Forecasting Models & Their Applications

Operations Management
Forecasting
Models & Their Applications

OperationsManagement
Lecture Outline
 Definitions of forecasting
 Roles of Forecasting and applications
 Components of Forecasting Demand
 List the elements of a good forecast
 The steps in the forecasting process
 Compare and contrast qualitative and
quantitative approaches to forecasting
 Advantages and disadvantages of each
 Time Series Methods
 Forecast Accuracy
 Time Series Forecasting Using Excel (if possible)
 Regression Methods
Forecasting: Models and Applications

Forecasting ?
• Predicting the future based on the historical data.
• A statement about the future value of a variable of interest
such as demand.
• Forecasting is used to make informed decisions.
- Long-range
- Short-range
 It is the basis for budgeting, planning capacity, sales,
production and inventory, personnel, purchasing, and more.
Forecasts play an important role in the planning process to
anticipate the future plan accordingly.
Forecasting

Data based - expecting that history repeats itself in a certain
way; usually given in the form of a time series, a
chronological sequence of observed data with respect to a
certain variable.
Theory based - where the external factors determine events.
Qualitative forecast methods
- subjective
Quantitative forecast methods
- based on mathematical formulas
Types of Forecasting
Two main methods:
Another distinction consists of:

Decisions and activities throughout an organization
Accounting Cost/profit estimates
Finance Cash flow and funding
Human Resources Hiring/recruiting/training
Marketing Pricing, promotion, strategy
MIS IT/IS systems, services
Operations Schedules, MRP, workloads
Product/service design New products and services
Uses of Forecasting

• Assumes causal system
Past => Present => Future
• Forecasts rarely perfect because of randomness
• Forecasts more accurate for groups vs. individuals
• Forecast accuracy decreases as time horizon increases
Features of Forecasting
I see that you will
get an A this semester.Timely
AccurateReliable
Written
Elements of a
Good Forecast

Depend on
• time frame
• demand behavior
• causes of behavior
Indicates how far into the future is forecast
• Short- to mid-range forecast
• typically encompasses the immediate future
• daily up to two years
• Long-range forecast
• usually encompasses a period of time longer
than two years
Types of Forecasting Methods
Time Frame

 Trend
• a gradual, long-term up or down movement of
demand
 Random variations
• movements in demand that do not follow a pattern
 Cycle
• an up-and-down repetitive movement in demand
 Seasonal pattern
• an up-and-down repetitive movement in demand
occurring periodically
Demand Behavior

Time
(a) Trend
Time
(d) Trend with seasonal pattern
Time
(c) Seasonal pattern
Time
(b) Cycle
DemandDemand
DemandDemand
Random
movement
Demand Behavior

 Time series
• statistical techniques that use historical demand
data to predict future demand
 Regression methods
• attempt to develop a mathematical relationship
between demand and factors that cause its behavior
 Qualitative
• use management judgment, expertise, and opinion
to predict future demand
Regular Behavior

Steps of Forecasting Technique
Step 1 Determine purpose of forecast
Step 2 Establish a time horizon
Step 3 Select a forecasting technique
Step 4 Obtain, clean and analyze data
Step 5 Make the forecast
Step 6 Monitor the forecast
“The forecast”

OperationsManagement Forecasting: Models and Applications
6. Check forecast
accuracy with one
or more measures
4. Select a forecast
model that seems
appropriate for data
5. Develop/compute
forecast for period
of historical data
8a. Forecast over
planning horizon
9. Adjust forecast
based on additional
qualitative information
and insight
10. Monitor results
and measure
forecast accuracy
8b. Select new
forecast model or
adjust parameters
of existing model
7.
Is accuracy
of forecast
acceptable?
1. Identify the
purpose of forecast
3. Plot data and
identify patterns
2. Collect
historical data
No
Yes
Copyright 2011 John Wiley & Sons, Inc.
Steps of Forecasting Technique

 Judgmental
- uses subjective inputs for qualitative methods
 Time series
- uses historical data assuming the future will be like
the past or present data
 Associative models
- uses explanatory variables to predict the future
Forecasting Techniques

Forecasts are largely intuitive, whereas others integrate data
and perhaps even mathematical or statistical techniques.
Judgmental forecasts consist of:
 forecasts by experts in the same field,
 forecasts by individual sales people,
 forecasts by division or product-line managers,
 consumer surveys,
 outside/ external experts or technical reports
Historical analogy relies on comparisons; Delphi method
o Opinions of managers and staff
o Achieves a consensus forecast
Opinion and Judgmental Methods

Time series Analysis
 A time series is a set of observations of a variable at
regular intervals over time.
 Assume that what has occurred in the past will continue
to occur in the future.
 Components of a time series are generally classified as
trend T, cyclical C, seasonal S, and random or irregular R.
 Time series analysis includes:
• moving average
• exponential smoothing
• linear trend line
 Data are tabulated or graphed to show the nature of the
time dependence.

Following are the steps in time series forecasting:
1. Plot historical data to confirm relationship (e.g.,
linear, exponential, logarithmic etc).
2. Develop a trend equation (T ) to describe the data.
3. Develop a seasonal index (e.g., monthly index values).
4. Project trend into the future (e.g., monthly trend values).
5. Multiply trend values by corresponding seasonal
index values.
6. Modify projected values by any knowledge of:
• Cyclical business conditions (C) ,
• Anticipated irregular effects (R) .
Time series forecasting procedure

 Simple to use
 Virtually no cost
 Quick and easy to prepare
 Data analysis is nonexistent
 Easily understandable
 Cannot provide high accuracy
 Can be a standard for accuracy
Naïve Forecasts
 The forecast for any period equals the previous period’s
actual value.
 Demand in current period is used as next period’s
forecast
Why Naïve Forecasts ?
Uh, give me a minute....
We sold 250 wheels last week....
Now, next week we should
sell.... 250???

Jan 120
Feb 90
Mar 100
Apr 75
May 110
June 50
July 75
Aug 130
Sept 110
Oct 90
ORDERS
Month Per Month
-
120
90
100
75
110
50
75
130
110
90Nov - ??
Forecast
Naïve Forecasts
Mathematical formula
used in Naïve:
• Stable time series
data
F (t ) = A (t -1)
• Seasonal variations
F (t ) = A (t – n )
• Data with trends
F (t ) = A ( t - 1) +
(A (t -1) – A(t – 2 ))

Three methods for describing trend are:
1. Moving average,
2. Hand fitting, and
3. Least squares.
A centered moving average is obtained by summing and
averaging the values from a given number of periods
repetitively, each time deleting the oldest value and adding
a new value.
Moving averages can smooth out fluctuations in any data,
while preserving the general pattern of the.
Trend Technique
Moving Average Method:

The generalized formula for moving average method is:
 Moving average / simple moving average
 Weighted moving average
 Exponential smoothing
Moving Average Method Cont…
𝑴𝑨 =
𝒙
Number of Period
Techniques for Averaging
– Averaging method
– Weights most recent data more strongly
– Reacts more to recent changes
– Widely used, accurate method

A technique that averages a number of recent actual
values, updated as new values become available.
MAn =
n
i = 1

Di
n
Simple Moving average
where
n = number of periods
in the moving
average
Di = demand in period i
Ft = MAn=
n
At-n + … At-2 + At-1
Or,

3-month Simple Moving Average
Jan 120
Feb 90
Mar 100
Apr 75
May 110
June 50
July 75
Aug 130
Sept 110
Oct 90
Nov -
Orders
Month Per Month
MA3 =
3
i = 1
 Di
3
=
90 + 110 + 130
3
= 110 orders for Nov
–
–
–
103.3
88.3
95.0
78.3
78.3
85.0
105.0
110.0
Moving
Average

Jan 120
Feb 90
Mar 100
Apr 75
May 110
June 50
July 75
Aug 130
Sept 110
Oct 90
Nov -
Orders
Month Per Month
–
–
–
–
–
99.0
85.0
82.0
88.0
95.0
91.0
Moving
Average
5-month Simple Moving Average
MA5 =
5
i = 1
 Di
5
=
90 + 110 + 130+75+50
5
= 91 orders for Nov

150 –
125 –
100 –
75 –
50 –
25 –
0 – | | | | | | | | | | |
Jan Feb Mar Apr May June July Aug Sept Oct Nov
Actual
Orders
Month
5-month
3-month
Effect of 3-month and 5-month moving average

 More recent values in a series are given more weight in
computing the forecast.
 Adjusts moving average method to more closely reflect
data fluctuations
Weighted Moving Average
WMAn =
i = 1
 Wi Di
where
Wi = the weight for period i,
between 0 and 100 %
Wi = 1.00
n
Ft = WMAn=
wnAt-n + … wn-1At-2 + w1At-1
n

MONTH WEIGHT DATA
August 17% 130
September 33% 110
October 50% 90
WMA3 =
3
i = 1
 Wi Di
= (0.50)(90) + (0.33)(110) + (0.17)(130)
= 103.4 orders
November Forecast
Example: Weighted Moving Average

Example: Weighted Moving Average
Shipments (in tons) of welded tube by an aluminum producer
are shown below:
a) Graph the data, and comment on the relationship.
b) Compute a 3-year moving average, plot it as a dotted
line, and use it to forecast shipments in year 12.
c) Using a weight of 3 for the most recent data, 2 for
the next, and 1 for the oldest, forecast shipments in
year 12.
Ref. Operations management, A. Kumar and N. Suresh, New Age, pp. 108-109

Solution:
Year Shipments 3-y moving
average
1 2 -
2 3 3.7
3 6 6.3
4 10 8.0
5 8 8.3
6 7 9.0
7 12 11.0
8 14 13.3
9 14 15.3
10 18 17.0
11 19 -
The MA forecast for year 12 would be
that of the latest average, 17.0 tons.
The data are plotted as shown:
Moving average:
= 17.8 tons
Example: WMA Cont…

The equation used for forecast for next period is:
where:
Ft +1 = forecast for next period
Dt = actual demand for present period
Ft = previously determined forecast for present period
𝜶 = weighting factor, smoothing constant
Exponential Smoothing
𝑭 𝒕+𝟏 = 𝜶𝑫 𝒕 + 𝟏 − 𝜶 𝑭 𝒕
Effect of Smoothing Constant
0.0  1.0
If = 0.20, then Ft +1 = 0.20 Dt + 0.80 Ft If = 0, then Ft +1 = 0 Dt + 1 Ft = Ft
Forecast does not reflect recent data
If = 1, then Ft +1 = 1 Dt + 0 Ft = Dt ; Forecast based only on most recent data

Example: Exponential Smoothing
Period Month Demand
1 Jan 37
2 Feb 40
3 Mar 41
4 Apr 37
5 May 45
6 Jun 50
7 Jul 43
8 Aug 47
9 Sep 56
10 Oct 52
11 Nov 55
12 Dec 54
F2 = D1 + (1 - )F1
= (0.30)(37) + (0.70)(37)
= 37
F3 = D2 + (1 - )F2
= (0.30)(40) + (0.70)(37)
= 37.9
F13 = D12 + (1 - )F12
= (0.30)(54) + (0.70)(50.84)
= 51.79
Letting,  =0.30
and so on. Similarly …

Forecast, Ft + 1
Period Month Demand ( = 0.3) ( = 0.5)
1 Jan 37 – –
2 Feb 40 37.00 37.00
3 Mar 41 37.90 38.50
4 Apr 37 38.83 39.75
5 May 45 38.28 38.37
6 Jun 50 40.29 41.68
7 Jul 43 43.20 45.84
8 Aug 47 43.14 44.42
9 Sep 56 44.30 45.71
10 Oct 52 47.81 50.85
11 Nov 55 49.06 51.42
12 Dec 54 50.84 53.21
13 Jan – 51.79 53.61
Example: Exponential Smoothing

70 –
60 –
50 –
40 –
30 –
20 –
10 –
0 – | | | | | | | | | | | | |
1 2 3 4 5 6 7 8 9 10 11 12 13
Actual
Orders
Month
 = 0.50
 = 0.30

Parabolic
Exponential
Growth
Common Nonlinear Trends

The generalized equation
y = a + bx
Where,
a = intercept
b = slope of the line
x = time period
y = forecast for
demand for period x
where
n = number of periods
= mean of the x values
= mean of the y values
𝒃 =
𝒙𝒚 − 𝒏. 𝒙. 𝒚
𝒙 𝟐 − 𝒏 𝒙 𝟐
𝒂 = 𝒚 − 𝒃 𝒙
𝒙 =
𝒙
𝒏
𝒚 =
𝒚
𝒏
Linear Trend Line

Example: Linear Trend Line
x(Period) y(Demand) xy x2
1 73 37 1
2 40 80 4
3 41 123 9
4 37 148 16
5 45 225 25
6 50 300 36
7 43 301 49
8 47 376 64
9 56 504 81
10 52 520 100
11 55 605 121
12 54 648 144
78 557 3867 650
𝒙 =
𝟕𝟖
𝟏𝟐
= 𝟔. 𝟓 𝒚 =
𝟓𝟓𝟕
𝟏𝟐
= 𝟒𝟔. 𝟒𝟐
𝒃 =
𝒙𝒚−𝒏. 𝒙. 𝒚
𝒙 𝟐−𝒏 𝒙 𝟐 = 1.72
𝒂 = 𝒚 − 𝒃 𝒙
= 𝟒𝟔. 𝟒𝟐 − 𝟏. 𝟕𝟐 × 𝟔. 𝟓 = 𝟑𝟓. 𝟐
Linear trend line y = 35.2 + 1.72x
Forecast for period 13, y = 57.56 units

 Linear regression
• mathematical technique that relates a dependent
variable to an independent variable in the form of a
linear equation
 Correlation
• a measure of the strength of the relationship between
independent and dependent variables
Regression Method
The generalized equation, y = a + bx
Where, a = intercept, b = slope of the line, x = time
period, and y = forecast for demand for period x
Linear Regression
n = number of periods𝒃 =
𝒙𝒚 − 𝒏. 𝒙. 𝒚
𝒙 𝟐 − 𝒏 𝒙 𝟐
𝒂 = 𝒚 − 𝒃 𝒙

From data,
𝒙 = 𝟔. 𝟏𝟐𝟓
X
wins
Y
attendance
xy x2
4 36.3 145.2 16
6 40.1 240.6 36
6 41.2 247.2 36
8 53.0 424.0 64
6 44.0 264.0 36
7 45.6 319.2 49
5 39.0 195.0 25
7 47.5 332.5 49
49 346.7 2167.7 311
𝒚 = 𝟒𝟑. 𝟑𝟔
𝒃 = 𝟒. 𝟎𝟔 𝒂 = 𝟏𝟖. 𝟒𝟔
Example: Linear Regression

 Correlation, r
• Measure of strength of relationship
• Varies between -1.00 and +1.00
 Coefficient of determination, r2
• Percentage of variation in dependent variable resulting
from changes in the independent variable
Computing coefficient of correlation:
Correlation
n xy -  x y
[n x2 - ( x)2] [n y2 - ( y)2]
r =
(8)(2,167.7) - (49)(346.9)
[(8)(311) - (49)2] [(8)(15,224.7) - (346.9)2]
r = =0.947

Multiple Regression
Study the relationship of demand to two or more independent
variables
The relationship is expressed as:
y = 0 + 1x1 + 2x2 … + kxk
where
0 = the intercept
1, … , k = parameters for the independent variables
x1, … , xk = independent variables

r2, the coefficient
of determination
Regression equation
coefficients for x1 and x2
Multiple Regression
y = 19,094.42 + 3560.99 x1 + .0368 x2
y = 19,094.42 + 3560.99 (7) + .0368 (60,000)
= 46,229.35

Seasonal Adjustments
• Repetitive increase/ decrease in demand
• Use seasonal factor to adjust forecast
Seasonal factor = Si =
Di
D
year Demand ( in 1000 units)
1 2 3 4
2002 12.686 6.3 17.5 45.0
2003 14.110 7.5 18.2 50.1
2004 15.31 8.1 19.6 53.6
Total 42.029 21.9 55.3 148.7
𝑆1 =
𝐷1
𝐷
=
42.029
148.7
= 0.28
𝑆4 =
55.3
148.7
= 0.37
𝑆3 =
21.9
148.7
= 0.15
𝑆2 = 0.20
SF1 = (S1) (F5) = (0.28)(58.17) = 16.28
SF2 = (S2) (F5) = (0.20)(58.17) = 11.63
SF3 = (S3) (F5) = (0.15)(58.17) = 8.73
SF4 = (S4) (F5) = (0.37)(58.17) = 21.53
y = 40.97 + 4.30x =
40.97 + 4.30(4) = 58.17
For 2005

=B5*(C11-C10)+
(1-B5)*D10
=C10+D10
=ABS(B10-E10)
=SUM(F10:F20)
=G22/11
Exponentially Smoothing using Excel

Click on “Insert” then “Line”

=INTERCEPT(B5:B12,A5:A12)
=CORREL(B5:B12,A5:A12)=SUM(B5:B12)

 No single technique works in every situation
 Two most important factors
o Cost and Accuracy
 Other factors include the availability of:
 Historical data
 Computers
 Time needed to gather and analyze the data
 Forecast horizon
 Forecasts are the basis for many decisions
 Work to improve short-term forecasts
 Accurate short-term forecasts improve
• Profits
• Lower inventory levels
• Reduce inventory shortages
• Improve customer service levels
• Enhance forecasting credibility
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