Bullwhip Effect

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Bullwhip Effect Demand Information Sharing
John Boylan Mohammad AliBuckinghamshire New
UniversityEPSRC 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
• Demand follows ARIMA process
• Residual noise is Gaussian
• Linear hierarchy, one node at each echelon
• 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(maxq1,q2)
• AR(p1) AR(p2) ARMA(p1p2,maxp1,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/(ph)) ? vv
• 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, qM) where qM max pd, qR-L
Manufacturer (Upstream Link)
Forecasting Method
MMSE
ARIMA (p, d, qR)
Retailer (Downstream Link)
Alwan et al (2003), Zhang (2004), Gilbert (2005)
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Upstream Translation of Demand (SMA)
ARIMA (p, d, qR n)
Manufacturer (Upstream Link)
Forecasting Method
SMA
ARIMA (p, d, qR)
Retailer (Downstream Link)
Where n is the number of historical terms used in
forecasting
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Upstream Translation of Demand (SES)
ARIMA (p, d, t - 1) term
Manufacturer (Upstream Link)
Forecasting Method
SES
ARIMA (p, d, qR)
Retailer (Downstream Link)
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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Lead Time Forecast
by Manufacturer AR(1)
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No Information Sharing
Take
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Demand Information Sharing
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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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Principle I(applies when pdltqM)
ARIMA (p, d, qM)
ARIMA (1, 0, 2)
L1
qM max pd, qR-L
qM qR-L qR-1
ARIMA (p, d, qR)
ARIMA (1, 0, 3)
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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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Principle II (applies when pdqM)
ARIMA (p, d, qM)
ARIMA (p, d, qML)
ARIMA (p, d, 1)
ARIMA (p, d, 0)
ARIMA (p, d, qM1)
ARIMA (p, d, qM)


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New Scenario No Information
Sharing estimation of noise

• There are two estimation methods for the above
• Recursive Estimation Method
• Forecast Error Method

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New Scenario Centralised Demand Information
Sharing
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Scenarios in our Research
New Scenarios Introduced
Current Literature
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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