Statistical Physics Framework for Analysis of the Economic Impact of Technology

1
Statistical Physics Framework for Analysis of the
Economic Impact of Technology

• Ken Dozier
• David Chang
• USC Viterbi School of Engineering Technology
  Transfer Center
• 8/11/05

2
A System of Forces in Organization
Direction
Cooperation
Efficiency
Proficiency
Competition
Concentration
Innovation
Source The Effective Organization Forces and
Form, Sloan Management Review, Henry Mintzberg,
McGill University 1991
3
Make Sell vs Sense Respond
Chart SourceCorporate Information Systems and
Management, Applegate, 2000
4
Supply Chain (Firm)
Source Gus Koehler, University of Southern
California Department of Policy and Planning,
2002
5
Supply Chain (Government)
Source Gus Koehler, University of Southern
California Department of Policy and Planning,
2002
6
Supply Chain (Framework)
Source Gus Koehler, University of Southern
California Department of Policy and Planning,
2002
7
Supply Chain (Interactions)
Source Gus Koehler, University of Southern
California Department of Policy and Planning,
2002
8
Theoretical Environment
Seven Organizational Change Propositions
Framework, Framing the Domains of IT
Management Zmud 2002
9
Data Provider

• 52 acre complex located on the Alameda Corridor
  in Lynwood, CA.
• The Business Park is a master planned development
  with 12 separate facilities consisting 15,000 to
  200,000 square foot buildings.
• Houses 45 tenants who occupy anywhere from 2000
  square feet to 100,000 square feet and employing
  approximately 1300 individuals.

10
Statistical Physics Approach
11
Outline

• Introduction 1
• Why a framework?
  3
• Why statistical physics? 4
• What technology transfer measures? 5
• Statistical physics program tasks for technology
  transfer to an industrial sector
• Quasi-static phenomena
• Task 1. Reduce unit cost of production T2S
  2004 6-12
• Task 2. Improve productivity (output/employee)
  CITSA 04 JITTA
  13-16
• Task 3. Increase total output 17
• Task 4. Reduce RD costs 18
• Dynamic phenomena
• Task 5. Understand implications of supply chain
  oscillations for tech. transfer CITSA 05
  19-20
• Task 6. Increase rate of production T2S
  2005 21
• Task 7. Understand T2 implications of
  instabilities in supply chain oscillations
  22
• Task 8. Dampen disruptive cyclic phenomena by
  technology transfer
  23

12
Why a framework?

• Current understanding of technology transfer
  impact
• Anecdotally-based
• Not comprehensive or convincing
• Advantages of an non-anecdotal framework
• Impact on relevant performance parameters and
  interrelationships
• Comprehensive and systematic approach

13
Why statistical physics?

• Proven formalism for seeing the forest past the
  trees
• Well established in physical and chemical
  sciences
• Our recent verification with data in economic
  realm
• Simple procedure for focusing on macro-parameters
• Most likely distributions obtained by maximizing
  the number of micro-states corresponding to a
  measurable macro-state
• Straightforward extension from original focus on
  energy to economic quantities
• Unit cost of production
• Productivity
• RD costs
• Self-consistency check provided by distribution
  functions

14
What technology transfer measures?

• Value-added goals for an industrial sector
• Reduce unit cost of production reduce entropy
• Improve productivity (output/employee)
• Increase total output
• Reduce RD costs
• Increase rate of production
• Dampen disruptive cyclic phenomena
• Increase rate of technology spread

15

Technology Transfer Quasi-static

• Task 1. Reduce unit cost of productionPresented
  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 approach 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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Technology Transfer Quasi-static
Task 1 approach Why does unit production cost
play the role of energy in a statistical physics
of production? Problem simplest
case Given Total output N of
sector Total costs of production for sector
C Unit costs c(i) of production at sites i
within sector Find Most likely distribution
of outputs n(i) within sector Approach Let
Wn(i) be the number of possible ways that a set
of outputs n(i) can be realized. Maximize
Wn(i) subject to given constraints N, C, and
c(i) d /d n(i) lnW ?N-Sn(i)
ßC-Sc(i) 0

1 Solution for simplest case n(i) P
exp-ßc(i) Maxwell-Boltzmann
distribution 2 where the
parameters characterizing the sector are P is
a productivity factor for the sector ß is an
inverse temperature or bureaucratic factor
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Technology Transfer Quasi-static
Task 1. Comparison of Statistical Formalism in
Physics and in Economics Variable Physics Eco
nomics State (i) Hamiltonian
eigenfunction Production site Energy Hamiltoni
an eigenvalue Ei Unit prod. cost
Ci Occupation number Number in state Ni
Output Ni exp-ßCißF Partition function Z
?exp-(1/kBT)Ei ?exp-ßCi Free energy F kBT
lnZ (1/ß) lnZ Generalized force f?
?F/?? ?F/?? Example Pressure Technology Ex
ample Electric field x charge Knowledge Entropy
(randomness) - ?F / ?T kBß2?F/?b
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Technology Transfer Quasi-static
Task 1 approach. Conservation law for Technology
Transfer
Total cost of production C ? C(?i) exp
-ß(C(?i) F(? )) 1
Effect of a change d? in a parameter ? in the
system and a change dß In bureaucratic factor
dC - ltf? gt d? ß d2F/ dßd? d? d2ßF/
dß2 dß 2
which can be rewritten
dC - ltf? gt d? TdS 3
Significance First term on the RHS
describes lowering of unit cost of production.
Second term on RHS describes increase in
entropy (temperature)
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Technology Transfer Quasi-static
Task 1. Approach
High output N, High temperature 1/b
Ln Output
Costs down
High output N, Low temperature 1/b
Low output N, High temperature 1/b
Entropy up
Low output N, Low temperature 1/b
Unit costs
20
Technology Transfer Quasi-static
Task 1. Semiconductor example Movement
between 1992 and 1997 on Maxwell Boltzmann plot
1997 High output N, Low temperature 1/b
Ln Output
1992 Low output N, High temperature 1/b
Unit costs
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Technology Transfer Quasi-static
Task 1. 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
22
Technology Transfer Quasi-static

• Task 2. Improve productivity (output/employee)P
  aper submitted to JITTA for publication (March,
  2005) following well-received presentation at
  CITSA 04 conference (July, 2004)
• 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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Technology Transfer Quasi-static
Task 2. Normalized cumulative distribution of
companies N(S)/N vs shipments per company S for
ß 0.5 (bottom curve), 1, and 5
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Technology Transfer Quasi-static
Task 2. 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 ß 0.167
per 106
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Technology Transfer Quasi-static
Task 2. Ratio (97/92) of the statistical
parameters

• Company size Large Intermediate
  Small
• IT rank 59 70 81
• 0.86 1.0
  0.90
• E(1000s) 0.78
  0.98 1.08
• /company 0.91 1.0 1.21
• Sh (million) 1.53 1.24
  1.42
• Sh/E (1000) 1.66 1.34
  1.35
• ß 1.11 0.90 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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Technology Transfer Quasi-static
Task 3. Increase total output

• Background question
• What are the parameters involved in determining
  an increase in output as well as a decrease in
  unit costs of production?
• Approach
• Maximize number of microstates corresponding to
  macrostate defined by
• total cost of production
• ratio of total output/total cost of production
• Obtain equivalent of a chemical potential
• Result
• Conservation equation containing a uniquely
  defined technology transfer force that affects
  chemical potential for increasing output

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Technology Transfer Quasi-static
Task 4. Reduce RD costs

• Background question
• Is there a systematic way of reducing barriers to
  industry use of government RD and vice versa
  (diffusion and infusion)?
• Approach
• Maximize number of microstates corresponding to
  macrostate defined by
• total cost of RD
• ratio of total innovation output/total RD cost
• Obtain equivalent of an innovation potential
• Result significance
• Conservation equation containing a uniquely
  defined technology transfer force that affects
  innovation potential for increasing innovation
  output

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Technology Transfer Dynamic
Task 5. Understand implications of supply chain
oscillations for technology transfer Paper
accepted for CITSA 05 conference in July, 2005

• Background
• National resources are wasted by disruptive and
  ubiquitous economic cycles
• Collective oscillations are evident in industry
  sector supply chains
• 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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Technology Transfer Dynamic
Task 5. Normal modes in a supply chain with
uniform processing times

• Supply chain normal mode equation
• y(n-1) 2y(n) y(n1) (?T)2 y(n)
  0 1
• Normal mode form for N companies in chain
• y(p(n) expi2?pn/N 2
• Normal mode dispersion relation
• ? ? (2/T) sin(?p/N) where p is any
  integer 3

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Technology Transfer Dynamic
Task 6. Increase rate of productionPaper
accepted for presentation at T2S meeting in
September, 2005

• Background question
• How should government technology transfer policy
  be focused to realize the value associated with
  increased production rates?
• Approach
• Understand flow (overall production rate) in a
  supply chain
• Develop normal modes for flow oscillations
• Apply quasilinear theory to describe effect of
  resonant interactions with normal modes on
  overall flow velocity
• Results significance
• Find criteria for timing and position focus of
  technology transfer efforts that will maximize
  impact on rate of production throughout a supply
  chain

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Technology Transfer Dynamic
Task 7. Understand technology transfer
implications of instabilities in supply chain
oscillations

• Background
• MITs beer game simulation has demonstrated
  that costly and disruptive supply chain inventory
  oscillations with phase change and growing
  amplitudes occur consistently.
• Approach
• Extend normal mode analysis of supply chains to
  accommodate instabilities due to overcompensation
• Apply eikonal (Hamilton-Jacobi) analysis to
  identify critical damping potential
• Result significance
• Determine the degree to which slowly-responding
  government technology transfer efforts can impact
  instabilities

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Technology Transfer Dynamic
Task 8. Optimize damping of disruptive cyclic
phenomena by focusing technology transfer

• Background questions
• Inventory oscillations in supply chains can be
  reduced somewhat by adiabatic technology transfer
  efforts, but is there a more effective technology
  transfer focus?
• Asynchronous SBIR program more appropriate?
• Approach
• Introduce a Wigner-type distribution function
• Develop associated Fokker-Planck equation for
  describing the evolution of oscillatory phenomena
  in supply chains
• Solve evolution equation by multi-time-scale
  formalism
• Result significance
• The effects of adiabatic, resonant, and short
  time-scale technology transfer efforts will be
  systematically described.
• Criteria will be established for the timing and
  focus of technology transfer efforts for most
  effectively controlling instabilities

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Technology Transfer Dynamic
Task 9. Increase rate of technology spread and
adoption

• Background
• W. Mansfield and others have pointed out the
  economic benefits of rapidly spreading new
  technology within and between industry sectors
• Approach
• Adapt the Pastor-Satorras equation for virus
  spreading in scale-free networks to technology
  transfer
• Generalize further by adding a Fokker-Planck term
  to the PS equations
• Result significance
• Identify thresholds for successful technology
  spread, and determine parameter-dependencies of
  spreading rates

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Technology Transfer Reality Check
Task 10. Compare the theory with actual data

• Background
• Applications of statistical physics to understand
  the impact of information on productivity growth
  has been demonstrated with U.S. economic census
  data for the Los Angeles area. A more general
  test of the predictions for technology transfer
  is needed.
• Approach
• Mine the technology transfer data of government
  agencies (NASA, DOE, DOD) to determine the impact
  on specific statistical physics parameters
  (e.g. productivity, output, bureaucratic factor)
  and on their distribution functions
• Result significance
• This should providing convincing support for the
  statistical physics framework for the guidance
  and analysis of technology transfer efforts.
• Actual data in statistical physics framework will
  provide calibration for assessing DOLLAR VALUE of
  technology transfer

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SUMMARY

• This statistical physics-based program should
  help put
• NASA in a leadership position to
• design and implement optimal technology transfer
  programs
• systematically measure value-added impact

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Future Work

• Examine NAICS consistent 2002 and 1997 U.S.
  manufacturing economic census data
• Use seven organizational change proposition
  strata to further explore the linkage between
  organizational size and productivity.
• Compare results across the strata and within each
  stratum
• Check for compliance to thermodynamic model
• Expand to technology transfer