Operations Forecasting
|
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? |
||||
|
|
|
||||
|
|
|
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? |
||||||||
|
|
|
||||||||
|
|
|
*******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 models.