National Scan, Inc., sells radio frequency inventory tags.
Problem 3-2
National Scan, Inc., sells radio frequency inventory tags. Monthly sales for a sevenmonth period were as follows:
Month Sales
(000)Units Feb. 19 Mar. 18 Apr. 15 May 20 Jun. 18 Jul. 22 Aug. 20
b. Forecast September sales volume using each of the following:
(1) A linear trend equation. (Round your intermediate calculations and final answer to 2 decimal places.)
Yt 20.86 thousands
(2) A fivemonth moving average.
Moving average 19 thousands
(3) Exponential smoothing with a smoothing constant equal to .20, assuming a March forecast of 19(000). (Round your intermediate calculations and final answer to 2 decimal places.)
Forecast 19.26 thousands
(4) The naive approach.
Naive approach 20 thousands
(5) A weighted average using .60 for August, .30 for July, and .10 for June. (Round your answer to 2 decimal places.)
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Weighted average 20.40 thousands
References
Worksheet Learning Objective: 0307 Use a naive method to make a forecast.
Learning Objective: 0310 Prepare an exponential smoothing forecast.
Problem 32 Learning Objective: 0308 Prepare a moving average forecast.
Problem 3-2
National Scan, Inc., sells radio frequency inventory tags. Monthly sales for a sevenmonth period were as follows:
Month Sales
(000)Units Feb. 19 Mar. 18 Apr. 15 May 20 Jun. 18 Jul. 22 Aug. 20
b. Forecast September sales volume using each of the following:
(1) A linear trend equation. (Round your intermediate calculations and final answer to 2 decimal places.)
Yt 20.86 ± 0.10 thousands
(2) A fivemonth moving average.
Moving average 19 thousands
(3) Exponential smoothing with a smoothing constant equal to .20, assuming a March forecast of 19(000). (Round your intermediate calculations and final answer to 2 decimal places.)
Forecast 19.26 ± 0.10 thousands
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2. Award: 25 out of 25.00 points
(4) The naive approach.
Naive approach 20 thousands
(5) A weighted average using .60 for August, .30 for July, and .10 for June. (Round your answer to 2 decimal places.)
Weighted average 20.40 ± 0.01 thousands
Explanation:
b. (1)
t Y tY 1 19 19 2 18 36 3 15 45 4 20 80 5 18 90 6 22 132 7 20 140 28 132 542
with n = 7, Σt = 28, Σt2 = 140
b = nΣty − ΣtΣy
= 7(542) − 28(132)
= .50 nΣt2 − (Σt)2 7(140) − 28(28)
a = Σy − bΣt
= 132 − .50(28)
= 16.86 n 7
For Sept., t = 8, and Yt = 16.86 + .50(8) = 20.86 (000)
(2) MA5 =
15 + 20 + 18 + 22 + 20 = 195
(3) Month Forecast = F(old) + .20 [Actual − F(Old)] April 18.8 = 19 + .20 [18 − 19] May 18.04 = 18.8 + .20 [15 − 18.8] June 18.43 = 18.04 + .20 [20 − 18.04] July 18.34 = 18.43 + .20 [18 − 18.43] August 19.07 = 18.34 + .20 [22 − 18.34] September 19.26 = 19.07 + .20 [20 − 19.07]
(5) .60(20) + .30(22) + .10(18) = 20.40
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Problem 3-3
A dry cleaner uses exponential smoothing to forecast equipment usage at its main plant. August usage was forecasted to be 88 percent of capacity; actual usage was 89.6 percent of capacity. A smoothing constant of .1 is used. a. Prepare a forecast for September. (Round your answer to 2 decimal places.)
Forecast for September 88.16 percent of capacity b. Assuming actual September usage of 92 percent, prepare a forecast for October usage.(Round your
answer to 2 decimal places.)
Forecast for October 88.54 percent of capacity
References
Worksheet Problem 33 Learning Objective: 0310 Prepare an exponential smoothing forecast.
Problem 3-3
A dry cleaner uses exponential smoothing to forecast equipment usage at its main plant. August usage was forecasted to be 88 percent of capacity; actual usage was 89.6 percent of capacity. A smoothing constant of .1 is used. a. Prepare a forecast for September. (Round your answer to 2 decimal places.)
Forecast for September 88.16 ± 0.05 percent of capacity b. Assuming actual September usage of 92 percent, prepare a forecast for October usage.(Round your
answer to 2 decimal places.)
Forecast for October 88.54 ± 0.05 percent of capacity
Explanation:
a. 88 + .1(89.6 − 88) = 88.16
b. 88.16 + .1(92 − 88.16) = 88.54
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3. Award: 25 out of 25.00 points
Problem 3-4
An electrical contractor’s records during the last five weeks indicate the number of job requests: Week: 1 2 3 4 5 Requests: 20 22 18 21 22 Predict the number of requests for week 6 using each of these methods: a. Naive.
Number of requests 22 b. A fourperiod moving average. (Round your answer to 2 decimal places.)
Number of requests 20.75
c. Exponential smoothing with α = .30. Use 20 for week 2 forecast. (Round your intermediate
calculations and final answers to 2 decimal places.)
Number of Requests F3 20.6 F4 19.82 F5 20.17 F6 20.72
References
Worksheet Learning Objective: 0307 Use a naive method to make a forecast.
Learning Objective: 0310 Prepare an exponential smoothing forecast.
Problem 34 Learning Objective: 0308 Prepare a moving average forecast.
Problem 3-4
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4. Award: 25 out of 25.00 points
An electrical contractor’s records during the last five weeks indicate the number of job requests: Week: 1 2 3 4 5 Requests: 20 22 18 21 22 Predict the number of requests for week 6 using each of these methods: a. Naive.
Number of requests 22 b. A fourperiod moving average. (Round your answer to 2 decimal places.)
Number of requests 20.75 ± 0.01
c. Exponential smoothing with α = .30. Use 20 for week 2 forecast. (Round your intermediate
calculations and final answers to 2 decimal places.)
Number of Requests F3 20.6 ± 0.05 F4 19.82 ± 0.05 F5 20.17 ± 0.05 F6 20.72 ± 0.05
Explanation:
b. 22 + 18 + 21 + 22 = 20.754
c. F3 = 20 + .30(22 − 20) = 20.6 F4 = 20.6 + .30(18 − 20.6) = 19.82 F5 = 19.82 + .30(21 − 19.82) = 20.17 F6 = 20.17 + .30(22 − 20.17) = 20.72
Problem 3-32
A manager has just received an evaluation from an analyst on two potential forecasting alternatives. The analyst is indifferent between the two alternatives, saying that they should be equally effective. Period: 1 2 3 4 5 6 7 8 9 10 Data: 37 39 37 39 45 49 47 49 51 54 Alt. 1: 36 38 40 42 46 46 46 48 52 55 Alt. 2: 36 37 38 38 41 52 47 48 52 53
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What would cause the analyst to reach this conclusion? (Round your answers to 2 decimal places.) MAD1 1.60 MAD2 1.50 MSE1 3.78 MSE2 3.89 rev: 11_18_2014_QC_59428
References
Worksheet Learning Objective: 0315 Construct control charts and use them to monitor forecast errors.
Problem 332 Learning Objective: 0316 Describe the key factors and tradeoffs to consider when choosing a forecasting technique.
Problem 3-32
A manager has just received an evaluation from an analyst on two potential forecasting alternatives. The analyst is indifferent between the two alternatives, saying that they should be equally effective. Period: 1 2 3 4 5 6 7 8 9 10 Data: 37 39 37 39 45 49 47 49 51 54 Alt. 1: 36 38 40 42 46 46 46 48 52 55 Alt. 2: 36 37 38 38 41 52 47 48 52 53 What would cause the analyst to reach this conclusion? (Round your answers to 2 decimal places.) MAD1 1.60 ± 0.05 MAD2 1.50 ± 0.05 MSE1 3.78 ± 0.05 MSE2 3.89 ± 0.05 rev: 11_18_2014_QC_59428
Explanation:
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Period Actual Forecast 1 Forecast 2 error 1 error 2 e12 e22 |e1| |e2| 1 37 36 36 +1 +1 1 1 1 1 2 39 38 37 +1 +2 1 4 1 2 3 37 40 38 –3 –1 9 1 3 1 4 39 42 38 –3 +1 9 1 3 1 5 45 46 41 –1 +4 1 16 1 4 6 49 46 52 +3 –3 9 9 3 3 7 47 46 47 1 0 1 0 1 0 8 49 48 48 1 +1 1 1 1 1 9 51 52 52 –1 –1 1 1 1 1 10 54 55 53 –1 +1 1 1 1 1
Total –2 +5 34 35 16 15
MSE1 =
34 = 3.789 MSE2 =
35 = 3.899 MAD1 =
16 = 1.610 MAD2 =
15 = 1.510 Both forecasting methods have MADs that are approximately equal (MAD1 = 1.6, MAD2 = 1.5), and MSEs that are also approximately equal (MSE1 = 3.78, MSE2 = 3.89).
