Viterbi School of Engineering Technology Transfer Center A Statistical Physics Model of Technology Transfer Ken Dozier USC Viterbi School of Engineering

Viterbi School of Engineering Technology Transfer Center

A Statistical Physics Model of Technology Transfer

Ken DozierUSC Viterbi School of Engineering

Technology Transfer Center Technology Transfer Society (T2S)

26th Annual ConferenceAlbany, NY

October 1, 2004


Presentation

• Problem (7 slides)

• Approach (9 slides)

• Results (5 slides)

• Conclusions (1 slide)

• Future (1 slide)


A System of Forces in Organization

Efficiency

Direction

Proficiency

Competition

Concentration Innovation

Cooperation

Source: “The Effective Organization: Forces and Form”,Sloan Management Review, Henry Mintzberg, McGill University 1991


Make & Sell vs Sense & Respond

Chart Source:“Corporate Information Systems and Management”, Applegate, 2000


Supply Chain (Firm)

Source: Gus Koehler, University of Southern California Department of Policy and Planning, 2002


Supply Chain (Government)



Supply Chain (Framework)



Supply Chain (Interactions)



Theoretical Environment

Seven Organizational Change Propositions Framework, “Framing the Domains of IT Management” Zmud 2002

Business Process Improvement

Business Process Redesign

Business Model Refinement

Business Model Redefinition

Supply-chain Discovery

Supply-chain Expansion

Market Redefinition


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


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


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


• 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”

Constrained Optimization Approach


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)/ (Chang Simplification)

where 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?


• Relations between total metropolitan employee number E and output N and sector employee numbers e(i) and outputs n(i)

E = Σ e(i)

N = Σ n(i)

• Relation between sector outputs, employee numbers, and productivities

n(i) = e(i) p(i)

n(i) = e(i)p(i)

• Accordingly,

N = Σ n(i) = Σ e(i) p(i)



• 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 β 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

ln{n!} => n ln{n}- n when n >>1



• Maximization of lnW with Lagrange multipliers

/ e(i) [ lnW + {N-Σn(i)} +β{E-Σe(i)}] = 0

• Use of relation between n(i) and e(i) and p(i):

/ e(i) [ lnW + {N-Σ e(i)p(i)} +β{E-Σe(i)}] =0

where, using Stirling’s approximation:

lnW = N(lnN-1) +E(lnE-1) - Σ e(i)p(i)[ln{e(i)p(i)}-1]

- Σ e(i)[ln{e(i)}-1]

Optimization


• Employee distribution over manufacturing sectors e(i)

e(i) = D p(i)-[p(i)/{p(i)+1}] Exp [- βp(i)/{1+p(i)}]

where the constants D and β are expressible in terms of the Lagrange multipliers that allow for the constraint relations

• Output distribution over manufacturing sectors n(i)

n(i) = D p(i) [1/{p(i)+1}] Exp [- βp(i)/{1+p(i)}]

• Two interesting features:

– NonMaxwellian – i.e. Not a simple exponential– An inverse temperature factor (or bureacratic factor) β that

gives the disperion of the distribution

Resulting Distributions


Figure 1: Predicted shape of output n(i) vs. productivity p(i) for a sector bureaucratic factor β = 0.1 [lower curve] and β=1 [upper curve].

n(i)

p(i)

Output


Figure 2. Predicted shape of employee number e(i) vs. productivity p(i) for a sector bureaucratic factor β = 0.1 [lower curve] and β=1 [upper curve].

e(i)

p(i)

Employment


Figure 3. Data Employment vs productivity for the 140 manufacturing sectors in the Los Angeles consolidated metropolitan statistical area in 1997

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00

100.00

0 100 200 300 400 500 600 700 800 900

Productivity in $ thousands/employee

Nu

mb

er o

f jo

bs

in t

ho

usa

nd

s p

er p

rod

uct

ivit

y b

in w

idth

s o

f $5

0K/e

mp

loye

e

Data


Productivity Paradox

Figure 4. Productivities in Los Angeles consolidated metropolitan statistical area. (Ignore Industry Sector Average Company Size)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 15 30 45 60 75 90 105 120 135

Average rank of per capita information technology expenditure

Rat

io o

f 199

7 pr

oduc

tivity

to 1

992

prod

uctiv

ity


0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 15 30 45 60 75 90 105 120 135

Average rank of per capita information technology expenditure

Rat

io o

f 199

7 pr

oduc

tivity

to 1

992

prod

uctiv

ity

Stratified

Figure 5. Productivities in Los Angeles consolidated metropolitan statistical area. (3 Industry sector sizes)

26 largest company size sectors

26 intermediate company size sectors

24 smallest company size sectors


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


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


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[-βCi]

Free energy F kBT lnZ (1/β) lnZ

Generalized force fξ ∂F/∂ξ ∂F/∂ξ

Example Pressure TechnologyExample Electric field x charge Knowledge

Entropy (randomness) - ∂F / ∂T kBβ2∂F/∂ξ

Comparison of Statistical Formalism in Physics and in Economics


0.5 1 1.5 2

1

2

3

4High temperature flatter curves

High productivity

Low productivity

Output

Unit cost

Maxwell-Boltzmann distributions for different effective industry sector “temperatures” and productivities


Ln Output

Unit costs

High productivity,High “temperature”

High productivity,Low “temperature”

Low productivity,High “temperature”

Low productivity,Low “temperature”

Example: Maxwell-Boltzmann dependence of output on unit costs


Total cost of production

C = ∑ C(i) exp [-β(C(i) – F)]

Effect of a change dξ in a parameter ξ in the system and a change d βIn bureaucratic factor

dC = - <fξ > dξ + β [2F/ βξ] dξ + [2[βF]/ β2] dβ

which can be rewritten

dC = - <fξ > dξ + TdS

Significance First term on the RHS describes lowering of unit cost of production. Second term on RHS describes increase in entropy (temperature)

Conservation law for Technology Transfer


Ln Output

Unit costs





Costs down

Entropy up

Effects of Technology Transfer


(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 (PMSA’s)

• 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 PMSA’s

– Semiconductor manufacturing sector investment in information technology high while heavy spring manufacturing sector investment in information is low

Very preliminary examples:


• Observations on a sector with large investment in information

– Correlation between PMSA’s 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

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


Ln Output

Unit costs





Semiconductor example: Movement between 1992 and 1997 on Maxwell Boltzmann plot


• 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 PMSA’s around (M+C)/S = 0.5

– Virtually no increase in productivity per employee between 1992 and 1997

• Close to $120K/employee both years

Example 2. Heavy springs production in consolidated LA metropolitan area in 1992 and 1987


Ln Output

Unit costs





Heavy spring example: Movement between 1992 and 1997 on Maxwell Boltzmann plot

Documents

Viterbi School of Engineering Technology Transfer Center A Statistical Physics Model of Technology Transfer Ken Dozier USC Viterbi School of Engineering