-Month Weighted Moving Average
Absolute Deviation
Ft
Absolute Deviation
Ft
Tt
FITt
Absolute Deviation
1
61
66.000
65.000
1.700
66.700
2
64
64.500
64.990
1.358
66.348
3
67
64.350
65.644
1.217
66.861
4
66
64.000
2.000
64.6
1.400
65.145
0.855
66.903
1.225
68.128
2.128
5
71
65.667
5.333
66.0
5.000
65.402
5.598
67.490
1.098
68.587
2.413
6
70
68.000
2.000
68.2
1.800
67.081
2.919
69.311
1.243
70.554
0.554
7
73
69.000
4.000
69.6
3.400
67.957
5.043
70.388
1.209
71.597
1.403
8
74
71.333
2.667
71.4
2.600
69.470
4.530
72.018
1.294
73.311
0.689
9
74
72.333
1.667
72.8
1.200
70.829
3.171
73.518
1.335
74.853
0.853
10
83
73.667
9.333
73.8
9.200
71.780
11.220
74.597
1.284
75.881
7.119
11
84
77.000
7.000
77.6
6.400
75.146
8.854
78.016
1.711
79.727
4.273
12
86
80.333
5.667
81.6
4.400
77.802
8.198
81.009
1.967
82.976
3.024
MAD
4.407
3.933
5.599
2.495
Based upon MAD, the exponential smoothing with trend forecast component appears to be the best method.
References
WorksheetDifficulty: Challenge
Problem 18-22Learning Objective: 18-02 Evaluate demand using quantitative forecasting
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