Viterbi School of Engineering Technology Transfer Center
Thermodynamics of Productivity Framework for Impact of
Information/Communication Investments
Ken Dozier
USC Viterbi School of Engineering
Technology Transfer Center
Viterbi School of Engineering Technology Transfer Center
Presentation Outline
• Problem (7 slides)
• Approach (9 slides)
• Results (8 slides)
• Conclusions (1 slide)
• Future (1 slide)
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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
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Make & Sell vs Sense & Respond
Chart Source:“Corporate Information Systems and Management”, Applegate, 2000
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Supply Chain (Firm)
Source: Gus Koehler, University of Southern California Department of Policy and Planning, 2002
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Supply Chain (Government)
Source: Gus Koehler, University of Southern California Department of Policy and Planning, 2002
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Supply Chain (Framework)
Source: Gus Koehler, University of Southern California Department of Policy and Planning, 2002
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Supply Chain (Interactions)
Source: Gus Koehler, University of Southern California Department of Policy and Planning, 2002
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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
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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
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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
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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
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• 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
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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)/<P> (Chang Simplification)
where <P> 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?
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• 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>p(i)
• Accordingly,
N = Σ n(i) = Σ e(i) <P> p(i)
Pseudo-Thermodynamic Approach
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• 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
Pseudo-Thermodynamic Approach
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• 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>p(i)} +β{E-Σe(i)}] =0
where, using Stirling’s approximation:
lnW = N(lnN-1) +E(lnE-1) - Σ e(i)p(i)<P>[ln{e(i)p(i)<P>}-1]
- Σ e(i)[ln{e(i)}-1]
Optimization
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• 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> 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
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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
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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
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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
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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
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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
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Effects of Technology Transfer
Ln Output
Unit costs
High output N,High “temperature”
High output N,Low “temperature” 1/
Low output N,High “temperature” 1/
Low output N,Low “temperature” 1/
Costs down
Entropy up
Task 1. Approach
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Task 1. Semiconductor example: Movement between 1992 and 1997 on Maxwell Boltzmann plot
Ln Output
Unit costs
1997:High output N,Low “temperature” 1/
1992:Low output N,High “temperature” 1/
Effects of Technology Transfer
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Task 1. Heavy spring example: Movement between 1992 and 1997 on Maxwell Boltzmann plot
Ln Output
Unit costs
1997:Low output N,High “temperature” 1/
1992: Low output N,Low “temperature” 1/
Effects of Technology Transfer
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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
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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