132) Favors Distribution
Company purchases small imported trinkets in bulk, packages them, and sells
them to retail stores. They are conducting an inventory control study of all
their items. The following data are for one such item, which is not seasonal.
a. Use trend projection to
estimate the relationship between time and sales (state the equation).
b. Calculate forecasts for
the first four months of the next year.
|
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
|
Month
|
Jan
|
Feb
|
Mar
|
Apr
|
May
|
Jun
|
Jul
|
Aug
|
Sep
|
Oct
|
Nov
|
Dec
|
|
Sales
|
51
|
55
|
54
|
57
|
50
|
68
|
66
|
59
|
67
|
69
|
75
|
73
|
Answer: The trend projection equation is Y = 48.32 +
2.105 T. The next four months are forecast to be 75.68, 77.79, 79.89, and
82.00.
Diff: 2
Topic: Time-series forecasting
AACSB: Analytic Skills
Objective: LO4-6
133) Use exponential
smoothing with trend adjustment to forecast deliveries for period 10. Let alpha
= 0.4, beta = 0.2, and let the initial trend value be 4 and the
initial forecast be 200.
|
Period
|
Actual
Demand
|
|
1
|
200
|
|
2
|
212
|
|
3
|
214
|
|
4
|
222
|
|
5
|
236
|
|
6
|
221
|
|
7
|
240
|
|
8
|
244
|
|
9
|
250
|
|
10
|
266
|
Answer:
|
|
Actual
|
Forecast
|
Trend
|
FIT
|
|
1
|
200
|
200.00
|
4.00
|
|
|
2
|
212
|
202.40
|
3.68
|
206.08
|
|
3
|
214
|
208.45
|
4.15
|
212.60
|
|
4
|
222
|
213.16
|
4.27
|
217.43
|
|
5
|
236
|
219.26
|
4.63
|
223.89
|
|
6
|
221
|
228.73
|
5.60
|
234.33
|
|
7
|
240
|
229.00
|
4.53
|
233.53
|
|
8
|
244
|
236.12
|
5.05
|
241.17
|
|
9
|
250
|
242.30
|
5.28
|
247.58
|
|
10
|
266
|
248.55
|
5.47
|
254.02
|
Diff: 2
Topic: Time-series forecasting
AACSB: Analytic Skills
Objective: LO4-3
134) A small family-owned restaurant uses a seven-day moving average model to determine manpower
requirements. These forecasts need to be seasonalized because each day of the
week has its own demand pattern. The seasonal indices for each day of the week
are: Monday, 0.445; Tuesday, 0.791; Wednesday, 0.927; Thursday, 1.033; Friday,
1.422; Saturday, 1.478; and Sunday 0.903. Average daily demand based on the
most recent moving average is 194 patrons. What is the seasonalized forecast
for each day of next week?
Answer: The average value multiplied by each day's
seasonal index. Monday: 194 x .445 = 86; Tuesday: 194 x .791 = 153; Wednesday: 194 x .927 = 180; Thursday: 194 x 1.033 = 200; Friday: 194 x 1.422 = 276; Saturday: 194 x 1.478 = 287; and Sunday: 194 x .903 = 175.
Diff: 2
Topic: Associative forecasting methods: Regression
and correlation
AACSB: Analytic Skills
Objective: LO4-5
135) A restaurant has
tracked the number of meals served at lunch over the last four weeks. The data shows little in terms of trends, but
does display substantial variation by day of the week. Use the following information to determine
the seasonal (daily) index for this restaurant.
|
|
Week
|
|||
|
Day
|
1
|
2
|
3
|
4
|
|
Sunday
|
40
|
35
|
39
|
43
|
|
Monday
|
54
|
55
|
51
|
59
|
|
Tuesday
|
61
|
60
|
65
|
64
|
|
Wednesday
|
72
|
77
|
78
|
69
|
|
Thursday
|
89
|
80
|
81
|
79
|
|
Friday
|
91
|
90
|
99
|
95
|
|
Saturday
|
80
|
82
|
81
|
83
|
Answer:
|
Day
|
Index
|
|
Sunday
|
0.5627
|
|
Monday
|
0.7855
|
|
Tuesday
|
0.8963
|
|
Wednesday
|
1.0618
|
|
Thursday
|
1.1800
|
|
Friday
|
1.3444
|
|
Saturday
|
1.1692
|
Diff: 2
Topic: Time-series forecasting
AACSB: Analytic Skills
Objective: LO4-5
136) A firm has modeled its
experience with industrial accidents and found that the number of accidents per
year (Y) is related to the number of employees (X) by the regression equation Y
= 3.3 + 0.049*X. R-Square
is 0.68. The regression is based on 20 annual observations. The firm intends to
employ 480 workers next year. How many accidents do you project? How much
confidence do you have in that forecast?
Answer: Y =
3.3 + 0.049 * 480 = 3.3 +
23.52 = 26.82 accidents. This
is not a time series, so next year =
year 21 is of no relevance. Confidence comes from the coefficient of
determination; the model explains 68% of the variation in number of accidents,
which seems respectable.
Diff: 2
Topic: Associative forecasting methods: Regression
and correlation
AACSB: Analytic Skills
Objective: LO4-6
137) Demand for a certain
product is forecast to be 8,000 units per month, averaged over all 12 months of
the year. The product follows a seasonal pattern, for which the January monthly
index is 1.25. What is the seasonally-adjusted
sales forecast for January?
Answer: 8,000 x 1.25 = 10,000
Diff: 1
Topic: Time-series forecasting
AACSB: Analytic Skills
Objective: LO4-5
138) A seasonal index for a
monthly series is about to be calculated on the basis of three years' accumulation
of data. The three previous July values were 110, 135, and 130. The average
over all months is 160. The approximate seasonal index for July is:
Answer: (110 +
135 + 130)/3 = 125; 125/160 = 0.781
Diff: 2
Topic: Time-series forecasting
AACSB: Analytic Skills
Objective: LO4-5
139) Marie Bain is the
production manager at a company that manufactures hot water heaters. Marie
needs a demand forecast for the next few years to help decide whether to add
new production capacity. The company's sales history (in thousands of units) is
shown in the table below. Use exponential smoothing with trend adjustment, to
forecast demand for period 6. The initial forecast for period 1 was 11 units;
the initial estimate of trend was 0. The smoothing constants are α = .3 and β =
.3
|
Period
|
Actual
|
|
1
|
12
|
|
2
|
15
|
|
3
|
16
|
|
4
|
16
|
|
5
|
18
|
|
6
|
20
|
Answer:
|
Period
|
Actual
|
Forecast
|
Trend
|
FIT
|
|
1
|
12
|
11.00
|
0.00
|
|
|
2
|
15
|
11.30
|
0.09
|
11.39
|
|
3
|
16
|
12.47
|
0.41
|
12.89
|
|
4
|
16
|
13.82
|
0.69
|
14.52
|
|
5
|
18
|
14.96
|
0.83
|
15.79
|
|
6
|
20
|
16.45
|
1.03
|
17.48
|
Diff: 2
Topic: Time-series forecasting
AACSB: Analytic Skills
Objective: LO4-3
140) The quarterly sales for
specific educational software over the past three years are given in the
following table. Compute the four seasonal factors.
|
|
YEAR 1
|
YEAR 2
|
YEAR 3
|
|
Quarter 1
|
1710
|
1820
|
1830
|
|
Quarter 2
|
960
|
910
|
1090
|
|
Quarter 3
|
2720
|
2840
|
2900
|
|
Quarter 4
|
2430
|
2200
|
2590
|
Answer:
|
|
Avg.
|
Sea. Fact.
|
|
Quarter 1
|
1786.67
|
0.8933
|
|
Quarter 2
|
986.67
|
0.4933
|
|
Quarter 3
|
2820.00
|
1.4100
|
|
Quarter 4
|
2406.67
|
1.2033
|
|
Grand Average
|
2000.00
|
|
Diff: 2
Topic: Time-series forecasting
AACSB: Analytic Skills
Objective: LO4-5
141) An innovative
restaurateur owns and operates a dozen "Ultimate Low-Carb" restaurants in northern Arkansas. His
signature item is a cheese-encrusted beef
medallion wrapped in lettuce. Sales (X, in millions of dollars) is related to
Profits (Y, in hundreds of thousands of dollars) by the regression equation Y = 8.21 +
0.76 X. What is your forecast of profit
for a store with sales of $40 million? $50 million?
Answer: Students must recognize that sales is the
independent variable and profits is dependent; the problem is not a time
series. A store with $40 million in sales: 40 x 0.76 = 30.4; 30.4 +
8.21 = 38.61, or $3,861,000
in profit; $50 million in sales is estimated to profit 46.21 or $4,621,000.
Diff: 2
Topic: Associative forecasting methods: Regression
and correlation
AACSB: Analytic Skills
Objective: LO4-6
142) Arnold Tofu owns and
operates a chain of 12 vegetable protein "hamburger" restaurants in
northern Louisiana. Sales figures and profits for the stores are in the table
below. Sales are given in millions of dollars; profits are in hundreds of
thousands of dollars. Calculate a regression line for the data. What is your
forecast of profit for a store with sales of $24 million? $30 million?
|
Store
|
Profits
|
Sales
|
|
1
|
14
|
6
|
|
2
|
11
|
3
|
|
3
|
15
|
5
|
|
4
|
16
|
5
|
|
5
|
24
|
15
|
|
6
|
28
|
18
|
|
7
|
22
|
17
|
|
8
|
21
|
12
|
|
9
|
26
|
15
|
|
10
|
43
|
20
|
|
11
|
34
|
14
|
|
12
|
9
|
5
|
Answer: Students must recognize that
"sales" is the independent variable and profits is dependent. Store
number is not a variable, and the problem is not a time series. The regression
equation is Y = 5.936 + 1.421 X (Y =
profit, X = sales). A store with
$24 million in sales is estimated to profit 40.04 or $4,004,000; $30 million in
sales should yield 48.566 or $4,856,600 in profit.
Diff: 2
Topic: Associative forecasting methods: Regression
and correlation
Objective: LO4-6
143) The department manager
using a combination of methods has forecast sales of toasters at a local
department store. Calculate the MAD for
the manager's forecast. Compare the
manager's forecast against a naive forecast.
Which is better?
|
Month
|
Unit Sales
|
Manager's Forecast
|
|
January
|
52
|
|
|
February
|
61
|
|
|
March
|
73
|
|
|
April
|
79
|
|
|
May
|
66
|
|
|
June
|
51
|
|
|
July
|
47
|
50
|
|
August
|
44
|
55
|
|
September
|
30
|
52
|
|
October
|
55
|
42
|
|
November
|
74
|
60
|
|
December
|
125
|
75
|
Answer:
|
Month
|
Actual
|
Manager's
|
Abs. Error
|
|
Naive
|
Abs. Error
|
|
January
|
52
|
|
|
|
|
|
|
February
|
61
|
|
|
|
|
|
|
March
|
73
|
|
|
|
|
|
|
April
|
79
|
|
|
|
|
|
|
May
|
66
|
|
|
|
|
|
|
June
|
51
|
|
|
|
|
|
|
July
|
47
|
50
|
3
|
|
51
|
4
|
|
August
|
44
|
55
|
11
|
|
47
|
3
|
|
September
|
30
|
52
|
22
|
|
44
|
14
|
|
October
|
55
|
42
|
13
|
|
30
|
25
|
|
November
|
74
|
60
|
14
|
|
55
|
19
|
|
December
|
125
|
75
|
50
|
|
74
|
51
|
The manager's forecast has a
MAD of 18.83, while the naive is 19.33.
Therefore, the manager's forecast is slightly better than the naive.
Diff: 2
Topic: Monitoring and controlling forecasts
AACSB: Analytic Skills
Objective: LO4-4
144) The last seven weeks of
demand at a new car dealer are shown below.
Use a three-period
weighted-moving average to
determine a forecast for the 8th week
using weights of 1, 2, and 3. Calculate
the MAD for this forecast. What does the
MAD indicate?
Week Sales
1 25
2 30
3 27
4 31
5 27
6 29
7 30
Answer:
Week Sales 3WMA |error|
1 25
2 30
3 27
4 31 28 3
5 27 30 3
6 29 28 1
7 30 29 1
8 29
MAD = 8/4 =
2
An MAD of 2 means that the
forecasting technique used was typically off by 2 units each period.
Diff: 2
Topic: Time-series forecasting, moving averages,
and measuring forecast error
Objective: LO4-4
No comments:
Post a Comment