D Lab: Supply Chains
Lectures 4 and 5
Class outline:
• What is Demand?
• Demand management
• Forecasting Demand
– Bass Model
– Causal Models
– Exponential Smoothing
© Stephen C. Graves 2014
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ARTI
Sinead Cheung
Neha Doshi
Emily Grandjean
Shannon Kizilski
Cherry Park
Sanjana Puri
Jessica Shi
Spencer Wenck
Chelsea Yeh
Daniel
Air Liquide Wecycler Ghonsla
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BPS
1
1
1
2
2
1
1
1
1
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Who is Alex Rogo? If you don’t know, it means you are not reading
“The Goal”…
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Assignment: Next Monday
• Book Review
This assignment is due at the beginning of class.
Prepare a one page summary of The Goal formatted
as follows:
1. List your (at most) 5 main take-aways from the
book (at most 2-3 sentence each); and
2. List the (at most) 3 main critiques (at most 2-3 sentence each) you would make about this book
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Demand Management
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Demand Management
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What is demand?
From the Merriam-Webster dictionary,
Demand is the quantity of a commodity or service wanted at a specified price and time. •How can we deal with demand from a SC
point of view?
•Why is anticipating demand important?
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Why forecast? - Two SC strategies
Two supply chain strategies for dealing with
demand are
•Make-to-order (MTO): the company chooses
to manufacture a product only after a request
from a customer is received.
•Make-to-stock (MTS): based on forecasts
production is done in anticipation of future
demand.
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Two SC strategies - Examples
Make-to-order (MTO)
• Construction Industry
• Customized products
• Services/Food
Make-to-stock (MTS)
• Vaccines and medicine
• Most consumer goods
• Agricultural Products
More examples?
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Two SC strategies - Tradeoffs
MTS
Economies of Scale
✔
More dependent on demand
forecasts
Longer lead time for customers
✔
Easier to scale-up
✔
MTO
✔
Customizable products
✔
Forecasting is important for both models
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Two SC strategies - Emerging Markets
In the context of emerging markets, think about the
following question:
Can you give examples of products for which a MTO model
“makes sense” in a developed economy but not in an
emerging economy?
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More reasons why forecasting is important
•Forecast used for inventory planning at retail
store level and at DC level for products held in
stock (ie, MTS)
•Forecast used to determine when to order
more inventory
•Need for simple, robust methods applicable
for wide range of contexts
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Forecast principles
Value
1. Forecasts are always wrong and should always
include some measure of error
2. The longer the horizon, the larger the error
3. Method should be chosen based on need and
context
Now
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Time
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Forecasting – formal definition
Previous observations of demand
Additional info:
Forecast
System Model
Forecast period
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Forecasting – formal definition
Previous observations of demand
Additional info:
Forecast
Forecast period
How would you forecast seminar lunch boxes?
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Factors for choosing forecast method
• How is forecast to be used? Need for accuracy?
Units? Time period? Forecast horizon? Frequency of
revision?
• Availability and accuracy of relevant data? censored?
• Computational complexity? Data requirements?
• How predictable is the entity? Are there independent
factors that affect it or are correlated to it?
• Level of aggregation? Across geographies? Time?
Product categories?
• Type of product? New or old?
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Types of forecasts
•
•
•
•
•
•
Qualitative; expert opinions
Diffusion models
Causal models, eg, regression
Disaggregation of an aggregate forecast
Aggregation of detailed forecasts
Time series methods
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Types of forecasts
Forecasting Methods
New Products
Bass Diffusion Model
Existing products
Time Series Methods
Causal Models
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Forecasting the adoption of new products
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Example: Water Purifier
Assume you are responsible for estimating a
demand for a new cheap and efficient water
purifier. How would you do it?
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The Bass Diffusion Model
•Is a model for adoption of new products
(consumer durables)
•One of the 10 most influential papers of
“Management Science” in the last 50 years
•Widely used in marketing and strategy
•We will build the model from first
principles
Frank Bass
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© Stephen C. Graves 2014
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The Bass Diffusion Model
Key idea: consumers are divided into 2 groups:
Innovators
• Early adopters
• Not influenced by other
individuals
• Driven by advertisement or some other external effect
Imitators
• Influenced by other buyers
• Word of mouth
• Network effects
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Motivation for the Bass model
Total: N
. . .
Innovators with prob. r
Imitators with prob. 1‐r
. . .
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Innovators
Total: N
Imitators
. . .
Innovators
Probability of adoption =
Imitators
Probability of adoption =
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Innovators
t = 1
Total: N
Imitators
. . .
Innovators
Probability of adoption =
Imitators
Probability of adoption = =0
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t = 2
Total: N
...
Innovators
Probability of adoption =
Imitators
Probability of adoption =
=
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t = 3
Total: N
...
Innovators
Probability of adoption =
Imitators
Probability of adoption =
=
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Motivation (board)
•
•
•
•
•
•
Market size:
Number of new adopters at time t:
Total number of adopters at time t:
Probability of being an innovator:
Probability of an innovator adopting at time t:
Probability of an imitator adopting at time t:
• Define
p  pr;
q  1  r  q
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Bass Model
• We can approximate the model we just
described by
• The continuous differential equation becomes Innovators
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Imitators
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Bass Model
•Thus, for the continuous approximation, we
have, for
, the solution
Imitators
New adopters
Total adoption
Innovators
Time
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Total
Time
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Estimation of parameters
• What parameters do we need to estimate?
– Market Size
– Imitation
– Innovation
• How do we estimate?
–
–
–
–
Early data + linear regression
Analogy (priors)
Focus groups
Macro Data
• What is missing?
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Generalized Bass Model
• Let “marketing effort” evolve as x(t). The new equation is: • When estimating or doing focus groups, try to map price vs. demand group
• Create a model for different prices
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Bass Model Examples © Stephen C. Graves 2014
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DIRECTV
• Launched in 1992
• How many people would subscribe to satellite
TV and when?
• New technology
• p and q were estimated by analogy
• N was determined by market research and
focus groups
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DIRECTV
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Fitting the Bass Model
The Bass difference equation is We can fit this equation to the data!
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Causal Models
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Example – Dengue in India
• Dengue is transmitted by a
mosquito, the Ades Aegypti
• During Summer monsoon,
stagnant water accumulates
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Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
• This leads to a proliferation of
mosquito reproduction
• A increase in mosquitos
increases dengue transmission
During rainy season
there is a lot of
stagnant water
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Example – Dengue in India
• Causal models are very useful to estimate
the occurrence of weather related
diseases (and the demand for
medicine/vaccines).
• Consider the relationship between monthly
rainfall and the occurrence of Dengue
Fever in India
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Google Dengue Index
0.8
0.0
500
0.2
0.4
0.6
1000 1500 2000 2500 3000
Rainfall
Dengue Index
0
Rainfall (mm/month)
Example – Dengue in India
2004
2006
2008
Time - Years
2010
The index is an estimate by Google.org of Dengue Activity.
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Causal Models
Can you think of other examples? © Stephen C. Graves 2014
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Types of forecasts Forecasting Methods
New Products
Bass Diffusion Model
Existing products
Time Series Methods
Causal Models
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Time Series Methods
• Used when there is limited information
available about exogenous factors that
influence demand
• Short horizon forecast (usually < 1 year)
• We will discuss methods that are easy to
implement
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Time Series – Components of Demand
In practice, it is useful to understand and estimate 4
components of demand: mean, trend, seasonality
and randomness.
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Randomness • Usually modeled using probability
distributions
• Two components: mean and variance
– Mean: Average Value
– Variance: “spread”
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Time Series Methods
Assume demand has the form
10
Randomness
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-10
In addition, assume that
Mean:
Variance:
0
5
Permanent component:
Mean, trend, seasonality
0
20
40
60
80
Randomness
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100
Time Series Methods
Assume demand has the form
In addition, assume that
Forecast method determines
: Expost estimate of the permanent
component
: forecast at time
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Time Series Methods
• What is permanent component and expost
estimate?
Expost estimate is where we “think” that the
permanent component is in the time period
• We are ready to discuss forecasting
methods
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Moving Average
• Recent observations are more “informative”
than old observations
• Uses n previous observations
• Expost estimate of the permanent
component
is
• Forecast is © Stephen C. Graves 2014
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Moving Average
• Advantages: Simple, only one “knob” (n)
• Disadvantages: weighs all previous
demand equally
• Example
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Weighted Moving Average
• Weighs previous observations using
weights
where
• We have the expost estimate
and the forecast (again) is
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Weighted Moving Average
• Advantages: Flexibility
• Disadvantages: too many “knobs” • Solution: Exponential Smoothing © Stephen C. Graves 2014
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Exponential Smoothing
• Weighs previous observations using a
geometric time series such that
Note that
Thus,
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Exponential Smoothing
• Only one parameter to adjust • Doesn’t weigh previous forecasts equally
• Very simple update equation
• Examples
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Exponential Smoothing vs. Moving Average
• Assume permanent component is constant
• For exponential smoothing:
,
• For moving average
,
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Holt-Winters Method
• So far, we did not explicitly estimate
seasonality or trend
0
10
• Assume that the permanent component is
Seasonality
-20
-10
-5
-15
0
-10
5
-5
Trend
0
20
40
60
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100
0
20
40
60
80
100
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Holt-Winters Method
• So far, we did not explicitly estimate
seasonality or trend
• Assume that the permanent component is
• Demand is © Stephen C. Graves 2014
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Holt-Winters Method
• Assume we know that the length of a
season is L
• Let be the deseasonalized
permanent component
• We now need to estimate,
Idea: Exponential smoothing on all the parameters!
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Expost Estimates
• Deseasonalized demand
• Trend
• Seasonal factor
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Expost Estimates
Deseasonalized demand
Where we think the
deaseason. permanent
component will be
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Expost Estimates
Deseasonalized demand
Deaseasonalized demand
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Expost Estimates
Deseasonalized demand
Trend
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Expost Estimates
Deseasonalized demand
Trend
Smoothing coefficient
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Expost Estimates
Deseasonalized demand
Trend
Estimate of slope
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Expost Estimates
Deseasonalized demand
Trend
Seasonality © Stephen C. Graves 2014
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Expost Estimates
Deseasonalized demand
Trend
Seasonality
Another smoothing coef.
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Expost Estimates
Deseasonalized demand
Trend
Seasonality
Another smoothing coef.
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Expost Estimates
Deseasonalized demand
Trend
Seasonality
Seasonality factor
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Forecast
• Given
• The forecast is
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Holt-Winters Method
Get new
data
Update X
Update C
Update B
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Wrap-up
Variables
Info
Moving Average
none
Weighted moving Average
none
Exponential Smoothing
none
Holt-Winters
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MIT OpenCourseWare
http://ocw.mit.edu
15.772J / EC.733J D-Lab: Supply Chains
Fall 2014
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