# Operations Management- Manchester United Case Study

Topics: Time series, Time series analysis, Seasonal variation Pages: 2 (400 words) Published: March 27, 2012
Manchester United

The following data for orders per quarter during the last two years. Orders (1000s) 2009 January – March April – June July – September October – December 18 23 20 41 2010 19 25 22 45

(a) Compute the seasonal indices for the four quarters. (b) Develop the trend line and forecast for the four quarters in 2011.

1. (a) Year Computation of seasonal indices: Quart er Sales (1000 s) 18 23 102/4 = 25.5 3 20 103/4 = 25.75 4 41 105/4 = 26.25 1 2 19 107/4 = 26.75 2 25 111/4 = 27.75 3 4 22 45 27.25 0.9194 (S2) 26.5 0.7170 (S1) 26 1.5769 (S4) 25.625 0.7805 (S3) 4-Qtr. Moving Average Centered Moving Avg. Seasonal Irregular Compone nt

1 2 1

Sum of the indices is 3.9938  4.00. Seasonal irregular components are considered as indices of the corresponding quarters.

(b)

Deseasonalization of the time series data

Year

Quart er 1

Yt 18

St 0.7170

Yt/St 25.10= 18/0.71 70 25.01 25.62

1 2 3 23 20 0.9194 0.7805

4 1 2 2 3 4

41 19 25 22 45

1.5769 0.7170 0.9194 0.7805 1.5769

26 26.50 27.19 28.19 28.54

Trend projection calculation: t 1 2 3 4 5 6 7 8 Total 36 Yt 25.10 25.01 25.62 26 26.50 27.19 28.19 28.54 212.15 t Yt 25.10 50.02 76.86 104 132.5 163.14 197.33 228.32 977.27 t2 1 4 9 16 25 36 49 64 204

We have

t

36 212.15  4.5, Y   26.52 8 8 977.27  (36  212.15) / 8 b1   0.5381. 204  (36  36) / 8 b0  26.52  0.5381  4.5  24.10 Tt  24.10  0.5381t.

Forecasting without seasonal effect: T9 = 24.10 + 0.5381  9 = 28.94 T10 = 24.10 + 0.5381  10 = 29.48

T11 = 24.10 + 0.5381  11 = 30.02 T12 = 24.10 + 0.5381  12 = 30.56 Forecasting with seasonal adjustment: t 9 10 11 12 Trend Forecast 28.94 29.48 30.02 30.56 Seasonal Index 0.7170 0.9194 0.7805 1.5769 Quarterly forecast 20.75 27.10 23.43 48.19