1. Quantitative Analysis for Management
Forecasting
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-1

2. Exponential Smoothing Forecasting Techniques
Forecasting Models
Moving
Average
Exponential Smoothing
Trend Projections
Time Series Methods
Forecasting Techniques
Delphi
Methods
Jury of Executive
Opinion
Sales Force
Composite
Consumer
Market Survey
Qualitative Models
Causal Methods
Regression Analysis
Multiple Regression
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-2

3. Scatter Diagram for Sales
Radios
Televisions
Compact Discs
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-3

4. Decomposition of Time Series
Time series can be decomposed into:
Trend (T): gradual up or down movement over time
Seasonality (S): pattern of fluctuations above or below trend line that occurs every year
Cycles(C): patterns in data that occur every several years
Random variations (R): “blips”in the data caused by chance and unusual situations
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-4

5. Product Demand Showing Components
Actual Data
Trend
Cyclic
Random
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-5

6. Moving Averages Moving average : å (demand in period n ) n 5-6
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-6

7. Calculation of Three-Month Moving Average
Actual Shed
Sales
Three-Month Moving
Average
January 10
February 12
March 13
April 16 3 2 11
13)/3
(10 = +
May 19
16)/3
(12
June 23
19)/3
(13
July 26 1
23)/3
(16
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-7

8. Weighted Moving Averages
weights )
period in
)(demand
for
(weight
average
moving
Weighted å = n
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-8

9. Calculating Weighted Moving Averages
Weights Applied
Period 3
Last month 2
Two months ago 1
Three months ago 3
*Sales last month + 2
*Sales two months ago + 1
*Sales three months ago 6
Sum of weights
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-9

10. Calculation of Three-Month Moving Average
Actual
Shed
Sales
Three-Month Moving
Average
January 10
February 12
March 13
April 16 6 1
10)]/6 * (1
12) (2
13)
[(3 = +
May 19 3 14
12)]/6
16)
June 23 17
13)]/6
19)
July 26 2 20
16)]/6
23)
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-10

11. Exponential Smoothing
New forecast =
previous forecast + (previous actual - previous)
or:
where ( ) 1 a - + = t F A
actual
period
previous
constant between 0~1
smoothing
forecast
new t-
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-11

12. Table 5.5
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-12

13. Actual Tonnage Unloaded
Table 5.5 Continued  =0.50
Qtr
Actual Tonnage Unloaded
Forecast using  =0.50 1
180
175 2
168
= ( ) 3
159
= ( ) 4
= ( ) 5
190
= ( ) 6
205
= ( ) 7
= ( ) 8
182
= ( ) 9 ?
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-13

14. Trend Projection General regression equation: + = 2 X n Y XY b a wherebX - å
intercept
axis
variable)
(dependent
predicted be to
variable
the of
value
computed
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-14

15. Table5.7
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-15

16. Solved Formula
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-16

17. Midwestern Manufacturing’s Demand
Trend Line
Forecast points
Actual demand line
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-17

18. Computing Seasonality Indices Using Answering Machine Sales
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-18

19. Trend Analysis with Seasonal Indices
Y = x
Where x=1,2,…12 for Jan, Feb,….Dec
So;
Jan =[ (1)]*.957 =
Feb =[ (2)]*.851 =
Mar =[ (3)]*.904 = .
Dec = [1150*20(12)]*.851 =
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-19

20. Trend Analysis Example with Seasonality:
Trend analysis was used to forecast the number of new hotel registrants (in ooo’s). The following data was used.
yr1 yr2
1 Jan
2 Feb
3 Mar
4 Apr
5 May
6 June
7 July
8 Aug
9 Sep
10 Oct
11 Nov
12 Dec
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-20

21. Trend Analysis Example :
The trend analysis, using year1 data was
Y= X
Compute the seasonal index
Forecast July of year3, October of year3
What is the forecast for December if the average yearly demand for year is thought to increase by 10% higher than year1?
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-21

22. Using Regression Analysis to Forecast(Causal)
Triple A' Sales
($100,000's) X
Local Payroll
($100,000,000)
2.0 1
3.0 3
2.5 4 2
3.5 7
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-22

23. Using Regression Analysis to Forecast - continued
Sales, Y
Payroll, X X 2 XY
2.0 1
3.0 3 9
9.0
2.5 4 16
10.0
4.0
3.5 7 49
24.5 S
Y = 15.0
X = 18
= 80
XY = 51.5
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-23

24. Using Regression Analysis to Forecast - continued
Calculating the required parameters: ( ) X . Y ˆ b a n XY 25 75 1 3 5 2 6 80 51 15 18 + = - å
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-24

25. Regression Equation Y = 1.75 + 0.25x 5-25
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-25

26. Methods to evaluate the Casual Regression Equation
Standard Error of the Estimate (the standard deviation)
Correlation Coefficient
-1 < r <1
Coefficient of Determination
0 < r <1
the percent of variation in Y ( the dependent variable ) that is described by the X’s
(independent variables ) 2
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-26

27. Standard Error of the Estimate - continued( )
points
data of
number
equation
regression
the
from
computed
variable
dependent
value
point
each = - å n Y
where S c X , 2
For Payroll example, S = 0.306
Y,X
This is the standard deviation of the regression
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-27

28. Correlation Coefficient= ( ) [ ] å - 2 Y n X XY r
For Payroll example, r = 0.91
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-28

29. Coefficient - Four Values Fig. 5.7
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-29

30. Multiple Regression to Forecast #5-32
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-30

31. Multiple Regression to Forecast #5-32
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-31

32. Regression SAS printout Problem
Attendance Wins
40,
60,
60,
50,
45,
55,
50,
a) What is the dependent variable?
b) Plot the data is it correlated?
To accompany Quantitative Analysis for Management, 7e by Render/ Stair
5-32