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Thermodynamics of Productivity Framework for Impact of Information/Communication Investments

Thermodynamics of Productivity Framework for Impact of Information/Communication Investments. Ken Dozier USC 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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Thermodynamics of Productivity Framework for Impact of Information/Communication Investments

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  1. Thermodynamics of Productivity Framework for Impact of Information/Communication Investments Ken Dozier USC Viterbi School of Engineering Technology Transfer Center

  2. Presentation Outline • Problem (7 slides) • Approach (9 slides) • Results (8 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 Source:“Corporate 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. Market Redefinition Supply-chain Expansion Supply-chain Discovery Business Model Redefinition Business Model Refinement Business Process Redesign Business Process Improvement 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)/<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?

  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 = 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)

  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 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

  17. Optimization • 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]

  18. Resulting Distributions • 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

  19. 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]. Output n(i) p(i)

  20. 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]. 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. Effects of Technology Transfer Task 1. Approach 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 Entropy up Low output N, Low “temperature” 1/b Unit costs

  25. Effects of Technology Transfer 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

  26. Effects of Technology Transfer 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

  27. 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

  28. 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

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