A Statistical Physics Model of Technology Transfer

1
A Statistical Physics Model of Technology
Transfer

• Ken Dozier
• USC Viterbi School of Engineering Technology
  Transfer Center
• Technology Transfer Society (T2S) 26th Annual
  Conference
• Albany, NY
• October 1, 2004

2
Presentation

• Problem (7 slides)
• Approach (9 slides)
• Results (5 slides)
• Conclusions (1 slide)
• Future (1 slide)

3
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
4
Make Sell vs Sense Respond
Chart SourceCorporate Information Systems and
Management, Applegate, 2000
5
Supply Chain (Firm)
Source Gus Koehler, University of Southern
California Department of Policy and Planning,
2002
6
Supply Chain (Government)
Source Gus Koehler, University of Southern
California Department of Policy and Planning,
2002
7
Supply Chain (Framework)
Source Gus Koehler, University of Southern
California Department of Policy and Planning,
2002
8
Supply Chain (Interactions)
Source Gus Koehler, University of Southern
California Department of Policy and Planning,
2002
9
Theoretical Environment
Seven Organizational Change Propositions
Framework, Framing the Domains of IT
Management Zmud 2002
10
Framework Assumptions

• U.S. Manufacturing Industry Sectors can be
  Stratified using Average Company Size and
  Assigned to Layers of the Change Propositions
• Layers with Large Average Firm Size Will Have
  High B and Lowest T(1/B)
• Layers with Small Average Firm Size Will Have Low
  B and High T (1/B)
• The B and T Values Provide the Entry Point to
  Thermodynamics

11
Thermodynamics ?

• Ample Examples of Support
• Long Term Association with Economics
• Krugman, 2004
• Systems Far from Equilibrium can be Treated by
  (open systems) Thermodynamics
• Thorne, Fernando, Lenden, Silva, 2000
• Thermodynamics and Biology Drove New Growth
  Economics
• Costanza, Perrings, and Cleveland, 1997
• Economics and Thermodynamics are Constrained
  Optimization Problems
• Smith and Foley, 2002

12
Thermodynamics ?

• Mathematical Complexity Could Discourage
  Practitioners
• Requires an Extension of Traditional Energy
  Abstractions
• Expansion May Require Knowledge to be Considered
  Pseudo Form of Energy?!
• Knowledge Potential and Kinetic States?!
• Patent potential
• Technology Transfer Kinetic
• Tacit versus Explicit

13
Constrained Optimization Approach

• Thermodynamics
• A systematic mathematical technique for
  determining what can be inferred from a minimum
  amount of data
• Key Many microstates possible to give an
  observed macrostate
• Basic principle Most likely situation given by
  maximization of the number of microstates
  consistent with an observed macrostate
• Why pseudo?
• Conventional thermodynamics energy rules
  supreme
• Thermodynamics of economics phenomena energy
  shown by statistical physics analysis to be
  replaced by quantities related to productivity,
  i.e. output per employee

14
Pseudo-Thermodynamic Approach

• Macrostate givens N and E, and census-reported
  sector productivities p(i)
• Total manufacturing output of a metropolitan area
  N
• Total number of manufacturing employees in
  metropolitan area E
• Productivities p(i), where p(i) is the
  output/employee of manufacturing sector I
• Convenient to work with a dimensionless
  productivity
• p(i) p(i)/ltPgt (Chang Simplification)
• where ltPgt is the average value for the
  manufacturing sectors of the output/employee for
  the metropolitan area.
• Thermodynamic problem with the foregoing
  givens
• What is the most likely distribution of employees
  e(i) over the sectors that comprise the
  metropolitan manufacturing activity ?
• What is the most likely distribution of output
  n(i) over the sectors?

15
Pseudo-Thermodynamic Approach

• Relations between total metropolitan employee
  number E and output N and sector employee numbers
  e(i) and outputs n(i)
• E S e(i)
• N S n(i)
• Relation between sector outputs, employee
  numbers, and productivities
• n(i) e(i) p(i)
• n(i) e(i)ltPgtp(i)
• Accordingly,
• N S n(i) S e(i) ltPgt p(i)

16
Pseudo-Thermodynamic Approach

• Look for the (microstate) distribution e(i) that
  will give the maximum number of ways W in which a
  known (macrostate) N and E can be achieved.
• Number of ways (distinguishable permutations) in
  which N and E can be achieved
• W N! / ? n(i)!E! / ? e(i)!
• Maximization of W subject to constraint
  equations of previous slide
• Introduce Lagrange multipliers ? and ß to take
  into account constraint equations
• Deal with lnW rather than W in order to use
  Stirling approximation for natural logarithm of
  factorials for large numbers
• lnn! gt n lnn- n when n gtgt1

17
Optimization

• Maximization of lnW with Lagrange multipliers
• ? / ? e(i) lnW ?N-Sn(i) ßE-Se(i)
  0
• Use of relation between n(i) and e(i) and p(i)
• ?/ ? e(i) lnW ?N-S e(i)ltPgtp(i)
  ßE-Se(i) 0
• where, using Stirlings approximation
• lnW N(lnN-1) E(lnE-1) - S e(i)p(i)ltPgtlne(i)
  p(i)ltPgt-1
• - S e(i)lne(i)-1

18
Resulting Distributions

• Employee distribution over manufacturing sectors
  e(i)
• e(i) D p(i)-p(i)/p(i)1 Exp -
  ßp(i)/1p(i)
• where the constants D and ß are expressible
  in terms of the Lagrange multipliers that allow
  for the constraint relations
• Output distribution over manufacturing sectors
  n(i)
• n(i) DltPgt p(i) 1/p(i)1 Exp -
  ßp(i)/1p(i)
• Two interesting features
• NonMaxwellian i.e. Not a simple exponential
• An inverse temperature factor (or bureacratic
  factor) ß that gives the disperion of the
  distribution

19
Figure 1 Predicted shape of output n(i) vs.
productivity p(i) for a sector bureaucratic
factor ß 0.1 lower curve and ß1 upper
curve.
Output
n(i)
p(i)
20
Figure 2. Predicted shape of employee number
e(i) vs. productivity p(i) for a sector
bureaucratic factor ß 0.1 lower curve and ß1
upper curve.
Employment
e(i)
p(i)
21
Figure 3. Data Employment vs productivity for
the 140 manufacturing sectors in the Los Angeles
consolidated metropolitan statistical area in 1997
Data
22
Productivity Paradox
Figure 4. Productivities in Los Angeles
consolidated metropolitan statistical area.
(Ignore Industry Sector Average Company Size)
1.8
1.6
1.4
1.2
1
Ratio of 1997 productivity to 1992 productivity
0.8
0.6
0.4
0.2
0
0
15
30
45
60
75
90
105
120
135
Average rank of per capita information technology
expenditure
23
Stratified
Figure 5. Productivities in Los Angeles
consolidated metropolitan statistical area. (3
Industry sector sizes)
1.8
1.6
26 largest company size sectors
1.4
1.2
26 intermediate company size sectors
24 smallest company size sectors
1
Ratio of 1997 productivity to 1992 productivity
0.8
0.6
0.4
0.2
0
0
15
30
45
60
75
90
105
120
135
Average rank of per capita information technology
expenditure
24
Conclusions

• Agreement with industry sector behavior to
  thermodynamic model.
• Consistent across multiple definitions of
  productivity.
• Interaction between average per capita
  expenditure on information technology,
  organizational size and the average increase in
  productivity
• IT investment alters B
• High IT (electronics) Investor changed their B,
  Low IT Investor (heavy springs) did not

25
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

26
Comparison of Statistical Formalism in Physics
and in Economics
Variable Physics Economics State
(i) Hamiltonian eigenfunction Production
site Energy Hamiltonian eigenvalue Ei
Unit production cost Ci Occupation number
Number in state Ni Production output
Ni 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/??
27
Maxwell-Boltzmann distributions for different
effective industry sector temperatures and
productivities
Output
High temperature flatter curves
High productivity
Low productivity
Unit cost
28
Example Maxwell-Boltzmann dependence of output
on unit costs
Ln Output
High productivity, High temperature
High productivity, Low temperature
Low productivity, High temperature
Low productivity, Low temperature
Unit costs
29
Conservation law for Technology Transfer
Total cost of production C ? C(i) exp
-ß(C(i) F)
Effect of a change d? in a parameter ? in the
system and a change d ß In bureaucratic factor
dC - ltf? gt d? ß ?2F/ ?ß?? d? ?2ßF/
?ß2 dß
which can be rewritten
dC - ltf? gt d? TdS
Significance First term on the RHS
describes lowering of unit cost of production.
Second term on RHS describes increase in
entropy (temperature)
30
Effects of Technology Transfer
Ln Output
High productivity, High temperature
Costs down
High productivity, Low temperature
Low productivity, High temperature
Entropy up
Low productivity, Low temperature
Unit costs
31
Very preliminary examples
(1) Semiconductor and (2) Heavy spring
manufacturing in consolidated LA metropolitan
area US Economic census data for 1992 and 1997

• LA consolidated metropolitan statistical area
  (CMSA) comprised of 4 primary metropolitan
  statistical areas (PMSAs)
• Los Angeles-Long Beach PMSA
• Orange County PMSA
• Riverside-San Bernardino County PMSA
• Ventura County PMSA
• Semiconductor and heavy spring production spread
  over all 4 PMSAs
• Semiconductor manufacturing sector investment in
  information technology high while heavy spring
  manufacturing sector investment in information is
  low

32
Example 1. Semiconductor production in
consolidated LA metropolitan area in 1992 and 1987

• Observations on a sector with large investment in
  information
• Correlation between PMSAs with highest
  production and lowest unit costs
• Qualitatively consistent with a Boltzmann
  distribution
• Large decrease in temperature (increase in
  bureaucratic factor) between 1992 and 1997
• slope 7 x larger in 1997 than in 1992
• Large increase in employee productivity between
  1992 and 1997
• Value of shipments per employee 1.8 x larger in
  1997 230K/employee than in 1992

33
Semiconductor example Movement between 1992 and
1997 on Maxwell Boltzmann plot
Ln Output
High productivity, High temperature
High productivity, Low temperature
Low productivity, High temperature
Low productivity, Low temperature
Unit costs
34
Example 2. Heavy springs production in
consolidated LA metropolitan area in 1992 and 1987

• Observations on a sector with small investment in
  information
• A lower sector temperature in 1992 than
  semiconductor sector slope of -5.5 compared to
  -1.2 for semiconductor sector
• Possibly higher sector temperature in 1997
• Clustering of PMSAs around (MC)/S 0.5
• Virtually no increase in productivity per
  employee between 1992 and 1997
• Close to 120K/employee both years

35
Heavy spring example Movement between 1992 and
1997 on Maxwell Boltzmann plot
Ln Output
High productivity, High temperature
High productivity, Low temperature
Low productivity, High temperature
Low productivity, Low temperature
Unit costs