FORECASTING

Dr.G.V.R.K.Acharyulu
Professor
School of Management Studies
University of Hyderabad
Hyderabad
• Forecasting is the process of projecting the
values of one or more variables (demand,
price, labor availability) into the future.
• Poor forecasting can result in poor inventory
and staffing decisions, resulting in part
shortages, inadequate customer service, and
many customer complaints.
• All forecasts are wrong, to a degree.
• Good forecasting results in more sales, less
safety stock, better customer service, better
staffing. Key is to reduce error as much as
possible.
 What is Forecasting?
• Educated Guessing
• Process of predicting
a future event Sales will
be $200
• Underlying basis of Million!
all business decisions
– Production
– Inventory
– Personnel
– Facilities
 Types of Forecasts by Time
Horizon
• Short-range forecast
– Up to 1 year; usually less than 3 months
– Job scheduling, worker assignments
• Medium-range forecast
– 3 months to 3 years
– Sales & production planning, budgeting
• Long-range forecast
– 3+ years
– New product planning, facility location
 Types of Forecasts
• Economic forecasts
– Address business cycle, e.g., inflation rate,
money supply, etc.
• Technological forecasts
– Predict technological change
– Predict new product sales
• Demand forecasts
– Predict existing product sales
 Approaches Forecasting
• Qualitative Techniques
–Nonquantitative forecasting techniques based
on expert opinions and intuition. Typically used
when there are no data available.
• Time Series Analysis
–Analyzing data by time periods to determine if
trends or patterns occur.
• Causal Relationship Forecasting
–Relating demand to an underlying factor other
than time.
 Forecasting Approaches

Qualitative Methods Quantitative Methods

 Used when situation is  Used when situation is stable
vague & little data exist & historical data exist
 New products  Existing products
 New technology  Current technology
 Involves intuition,  Involves mathematical
experience techniques
 e.g., forecasting sales  e.g., forecasting sales of
on Internet color televisions
Basic Concepts in Forecasting
• Time series data pattern -- a set of
observations measured over successive
periods of time. A time series pattern may
have one or more of the following five
characteristics:
 Trend
 Seasonal patterns
 Cyclical patterns
 Random variation (or noise)
 Irregular (one time) variation
Use of Forecasting: Operations Decisions

Time Accuracy Number of Management Forecasting

Horizon Required Forecasts Level Method
Process Qualitative
design Long Medium Single or few Top
or causal
Capacity
Qualitative
planning, Long Medium Single or few Top
and causal
facilities
Aggregate Causal and
planning Medium High Few Middle
time series

Scheduling Short Highest Many Lower Time series

Inventory
management Short Highest Many Lower Time series

11-9
Use of Forecasting: Marketing & Finance

Time Accuracy Number of Management Forecasting

Horizon Required Forecasts Level Method
Long-range
marketing Long Medium Single or few Top Qualitative
programs
Pricing
decisions Short High Many Middle Time series

New product Qualitative

introduction Medium Medium Single Top
and causal

Cost
Short High Many Lower Time series
estimating
Capital Causal and
budgeting Medium Highest Few Top
time series

11-10
 Types of Forecasting Models
• Qualitative methods:
– Forecasts generated subjectively by the
forecaster

• Quantitative methods:
– Forecasts generated through mathematical
modeling
 Qualitative Methods

Type Characteristics Strengths Weaknesses

Executive A group of managers Good for strategic or One person's opinion
opinion meet & come up with new-product can dominate the
a forecast forecasting forecast

Market Uses surveys & Good determinant of It can be difficult to

research interviews to identify customer preferences develop a good
customer preferences questionnaire

Delphi Seeks to develop a Excellent for Time consuming to

method consensus among a forecasting long-term develop
group of experts product demand,
technological
changes, and
Overview of Qualitative Methods
• Jury of executive opinion
– Pool opinions of high-level executives, sometimes
augment by statistical models
• Sales force composite
– Estimates from individual salespersons are reviewed
for reasonableness, then aggregated
• Delphi method
– Panel of experts, queried iteratively
• Consumer Market Survey
– Ask the customer
 Jury of Executive Opinion
• Involves small group of high-level managers
– Group estimates demand by working
together
• Combines managerial experience with statistical
models
• Relatively quick
• ‘Group-think’
disadvantage

© 1995 Corel Corp.

 Sales Force Composite

• Each salesperson
projects his or her sales Sales

• Combined at district &

national levels
• Sales reps know
customers’ wants
• Tends to be overly
optimistic
© 1995 Corel Corp.
 Consumer Market Survey
How many hours will
• Ask customers you use the Internet
about purchasing next week?
plans
• What consumers
say, and what
they actually do
are often different
• Sometimes
difficult to answer © 1995 Corel
Corp.
Forecasting Techniques and Common Models:
Time Series Analysis
 Overview of Quantitative Approaches

• Naïve approach
• Moving averages
• Exponential smoothing Time-series
models
• Trend projection

• Linear regression Associative

models
 Naive Approach

Assumes demand in next period is the

same as demand in most recent period
 If May sales were 48, then June sales will
be 48
Sometimes can be cost effective &
efficient
 Quantitative Methods

• Time Series Models:

– Assumes the future will follow same patterns
as the past
 Quantitative Methods

 Causal Models:
Explores cause-and-effect relationships


Uses leading indicators to predict the

future
Time Series Data Composition

• Data = historic pattern + random variation

• Historic pattern to be forecasted:
– Level (long-term average)
– Trend
– Seasonality
– Cycle
• Random Variation cannot be predicted
Time Series Patterns
Components of Time Series
Data
 Product Demand Charted over 4
Years with Trend and Seasonality
Seasonal peaks Trend component
Demand for product or service

Actual
demand line

Average demand
over four years
Random
variation
Year Year Year Year
1 2 3 4
Common
Types of
Trends
 Time Series Models
• Naive:
– The forecast is equal to the actual value observed during the
last period – good for level patterns
• Simple Mean:
– The average of all available data - good for level patterns
• Moving Average:
– The average value over a set time period
(e.g.: the last four weeks)
– Each new forecast drops the oldest data point & adds a new
observation
– More responsive to a trend
 Time Series Models (continued)
• Weighted Moving Average: Ft 1  C t A t

• All weights must add to 100% or 1.00

e.g. Ct .5, Ct-1 .3, Ct-2 .2 (weights add to 1.0)

• Allows emphasizing one period over others; above

indicates more weight on recent data (Ct=.5)

• Differs from the simple moving average that weighs all

periods equally - more responsive to trends
Time Series Models (continued)
• Exponential Smoothing:
Ft 1 αA t  1  α Ft
• Most frequently used time series method because of ease of use and
minimal amount of data needed
• Need just three pieces of data to start:
– Last period’s forecast (Ft)
– Last periods actual value (At)
– Select value of smoothing coefficient, ,between 0 and 1.0
• If no last period forecast is available, average the last few periods or
use naive method
• Higher values (e.g. .7 or .8) may place too much weight on last
period’s random variation
 Causal Models
• Often, leading indicators can help to predict
changes in future demand
• Causal models establish a cause-and-effect
relationship between independent and
dependent variables
• A common tool of causal modeling is linear
regression: Y a  bx
• Additional related variables may require
multiple regression modeling
‘Qualitative’ Forecasting Methods
• Based upon managerial judgment when
there is a lack of data. No specific
model.
• Major methods:
– Delphi Technique
– Market Surveys
– Life-cycles Analogy
– Informed Judgment (naïve models)

11-32
 Time-Series Forecasting
• Components of time-series data:
– Average level
– Trend—general direction (up or down)
– Seasonality—short term recurring cycles
– Cycle—long term business cycle
– Error (random or irregular component)
• “Decomposition” of time-series
– Data are decomposed into the four components
• Moving Averages
• Exponential Smoothing

11-33
Exhibit 11.2 Example of Linear and Nonlinear Trend Patterns
 Seasonal Pattern of Home Natural Gas Usage

Seasonal patterns -- repeatable periods of

ups and downs over time.
 Trend and Business Cycle Characteristics (each data point is
1 year apart)

Cyclical patterns -- regular patterns in a data

series that take place over long periods of
time.
Random variation (sometimes called
noise) is the unexplained deviation of a time
series from a predictable pattern, such as a
trend, seasonal, or cyclical pattern.
Because of these random variations,
forecasts are never 100 percent accurate
(thus the need for contingency
planning).
Examples?
Quarterly Call
Center Volumes
6 yrs.
 Chart of Call Volume

Call center volumes plotted -- an increasing

trend over the six years, along with seasonal
patterns.
 Forecast Errors
In addition to the forecast, one should
compute an estimate of forecast error.
Its uses include:
• To monitor erratic demand observations or
“outliers.”
• To determine when the forecasting method is
no longer tracking actual demand.
• To determine the parameter values that
provide the forecast with the least error.
• To set safety stocks or safety capacity.
 Forecast Errors
• Cumulative Sum of Forecast Error (CFE)
and Mean Error (ME)
• Mean Square Error (MSE)
• Mean Absolute Deviation (MAD)—measure
of deviation in units.
• Mean Absolute Percentage Error (MAPE)
• Tracking Signal (TS)—relative measure of
bias
 Forecast Errors: Formulas

n n
et
Cumulative sum of Mean Absolute | D
CFE =  et | 100
Forecast Errors i=1 Percentage Error MAPE = i=1 t
n

n
n

Mean Square Error e

i=1
2
t
Tracking Signal e t
MSE = TS = i=1

n MAD

n n
Mean Absolute |e | t
Mean Error e t
Deviation MAD = i=1
ME = i=1
n
n
 Tracking Signal

Analogous to control charts in quality

control, viz. if there is no bias, its values
should fluctuate around zero.
Is a relative measure, i.e. the numbers mean
the same for any forecast.
 Tracking Signal
• Measures how well the forecast is predicting
actual values
• Ratio of running sum of forecast errors
(RSFE) to mean absolute deviation (MAD)
– Good tracking signal has low values
• Should be within upper and lower control
limits
Tracking Signal Equation

RSFE
TS 
MAD

n
 y i  ŷ i 
i 
MAD

 forecast error

MAD
 Tracking Signal Computation
Mo Forc Act Error RSFE Abs Cum MAD TS
Error |Error|
1 100 90 -10 -10
2 100 95
3 100 115 RSFE==Errors
RSFE Errors
==NA
NA++(-10)
(-10)==-10
-10
4 100 100
5 100 125
6 100 140
 Tracking Signal Computation
Mo Forc Act Error RSFE Abs Cum MAD TS
Error |Error|
1 100 90 -10 -10 10
2 100 95
3 100 115 Abs
AbsError
Error==|Error|
|Error|
==|-10|
|-10|==10
10
4 100 100
5 100 125
6 100 140
 Tracking Signal Computation
Mo Forc Act Error RSFE Abs Cum MAD TS
Error |Error|
1 100 90 -10 -10 10 10
2 100 95
3 100 115 Cum |Error|== |Errors|
Cum|Error| |Errors|
==NA
NA++10 10==10
10
4 100 100
5 100 125
6 100 140
 Tracking Signal Computation

Mo Forc Act Error RSFE Abs Cum MAD TS

Error |Error|
1 100 90 -10 -10 10 10 10.0
2 100 95
3 100 115 MAD==|Errors|/n
MAD |Errors|/n
==10/1
10/1==10
10
4 100 100
5 100 125
6 100 140
 Tracking Signal Computation
Mo Forc Act Error RSFE Abs Cum MAD TS
Error |Error|
1 100 90 -10 -10 10 10 10.0 -1
2 100 95
3 100 115 TS
TS==RSFE/MAD
RSFE/MAD
==-10/10
-10/10==-1
-1
4 100 100
5 100 125
6 100 140
 Tracking Signal Computation
Mo Forc Act Error RSFE Abs Cum MAD TS
Error |Error|
1 100 90 -10 -10 10 10 10.0 -1
2 100 95 -5
3 100 115
4 100 100 Error
Error==Actual
Actual--Forecast
Forecast
==95
95--100
100==-5
-5
5 100 125
6 100 140
 Tracking Signal Computation
Mo Forc Act Error RSFE Abs Cum MAD TS
Error |Error|
1 100 90 -10 -10 10 10 10.0 -1
2 100 95 -5 -15
3 100 115
4 100 100 RSFE==Errors
RSFE Errors
==(-10)
(-10)++(-5)
(-5)==-15
-15
5 100 125
6 100 140
 Tracking Signal Computation
Mo Forc Act Error RSFE Abs Cum MAD TS
Error |Error|
1 100 90 -10 -10 10 10 10.0 -1
2 100 95 -5 -15 5
3 100 115
4 100 100 Abs
AbsError
Error==|Error|
|Error|
==|-5|
|-5|==55
5 100 125
6 100 140
 Tracking Signal Computation
Mo Forc Act Error RSFE Abs Cum MAD TS
Error |Error|
1 100 90 -10 -10 10 10 10.0 -1
2 100 95 -5 -15 5 15
3 100 115
4 100 100 Cum Error==|Errors|
CumError |Errors|
==10
10++55==15
15
5 100 125
6 100 140
 Tracking Signal Computation
Mo Forc Act Error RSFE Abs Cum MAD TS
Error |Error|
1 100 90 -10 -10 10 10 10.0 -1
2 100 95 -5 -15 5 15 7.5
3 100 115
4 100 100 MAD==|Errors|/n
MAD |Errors|/n
==15/2
15/2==7.5
7.5
5 100 125
6 100 140
 Tracking Signal Computation
Mo Forc Act Error RSFE Abs Cum MAD TS
Error |Error|
1 100 90 -10 -10 10 10 10.0 -1
2 100 95 -5 -15 5 15 7.5 -2
3 100 115
4 100 100 TS
TS==RSFE/MAD
RSFE/MAD
==-15/7.5
-15/7.5==-2
-2
5 100 125
6 100 140
 Plot of a Tracking Signal
Signal exceeded limit

Tracking signal
Upper control limit
+

0
MAD

Acceptable range

-
Lower control limit

Time
 Tracking Signals
160 3
140 2
120

Tracking Singal
Actual Demand

Forecast 1
100
80 Actual demand
0
60 Tracking Signal
-1
40
20 -2
0 -3
0 1 2 3 4 5 6 7
Time
• Forecast error -- the difference
between the actual value and the forecast,
or At – Ft.
• Objective is to minimize forecast
errors with good forecasating.
• Mean AbsoluteΣDeviation
‫(׀‬At – Ft ) ‫ ׀‬Error (MAD)
MAD =
T

• The best MAD?

 Computing the Mean Absolute Deviation
(MAD), the Running Sum of Forecast Errors
(RSFE), and the Tracking Signal from
Forecast and Actual Data
A Plot of the Tracking Signals Calculated
A Normal Distribution with
a Mean = 0 and a MAD = 1
The Percentages of Points Included within the
Control Limits for a Range of 0 to 4 MADs
 Time Series vs. Causal Models

• Time series compares data being forecast

over time, i.e. Time is the independent
variable or x- axis or x-variable.
• Causal models compare data being
forecast against some other data set which
the forecaster may think is a cause of the
forecasted data, e.g. population size
causes newspaper sales.

11-64
 Moving Average Method
• MA is a series of arithmetic means
• Used if little or no trend
• Used often for smoothing
– Provides overall impression of data over time
• Equation

MA   Demand in Previous n Periods

n
 Moving Average Solution
Time Response Moving Moving
Yi Total Average
(n=3) (n=3)
1998 4 NA NA
1999 6 NA NA
2000 5 NA NA
2001 3 4+6+5=15 15/3=5.0
2002 7 6+5+3=14 14/3=4.7
2003 NA 5+3+7=15 15/3=5.0
Forecast Error of Example Time Series Data
 Simple Moving Average
Forecasting
• Not “Single” moving average
• A type of statistical forecast (projects past data into future)
• An average of the most recent n-periods
• Ft+1 = (At + At-1 + At-2) / 3
– A is actual or observed data
– For a 3-period moving average forecast
– Best for short-term, stable data
– The larger the n, the smoother the forecast

• Assumes no trend, seasonal or cyclical

components.
 Summary of 3-Month Moving-Average Forecasts

MAD = ?
 Comparing 2, 3, 4 period simple moving avg. forecasts

MAD = ?
Simple Exponential Smoothing
Forecast -- a forecasting technique that
uses a weighted average of previous
period's forecast and demand. “Simple” not
“Single”
• “smoothes out” the irregular fluctuations
in the time series.
• Ft+1 = Ft + α(A t – Ft)
• α = smoothing constant (0 to 1)
• Must guess for F1 (typically = A1)
•No trend, cyclical or seasonal components
Example of Simple Exponential Smoothing Milk Sales
Forecasts with α = 0.2

MAD = ?
Graph of Simple Exponential Smoothing
Milk Sales Forecasts with α = 0.2
Solved Problem: Develop three-period and
four-period simple moving-average forecasts and
simple exponential smoothing forecast with α =
0.5. Compute the MAD for each. Which
method is best?
Period Demand Period Demand
1 86 7 91
2 93 8 93
3 88
4 89
5 92
6 94
 Exponential Smoothing-
calculation
• Facts:
– September forecast for sales was 15
– September actual sales were 13
– Alpha ( α) is 0.2
– What is the forecast for October?
• Calculation
– October Forecast = September forecast +
α(September actual-September forecast)
=15+0.2(13-15)=15+0.2(-2)=15-0.4=14.6

11-76
• Regression analysis Forecast –
determines the relationship between a single
dependent variable and one or more
independent variables.
Yt = a + bt

• Simple linear regression finds the best values of

a and b using the method of least squares. (Fits
a line between the data points). Y could be
energy costs, t could be time.
• Excel provides a very simple tool to find the
best-fitting regression model for a time series
by selecting the Add Trendline option from the
Chart menu.
 Trend & Linear Regression
Model
• Shows linear relationship between
dependent & explanatory variables
– Example: Sales & advertising (not time)

Y-intercept Slope
^
Y i = a + b X i
Dependent Independent (explanatory)
(response) variable variable
Linear Regression Equations

Equation: Ŷi a  bx i
n
 x i y i  nx y
Slope: b  i n
 x i  nx 
i 

Y-Intercept: a y  bx
 How Good is the Fit?
• Correlation coefficient (r) measures the direction and strength of the linear
relationship between two variables. The closer the r value is to 1.0 the better
the regression line fits the data points.

n  XY  X  Y 
r
n  X   X  * n  Y  Y 
2 2 2 2

428202 189589
r 0.982
4(9253) - (189) * 487,165 589
2 2

R 2 0.982 0.964
2

• Coefficient of determination
R 2 ( ) measures the amount of variation in the
dependent variable about its mean that is explained by the regression line.
Values of ( R 2) close to 1.0 are desirable.
Factory Energy Costs
Least-Squares Regression Model for Energy Cost Forecasting
Judgmental Forecasting
• When no historical data is available, or
when forecasting far into the future,
judgmental forecasting is best (educated
guess).
• The Delphi method consists of
forecasting by expert opinion by gathering
judgments and opinions of key personnel
based on their experience and knowledge
of the situation.
• Can do several rounds of forecasting with
members.
Judgmental Forecasting (cont.)
• Another common approach for making a
judgemental forecast is to gather data using a
consumer survey. Cost of such surveys can be
high.
• The major reasons for using judgmental
methods are:
 Too into future to project current data
 Ability to incorporate unusual or one-time
events
 The difficultly of obtaining the data
necessary for quantitative techniques
Forecasting in Practice
• Managers use a combination of
judgmental and quantitative forecasting
techniques.
• Statistical methods alone cannot account
for such factors as sales promotions,
competitive strategies, unusual economic
disturbances, new products, large one-
time orders, natural disasters, or a “feel”
for the data.
 Selecting a Forecasting Method
• User and system sophistication
– People reluctant to use what they don’t understand
• Time and resources available
– When is forecast needed?
– What is value of forecast?
• Use or decision characteristics, e.g. horizon
• Data availability and quality
• Data pattern
• Don’t force the data to fit the model!
Selecting the Right Forecasting
Model

• The amount & type of available data

– Some methods require more data than
others
• Degree of accuracy required
– Increasing accuracy means more data
• Length of forecast horizon
– Different models for 3 month vs. 10 years