Operations Management Essay

Winter 2009
Problem 1
(a) Moving average (N=3)
F37 = (A36 + A35 + A34)/3 = (505 + 1851 + 1044)/3 = 1133.33
Exponential Smoothing (α=0.3)
F37 = F36 + α*(A36 - F36) = 1976.3 + 0.3*(505-1976.5) = 1534.85
Regression
F37 = 1367+20.5*(37) =
(b) MAD
The 36th error will need to be added to the sum of the 35 errors given for each of the 3 methods.
Moving Average MAD = = = = 676.454
Linear Regression MAD = = = = 537.694
(c) SD
Exponential Smoothing = = = 760.873
Linear Regression = = = 715.426
(d) Analysis of Chart
The r-squared value for the regression method is 0.082, this is very low, meaning the regression method is not doing a good job of forecasting future demand. We can see from the chart that there are peaks and valleys in the date. This suggest a season component, so multiplicative decomposition should be used.

Problem 2
(a) Double Exponential Smoothing (α = 0.5, β = 0.1, F2008-2009 = 21425, T2008-2009 = 1027.5)
2008-2009 Calculations
FIT2008-2009 = F2008-2009 + T2008-2009 = 21425 + 1027.5 = 22452.5
2009-2010 Calculations
F2009-2010 = α*A2008-2009 + (1-α)*FIT2008-2009 = 0.5*23100 + (1-0.5)*22452.5 = 22776.25
T2009-2010 = β*(F2009-2010 - F2008-2009) + (1-β)*T2008-2009 = 0.1*(22776.25 - 21425) + (1-0.1)*1027.5 = 1059.875
FIT2009-2010 = F2009-2010 + T2009-2010 = 22776.25 + 1059.875 = 23836.13
2010-2011 Calculations
F2010-2011 = α*A2009-2010 + (1-α)*FIT2009-2010 = 0.5*25000 + (1-0.5)*23836.13 = 24418.06
T2010-2011 = β*(F2010-2011 - F2009-2010) + (1-β)*T2009-2010 = 0.1*(24418.06 - 22776.25) + (1-0.1)*1059.875 = 1118.069
FIT2010-2011 = F2010-2011 + T2010-2011 = 24418.06 + 1118.069= 25536.13

(b) Exponential Smoothing (a=0.2)
The current year is 2010. A mistake was made in 2008 where the actual value of 1500 was used. The correct values should have been 5100. We will use the following formula:
Ft = α*At-1 + α*(1- α)*At-2 + α *(1- α)2*At-3 .........
Since the mistake was made in 2008, the number that was input incorrectly was At-2. So let us re-calculate.
Using 1500 α*(1- α)*At-2 = 0.2*(1-0.2)*1500 = 240
Using the correct value of 5100 α*(1- α)*At-2 = 0.2*(1-0.2)*5100 = 816
Therefore the forecast should be increased by 816-240 = 576 units

(c) A stable time series has no peaks or valleys and no slope, the date would look like a straight horizontal line. Of the average is 1300, it would suggest that the regression intercept = 1300. The slope would be 0. If there are no peaks and valleys then all the seasonal index must be equal. Remember also that all the season indexes must add up to the number of seasons. We are told there are 4 seasons so S1=S2=S3=S4, and S1 + S2 + S3 + S4 = 4, therefore S1=S2=S3=S4= 1.

(d)
First calculate each of the seasonal indexes, there are 4 seasons. Recall that to get the forecast we use the following formula:
Forecast = Trend * Adjusted S
Re-arranging, we get
Adjusted S = Forecast/Trend
Use the first 4 periods to calculate the seasonal indexes:
Adjusted S1 = F1/T1 = 2023.24394/2314.81 = 0.8740
Adjusted S2 = F2/T2 = 2332.57/2332.57 = 1
Adjusted S3 = F3/T3 = 2803.94369 /2350.33= 1.193
Adjusted S4 = F4/T4 = 2209.42797/2368.09 = 0.993
Since period 21 is season 1, we know Adjusted S21 = 0.8740
Since period 22 is season 2, we know Adjusted S22 = 1
Since period 23 is season 3, we know Adjusted S23 = 1.193
Since period 24 is season 4, we know Adjusted S24 = 0.993
We now need to calculate the Trend component for periods 21-24, we will need the regression equation.
Slope = T2 - T1 = 2332.57 - 2314.81 = 17.76
Intercept = T0 = T1 - Slope = 2314.81 - 17.76 = 2297.05
So our regression equation would be as follows
Trend = 2297.05 + 17.76*period
We now need to calculate the trend for periods 21-24 using the above equation
T21 = 2297 + 17.76 * (21) = 2669.96
T22 = 2297 + 17.76 * (22) = 2687.72
T23 = 2297 + 17.76 * (23) = 2705.48
T24 = 2297 + 17.76 * (24) = 2723.24
Finally, we can calculate the forecast for periods

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