ch4 3

Chapter 4
Class 3
Seasonal Variations In Data
The multiplicative seasonal model can modify
trend data to accommodate seasonal variations in
demand
1. Find average historical demand for each season

2. Compute the average demand over all seasons
3. Compute a seasonal index for each season
4. Estimate next year’s total demand
5. Divide this estimate of total demand by the number of seasons,
then multiply it by the seasonal index for that season
Seasonal Index Example
Demand Average Average Seasonal
Month 2003 2004 2005 2003-2005 Monthly Index
Jan 80 85 105 90 94
Feb 70 85 85 80 94
Mar 80 93 82 85 94
Apr 90 95 115 100 94
May 113 125 131 123 94
Jun 110 115 120 115 94
Jul 100 102 113 105 94
Aug 88 102 110 100 94
Sept 85 90 95 90 94
Oct 77 78 85 80 94
Nov 75 72 83 80 94
Dec 82 78 80 80 94
Jan 80 85 105 90 94 0.957
Feb 70 85 85 80 94
Mar 80 93 82 85 94
average 2003-2005 monthly demand
Seasonal 90
Apr index 95
= 115 100 94
May 113 125 131 average 123 monthly demand
94
Jun 110 115 = 90/94
120 = .957 115 94
Jul 100 102 113 105 94
Aug 88 102 110 100 94
Sept 85 90 95 90 94
Oct 77 78 85 80 94
Nov 75 72 83 80 94
Dec 82 78 80 80 94
Jan 80 85 105 90 94 0.957
Feb 70 85 85 80 94 0.851
Mar 80 93 82 85 94 0.904
Apr 90 95 115 100 94 1.064
May 113 125 131 123 94 1.309
Jun 110 115 120 115 94 1.223
Jul 100 102 113 105 94 1.117
Aug 88 102 110 100 94 1.064
Sept 85 90 95 90 94 0.957
Oct 77 78 85 80 94 0.851
Nov 75 72 83 80 94 0.851
Dec 82 78 80 80 94 0.851
Jan 80 85 105 90 94 0.957
Feb 70 85 Forecast for 80
85 2006 94 0.851
Mar 80 93 82 85 94 0.904
Apr 90 Expected
95 115 annual demand
100 = 1,20094 1.064
May 113 125 131 123 94 1.309
Jun 110 115 120 1,200 115 94 1.223
Jul 100 102Jan113 x .957 = 96 94
105 1.117
12
Aug 88 102 110 100 94 1.064
Sept 85 90 95 1,200 90 94 0.957
Feb x .851 = 85
Oct 77 78 85 12 80 94 0.851
Nov 75 72 83 80 94 0.851
Dec 82 78 80 80 94 0.851
2006 Forecast
140 – 2005 Demand
130 – 2004 Demand
2003 Demand
120 –
Demand
110 –
100 –
90 –
80 –
70 –
| | | | | | | | | | | |
J F M A M J J A S O N D
Time
Problem 4.28
Attendance at Los Angeles's newest Disney-like
attraction, Vacation World, has been as follows:
Quarter Guests Quarter Guests
(in thousands) (in thousands)
Winter 07 73 Summer 08 124
Spring 07 104 Fall 08 52
Summer 07 168 Winter 09 89
Fall 07 74 Spring 09 146
Winter 08 65 Summer 09 205
Spring 08 82 Fall 09 98
Compute seasonal indices using all of the data

Problem 4.28
Problem 4.29
Central States Electric Company estimates its demand trend line (in
millions of kilowatt hours) to be:
D = 77 + 0.43Q
where Q refers to the sequential quarter number and Q = 1 for winter
1986. In addition, the multiplicative seasonal factors are as follows:
Quarter Factor (Index)
Winter 0.8
Spring 1.1
Summer 1.4
Fall 0.7
Forecast energy use for the four quarters of 2011, beginning with winter.
Problem 4.29
2011 is 25 years beyond 1986. Therefore, the 2011 quarter
numbers are 101 through 104
Associative Forecasting
Used when changes in one or more independent
variables can be used to predict the changes in the
dependent variable
Most common technique is linear

regression analysis
We apply this technique just as we did in the

time series example
Forecasting an outcome based on predictor
variables using the least squares technique
^
y = a + bx b=
Sxy - nxy
Sx2 - nx2
where ^ y = computed value of the
variable to be predicted (dependent
variable) a = y - bx
a = y-axis intercept
b = slope of the regression line
x = the independent variable
though to predict the value of the
dependent variable
Example
Sales Local Payroll
($000,000), y ($000,000,000), x
2.0 1
3.0 3
2.5 4
2.0 2 4.0 –
2.0 1
3.0 –
3.5 7 Sales
2.0 –
1.0 –
| | | | | | |
0 1 2 3 4 5 6 7
Area payroll
Example
Sales, y Payroll, x x2 xy
2.0 1 1 2.0
3.0 3 9 9.0
2.5 4 16 10.0
2.0 2 4 4.0
2.0 1 1 2.0
3.5 7 49 24.5
∑y = 15.0 ∑x = 18 ∑x2 = 80 ∑xy = 51.5
b= ∑xy - nxy = 51.5 - (6)(3)(2.5) = .25

x = ∑x/6 = 18/6 = 3
∑x2 - nx2 80 - (6)(32)
y = ∑y/6 = 15/6 = 2.5 a = y - bx = 2.5 - (.25)(3) = 1.75
Example
^
y = 1.75 + .25x Sales = 1.75 + .25(payroll)
If payroll next year is

estimated to be 4.0 –
$600 million, then: 3.25
3.0 –
Sales
Sales = 1.75 + .25(6) 2.0 –

Sales = $325,000
1.0 –
| | | | | | |
0 1 2 3 4 5 6 7
Area payroll
Standard Error of the Estimate
 A forecast is just a point estimate of a future
value
 This point is
4.0 –
actually the 3.25
mean of a 3.0 –
Sales
probability
2.0 –
distribution
1.0 –
| | | | | | |
0 1 2 3 4 5 6 7
Area payroll
Figure 4.9
∑(y - yc)2
Sy,x =
n-2
where y = y-value of each data point
yc = computed value of the dependent variable,
from the regression equation
n = number of data points
Computationally, this equation is
considerably easier to use
∑y2 - a∑y - b∑xy

Sy,x =
n-2
We use the standard error to set up prediction

intervals around the point estimate
∑y2 - a∑y - b∑xy 39.5 - 1.75(15) - .25(51.5)
Sy,x = =
n-2 6-2
Sy,x = .306 4.0 –

3.25
3.0 –
Sales
The standard error of the
estimate is 2.0 –
$30,600 in sales
1.0 –
| | | | | | |
0 1 2 3 4 5 6 7
Area payroll
Problem 4.24
Howard Weiss, owner of a musical instrument distributorship, thinks that
demand for bass drums may be related to the number of television
appearances by the popular group Stone Temple Pilots during previous
month. Weiss has collected the data shown in the following table:
Demand for Bass Drums 3 6 7 5 10 7
number of TV 3 4 7 6 8 5
appearances
A. Graph these data to see whether a linear equations might describe the
relationship between the group's television shows and bass drum sales.
B. use the least squares regression method to derive a forecasting
equation.
C. What is your estimate for bass drum sales if the Stone Temple Pilots
Performed on TV nine times last month?
Problem 4.24
(a) Graph of demand
The observations obviously do not form a straight line but do tend to
cluster about a straight line over the range shown.
Problem 4.24
(b) Least-squares regression:
Problem 4.24
The following figure shows both the data and the resulting equation:
Problem 4.24
(c) If there are nine performances by Stone Temple Pilots, the
estimated sales are:

ch4 3

Uploaded by

Copyright:

Available Formats

ch4 3

Uploaded by

Document Information

Original Description:

Original Title

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

ch4 3

Uploaded by

Copyright:

Available Formats

Chapter 4

1. Find average historical demand for each season

Compute seasonal indices using all of the data

Quarter Factor (Index)

Most common technique is linear

We apply this technique just as we did in the

b= ∑xy - nxy = 51.5 - (6)(3)(2.5) = .25

If payroll next year is

Sales = 1.75 + .25(6) 2.0 –

∑y2 - a∑y - b∑xy

We use the standard error to set up prediction

Sy,x = .306 4.0 –

Demand for Bass Drums 3 6 7 5 10 7

You might also like