Informs annual meeting 2014

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University of Illinois

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Bounded growth of the bullwhip effect under a class of nonlinear ordering policies

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Zhaodong Wang

Joint work with

Xin Wang

Yanfeng Ouyang*

University of Illinois in Urbana-Champaign

Outline

  • Background
  • Methodology
  • Numerical analysis
  • Conclusion

Background

What is the bullwhip effect?

bwe_illu

Stages

Upstream

Downstream

Product flow

rightarrow

Order flow

leftarrow
  • "No.1 issue" at Supply Chain Service at HP (Callioni, 2003)
  • 12.5%–25% extra costs, $30 billion potential benefits in the U.S. grocery industry (Lee et al., 1997a)
  • Excessive upstream inventory and insufficient order fulfillment

Ordering policy

Optimal (Karlin, 1958)

Stage n

Stage n+1

rightarrow

Linear system

rightarrow

Frequency domain

Exponential

Frequency domain

Disadvantage of linear approach

lin_nonlin

Linear

v.s.

Nonlinear (optimal)

  • Not realistic. Real suppliers use nonlinear ordering policies.
  • Not reasonable. The amplitudes shouldn’t go to infinity.
    • Empirical observations. (Cachon et al., 2007)

Predict the trend and the bound under nonlinear policy

lin_nonlin
  • Develop a integrated system-control framework
  • Incorporate general nonlinear ordering policies
  • Predict the fluctuation and the bound
  • Provide managerial insights

Methodology

Steady state

rightarrow

Nonlinear system

rightarrow
rightarrow
rightarrow
downarrow
downarrow
downarrow

Numerical analysis

conclusion

  • Analytical closed-form solutions are obtained to predict the bullwhip effect.
  • Existence of steady state are proved.
  • Numerical experiments verify the accuracy of proposed framework.

Future research:

  • Extend the framework to multi-input multi-output systems.
  • Generalize the system input into random processes.
  • Validate the framework using empirical data.

Thank you

Questions and comments