bullwhip effect & demand information sharing john boylan & mohammad ali buckinghamshire new...
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Bullwhip Effect & Demand Information Sharing
John Boylan & Mohammad AliBuckinghamshire New University
EPSRC Launch Meeting, 24 October 2007
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Outline
Approaches to the Bullwhip Effect Demand Information Sharing (DIS) and
standard assumptions Scenarios presented in current literature Uncertainty Principles New scenarios introduced
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Bullwhip Effect
Amplification of ‘noise’ as demand moves upstream
Amplification of upstream inventory requirements
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Approaches to the Bullwhip
Control Theory System Dynamics OR / Statistical approach :
Share downstream demand information with upstream links Lee et al (2000) Chen et al (2000) Raghunathan (2003)
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Demand Information Sharing
Papers share the following assumptions:
1. Demand follows ARIMA process
2. Residual noise is Gaussian
3. Linear hierarchy, one node at each echelon
4. Inventory rule is ‘Order Up To’ (OUT)
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1. ARIMA process
Advantages Convenient
mathematically Can be insightful
Disadvantages Even if process is
ARIMA, forecasting may not be ARIMA
Alternatives Assume ARIMA
process but use a non-optimal method (eg SMA, SES)
Use state-space approach
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2. Gaussian Residual Noise
Advantages Leads to tractable
results
Disadvantages May lead to low
safety stocks if data is skewed
NB: depends on inventory rule
Alternatives Use non-standard
ARIMA model with skewed noise distribution
For slow-moving items, use Integer ARMA models (with Poisson noise)
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3. Linear Hierarchy
Unrealistic to have single node at each echelon Upstream propagation based on sum of
demands: MA(q1) + MA(q2) = MA(max{q1,q2})
AR(p1) + AR(p2) = ARMA(p1+p2,max{p1,p2})
Even if backward inference allows for identification of the process for total demand, it does not allow identification at each node
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4. ‘OUT’ Inventory Rule
OUT leads to
Yt = Dt + (St – St-1)
If optimal (MMSE) forecasting method used: St = mt + -1(p/(p+h)) √v
Yt = Dt + (mt – mt-1)
Immediately apparent that Bullwhip or Anti-Bullwhip may occur
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Upstream Translation of Demand (MMSE)
ARIMA (p, d, qR)
ARIMA (p, d, qM)
where qM = max {p+d, qR-L}
Manufacturer(Upstream Link)
Retailer(Downstream Link)
Forecasting Method
MMSE
Alwan et al (2003), Zhang (2004), Gilbert (2005)Alwan et al (2003), Zhang (2004), Gilbert (2005)
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Upstream Translation of Demand (SMA)
ARIMA (p, d, qR)
ARIMA (p, d, qR +n)
Manufacturer(Upstream Link)
Retailer(Downstream Link)
Forecasting Method
SMA
Where n is the number of historical terms used in forecasting
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Upstream Translation of Demand (SES)
ARIMA (p, d, qR)
ARIMA (p, d, t - 1) + term
Manufacturer(Upstream Link)
Retailer(Downstream Link)
Forecasting Method
SES
Where t is the number of historical terms used in forecasting
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Scenarios
Current No information
sharing Demand information
sharing Downstream
Demand Inference
New No information
sharing (estimation of noise term)
Centralised demand information sharing
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1 11 (1 )ˆ 1 1
(Manufacturer's Lead Time Forecast)
L L
t t tY y
Lead Time Forecast by Manufacturer AR(1)
1ˆ ˆ( ) (Demand at Manufacturer)t t t ty d D D
1 (Demand at Retailer)t t td d
1(1 )ˆ (Retailer's Lead Time Forecast)1
L
t tD d
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No Information Sharing
0t
1 11 (1 )ˆ 1 1
L L
t t tY y
11ˆ
1
L
t tY y
Take
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t
1 1
is known, thus can be calculated
1 (1 )ˆ 1 1
t
L L
t t t
d
Y y
1 11 (1 )ˆ 1 1
L L
t t tY y
Demand Information Sharing
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t
1 1
ˆ is unknown, but can be estimated
1 (1 )ˆ ˆ 1 1
t
L L
t t t
d
Y y
1 11 (1 )ˆ 1 1
L L
t t tY y
Downstream Demand Inference
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Uncertainty Principle I
If the upstream member can identify the demand model at the downstream link, the demand value at the downstream link cannot be exactly calculated.
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ARIMA (p, d, qM)
Principle I(applies when p+d<qM)
ARIMA (p, d, qR)
ARIMA (1, 0, 2)
ARIMA (1, 0, 3)
L=1
qM = max {p+d, qR-L}
qM = qR-L = qR-1
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Uncertainty Principles
Principle II: “If the upstream member cannot identify the
demand model at the downstream link, then the demand value at the downstream link can be exactly calculated, if a certain model is assumed from a restrictive subset of the possible models.”
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ARIMA (p, d, qM+L)…
Principle II (applies when p+d=qM)
ARIMA (p, d, qM)
ARIMA (p, d, 1)
ARIMA(p, d, 0)
ARIMA(p, d, qM+1)…
ARIMA(p, d, qM)
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New Scenario : No Information Sharing – estimation of noise
1 11 (1 )ˆ 1 1
L L
t t tY y
t
1 1
ˆ is unknown but can be calculated
1 (1 )ˆ ˆ 1 1
t
L L
t t t
d
Y y
There are two estimation methods for the above1. Recursive Estimation Method
2. Forecast Error Method
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New Scenario: Centralised Demand Information Sharing
1 11 (1 )ˆ 1 1
L L
t t tY y
11ˆ
1
L
t t tY d
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New Scenarios Introduced
Current Literature
t t
NIS
Y , 0 t t
NIS-Est
ˆY ,
t
DIS
Y , t t t
CDIS
d ,
Scenarios in our Research
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Summary of Research
Downstream Demand Inference shown to be infeasible
No Information Scenario improved to include estimation of ‘noise’ term
Demand Information Sharing scenario enhanced by basing estimation on demand at retailer
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Further Research
Issue of batching Evaluation of multi-node supply chains Inventory rules other than OUT Challenging the nature of the rules