BSc. Recap:
Demand Forecasting
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#1
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
The Forecasting Horizon
Long term (multiple years):
• Plant relocation: forecasting economic trends
• Mergers & acquisitions:
forecasting market development
Medium term (few months – 2 years):
• Workforce planning: production forecasting
• Equipment purchasing:
forecasting capacity requirements
Short term (up to a few months):
• Inventory control: demand forecasting
• Distribution: demand forecasting
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#2
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Forecasting Methods
• Qualitative Methods
– Expert judgment (sales force, management,…)
– Customer polls
– Delphi-Method
• Quantitative Methods
– Univariate methods:
Our focus
• Time series of past demand data
– Multivariate methods:
• Include additional explanatory variables
(e.g. competition, economic development,…)
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#3
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Time Series Analysis
• Goal: Short-/medium-term demand forecast
• General setting & notation:
past
... t-3
t-2
today
t-1
... Dt-3 Dt-2 Dt-1
known demand
future
t
t+1
t+2
t+3
Dt
Dt+1
Dt+2
Dt+3
time
random variables
^
^
^
D
D
D
estimates
t+1
t+2
t+3
Caution: Sales ≠ demand…
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#4
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Time Series Forecasting
• Basic underlying assumption:
Historical trends are relevant for future development
• Appropriate only if underlying pattern remains
unchanged
• Regularly re-check your model to make sure it is still
valid!
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#5
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Time Series Analysis
General approach:
1) Choose forecasting model
2) Estimate model parameters
3) Forecasting (Extrapolation)
4) Ex-post comparison of forecast
and actual demand
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Updating
Recap: Forecasting
#6
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Time Series Models
• Analyze structural properties of the data series:
– Level
– Trend
– Seasonal fluctuations
– Impact of special events (e.g. marketing activity, price
changes,…)
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#7
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Time Series Models
• Identification of appropriate model:
structural properties + unexplained („random“) error term
Dt = f(t) + et, with E[et] = 0 und Var[et] = s2
• Common models:
1) Level model
f(t) = a
2) Linear trend model
f(t) = a + bt
3) Non-linear trend model
f(t) non-linear (e.g. exponential,…)
4) Seasonal fluctuations
additive: f(t) = a + bt + s(t)
multiplikative: f(t) = (a + bt)·s(t)
1.
t
2.
t
3.
t
4.
t
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#8
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Example
42
Demand
40
38
36
34
32
30
0
5
10
15
20
25
30
Month
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#9
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Level Model
•
Model: Dt = a + et
•
Estimation of â, based on D1 … Dt
•
^
Forecast Dt+i = â
(i = 1, 2, 3, …. )
 How to estimate â ?
 Least-squares approach (linear regression):
1
â = average = ( D1  ....  Dt )
t
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#10
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Level Model: Example
42
40
Demand
Forecast
38
36
34
32
30
0
5
10
15
20
25
30
Month
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#11
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Level Model: Linear Regression
• Issue: Up to which point in the past should data be
used?
• Drawbacks of including very old data:
– Model reacts very slowly to changes
– Is the data still representative?
• Alternative: Adaptive methods
– Moving average
– Exponential smoothing
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#12
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Moving Averages
Idea: Estimation uses only n most recent data points
1
ˆ
Dt i  aˆ  ( Dt  ...  Dt ( n 1) )
n
i=1, 2, ….
• Updating as new demand data becomes available:
Skip oldest data point, add newest data point
• How to choose n?
Choice of n determines length of the “memory” of
the forecast
 Trade-off:
Larger n  more stable forecast
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#13
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Example: Moving Average, n=6
42
Demand
40
Forecast
38
36
34
32
30
0
5
10
15
20
25
30
Month
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#14
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Moving Averages: Remarks
• Typical values of n in the range of 3 – 12
• Requires n historical values to be stored per SKU
• Basic moving average approach gives equal weight
to all n periods and makes a sharp cut thereafter
 Alternatives: weighted moving average,
exponential smoothing
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#15
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Exponential Smoothing
• Most common method in practice
• Also basis for more complex methods
Idea:
• Update forecast as weighted sum of old forecast and
new observation
• Control the extent of updating
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#16
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Exponential Smoothing
• Calculations:
o New forecast = Weighted sum of old forecast
and new demand observation
o Formula:
Dˆ t 1  aDt  (1  a ) Dˆ t
with smoothing parameter a  (0;1)
• Result:
Dˆ t 1  Dˆ t  a ( Dt  Dˆ t )
Forecast error in t
Dˆ t 1  aDt  (1  a )aDt 1  (1  a ) 2 aDt 2  ...  (1  a ) n aDt n  ...
Exponentially decreasing weight of past demand observations
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#17
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Example: Exponential Smoothing, a=0.1
42
Actual demand exceeds forecast
=> Forecast is updated upwards
Demand
40
38
36
34
32
30
0
5
10
15
20
25
30
Month
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#18
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Exponential Smoothing
• Initialization:
^
- Initialize Dt based on first few data points, e.g. by taking their
average
- Specific way of initializing is not crucial since impact of initial
value on forecast is smoothed out
• How to choose a?
- Common range: a  (0.05; 0.3)
- a large  strong impact of recent values, quick response
to changes, but also large impact of outliers
- a small  dampening of random effects / outliers
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#19
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Forecast Quality
• How to decide which method is most appropriate in a
given setting?
 Intuitive: Analyze which method would have performed
best in the past
 Measure forecast error on past data (use different data
than for estimating the model parameters)
Careful: Goal is to make estimates about the future, not
to match the past…!
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#20
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Measuring Forecast Errors
ˆ
• Forecast error in period t = Dt  D
t
• Measures of sample forecast error:
 D  Dˆ  / n
n
• Mean squared error (MSE):
t 1
• Mean absolute deviation (MAD):
2
t
t
n
 D  Dˆ
t
t 1
• Mean absolute percentage error (MAPE):
n

t
/n

100   Dt  Dˆ t / Dt / n
t 1
• For normally distributed forecast errors:
1.25  MAD = estimated variance of forecast errors
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#21
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Using Information on Forecast Errors
Ex post:
• Assessment and comparison of forecasting methods
• Identification of appropriate time series model
Ex ante:
• Calculation of confidence intervals for forecast values
• Calculation of safety buffers, in particular safety stocks
Golden rule of forecasting: All forecasts are wrong!
 Always specify forecast quality!
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#22
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Biased Forecasts
• Bias = systematic over- or underestimation
• To detect bias, monitor cumulative (signed) error
n

Cn   Dt  Dˆ t
t 1

or the ‘tracking signal’
Cn / MSEn
• Tracking signal should fluctuate around 0 for unbiased
forecasts
• Bias indicates that the chosen model is not appropriate
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#23
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Linear Trend Model
• Model: Dt = a + bt + et
• Estimation of a und b
- Initial estimate through linear regression
- Updating analogous to moving averages or
exponential smoothing
^
^
• Forecast: Dt+i = â+bi
(i = 1, 2, 3, …. )
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#24
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Example
45
demand (units)
40
35
Forecast
30
25
20
0
5
10
15
20
month
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#25
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Double Exponential Smoothing
• Also known as ‘Holt’s method’
• Applies smoothing approach to a linear trend model:
Dt = a +bt + et
• Update estimates for intercept and trend parameters:
aˆt  aDt  (1  a )(aˆt 1  bˆt 1 )
bˆ   (aˆ  aˆ )  (1   )bˆ
t
t
t 1
t 1
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#26
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Choosing the Smoothing Constants
• Again, initialize parameter estimates based on first few values
(results may be more sensitive to this than in basic model)
• Set smoothing parameters a and  to achieve small MSE
• Common ranges:
a in 0.02 - 0.5
 in 0.005 - 0.175
• For stability,  should be sufficiently smaller than a
• Empirical heuristic to facilitate parameter choice:
Set a = [1-(1-c)2]
 = c2 / a
and then vary c in [0.01 – 0.3]
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#27
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Example: Holt‘s Method, c=0.04
45
demand (units)
40
Forecast
35
30
25
20
0
5
10
15
20
month
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#28
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Forecasting Adjustments
• Do not trust blindly in the calculations!
• Always check critically, whether the forecasts make
sense
• Periodically review whether the chosen demand model is
still appropriate
• Eliminate outliers
• Incorporate information on non-random factors
(promotional campaign,…)
• Adjust model to business changes
(expanded sales area,…)
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#29
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Forecast-Based Planning
• Remember: All forecasts are wrong…
• Do not only use forecast, but also information on
forecast errors in your planning:
– Invest in information gathering
– Explicitly take forecast errors into account:
• Rolling horizon planning
• Use safety buffers, safety capacity, safety
stocks,…
• Build up flexibility
• Scenario-based planning (decision trees)
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#30
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Rolling-Horizon Planning
• Plan based on available data (forecasts)
– Look ahead, anticipate future impact of current decision
• Implement current decision
• Update available data
– Realized demand
– Updated forecasts
– Updated status of inventories, shipments,…
• Replanning
Planning horizon
Jan
Planning instant
Feb Mar
Apr
Feb
May June
July
Mar
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Aug
Recap: Forecasting
#31
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Example: Safety Stock
Inventory
level
Safety stock
Time
Replenishment
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#32
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Key Insights
 There is no ‘one-size-fits-all’ solution, different purposes
and scenarios require different forecasting methods
 For short-term forecasting, adaptive time series
forecasting methods, such as moving averages and
exponential smoothing, are particularly useful
 The farther out in the future, the less reliable the forecast
 Critically re-evaluate your basic underlying model!
 Forecasts are ‘best guesses’ no ‘crystal balls’
 The goal of forecasting is to make estimates about the
future, not to match the past!
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#33
Role of forecasting
Forecasting approaches
Stationary demand
Forecast quality
Demand with trend
Forecast-based planning
Wrap-up
Background Readings
• Thonemann, Operations Management, Pearson, 2010
Chapter 2: Nachfrageprognose
• Silver, Pyke, and Peterson, Inventory Management and
Production Planning and Scheduling, Wiley, 1998,
Chapter 4: Forecasting
• Stadtler / Kilger: Supply Chain Management and
Advanced Planning, Springer, 2007
Chapter 7: Demand Planning.
• Software Survey: (OR/MS Today)
http://lionhrtpub.com/orms/surveys/FSS/FSS.html
CHAIR OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
Prof. Dr. Moritz Fleischmann
Recap: Forecasting
#34