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The units sold during the last four years were 940, 920, 970 and 880 units. The forecast for the fourth year was 917 units. If the forecast for the fifth year (using simple exponential smoothing) is equal to the forecast using a three-period simple moving average, find the value of the exponential smoothing constant and find the forecast for the sixth year (if actual units sold in fifth year is 900)?
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The units sold during the last four years were 940, 920, 970 and 880 u...
Forecasting using Simple Exponential Smoothing and Simple Moving Average
Given data:
- Last four years' units sold: 940, 920, 970, 880
- Forecast for fourth year: 917 units
- Actual units sold in fifth year: 900 units
Step 1: Finding the Exponential Smoothing Constant
To find the exponential smoothing constant, we need to compare the forecast for the fourth year with the actual units sold in the fourth year.
Error for fourth year = Actual units sold in fourth year - Forecast for fourth year
= 880 - 917
= -37
To minimize the error, we can try different values of alpha (exponential smoothing constant) and see which one gives the lowest error. Let's start with alpha = 0.1.
Forecast for fifth year = alpha * Actual units sold in fourth year + (1 - alpha) * Forecast for fourth year
= 0.1 * 880 + 0.9 * 917
= 909.3
Error for fifth year = Actual units sold in fifth year - Forecast for fifth year
= 900 - 909.3
= -9.3
Let's try alpha = 0.2.
Forecast for fifth year = alpha * Actual units sold in fourth year + (1 - alpha) * Forecast for fourth year
= 0.2 * 880 + 0.8 * 917
= 903.6
Error for fifth year = Actual units sold in fifth year - Forecast for fifth year
= 900 - 903.6
= -3.6
Let's try alpha = 0.3.
Forecast for fifth year = alpha * Actual units sold in fourth year + (1 - alpha) * Forecast for fourth year
= 0.3 * 880 + 0.7 * 917
= 898.5
Error for fifth year = Actual units sold in fifth year - Forecast for fifth year
= 900 - 898.5
= 1.5
The error is lowest for alpha = 0.3, so the exponential smoothing constant is 0.3.
Step 2: Finding the Forecast for the Sixth Year
To find the forecast for the sixth year, we use the formula:
Forecast for sixth year = alpha * Actual units sold in fifth year + (1 - alpha) * Forecast for fifth year
Substituting the values:
Forecast for sixth year = 0.3 * 900 + 0.7 * 898.5
= 899.55
= 900 units (rounded to the nearest whole number)
Step 3: Comparing Simple Exponential Smoothing with Simple Moving Average
To find the three-period simple moving average, we take the average of the last three years' units sold:
Three-period simple moving average = (970 + 920 + 940) / 3
= 943.33
= 943 units (rounded to the nearest whole number)
Since the forecast for the fifth year using simple exponential smoothing (898.5) is not equal to the forecast using a three-period simple moving average (943), we cannot compare them.
Given data:
- Last four years' units sold: 940, 920, 970, 880
- Forecast for fourth year: 917 units
- Actual units sold in fifth year: 900 units
Step 1: Finding the Exponential Smoothing Constant
To find the exponential smoothing constant, we need to compare the forecast for the fourth year with the actual units sold in the fourth year.
Error for fourth year = Actual units sold in fourth year - Forecast for fourth year
= 880 - 917
= -37
To minimize the error, we can try different values of alpha (exponential smoothing constant) and see which one gives the lowest error. Let's start with alpha = 0.1.
Forecast for fifth year = alpha * Actual units sold in fourth year + (1 - alpha) * Forecast for fourth year
= 0.1 * 880 + 0.9 * 917
= 909.3
Error for fifth year = Actual units sold in fifth year - Forecast for fifth year
= 900 - 909.3
= -9.3
Let's try alpha = 0.2.
Forecast for fifth year = alpha * Actual units sold in fourth year + (1 - alpha) * Forecast for fourth year
= 0.2 * 880 + 0.8 * 917
= 903.6
Error for fifth year = Actual units sold in fifth year - Forecast for fifth year
= 900 - 903.6
= -3.6
Let's try alpha = 0.3.
Forecast for fifth year = alpha * Actual units sold in fourth year + (1 - alpha) * Forecast for fourth year
= 0.3 * 880 + 0.7 * 917
= 898.5
Error for fifth year = Actual units sold in fifth year - Forecast for fifth year
= 900 - 898.5
= 1.5
The error is lowest for alpha = 0.3, so the exponential smoothing constant is 0.3.
Step 2: Finding the Forecast for the Sixth Year
To find the forecast for the sixth year, we use the formula:
Forecast for sixth year = alpha * Actual units sold in fifth year + (1 - alpha) * Forecast for fifth year
Substituting the values:
Forecast for sixth year = 0.3 * 900 + 0.7 * 898.5
= 899.55
= 900 units (rounded to the nearest whole number)
Step 3: Comparing Simple Exponential Smoothing with Simple Moving Average
To find the three-period simple moving average, we take the average of the last three years' units sold:
Three-period simple moving average = (970 + 920 + 940) / 3
= 943.33
= 943 units (rounded to the nearest whole number)
Since the forecast for the fifth year using simple exponential smoothing (898.5) is not equal to the forecast using a three-period simple moving average (943), we cannot compare them.
Community Answer
The units sold during the last four years were 940, 920, 970 and 880 u...
Solution:
Given Data:
- Units sold in the last four years: 940, 920, 970, 880
- Forecast for the fourth year: 917 units
- Actual units sold in the fifth year: 900 units
Finding the Exponential Smoothing Constant:
- Let alpha (α) be the exponential smoothing constant
- The forecast for the fifth year using simple exponential smoothing will be: F5 = α(Actual fifth year sales) + (1-α)F4
- The forecast using a three-period simple moving average will be: F5 = (Last 3 years' sales)/3
- Equating both the forecasts:
α(Actual fifth year sales) + (1-α)F4 = (Last 3 years' sales)/3
- Substituting the given values:
α(900) + (1-α)(917) = (940 + 920 + 970)/3
α = 0.2 (approx.)
Finding the Forecast for the Sixth Year:
- Using simple exponential smoothing, the forecast for the sixth year will be:
F6 = 0.2(Actual sixth year sales) + 0.8F5
- Substituting the given values:
F6 = 0.2(unknown) + 0.8(900)
F6 = 900.8 (approx.)
Explanation:
- The given data includes the units sold in the last four years and the forecast for the fourth year.
- The exponential smoothing constant is found by equating the forecast using simple exponential smoothing and the forecast using a three-period simple moving average.
- The forecast for the sixth year is found using the exponential smoothing constant and the actual units sold in the fifth year.
- Simple exponential smoothing is a forecasting method that takes into account past data and gives more weight to recent data. It is useful in predicting trends and detecting seasonality.
Given Data:
- Units sold in the last four years: 940, 920, 970, 880
- Forecast for the fourth year: 917 units
- Actual units sold in the fifth year: 900 units
Finding the Exponential Smoothing Constant:
- Let alpha (α) be the exponential smoothing constant
- The forecast for the fifth year using simple exponential smoothing will be: F5 = α(Actual fifth year sales) + (1-α)F4
- The forecast using a three-period simple moving average will be: F5 = (Last 3 years' sales)/3
- Equating both the forecasts:
α(Actual fifth year sales) + (1-α)F4 = (Last 3 years' sales)/3
- Substituting the given values:
α(900) + (1-α)(917) = (940 + 920 + 970)/3
α = 0.2 (approx.)
Finding the Forecast for the Sixth Year:
- Using simple exponential smoothing, the forecast for the sixth year will be:
F6 = 0.2(Actual sixth year sales) + 0.8F5
- Substituting the given values:
F6 = 0.2(unknown) + 0.8(900)
F6 = 900.8 (approx.)
Explanation:
- The given data includes the units sold in the last four years and the forecast for the fourth year.
- The exponential smoothing constant is found by equating the forecast using simple exponential smoothing and the forecast using a three-period simple moving average.
- The forecast for the sixth year is found using the exponential smoothing constant and the actual units sold in the fifth year.
- Simple exponential smoothing is a forecasting method that takes into account past data and gives more weight to recent data. It is useful in predicting trends and detecting seasonality.
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The units sold during the last four years were 940, 920, 970 and 880 units. The forecast for the fourth year was 917 units. If the forecast for the fifth year (using simple exponential smoothing) is equal to the forecast using a three-period simple moving average, find the value of the exponential smoothing constant and find the forecast for the sixth year (if actual units sold in fifth year is 900)?
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The units sold during the last four years were 940, 920, 970 and 880 units. The forecast for the fourth year was 917 units. If the forecast for the fifth year (using simple exponential smoothing) is equal to the forecast using a three-period simple moving average, find the value of the exponential smoothing constant and find the forecast for the sixth year (if actual units sold in fifth year is 900)? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The units sold during the last four years were 940, 920, 970 and 880 units. The forecast for the fourth year was 917 units. If the forecast for the fifth year (using simple exponential smoothing) is equal to the forecast using a three-period simple moving average, find the value of the exponential smoothing constant and find the forecast for the sixth year (if actual units sold in fifth year is 900)? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The units sold during the last four years were 940, 920, 970 and 880 units. The forecast for the fourth year was 917 units. If the forecast for the fifth year (using simple exponential smoothing) is equal to the forecast using a three-period simple moving average, find the value of the exponential smoothing constant and find the forecast for the sixth year (if actual units sold in fifth year is 900)?.
The units sold during the last four years were 940, 920, 970 and 880 units. The forecast for the fourth year was 917 units. If the forecast for the fifth year (using simple exponential smoothing) is equal to the forecast using a three-period simple moving average, find the value of the exponential smoothing constant and find the forecast for the sixth year (if actual units sold in fifth year is 900)? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The units sold during the last four years were 940, 920, 970 and 880 units. The forecast for the fourth year was 917 units. If the forecast for the fifth year (using simple exponential smoothing) is equal to the forecast using a three-period simple moving average, find the value of the exponential smoothing constant and find the forecast for the sixth year (if actual units sold in fifth year is 900)? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The units sold during the last four years were 940, 920, 970 and 880 units. The forecast for the fourth year was 917 units. If the forecast for the fifth year (using simple exponential smoothing) is equal to the forecast using a three-period simple moving average, find the value of the exponential smoothing constant and find the forecast for the sixth year (if actual units sold in fifth year is 900)?.
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