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Introduction to Business
Logistics Management
Lecture 5
Forecasting
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Outline
Forecasting and Evaluation of Forecasting Methods
Forecasting Methods:
Methods for Stationary Series:
Simple and Weighted Moving Average
Exponential smoothing
Trend-Based Methods
Regression
Double Exponential Smoothing: Holts Method
Methods for Seasonality and Trend
Seasonal factors for Stationary series
Seasonal Decomposition
Winterss method
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1. Forecasting
http://www.eduvinet.de/eduvinet/pictures/de01120.gif
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Example: real data
Real Data in 2001:
NA: 9.54
Western Europe: 14.126
Central and Easting Europe : 1.774
Asia: 8.05
Demand Processes
Demand Forecasting
Predict what will happen in the future
Typically involves statistical, causal or other model
Conducted on a routine basis (monthly, weekly, etc.)
Demand Planning
Develop plans for creating or affecting future demand
Results in marketing & sales plans builds unconstrained forecast
Conducted on a routine basis (monthly, quarterly, etc.)
Demand Management
Make decisions in order to balance supply and demand within the
forecasting/planning cycle
Includes forecasting and planning processes
Conducted on an on-going basis as supply and demand changes
Includes yield management, real-time demand shifting, forecast
consumption tracking, etc.
Role of Forecasting in a Supply
Chain
The basis for all planning decisions in a supply
chain
Used for both push and pull processes
Production scheduling, inventory, aggregate planning
Sales force allocation, promotions, new production
introduction
Plant/equipment investment, budgetary planning
Workforce planning, hiring, layoffs
All of these decisions are interrelated
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Characteristics of Forecasts
They are usually wrong!
A good forecast is more than a single number
mean and standard deviation
range (high and low)
Aggregate forecasts are usually more accurate
Accuracy erodes as we go further into the future.
Forecasts should not be used to the exclusion of
known information
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Forecast Horizons
in Operation Planning
Basic Approach
1. Understand the objective of forecasting.
2. Integrate demand planning and forecasting
throughout the supply chain.
3. Identify the major factors that influence the
demand forecast.
4. Forecast at the appropriate level of aggregation.
5. Establish performance and error measures for the
forecast.
Steps in the Forecasting Process
Step 1: Decide what to forecast
Step 2: Analyze appropriate data
Common patterns include:
Level or horizontal
Trend
Seasonality
Cycles
In addition to patterns, data contain random variation
Step 3: Select the forecasting model
select the model best suited for the identified data pattern
Step 4: Generate the forecast
Step 5: Monitor forecast accuracy
measure forecast error
use to improve the forecast process
Types of Forecasting Methods
There are two groups of forecasting methods:
Qualitative
based on subjective opinions
often called judgmental methods
Quantitative
based on mathematical modeling
objective and consistent
can handle large amounts of data and uncover
complex relationships
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Approaches to Forecasting
Subjective Methods -human judgment
Sale force composites
Customer Surveys
Expert Opinion
Delphi -repeat process
Objective Methods -analysis of data
Causal Methods -Econometrics
Y= f (X
1,,,
X
2
, , X
n
)
X
i
is a variable related to Y
Time series Methods
Qualitative vs. Quantitative Methods
Qualitative Forecasting Methods
Strength Weakness
Highly responsive to latest changes in
environment.
Cannot consider many variables.
Can include inside and soft information
difficult to quantify.
Influenced by short term memory.
Can compensate for one-time or unusual events. Difficulty in understanding relationships.
Provide user with a sense of ownership. Biased (optimism, political manipulation, wishful
thinking, lack of consistency).
Quantitative Forecasting Methods
Strength Weakness
Can consider many variables and complex
relationships.
Only as good as the data and model.
Objective. Slow to react to changing environments.
Consistent. Costly and time consuming to model soft
information.
Can process large amounts of information. Requires technical understanding.
Delphi Method
1. Choose the experts to participate representing a variety of
knowledgeable people in different areas
2. Through a questionnaire (or E-mail), obtain forecasts (and any
premises or qualifications for the forecasts) from all participants
3. Summarize the results and redistribute them to the participants
along with appropriate new questions
4. Summarize again, refining forecasts and conditions, and again
develop new questions
5. Repeat Step 4 as necessary and distribute the final results to all
participants
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What is a Time Series?
Set of evenly spaced numerical data
Obtained by observing response variable at regular time
periods
Forecast based only on past values
Assumes that factors influencing past and present will
continue influence in future
Example
Year: 1993 1994 1995 1996 1997
Sales: 78.7 63.5 89.7 93.2 92.1
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Time Series Components
(Components of Demand)
Average demand
Trend
Gradual shift in average demand
Seasonal pattern
Periodic oscillation in demand which repeats
Cycle
Similar to seasonal patterns, length and
magnitude of the cycle may vary
Random movements
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Notations
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Measures of Forecast Error
E
t
= error in period t
= F
t-t,t
D
t
= F
t
D
t
(One Step)
2. Evaluation of Forecast
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E|E
t
|
n
EE
t
2
n
MAD =
MSE =
MAPE =
o = MSE
E[ |E
t
| (100) ] / D
t
n
MSE: Mean Squared Error
MAD: Mean Absolute Deviation
MAPE: Mean Absolute Percentage Error
N: the total number of periods
| |: Absolute value
Evaluation of Forecast
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Evaluation of Forecast:
Example
Month t
Demand
D_t
Foecast F_t Error E_t |E_t| E_t^2 |E_t|/D_t*100
1 200 225
2 240 220
3 300 285
4 270 290
5 230 250
6 260 240
7 210 250
8 275 240
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Evaluation of Forecast:
Example
Month t
Demand
D_t
Foecast F_t Error E_t |E_t| E_t^2 |E_t|/D_t*100
1 200 225 -25 25 625 12.5
8 275 240 35 35 1225 12.73
Average
MSE=?
MAD=?
MAPE=?
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3. Methods for Stationary Series
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3.1 Moving Average Method
(A Time Series Method)
MA is the arithmetic average of the most
recent N observations
Used if little or no trend
Equation:
F
D
N
D D D
N
t
i
i t n
t
t t t n
= =
+ + +
=
1
1 2
...
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Example
Week # of Patient Moving total (n=3) Moving Average (n=3)
1 400
2 380
3 411
4 415
5 390
6 371
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Weighted Moving Average
Method
Used when trend is present
Older data usually less important
Weights based on intuition
Often lay between 0 & 1, & sum to 1.0
Equation
F D D D D
Where
t i i
i t n
t
t t t t t n t n
i
i t n
t
= = + + +
=
=
o o o o
o
1
1 1 2 2
1
1
...
:
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Time Series Methods
Weighted Moving Average
450
430
410
390
370
P
a
t
i
e
n
t
a
r
r
i
v
a
l
s
Week
| | | | | |
0 5 10 15 20 25 30
Actual patient
arrivals
3-week MA
forecast
Weighted Moving Average
Assigned weights
t-1 0.70
t-2 0.20
t-3 0.10
F
4
=
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Time Series Methods
Weighted Moving Average
450
430
410
390
370
P
a
t
i
e
n
t
a
r
r
i
v
a
l
s
Week
| | | | | |
0 5 10 15 20 25 30
Actual patient
arrivals
3-week MA
forecast
Weighted Moving Average
Assigned weights
t-1 0.70
t-2 0.20
t-3 0.10
F
5
=
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3.2 Exponential Smoothing
(Time Series Method)
Form of weighted moving average
Weights decline exponentially
Most recent data weighted most
Requires smoothing constant (o)
Ranges from 0 to 1
Subjectively chosen
Equation:
F D F
t t t
= +
o o
1 1
1 ( )
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Time Series Methods
Exponential Smoothing
450
430
410
390
370
P
a
t
i
e
n
t
a
r
r
i
v
a
l
s
Week
| | | | | |
0 5 10 15 20 25 30
Exponential Smoothing
o = 0.10
F
t
= o D
t-1
+ (1 - o)F
t - 1
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Time Series Methods
Exponential Smoothing
450
430
410
390
370
P
a
t
i
e
n
t
a
r
r
i
v
a
l
s
Week
| | | | | |
0 5 10 15 20 25 30
Exponential Smoothing
o = 0.10
F
t
= o D
t-1
+ (1 - o)F
t - 1
F
3
= (400 + 380)/2=390
D
3
= 411
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Time Series Methods
Exponential Smoothing
450
430
410
390
370
P
a
t
i
e
n
t
a
r
r
i
v
a
l
s
Week
| | | | | |
0 5 10 15 20 25 30
F
4
=
Exponential Smoothing
o = 0.10
F
t
= o D
t-1
+ (1 - o)F
t - 1
F
3
= (400 + 380)/2=390
D
3
= 411
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Time Series Methods
Exponential Smoothing
Week
450
430
410
390
370
P
a
t
i
e
n
t
a
r
r
i
v
a
l
s
| | | | | |
0 5 10 15 20 25 30
F
4
=
D
4
= 415
Exponential Smoothing
o = 0.10
F
t
= o D
t
+ (1 - o)F
t - 1
F
5
=
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Time Series Methods
Exponential Smoothing
450
430
410
390
370
P
a
t
i
e
n
t
a
r
r
i
v
a
l
s
Week
| | | | | |
0 5 10 15 20 25 30
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Comparison of Exponential Smoothing
and Simple Moving Average
Both Methods
Are designed for stationary demand
Require a single parameter
Lag behind a trend, if one exists
Have the same distribution of forecast error if
) 1 /( 2 + = o N
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Comparison of Exponential Smoothing and
Simple Moving Average
Moving average uses only the last N periods
data, exponential smoothing uses all data
Exponential smoothing uses less memory and
requires fewer steps of computation; store only
the most recent forecast!
