Forecasting
August 29, Wednesday
Course
Structure
Introduction
Operations Strategy & Competitiveness
Quality Management
Strategic Decisions (some)
Design of Products
and Services
Process Selection
and Design
Capacity and
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
Outline
 What is forecasting?
 Types of forecasts
 Time-Series forecasting
 Naïve
 Moving Average
 Exponential Smoothing
 Regression
 Good forecasts
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
Why do we need to forecast?
In general, forecasts are almost always 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 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
Quantitative
methods
 Short-range forecast
 Usually < 3 months
 Job scheduling, worker assignments
 Medium-range forecast
Detailed
use of
system
 3 months to 2 years
 Sales/production planning
 Long-range forecast
 > 2 years
 New product planning
Design
of system
Qualitative
Methods
Forecasting During the Life Cycle
Introduction
Qualitative models
- Executive judgment
- Market research
-Survey of sales force
-Delphi method
Sales
Growth
Maturity
Quantitative models
- Time series analysis
- Regression analysis
Time
Decline
Qualitative Forecasting Methods
Qualitative
Forecasting
Executive
Judgement
Sales
Force
Composite
Market
Research/
Survey
Smoothing
Models
Delphi
Method
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.
Qualitative Methods
Delphi Method: 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.
.
Quantitative Forecasting Methods
Quantitative
Forecasting
Regression
Models
Time Series
Models
1. Naive
2. Moving
Average
a) simple
b) weighted
3. Exponential
Smoothing
a) level
b) trend
c) seasonality
Quantitative Forecasting Methods
Quantitative
Forecasting
Regression
Models
Time Series
Models
1. Naive
2. Moving
Average
a) simple
b) weighted
3. Exponential
Smoothing
a) level
b) trend
c) seasonality
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
Demand for product or service
Product Demand over Time
Year
1
Year
2
Year
3
Year
4
Product Demand over Time
Trend component
Demand for product or service
Seasonal peaks
Random
variation
Year
1
Year
2
Actual
demand line
Year
3
Year
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
Models
Models
1. Naive
2. Moving
Average
a) simple
b) weighted
3. Exponential
Smoothing
a) level
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
2a. Simple Moving Average
 Assumes an average is a good estimator of
future behavior
 Used if little or no trend
 Used for smoothing
A t + A t -1 + A t -2 + ... + A t -n 1
Ft 1 =
n
Ft+1
n
At
= Forecast for the upcoming period, t+1
= Number of periods to be averaged
= Actual occurrence in period t
2a. Simple Moving Average
A t + A t -1 + A t -2 + ... + A t -n 1
Ft 1 =
n
You’re manager in Amazon’s electronics
department. You want to forecast ipod sales for
months 4-6 using a 3-period moving average.
Month
1
2
3
4
5
6
Sales
(000)
4
6
5
?
?
?
2a. Simple Moving Average
A t + A t -1 + A t -2 + ... + A t -n 1
Ft 1 =
n
You’re manager in Amazon’s electronics
department. You want to forecast ipod sales for
months 4-6 using a 3-period moving average.
Month
1
2
3
4
5
6
Sales
(000)
4
6
5
?
?
?
Moving Average
(n=3)
NA
NA
NA
(4+6+5)/3=5
2a. Simple Moving Average
What if ipod sales were actually 3 in month 4
Month
1
2
3
4
5
6
Sales
(000)
4
6
5
3?
?
?
Moving Average
(n=3)
NA
NA
NA
5
2a. Simple Moving Average
Forecast for Month 5?
Month
1
2
3
4
5
6
Sales
(000)
4
6
5
3
?
?
Moving Average
(n=3)
NA
NA
NA
5
(6+5+3)/3=4.667
2a. Simple Moving Average
Actual Demand for Month 5 = 7
Month
1
2
3
4
5
6
Sales
(000)
4
6
5
3
?7
?
Moving Average
(n=3)
NA
NA
NA
5
4.667
2a. Simple Moving Average
Forecast for Month 6?
Month
1
2
3
4
5
6
Sales
(000)
4
6
5
3
7
?
Moving Average
(n=3)
NA
NA
NA
5
4.667
(5+3+7)/3=5
2b. Weighted Moving Average
Gives more emphasis to recent data
Ft 1 = w1A t + w 2 A t -1 + w 3A t -2 + ... + w n A t -n 1
Weights
decrease for older data
sum to 1.0
Simple moving
average models
weight all previous
periods equally
Ft 1 = w1A t + w 2 A t -1 + w 3A t -2 + ... + w n A t -n 1
2b. Weighted Moving Average: 3/6, 2/6, 1/6
Month
1
2
3
4
5
6
Sales
(000)
4
6
5
?
?
?
Weighted
Moving
Average
NA
NA
NA
31/6 = 5.167
Ft 1 = w1A t + w 2 A t -1 + w 3A t -2 + ... + w n A t -n 1
2b. Weighted Moving Average: 3/6, 2/6, 1/6
Month
1
2
3
4
5
6
Sales
(000)
4
6
5
3
7
Weighted
Moving
Average
NA
NA
NA
31/6 = 5.167
25/6 = 4.167
32/6 = 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 + a(At - Ft)
et
Ft+1 = Forecast value for time t+1
At
= Actual value at time t
a
= Smoothing constant
Need initial
forecast Ft
to start.
3a. Exponential Smoothing – Example 1
Ft+1 = Ft + a(At - Ft)
i
Week
1
2
3
4
5
6
7
8
9
10
Ai
Demand
820
775
680
655
750
802
798
689
775
Given the weekly demand
data what are the exponential
smoothing forecasts for
periods 2-10 using a=0.10?
Assume F1=D1
3a. Exponential Smoothing – Example 1
Ft+1 = Ft + a(At - Ft)
i
Week
1
2
3
4
5
6
7
8
9
10
Ai
Fi
a = 0.1
Demand
0.6
820
820.00
820.00
775
820.00
820.00
= F1+ a(A793.00
680 F2815.50
1–F1) =820+.1(820–820)
655
801.95
725.20=820
750
787.26
683.08
802
783.53
723.23
798
785.38
770.49
689
786.64
787.00
775
776.88
728.20
776.69
756.28
3a. Exponential Smoothing – Example 1
Ft+1 = Ft + a(At - Ft)
i
Week
1
2
3
4
5
6
7
8
9
10
Ai
Fi
a = 0.1
Demand
0.6
820
820.00
820.00
775
820.00
820.00
680
815.50
793.00
F3 = F2+ a(A2–F2) =820+.1(775–820)
655
801.95
725.20
750
787.26
683.08=815.5
802
783.53
723.23
798
785.38
770.49
689
786.64
787.00
775
776.88
728.20
776.69
756.28
3a. Exponential Smoothing – Example 1
Ft+1 = Ft + a(At - Ft)
i
Week
1
2
3
4
5
6
7
8
9
10
Ai
Demand
820
775
680
655
750
802
798
689
775
Fi
a = 0.1
820.00
820.00
815.50
801.95
787.26
783.53
785.38
786.64
776.88
776.69
0.6
820.00
820.00
793.00
725.20
683.08
This process
723.23
continues
770.49
through week
787.00
10
728.20
756.28
3a. Exponential Smoothing – Example 1
Ft+1 = Ft + a(At - Ft)
i
Week
1
2
3
4
5
6
7
8
9
10
Ai
Demand
820
775
680
655
750
802
798
689
775
Fi
a = 0.1
a = 0.6
820.00
820.00
815.50
801.95
787.26
783.53
785.38
786.64
776.88
776.69
820.00
820.00
793.00
725.20
683.08
723.23
770.49
787.00
728.20
756.28
What if the
a constant
equals 0.6
3a. Exponential Smoothing – Example 2
Ft+1 = Ft + a(At - Ft)
i
Ai
Month Demand
January
120
February
90
March
101
April
91
May
115
June
83
July
August
September
Fi
a = 0.3
a = 0.6
100.00
106.00
101.20
101.14
98.10
103.17
97.12
100.00
112.00
98.80
100.12
94.65
106.86
92.54
What if the
a 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 past 5
months is given in the following table.
3a. Exponential Smoothing – Example 3
Ft+1 = Ft + a(At - Ft)
i
Month
January
February
March
April
May
June
July
Ai
Fi
Demand
80
84
82
85
89
??
a = 0.3
a = 0.5
84.00
82.80
83.16
82.81
83.47
85.13
84.00
82.00
83.00
82.50
83.75
86.38
??
What if the
a 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 a
or
Ft+1 = Ft + a (At - Ft)
Ft+1 = a At + a(1- a) At - 1 + a(1- a)2At - 2 + ...
w1
w2
w3
Weights
a=
a= 0.10
a= 0.90
Prior Period
2 periods ago 3 periods ago
a
a(1 - a)
a(1 - a)2
10%
9%
8.1%
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 a
 Selections should produce a good forecast
…but what is a good forecast?
A Good Forecast
 Has a small error
 Error = Demand - Forecast
Measures of Forecast Error
et
n
A
a. MAD = Mean Absolute Deviation
t
- Ft
t=1
MAD =
n
n
b. MSE = Mean Squared Error
2


A
F
 t t
MSE =
t =1
n
c. RMSE = Root Mean Squared Error RMSE = MSE
 Ideal values =0 (i.e., no forecasting error)
n
A
MAD Example
MAD =
t
- Ft
t=1
n
What is the MAD value given the
forecast values in the table below?
At
Month
1
2
3
4
5
Ft
Sales Forecast
220
n/a
250
255
210
205
300
320
325
315
|At – Ft|
5
5
20
10
= 40
= 40 =10
4
n
2


A
F
 t t
MSE/RMSE Example
MSE =
t =1
n
= 550 =137.5
4
RMSE = √137.5
What is the MSE value?
=11.73
At
Month
1
2
3
4
5
Ft
Sales Forecast
220
n/a
250
255
210
205
300
320
325
315
|At – Ft| (At – Ft)2
5
5
20
10
25
25
400
100
= 550
Measures of Error
1. Mean Absolute Deviation
(MAD)
t
At
Ft
Jan
120
100
Feb
90
106
Mar
101
102
et
20
20
-16
16
-1
1
May
June
91
115
83
400
256
1
10
103
t
1
n
84
6
= 14
2a. Mean Squared Error
(MSE)
100
101
98
MAD 
e
n
-10
April
|et|
n
et2
17
17
289
-20
20
400
-10
84
1,446
MSE 
2
e


 t
1
n
1,446
= 241
6
2b. Root Mean Squared Error
(RMSE)
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 or the
parameters such as α used in the method are wrong.
Note: In the above, n is the number of periods, which is
RMSE  MSE
= SQRT(241)
=15.52
Forecast Bias
 How can we tell if a forecast has a positive or
negative bias?
 TS = Tracking Signal
Good tracking signal has low values
 (actual
t
 forecastt )
RSFE
TS =
= t
MAD
MAD Mean absolute
deviation
30
Quantitative Forecasting Methods
Quantitative
Forecasting
Regression
Models
Time Series
Models
1. Naive
2. Moving
Average
a) simple
b) weighted
3. Exponential
Smoothing
a) level
b) trend
c) seasonality
Exponential Smoothing (continued)
 We looked at using exponential
smoothing to forecast demand with
only random variations
Ft+1 = Ft + a (At - Ft)
Ft+1 = Ft + a At – a Ft
Ft+1 = a At + (1-a) 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.
Sales of Autos (100,000)
Formulas
y=a+bx
where,
x
y
xy  n x y

b
 x  nx
2
x
y
a  y  bx
2
Regression – Example
y = a+ b X
xy  n x y

b
 x  nx
2
MonthAdvertising
January
3
February
4
March
2
April
5
May
4
June
2
July
TOTAL
20
Sales
1
2
1
3
2
1
10
2
a  y  bx
X 2 XY
9.00
3.00
16.00
8.00
4.00
2.00
25.00
15.00
16.00
8.00
4.00
2.00
74
38
General Guiding Principles for
Forecasting
1.
2.
3.
4.
Forecasts are more accurate for larger groups of items.
Forecasts are more accurate for shorter periods of time.
Every forecast should include an estimate of error.
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
FOR JULY 2nd MONDAY
 READ THE CHAPTERS ON
 Forecasting
 Product and service design