CASE PROBLEM

THE UNIVERSITY BOOKSTORE STUDENT COMPUTER PURCHASE PROGRAM

Year Bikes Sold1 2252 3133 4754 4085 7926 8067 8998 9539 106910 98611 109812 125613 117814 1607

Based on the question, most inventory is sold at the beginning of the semester. However,

based on the data above, the total quantity is given for the year. Therefore, the data is not

detailed enough to show a seasonal pattern.

Overall, it looks like the sales keep increasing in the past 14 years even though the sales for

some years are lower than the previous year on 3 occasions ( Year 4, 10 and 13). Therefore,

the linear regression seem to be the appropriate forecast method for this case. The accuracy of

this method is represented by its MAD value, compared to the MAD value of various other

methods that will also be demonstrated below. The method that gives the lowest MAD (Mean

Absolute Deviation) value corresponds to the most accurate forecast value.

1) Linear regression forecast method result

Linear Relationship

Y = 183.44 + 90.45 X

Forecast of bikes to be sold in coming year : 1540 bikes

MAD Value : 87.67

In terms of correlation, the closer the correlation coefficient value is to 1, the closer the linear

relationship. The correlation coefficient in this is 0.96. This shows that there is high strength

for relationship between the year and bikes sold.

Therefore, the given forecast value of 1540 bikes sales for the coming year could be quite

accurate.

The MAD value will later be compared to other MAD values resulting from various other

forecast methods to further demonstrate the accuracy of this forecasted value.

The graph for linear regression is illustrated below :

2) Different forecast methods and results are illustrated below:

a) 3 year moving average

Forecast for beginning of next semester is 1347 bikes.

The MAD value is 186.58

b) 5 year moving average

Forecast for beginning of next semester is 1225 bikes.

The MAD value is 262.8

c) Exponential smoothing with α 0.3

Forecast for beginning of next semester is 1241 bikes.

The MAD value is 260.55

d) Exponential smoothing with α 0.5

Forecast for beginning of next semester is 1384 bikes.

The MAD value is 178.43

e) Exponential smoothing with α 0.8

Forecast for beginning of next semester is 1522 bikes.

The MAD value is 144.83

f) Exponential smoothing with trend α 0.8 β 0.8

Forecast for next period is 1791

The MAD value is 150.7

g) Exponential smoothing with trend α 0.5 β 0.5

Forecast for beginning of next semester is 1520 bikes.

The MAD value is 134.42

h) Exponential smoothing with trend α 0.5 β 0.3

Forecast for beginning of next semester is 1493 bikes.

The MAD value is 136.58

i) Exponential smoothing with trend α 0.5, β 0.8

Forecast for beginning of next semester is 1568 bikes.

The MAD value is 137.74

j) Exponential smoothing with trend α 0.7, β 0.8

Forecast for beginning of next semester is 1719 bikes.

The MAD value is 139.77

k) Exponential smoothing with trend α 0.3, β 0.3

Forecast for beginning of next semester is 1333 bikes.

The MAD value is 206.03

l) Exponential smoothing with trend α 0.8, β 0.5

Forecast for beginning of next semester is 1706 bikes.

The MAD value is 134.05

m) Exponential smoothing with trend α 0.8 β 0.3

Forecast for beginning of next semester is 1658 bikes.

The MAD value is 122.74

n) Exponential smoothing with trend α 0.8 β 0.2

Forecast for beginning of next semester is 1634.74 bikes.

The MAD value is 119.81

o) Exponential smoothing with trend α 0.8 β 0.1

Forecast for beginning of next semester is 1602 bikes.

The MAD value is 127.15

Overall summary for different methods of forecasting

No Method Forecast Value (bikes)

MAD Error value

1 Linear agression 1540 87.67

2a 3 year moving average 1347 186.58

b 5 year moving average 1225 262.87

c Exponential smoothing with α 0.3

1241 260.55

d Exponential smoothing with α 0.5

1384 178.43

e Exponential smoothing with α 0.8

1522 144.83

f Exponential smoothing with α 0.8, β 0.8

1791 150.7

g Exponential smoothing with α 0.5, β 0.5

1520 134.42

h Exponential smoothing with α 0.5, β 0.3

1493 136.58

i Exponential smoothing with α 0.5, β 0.8

1568 137.74

j Exponential smoothing with α 0.7, β 0.8

1719 139.77

k Exponential smoothing with α 0.3, β 0.3

1333 206.03

l Exponential smoothing with α 0.8, β 0.5

1706 134.05

m Exponential smoothing with α 0.8, β 0.3

1658 122.74

n Exponential smoothing with α 0.8 , β .2

1634.74 119.81

o Exponential smoothing with α 0.8, β 0.1

1602 127.15

The forecasting method with the lowest MAD error value (87.67) is Trend Analysis.

The corresponding forecast value for this is 1540.13. This supports that this forecast

method is the most accurate method. This means Nomura can expect to sell 1540

bikes in the coming year.

With the linear trend established, Nomura can also do some long term forecast to

decide if he needs to expand his shop or open at another location to deal with the new

sales or open a business in a new market.