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 CITSA 2004 July 21-25, 2004

Viterbi School of Engineering Technology Transfer Center Presentation Problem (7 slides) Approach (9 slides) Results (5 slides) Conclusions (1 slide) Future (1 slide)

Viterbi School of Engineering Technology Transfer Center 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

Viterbi School of Engineering Technology Transfer Center Make & Sell vs Sense & Respond Chart Source:“Corporate Information Systems and Management”, Applegate, 2000

Viterbi School of Engineering Technology Transfer Center Supply Chain (Firm) Source: Gus Koehler, University of Southern California Department of Policy and Planning, 2002

Viterbi School of Engineering Technology Transfer Center Supply Chain (Government) Source: Gus Koehler, University of Southern California Department of Policy and Planning, 2002

Viterbi School of Engineering Technology Transfer Center Supply Chain (Framework) Source: Gus Koehler, University of Southern California Department of Policy and Planning, 2002

Viterbi School of Engineering Technology Transfer Center Supply Chain (Interactions) Source: Gus Koehler, University of Southern California Department of Policy and Planning, 2002

Viterbi School of Engineering Technology Transfer Center 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

Viterbi School of Engineering Technology Transfer Center 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

Viterbi School of Engineering Technology Transfer Center 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

Viterbi School of Engineering Technology Transfer Center 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

Viterbi School of Engineering Technology Transfer Center 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

Viterbi School of Engineering Technology Transfer Center 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?

Viterbi School of Engineering Technology Transfer Center 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) Accordingly, N = Σ n(i) = Σ e(i) p(i) Pseudo-Thermodynamic Approach

Viterbi School of Engineering Technology Transfer Center 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

Viterbi School of Engineering Technology Transfer Center 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

Viterbi School of Engineering Technology Transfer Center 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

Viterbi School of Engineering Technology Transfer Center 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

Viterbi School of Engineering Technology Transfer Center 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

Viterbi School of Engineering Technology Transfer Center Figure 3. Data Employment vs productivity for the 140 manufacturing sectors in the Los Angeles consolidated metropolitan statistical area in 1997 Data

Viterbi School of Engineering Technology Transfer Center Productivity Paradox Figure 4. Productivities in Los Angeles consolidated metropolitan statistical area. (Ignore Industry Sector Average Company Size) Average rank of per capita information technology expenditure Ratio of 1997 productivity to 1992 productivity

Viterbi School of Engineering Technology Transfer Center Average rank of per capita information technology expenditure Ratio of 1997 productivity to 1992 productivity 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

Viterbi School of Engineering Technology Transfer Center 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

Viterbi School of Engineering Technology Transfer Center 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