CYBERNETIC CONTROL IN A SUPPLY CHAIN WAVE PROPAGATION AND - PowerPoint by umsymums35

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									CYBERNETIC CONTROL IN A SUPPLY CHAIN: WAVE PROPAGATION AND RESONANCE

Ken Dozier and David Chang USC Engineering Technology Transfer Center July 14, 2005

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Outline • Background
– Application of statistical physics to economic phenomena 3 – Quasistatic examples 4-10 – Time-dependent phenomena 11

• Implications of supply chain oscillations for cybernetic control 12
– – – – Inventory oscillation observations Simple model of supply chain oscillations Normal mode equations Implications 13 14 15 16
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• Conclusions

Applications of statistical physics to economics
• Quasistatic phenomena
– Approach: Constrained maximization of microstates corresponding to a macrostate – Applications to date: unit cost of production & productivity

• Time-dependent phenomena
– Approach: normal mode analysis – Current application: supply chain oscillations
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Quasistatic example: reduction in unit cost of production
[Presented at 2004 T2S meeting in Albany, N.Y.]

• Background question
– What is required for technology transfer to reduce production costs throughout an industrial sector?

• Approach
– Apply statistical physics to develop a “first law of thermodynamics” for technology transfer, where “energy” is replaced by “unit cost of production”

• Result & significance
– Find that technology transfer impact can be increased if “entropy” term and “work” term act synergistically rather than antagonistically
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Quasistatic example: unit cost of production Ln Output
High output N, High “temperature” 1/b Costs down High output N, Low “temperature” 1/b Low output N, High “temperature” 1/b Low output N, Low “temperature” 1/b

Entropy up

Unit costs
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Semiconductor example: Movement between 1992 and 1997 on Maxwell Boltzmann plot
Ln output

1997: High output N, Low “temperature” 1/b

Ln Output
1992: Low output N, High “temperature” 1/b

Unit costs
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Heavy spring example: Movement between 1992 and 1997 on Maxwell Boltzmann plot Ln Output

1997: Low output N, High “temperature” 1/b

1992: Low output N, Low “temperature” 1/b

Unit costs
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Quasistatic example: Improve productivity
[CITSA ‟04 conference (July, 2004); Paper submitted to JITTA for publication (March, 2005) ]

• Background
– Information paradox: Value of technology transfer – and more generally, of information – on productivity has been called into question

• Approach
– Apply statistical physics approach to show how productivity is distributed across an industry sector – Compare evolution of distributions for information-rich and information-poor sectors [US economic census data for LA]

• Results & significance
– Find that productivity decreases but output increases in small company sectors that invest in information, while productivity increases in information-rich large company sectors
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Productivity: Comparison of U.S. economic census cumulative number of companies vs shipments/company (diamond points) in LACMSA in 1992 and the statistical physics cumulative distribution curve (square points) with β = 0.167 per $106
4000

3500

3000

2500

2000

1500

1000

500

0 0 10 20 30 40 50 60

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Productivity: Ratio („97/‟92) of the statistical parameters
Company size: IT rank # E(1000s) #/company Sh ($million) Sh/E ($1000) β Large 59 0.86 0.78 0.91 1.53 1.66 1.11 Intermediate 70 1.0 0.98 1.0 1.24 1.34 0.90 Small 81 0.90 1.08 1.21 1.42 1.35 0.99

Findings: Sectors with large companies spend a larger percentage on IT. Largest % increases in shipments are in large & small company sectors. Small companies increased in size while large companies decreased. Number of large and small companies decreased by 10%. Employment decreased 20% in large companies, but increased 8% in small companies. Largest productivity occurred in large companies.
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Time-dependent phenomena
• Cyclic phenomena in economics
– Ubiquitous – Resource wasteful & career disruptive

• Example: oscillations in supply chain inventories

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Implications of supply chain oscillations for cybernetic control
• Approach
– Develop a simple model of important interactions between supply chain companies that give rise to oscillations – Determine structure of normal mode oscillations – Find governing dispersion relation for supply chain normal modes • Results & significance – Identify opportunities for resonant, adiabatic, and short-time technology transfer efforts

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Observations of supply chain oscillations

• Prevalent inventory oscillations led to MIT’s “Beer game” simulation • Simulations and observations both show
– Oscillations – Phase dependence of oscillations on position in supply chain – Instabilities
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Development of a model for normal modes in a supply chain
• Assume oscillations in supply chain inventories of the form exp(it) • Obtain a simple form for normal modes by any of three approaches
– Inventory dependent on nearest neighbor inventories – Conservation equations for inventory and sales – Fluid flow model of a supply chain

• Derive dispersion relation giving dependence of oscillation frequency on form of normal mode
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Resulting normal modes in a supply chain with uniform processing times
• Supply chain normal mode equation

y(n-1) – 2y(n) + y(n+1) +(T)2 y(n) = 0
• Normal mode form for N companies in chain

[1]

y(p:n) = exp[i2pn/N]
• Normal mode dispersion relation  =  (2/T) sin(p/N) where p is any integer

[2]

[3]

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Implications of normal modes
• Supply chains naturally oscillate at frequencies below and up to inverse of processing times
– In agreement with observations

• Disturbances in inventories propagate through supply chain at different velocities
– Phase velocities increase to saturation as disturbance wavelength decreases – Group velocities decrease as disturbance wavelength decreases

• Maximum control exerted by resonant interactions (Landau damping) with propagating waves
– Control by surfing

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Conclusions
• Normal mode analysis provides a good framework for optimizing cybernetic control of undesirable oscillations in supply chains • Optimization of cybernetic control will involve development of quasilinear equations for calculating the impact of resonant interactions

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