Lenovo uses the ZX-81 chip in some of its laptop computers. The prices for the c
ID: 391061 • Letter: L
Question
Lenovo uses the ZX-81 chip in some of its laptop computers. The prices for the chip during the last 12 months were as follows:
Month
Price Per Chip
Month
Price Per Chip
January
$1.901.90
July
$1.801.80
February
$1.611.61
August
$1.821.82
March
$1.601.60
September
$1.601.60
April
$1.851.85
October
$1.571.57
May
$1.901.90
November
$1.621.62
June
$1.951.95
December
$1.751.75
This exercise contains only part d.
With
alpha
= 0.1 and the initial forecast for October of
$1.831.83,
using exponential smoothing, the forecast for periods 11 and 12 is (round your responses to two decimal places):
Month
Oct
Nov
Dec
Forecast
$1.831.83
1.801.80
1.791.79
With
alpha
= 0.3 and the initial forecast for October of
$1.761.76,
using exponential smoothing, the forecast for periods 11 and 12 is (round your responses to two decimal places):
Month
Oct
Nov
Dec
Forecast
$1.761.76
1.701.70
1.681.68
With
alpha
= 0.5 and the initial forecast for October of
$1.721.72,
using exponential smoothing, the forecast for periods 11 and 12 is (round your responses to two decimal places):
Month
Oct
Nov
Dec
Forecast
$1.721.72
1.651.65
1.641.64
Based on the months of October, November, and December, the mean absolute deviation using exponential smoothing where
alpha
= 0.1 and the initial forecast for
Octoberequals=$1.831.83
is
$0.1570.157
(round your response to three decimal places).
Based on the months of October, November, and December, the mean absolute deviation using exponential smoothing where
alpha
= 0.3 and the initial forecast for
Octoberequals=$1.761.76
is
$0.1130.113
(round your response to three decimal places).
Based on the months of October, November, and December, the mean absolute deviation using exponential smoothing where
alpha
= 0.5 and the initial forecast for
Octoberequals=$1.721.72
is
$0.0970.097
(round your response to three decimal places).
Based on the mean absolute deviation, the better forecast is achieved using alphaequals=
0.5
Month
Price Per Chip
Month
Price Per Chip
January
$1.901.90
July
$1.801.80
February
$1.611.61
August
$1.821.82
March
$1.601.60
September
$1.601.60
April
$1.851.85
October
$1.571.57
May
$1.901.90
November
$1.621.62
June
$1.951.95
December
$1.751.75
Explanation / Answer
Below is the given table
Formula for expontneital foreacst = @ * Actual demand of previous period + ( 1-@) * forecast of previous period.
1)
With
alpha
= 0.1 and the initial forecast for October of
$1.831.83,
The exponential forecast of novemer = 0.1 * 1571.57 ( actual demand of november) + (1-0.1) * 1831.83 ( forecast of october)
The forecast for november = 1805.80
The forecast for december = 0.3* 1621.62 ( demand for november) +(1-0.3) * 1805.80 ( forecast for november) = 1679.78
2)
With
alpha
= 0.3 and the initial forecast for October of
$1,761.76,
The exponential forecast of novemer = 0.3 * 1571.57 ( actual demand of november) + (1-0.3) * 1,761.76 ( forecast of october)
The forecast for november = $1704.70
3)
With
alpha
= 0.5 and the initial forecast for October of
$1,721.72,
The exponential forecast of novemer = 0.5 * 1571.57 ( actual demand of november) + (1-0.5) * 1,721.72 ( forecast of october)
The forecast for november = $1646.65
The forecast for december = 0.5* 1621.62 ( demand for november) +(1-0.5) * 1676.68 ( forecast for november) = $1634.13
4)
With
alpha
= 0.1 and the initial forecast for October of
$1.831.83,
The exponential forecast of novemer = 0.1 * 1571.57 ( actual demand of november) + (1-0.1) * 1831.83 ( forecast of october)
The forecast for november = 1805.80
The forecast for december = 0.3* 1621.62 ( demand for november) +(1-0.3) * 1805.80 ( forecast for november) = 1679.78
The error for october = Actual - forecast = 1571.57-1,831.83 = -260.26
Absolute value of error = 260.26
The error for November = Actual - forecast = 1621.62-1805.80 = -184.18
Absolute value of error = 184.18
The error for December = Actual - forecast = 1751.75 - 1679.78 = 71.97
Absolute value of error = 71.97
The total of absolute values = 260.26 + 184.18 +71.97 = 516.41
The average of these these periods = mean average deviation = 516.41/3 = 172.14
Month Actual ( $) January 1901.9 February 1611.61 March 1601.6 April 1851.85 May 1901.9 June 1951.95 July 1801.8 August 1821.82 September 1601.6 October 1571.57 November 1621.62 December 1751.75