Forecasting

What is Forecasting?

■ Process of predicting a future

event based on historical data
■ Educated Guessing
■ Underlying basis of
all business decisions
✔ Production
✔ Inventory
✔ Personnel
✔ Facilities
Course
Structure Introduction

Operations Strategy & Competitiveness

Quality Management
Strategic Decisions (some)
Design of Products Process Selection Capacity and
and Services and Design Facility Decisions

Forecasting

Tactical & Operational Decisions

Forecasting

■ Predict the next number in the pattern:

a) 3.7, 3.7, 3.7, 3.7, 3.7, ?

b) 2.5, 4.5, 6.5, 8.5, 10.5, ?

c) 5.0, 7.5, 6.0, 4.5, 7.0, 9.5, 8.0, 6.5, ?

Forecasting

■ Predict the next number in the pattern:

a) 3.7, 3.7, 3.7, 3.7, 3.7, 3.

7
b) 2.5, 4.5, 6.5, 8.5, 10.5, 12.
5
c) 5.0, 7.5, 6.0, 4.5, 7.0, 9.5, 8.0, 6.5, 9.
0
 Central Tendency

The mean, the median and the mode

■ Mean, median and mode are numbers
that represent a whole set of data or
information. Mean, median and mode are
together called the measures of central
tendency.
 Mean

Example
Find the mean of the following data set:
56, 35, 45, 67, 12, 24, 48, 55, 58, 30
56+35+45+67+12+24+48+55+58+30/10=430/10
= 43

The Mean is 43
 Median

■ The median is the number in an ordered

set of data that is in the middle.
■ If we have a set of data with an odd
number of data points then the median is
the data point in the middle.
■ 1,2,3,4,5,6,7
 Median
■ If we have a set of data with an even number
of data points, then the median is the mean
of the two data points in the middle
■ 1,2,3,4,5,6,7,8
4+5/2=9/2=4.5
 Mode

■ The mode is the most common number

in the set of data.
■ Example

■ 2,5,6,2,2,2,5,6,2

■ The mode=2
Outline

■ What is forecasting?
■ Types of forecasts
■ Time-Series forecasting
✔ Naïve
✔ Moving Average
✔ Exponential Smoothing
✔ Regression
■ Good forecasts
 Why do we need to
forecast?
In general, forecasts are mostly wrong. So,
Throughout the day we forecast very different
things such as weather, traffic, stock market, state
of our company from different perspectives.

Virtually every business attempt is based on

forecasting. Not all of them are derived from
sophisticated methods. However, “Best" educated
guesses about future are more valuable for
purpose of Planning rather than no forecasts and
hence no planning.
Importance of Forecasting in OM
Departments throughout the organization depend
on forecasts to formulate and execute their plans.

Finance needs forecasts to project cash flows and

capital requirements.

Human resources need forecasts to anticipate

hiring needs.

Production needs forecasts to plan production

levels, workforce, material requirements,
inventories, etc.
Importance of Forecasting in OM

Demand is not the only variable of interest to

forecasters.

Manufacturers also forecast worker

absenteeism, machine availability, material
costs, transportation and production lead
times, etc.

Besides demand, service providers are also

interested in forecasts of population, of other
demographic variables, of weather, etc.
Types of Forecasts by Time Horizon
Quantitativ
■ Short-range forecast e
methods
✔ Usually < 3 months
■ Job scheduling, worker assignments Detailed

■ Medium-range forecast use of

system
✔ 3 months to 2 years
■ Sales/production planning

■ Long-range forecast
✔ > 2 years Design
■ New product planning of
system Qualitativ
e
Forecasting During the Life Cycle

Introductio Growt Maturit Declin

n h y e

Qualitative models Quantitative models

- Executive judgment
- Time series analysis
- Market research
- Regression analysis
- Survey of sales force
- Delphi method
Sales

Time
Qualitative Forecasting Methods

Qualitative
Forecasting

Models
Sales Delphi
Executive Market
Force Metho
Judgemen Research
Composit d
t /
e
Survey
Smoothing
 Qualitative
Methods
Briefly, the qualitative methods are:

Executive Judgment: Opinion of a group of high level

experts or managers is pooled

Sales Force Composite: Each regional salesperson

provides his/her sales estimates. Those forecasts are then
reviewed to make sure they are realistic. All regional
forecasts are then pooled at the district and national levels
to obtain an overall forecast.

Market Research/Survey: Solicits input from customers

pertaining to their future purchasing plans. It involves the
use of questionnaires, consumer panels and tests of new
products and services.
Delphi Method
 Qualitative
Delphi Method: Methods
As opposed to regular panels where the individuals
involved are in direct communication, this method eliminates the
effects of group potential dominance of the most vocal members.
The group involves individuals from inside as well as outside the
organization.

Typically, the procedure consists of the following steps:

Each expert in the group makes his/her own forecasts in form of
statements
The coordinator collects all group statements and summarizes
them
The coordinator provides this summary and gives another set
of questions to each
group member including feedback as to the input of other
experts.
The above steps are repeated until a consensus is reached.

.
■ The Delphi method is a process used to arrive at
a group opinion or decision by surveying a panel of
experts. Experts respond to several rounds of
questionnaires, and the responses are aggregated
and shared with the group after each round.
■ For examples , social media surveys like especially
LinkedIn, Facebook, college groups; while
organising college fests cultural fests, university
fests, sponsor groups.
 Quantitative Forecasting

■ Quantitative forecasting are used to develop a

future forecast using past data. Math and statistics are
applied to the historical data to generate forecasts.
Models used in such forecasting are time series (such
as moving averages and exponential smoothing) and
causal (such as regression and econometrics).
Quantitative Forecasting Methods

Quantitative
Forecasting

Time Regression
Models
Series Models

2. 3. Exponential
1.
Average
Moving Smoothing
Naive
a) simple a) level
b) weighted b) trend
c) seasonality
1. Naive Approach

■ Demand in next period is the same as

demand in most recent period
✔ May sales = 48 → June forecast =
48

■ Usually not good

 Regression model

Regression analysis is a statistical technique for

quantifying the relationship between variables. In
simple regression analysis, there is one dependent
variable (e.g. sales) to be forecast and one
independent variable.
 Regression Analysis as a Method for
Forecasting
Regression analysis takes advantage
of the relationship between two
variables. Demand is then
forecasted based on the
knowledge of this relationship and
for the given value of the related
variable.

Ex: Sale of Tires (Y), Sale of Autos

(X) are obviously related

If we analyze the past data of these

two variables and establish a
relationship between them, we
may use that relationship to
forecast the sales of tires given
the sales of automobiles.

The simplest form of the relationship

is, of course, linear, hence it is
referred to as a regression line.
Simple Linear Regression Model
This is called the regression
line and it’s drawn (using a
statistics program like SPSS or
STATA or even Excel) to show
the line that best fits the data.
In other words, “The red line is
the best explanation of the
relationship between the
independent variable and
dependent variable.”
 Regression Method

In addition to drawing the line, your

statistics program also outputs a formula
that explains the slope of the line and
looks something like this:

Y = 200 + 5X+error term

Ignore the error term for now. It refers to

the fact that regression isn’t perfectly
precise. Just focus on the model:

Y = 200 + 5X
What this formula is telling you is
that if there is no “x” then Y = 200.
So, historically, when it didn’t rain at
all, you made an average of 200
sales and you can expect to do the
same going forward assuming other
variables stay the same. And in the
past, for every additional inch of rain,
you made an average of five more
sales. “For every increment that x
goes up one, y goes up by five,”
■ Now let’s return to the error term. You might be
tempted to say that rain has a big impact on
sales if for every inch you get five more sales,
but whether this variable is worth your attention
will depend on the error term. A regression line
always has an error term because, in real life,
independent variables are never perfect
predictors of the dependent variables. Rather the
line is an estimate based on the available data.
So the error term tells you how certain you can
be about the formula. The larger it is, the less
certain the regression line.
Time Series Models

■ Try to predict the future based on past

data

✔ Assume that factors influencing the past will

continue to influence the future
Time Series Models: Components

Random Trend

Seasonal Composite
Product Demand over Time
Demand for product or
service

Year Year Year Year

1 2 3 4
 Product Demand over Time
Trend component
Seasonal
peaks
Demand for product or

Actual
service

Random demand line

variation
Year Year Year Year
1 2 3 4
Now let’s look at some time series approaches to forecasting…
Borrowed from Heizer/Render - Principles of Operations Management, 5e, and Operations Management, 7e
Quantitative Forecasting Methods

Quantitative
Time
Series
Model
s
Models

2. 3. Exponential
1.
Average
Moving Smoothin
Naive
a) simple a)glevel
b) weighted b) trend
c) seasonality
2a. Simple Moving Average

■ Assumes an average is a good estimator of

future behavior
✔ Used if little or no trend
✔ Used for smoothing

Ft+1 = Forecast for the upcoming period,

t+1
n = Number of periods to be averaged
A t = Actual occurrence in period t
2a. Simple Moving Average
You’re manager in Amazon’s electronics
department. You want to forecast ipod sales for
months 4-6 using a 3-period moving average.
Sale
Mont s
h1 (000)
4
2 6
3 5
4 ?
5 ?
6 ?
2a. Simple Moving Average

What if ipod sales were actually 3 in month 4

Sale Moving Average

Mont s (n=3
h1 (000)
4 )N
2 6 A
N
3 5 A
N
4 3? A
5 ? 5
6 ?
2a. Simple Moving Average
You’re manager in Amazon’s electronics
department. You want to forecast ipod sales for
months 4-6 using a 3-period moving average.
Sale Moving Average
Mont s (n=3
h1 (000)
4 )N
2 6 A
N
3 5 A
N
4 ? (4+6+5)/3=
A
5 ? 5
6 ?
2a. Simple Moving Average

Forecast for Month 5?

Sale Moving Average

Mont s (n=3
h1 (000)
4 )N
2 6 A
N
3 5 A
N
4 3 A
5 ? (6+5+3)/3=4.667
5
6 ?
2a. Simple Moving Average

Actual Demand for Month 5 = 7

Sale Moving Average

Mont s (n=3
h1 (000)
4 )N
2 6 A
N
3 5 A
N
4 3 A
5 ?7 5
6 ? 4.667
2a. Simple Moving Average

Forecast for Month 6?

Sale Moving Average

Mont s (n=3
h1 (000)
4 )N
2 6 A
N
3 5 A
N
4 3 A
5 7 5
6 ? (5+3+7)/3=
4.667
2b. Weighted Moving Average
■ Gives more emphasis to recent data

■ Weights
✔ decrease for older data Simple moving
✔ sum to 1.0 average models
weight all
previous
periods equally
2b. Weighted Moving Average: 3/6, 2/6, 1/6

Mont Sale Weighted

h s(000 Moving
) Average
1 4 N
2 6 A
N
3 5 A
N
4 ? 31/6 =A
5 ? 5.167
6 ?
2b. Weighted Moving Average: 3/6, 2/6, 1/6

Mont Sale Weighted

h s(000 Moving
) Average
1 4 N
2 6 A
N
3 5 A
N
4 3 31/6 =A
5 7 25/6 =
5.167
6 32/6 =
4.167
5.333
3a. Exponential Smoothing

■ Assumes the most recent observations

have the highest predictive value
✔ gives more weight to recent time periods

Ft+1 = Ft + α(At -
Ft) e
t
Ft+1 = Forecast value for time t+1 Need
initial
At = Actual value at time t
forecast Ft
α = Smoothing constant to start.
3a. Exponential Smoothing – Example 1
Ft+1 = Ft + α(At -
Ft)
i A
i

Given the weekly demand

data what are the exponential
smoothing forecasts for
periods 2-10 using α=0.10?

Assume F1=D1
3a. Exponential Smoothing – Example 1
Ft+1 = Ft + α(At -
Ft)
i A
i
=
F
i
α

F2 = F1+ α(A1–F1)
=820+.1(820–820)
=820
3a. Exponential Smoothing – Example 1
Ft+1 = Ft + α(At -
Ft)
i A
i
=
F
i
α

F3 = F2+ α(A2–F2)
=820+.1(775–820)
=815.5
3a. Exponential Smoothing – Example 1
Ft+1 = Ft + α(At -
Ft)
i A
i
=
F
i
α

This process
continues
through week
10
3a. Exponential Smoothing – Example 2
Ft+1 = Ft + α(At -
Ft)
i A
i
=
F
i
α α=

What if the
α constant
equals 0.6
3a. Exponential Smoothing – Example 2
Ft+1 = Ft + α(At -
Ft)
i A
i
=
F
i
α α=

What if the
α constant
equals 0.6
 3a. Exponential Smoothing – Example 3

Company A, a personal computer

producer purchases generic parts and
assembles them to final product. Even
though most of the orders require
customization, they have many common
components. Thus, managers of Company
A need a good forecast of demand so that
they can purchase computer parts
accordingly to minimize inventory cost
while meeting acceptable service level.
Demand data for its computers for the
3a. Exponential Smoothing – Example 3
Ft+1 = Ft + α(At -
Ft)
i A
i
=
F
i
α α=

What if the
α constant
equals 0.5
3a. Exponential Smoothing

■ How to choose α
✔ depends on the emphasis you want to place
on the most recent data

■ Increasing α makes forecast more

sensitive to recent data
Forecast Effects of
Smoothing Constant α
Ft+1 = Ft + α (At - Ft)
or Ft+1 = α At + α(1- α) At - 1 + α(1- α)2At - 2 + ...
w1 w2 w3

Weights
α= Prior Period 2 periods ago 3 periods ago
α α(1 - α) α(1 - α)2

α= 0.10
10% 9 8.1
% %
α= 0.90 90% 9 0.9
% %
To Use a Forecasting Method

■ Collect historical data

■ Select a model
✔ Moving average methods
■ Select n (number of periods)
■ For weighted moving average: select weights
✔ Exponential smoothing
■ Select α

■ Selections should produce a good forecast

…but what is a good
 A Good Forecast

♦♦HasError
a small error
= Demand - Forecast
Measures of Forecast Error
e
t

a. MAD = Mean Absolute Deviation

b. MSE = Mean Squared Error

c. RMSE = Root Mean Squared Error

■ Ideal values =0 (i.e., no forecasting error)

 = =1
MAD Example 40 0
4
What is the MAD value given the
forecast values in the table below?
At Ft
Month Sales Forecast |At – Ft|
1 22 n/a
2 0
25 25 5
3 0
21 5
20 5
4 0
30 5
32 2
5 0
32 0
31 0
1
5 5 0
=
 = 550 =137.
MSE/RMSE Example 4 5

What is the MSE RMSE √137.

value? = 5
=11.7
At Ft 3
Month Sales Forecast |At – Ft| (At – Ft)2
1 22 n/a
2 0
25 25 5 2
3 0
21 5
20 5 2
5
4 0
30 5
32 2 5
40
5 0
32 0
31 0
1 0
10
5 5 0 0
=
 Measures of Error
1. Mean Absolute Deviation
(MAD)
t At Ft et |et| e t2
84 = 14
Jan 120 100 20 20 400
6
-1 1
Feb 90 106 6 6
256 2a. Mean Squared Error
- 1 1 (MSE)
Mar 101 102 1
-1 1 10
April 91 101 0 0 0 1,446
1 1 28 = 241
May 115 98 7 7 9 6
-2 2 40
0 0 0 2b. Root Mean Squared Error
June 83 103 (RMSE)
-10 84 1,446
An accurate forecasting system will have small MAD,
MSE and RMSE; ideally equal to zero. A large error
may indicate that either the forecasting method used
= SQRT(241)
or the parameters such as α used in the method are
wrong. =15.52
Note: In the above, n is the number of periods, which is
Forecast Bias

■ How can we tell if a forecast has a positive or

negative bias?

■ TS = Tracking Signal
✔ Good tracking signal has low values

MAD
30
Exponential Smoothing (continued)

■ We looked at using exponential

smoothing to forecast demand with
only random variations
Ft+1 = Ft +
Ft+1α=(AFtt -+
α Ft)– α
A
Ft+1 = αt At
Ftα)
+ (1-
Ft
Exponential Smoothing (continued)

■ We looked at using exponential

smoothing to forecast demand with
only random variations
■ What if demand varies due to
randomness and trend?

■ What if we have trend and seasonality

in the data?
 Regression Analysis as a Method for
Forecasting
Regression analysis takes advantage
of the relationship between two
variables. Demand is then
forecasted based on the
knowledge of this relationship and
for the given value of the related
variable.

Ex: Sale of Tires (Y), Sale of Autos

(X) are obviously related

If we analyze the past data of these

two variables and establish a
relationship between them, we
may use that relationship to
forecast the sales of tires given
the sales of automobiles.

The simplest form of the relationship

is, of course, linear, hence it is
referred to as a regression line.
Formulas

y=a+bx

where,
Regression Method – Example
y = a+ b
X
 General Guiding Principles for
Forecasting

1. Forecasts are more accurate for larger groups of

items.
2. Forecasts are more accurate for shorter periods of
time.
3. Every forecast should include an estimate of error.
4. Before applying any forecasting method, the total
system should be understood.
5. Before applying any forecasting method, the
method should be tested and evaluated.
6. Be aware of people; they can prove you wrong
very easily in forecasting
 Conclusions

■ A forecast can play a major role in

driving company success or failure. At the base
level, an accurate forecast keeps prices low by
optimizing a business operation - cash flow,
production, staff, and financial management. ...
Effective forecasting also has a positive impact on
product success rates.
■ Forecasting allows your company to be proactive
instead of reactive.
■ Forecasting is valuable to businesses because it
gives the ability to make
informed business decisions and develop data-
driven strategies