The document discusses quantitative forecasting methods, including exponential smoothing. Exponential smoothing assigns weights to past observations, with more recent observations receiving greater weight, to generate forecasts. Examples are provided to demonstrate how to calculate forecasts for upcoming time periods using exponential smoothing with different smoothing constants (a). Managers can use exponential smoothing on historical demand data to forecast future demand and support inventory and production planning.

1. Forecasting

2. Introduction
Operations Strategy & Competitiveness
Quality Management
Strategic Decisions (some)
Design of Products
and Services
Process Selection
and Design
Capacity and
Facility Decisions
Tactical & Operational Decisions
Course
Structure
Forecasting

3. 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, ?

4. 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,
3.7
12.5
9.0

5. Outline
 What is forecasting?
 Types of forecasts
 Time-Series forecasting
 Naïve
 Moving Average
 Exponential Smoothing
 Regression
 Good forecasts

6. 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

7. In general, forecasts are almost always wrong. So,
Why do we need to forecast?
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.

8. 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

9. 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.
Importance of Forecasting in OM

10.  Short-range forecast
 Usually < 3 months
 Job scheduling, worker assignments
 Medium-range forecast
 3 months to 2 years
 Sales/production planning
 Long-range forecast
 > 2 years
 New product planning
Types of Forecasts by Time Horizon
Design
of system
Detailed
use of
system
Quantitative
methods
Qualitative
Methods

11. Forecasting During the Life Cycle
Introduction Growth Maturity Decline
Sales
Time
Quantitative models
- Time series analysis
- Regression analysis
Qualitative models
- Executive judgment
- Market research
-Survey of sales force
-Delphi method

12. Qualitative Forecasting Methods
Qualitative
Forecasting
Models
Market
Research/
Survey
Sales
Force
Composite
Executive
Judgement
Delphi
Method
Smoothing

13. 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

14. 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.
.
Qualitative Methods

15. Quantitative Forecasting Methods
Quantitative
Forecasting
Regression
Models
2. Moving
Average
1. Naive
Time Series
Models
3. Exponential
Smoothing
a) simple
b) weighted
a) level
b) trend
c) seasonality

16. Quantitative Forecasting Methods
Quantitative
Forecasting
Regression
Models
2. Moving
Average
1. Naive
Time Series
Models
3. Exponential
Smoothing
a) simple
b) weighted
a) level
b) trend
c) seasonality

17. Time Series Models
 Try to predict the future based on past
data
 Assume that factors influencing the past will
continue to influence the future

18. Random
Seasonal
Trend
Composite
Time Series Models: Components

19. Product Demand over Time
Year
1
Year
2
Year
3
Year
4
Demand
for
product
or
service

20. Product Demand over Time
Year
1
Year
2
Year
3
Year
4
Demand
for
product
or
service
Trend component
Actual
demand line
Seasonal peaks
Random
variation
Now let’s look at some time series approaches to forecasting…
Borrowed from Heizer/Render - Principles of Operations Management, 5e, and Operations Management, 7e

21. Quantitative Forecasting Methods
Quantitative
Models
2. Moving
Average
1. Naive
Time Series
Models
3. Exponential
Smoothing
a) simple
b) weighted
a) level
b) trend
c) seasonality

22. 1. Naive Approach
 Demand in next period is the same as
demand in most recent period
May sales = 48 →
 Usually not good
June forecast = 48

23. 2a. Simple Moving Average
n
A
+
...
+
A
+
A
+
A
=
F 1
n
-
t
2
-
t
1
-
t
t
1
t


 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

24. 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.
n
A
+
...
+
A
+
A
+
A
=
F 1
n
-
t
2
-
t
1
-
t
t
1
t


Month
Sales
(000)
1 4
2 6
3 5
4 ?
5 ?
6 ?

25. 2a. Simple Moving Average
Month
Sales
(000)
Moving Average
(n=3)
1 4 NA
2 6 NA
3 5 NA
4 ?
5 ?
(4+6+5)/3=5
6 ?
n
A
+
...
+
A
+
A
+
A
=
F 1
n
-
t
2
-
t
1
-
t
t
1
t


You’re manager in Amazon’s electronics
department. You want to forecast ipod sales for
months 4-6 using a 3-period moving average.

26. What if ipod sales were actually 3 in month 4
Month
Sales
(000)
Moving Average
(n=3)
1 4 NA
2 6 NA
3 5 NA
4 3
5 ?
5
6 ?
2a. Simple Moving Average
?

27. Forecast for Month 5?
Month
Sales
(000)
Moving Average
(n=3)
1 4 NA
2 6 NA
3 5 NA
4 3
5 ?
5
6 ?
(6+5+3)/3=4.667
2a. Simple Moving Average

28. Actual Demand for Month 5 = 7
Month
Sales
(000)
Moving Average
(n=3)
1 4 NA
2 6 NA
3 5 NA
4 3
5 7
5
6 ?
4.667
2a. Simple Moving Average
?

29. Forecast for Month 6?
Month
Sales
(000)
Moving Average
(n=3)
1 4 NA
2 6 NA
3 5 NA
4 3
5 7
5
6 ?
4.667
(5+3+7)/3=5
2a. Simple Moving Average

30. Gives more emphasis to recent data
Weights
decrease for older data
sum to 1.0
2b. Weighted Moving Average
1
n
-
t
n
2
-
t
3
1
-
t
2
t
1
1
t A
w
+
...
+
A
w
+
A
w
+
A
w
=
F 

Simple moving
average models
weight all previous
periods equally

31. 2b. Weighted Moving Average: 3/6, 2/6, 1/6
Month Weighted
Moving
Average
1 4 NA
2 6 NA
3 5 NA
4 31/6 = 5.167
5
6 ?
?
?
1
n
-
t
n
2
-
t
3
1
-
t
2
t
1
1
t A
w
+
...
+
A
w
+
A
w
+
A
w
=
F 

Sales
(000)

32. 2b. Weighted Moving Average: 3/6, 2/6, 1/6
Month Sales
(000)
Weighted
Moving
Average
1 4 NA
2 6 NA
3 5 NA
4 3 31/6 = 5.167
5 7
6
25/6 = 4.167
32/6 = 5.333
1
n
-
t
n
2
-
t
3
1
-
t
2
t
1
1
t A
w
+
...
+
A
w
+
A
w
+
A
w
=
F 


33. 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.

34. 3a. Exponential Smoothing – Example 1
Week Demand
1 820
2 775
3 680
4 655
5 750
6 802
7 798
8 689
9 775
10
Given the weekly demand
data what are the exponential
smoothing forecasts for
periods 2-10 using a=0.10?
Assume F1=D1
Ft+1 = Ft + a(At - Ft)
i Ai

35. Week Demand 0.1 0.6
1 820 820.00 820.00
2 775 820.00 820.00
3 680 815.50 793.00
4 655 801.95 725.20
5 750 787.26 683.08
6 802 783.53 723.23
7 798 785.38 770.49
8 689 786.64 787.00
9 775 776.88 728.20
10 776.69 756.28
Ft+1 = Ft + a(At - Ft)
3a. Exponential Smoothing – Example 1
a =
F2 = F1+ a(A1–F1) =820+.1(820–820)
=820
i Ai Fi

36. Week Demand 0.1 0.6
1 820 820.00 820.00
2 775 820.00 820.00
3 680 815.50 793.00
4 655 801.95 725.20
5 750 787.26 683.08
6 802 783.53 723.23
7 798 785.38 770.49
8 689 786.64 787.00
9 775 776.88 728.20
10 776.69 756.28
Ft+1 = Ft + a(At - Ft)
3a. Exponential Smoothing – Example 1
a =
F3 = F2+ a(A2–F2) =820+.1(775–820)
=815.5
i Ai Fi

37. Week Demand 0.1 0.6
1 820 820.00 820.00
2 775 820.00 820.00
3 680 815.50 793.00
4 655 801.95 725.20
5 750 787.26 683.08
6 802 783.53 723.23
7 798 785.38 770.49
8 689 786.64 787.00
9 775 776.88 728.20
10 776.69 756.28
Ft+1 = Ft + a(At - Ft)
This process
continues
through week
10
3a. Exponential Smoothing – Example 1
a =
i Ai Fi

38. Week Demand 0.1 0.6
1 820 820.00 820.00
2 775 820.00 820.00
3 680 815.50 793.00
4 655 801.95 725.20
5 750 787.26 683.08
6 802 783.53 723.23
7 798 785.38 770.49
8 689 786.64 787.00
9 775 776.88 728.20
10 776.69 756.28
Ft+1 = Ft + a(At - Ft)
What if the
a constant
equals 0.6
3a. Exponential Smoothing – Example 1
a = a =
i Ai Fi

39. Month Demand 0.3 0.6
January 120 100.00 100.00
February 90 106.00 112.00
March 101 101.20 98.80
April 91 101.14 100.12
May 115 98.10 94.65
June 83 103.17 106.86
July 97.12 92.54
August
September
Ft+1 = Ft + a(At - Ft)
What if the
a constant
equals 0.6
3a. Exponential Smoothing – Example 2
a = a =
i Ai Fi

40. 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

41. Month Demand 0.3 0.5
January 80 84.00 84.00
February 84 82.80 82.00
March 82 83.16 83.00
April 85 82.81 82.50
May 89 83.47 83.75
June 85.13 86.38
July ?? ??
Ft+1 = Ft + a(At - Ft)
What if the
a constant
equals 0.5
3a. Exponential Smoothing – Example 3
a = a =
i Ai Fi

42. 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
3a. Exponential Smoothing

43. Ft+1 = a At + a(1- a) At - 1 + a(1- a)2At - 2 + ...
Forecast Effects of
Smoothing Constant a
Weights
Prior Period
a
2 periods ago
a(1 - a)
3 periods ago
a(1 - a)2
a=
a= 0.10
a= 0.90
10% 9% 8.1%
90% 9% 0.9%
Ft+1 = Ft + a (At - Ft)
or
w1 w2 w3

44.  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
To Use a Forecasting Method
…but what is a good forecast?

45. A Good Forecast
Has a small error
 Error = Demand - Forecast

46. Measures of Forecast Error
b. MSE = Mean Squared Error  
n
F
-
A
=
MSE
n
1
=
t
2
t
t

MAD =
A - F
n
t t
t=1
n

et
 Ideal values =0 (i.e., no forecasting error)
MSE
=
RMSE
c. RMSE = Root Mean Squared Error
a. MAD = Mean Absolute Deviation

47. MAD Example
Month Sales Forecast
1 220 n/a
2 250 255
3 210 205
4 300 320
5 325 315
What is the MAD value given the
forecast values in the table below?
MAD =
A - F
n
t t
t=1
n

5
5
20
10
|At – Ft|
Ft
At
= 40
= 40
4
=10

48. MSE/RMSE Example
Month Sales Forecast
1 220 n/a
2 250 255
3 210 205
4 300 320
5 325 315
What is the MSE value?
5
5
20
10
|At – Ft|
Ft
At
= 550
4
=137.5
(At – Ft)2
25
25
400
100
= 550
 
n
F
-
A
=
MSE
n
1
=
t
2
t
t

RMSE = √137.5
=11.73

49. Measures of Error
t At Ft et |et| et
2
Jan 120 100 20 20 400
Feb 90 106 256
Mar 101 102
April 91 101
May 115 98
June 83 103
1. Mean Absolute Deviation
(MAD)
n
e
MAD
n
t

 1
2a. Mean Squared Error
(MSE)
 
MSE
e
n
t
n


2
1
2b. Root Mean Squared Error
(RMSE)
RMSE MSE

-16 16
-1 1
-10
17
-20
10
17
20
1
100
289
400
-10 84 1,446
84
6
= 14
1,446
6
= 241
= SQRT(241)
=15.52
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

50. deviation
absolute
Mean
)
(
=
MAD
RSFE
=
TS
 
t
t
t forecast
actual
30
 How can we tell if a forecast has a positive or
negative bias?
 TS = Tracking Signal
Good tracking signal has low values
Forecast Bias
MAD

51. Quantitative Forecasting Methods
Quantitative
Forecasting
Regression
Models
2. Moving
Average
1. Naive
Time Series
Models
3. Exponential
Smoothing
a) simple
b) weighted
a) level
b) trend
c) seasonality

52.  We looked at using exponential
smoothing to forecast demand with
only random variations
Exponential Smoothing (continued)
Ft+1 = Ft + a (At - Ft)
Ft+1 = Ft + a At – a Ft
Ft+1 = a At + (1-a) Ft

53. 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?

54. 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)

55. Formulas
x
b
y
a 





 2
2
x
n
x
y
x
n
xy
b
x
y

x

y
y = a + b x
where,

56. MonthAdvertising Sales X 2
XY
January 3 1 9.00 3.00
February 4 2 16.00 8.00
March 2 1 4.00 2.00
April 5 3 25.00 15.00
May 4 2 16.00 8.00
June 2 1 4.00 2.00
July
TOTAL 20 10 74 38
y = a + b X
Regression – Example




 2
2
x
n
x
y
x
n
xy
b x
b
y
a 


57. 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

58. FOR JULY 2nd MONDAY
 READ THE CHAPTERS ON
 Forecasting
 Product and service design