Quantifying the Bullwhip Effect in a Simple Supply Chain: The Impact of Forecasting, Lead Times, and Information

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Quantifying the Bullwhip Effect in a Simple
Supply Chain The Impact of Forecasting, Lead
Times, and Information

• The Bullwhip Effect

Presented by Ali Koç January 13, 2014
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Outline

• Definition
• Analysis
• Impact of forecasting and lead times
• Centralization (value of information)
• Conclusion

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Bullwhip Effect

• Increase in demand variability as one moves up a
  supply chain

• Occasioned by
• Demand forecasts (sharing information)
• Lead times

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Case 1 Impact of Demand Forecasting
Model and Assumptions

• Only one retailer and one supplier

Fixed lead time Unfilled orders are backlogged
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Model and Assumptions

• Current periods demand depends on the previous
  one
• Error terms are i.i.d. from a symmetric
  distribution with mean ? and variance ?2

• Retailer uses simple moving average to estimate
  mean of the L-period demand and variance of the
  L-period forecast error

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Model Assumptions

• Periodic order, order up to policy
• Order up to level

• Excess inventory is returned without cost (qtlt0)

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Derivations

• From 1, 2, 3 and 4

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Theorem 1

• The bound is tight when z0

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Sensitivity Analysis
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Sensitivity Analysis
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Consequences

• Longer lead times inflates the variance of order
  quantity
• The smoother the demand forecasts, the smaller
  the increase in variability
• The larger the correlation the smaller the
  increase in variability
• For any value of L, p, and correlation, the way
  one treats excess inventory has little impact

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Case 2 Impact of Centralized Demand Information
Model and Assumptions

• Multi-stage supply chain

• Every stage has complete knowledge of the demand
  seen by the retailer

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Model and Assumptions

• Every stage uses the same forecasting technique

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Model and Assumptions

• Each stage uses the same inventory policy

• Order up to level is

• An immediate conclusion
• determine the impact of just demand forecasting,
  not different forecasting techniques or inventory
  policies

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System Protocol

• At the and of period t-1 Dt-1 retailer observes
  Dt-1, calculate yt1, and order qt1
• Stage 2 receives order qt1 with the information
  about Dt-1(no information lead time), calculate
  yt2, and order qt2
• Process continues

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Theorem 2

• Bullwhip effect is not completely eliminated

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Decentralized Model

• Same inventory policy for each stage,
  order up to level (z0)

• Demand is in the following form (?0)

• Same fore casting techniques for each stage

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Decentralized Model

• No retailer demand information for suppliers
• Each stage determines its forecast demand based
  on the order placed by the previous stage

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Theorem 3

• When z0, people usually use inflated lead times

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Comparison
Centralized
Decentralized
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Consequences

• Centralizing the customer demand information
  significantly reduces the bullwhip effect
• Difference between two system increases as we
  move up the supply chain

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Limitations

• Excess inventory is returned without a cost
• Not using optimal inventory policy
• Not using optimal forecasting techniques
• A simple system (not a multi-stage with multiple
  suppliers and manufacturers)

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Last word

• Lead time and forecast errors, increases the
  bullwhip effect, whereas correlation decreases.
• Treating excess inventory in any way does not
  change the bullwhip effect much
• Accessing the retailer demand information
  significantly reduces the bullwhip effect

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THANKS

• Q/A