Temporal and Focal Optimization of Technology Transfer in a Supply Chain

1. Temporal and Focal Optimization of Technology Transfer in a Supply Chain Ken Dozier & David Chang USC Engineering Technology Transfer Center T2S Annual Conference 2005September 29, 2005

2. Bio

3. Outline • Objective, approach, & significance 4-12 • Background • 1. Thermodynamics of technology transfer 13-17 • 2. Oscillations in supply chains 18-21 • Fluid flow model of supply chain • Rationale for fluid flow model 22 • Quasilinear equations • Basic flow equations 23 • Expansion and Fourier analyzed equations 24 • Treatment of singularities 25 • Resulting quasilinear equation for flow velocity 26 • Conclusions 27 • Moral 28

4. 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

5. Make & Sell vs Sense & Respond Chart Source:“Corporate Information Systems and Management”, Applegate, 2000

6. Supply Chain (Firm) Source: Gus Koehler, University of Southern California Department of Policy and Planning, 2002

7. Supply Chain (Government) Source: Gus Koehler, University of Southern California Department of Policy and Planning, 2002

8. Supply Chain (Framework) Source: Gus Koehler, University of Southern California Department of Policy and Planning, 2002

9. Supply Chain (Interactions) Source: Gus Koehler, University of Southern California Department of Policy and Planning, 2002

10. Plasma theories • Advanced plasma theories are extremely important when one tries to explain, for example, the various waves and instabilities found in the plasma environment. Since plasma consist of a very large number of interacting particles, in order to provide a macroscopic description of plasma phenomena it is appropriate to adopt a statistical approach. This leads to a great reduction in the amount of information to be handled. In the kinetic theory it is necessary to know only the distribution function for the system of particles. Source: University of Oulu, FInland

11. Why statistical physics? • Proven formalism for “seeing the forest past the trees” • Well established in physical and chemical sciences • Our recent verification with data in economic realm • Simple procedure for focusing on macro-parameters • Most likely distributions obtained by maximizing the number of micro-states corresponding to a measurable macro-state • Straightforward extension from original focus on energy to economic quantities • Unit cost of production • Productivity • R&D costs • Self-consistency check provided by distribution functions

12. Objective, approach, and significance • Objective • Optimize technology transfer policy to increase average production rate throughout a supply chain • Approach • Develop simple model for flow (overall production rate) in a supply chain • Develop normal modes for flow oscillations • Apply quasilinear theory to describe effects of resonant interactions with normal modes on overall flow velocity • Significance • Criteria for timing and position focus of technology transfer efforts that will maximize impact on rate of production throughout supply chain

13. Background 1: Thermodynamics of technology transfer (T2S 2004 Albany conference: Dozier & Chang) Technology Transfer • Question addressed • What is required for technology transfer to reduce production costs throughout an industrial sector? • Approach • Application of statistical physics approach to develop a “first law of thermodynamics” for technology transfer, where “energy” is replaced by “unit cost of production” • Result and significance • Found that technology transfer impact can be increased if “entropy” term and “work” term act synergistically rather than antagonistically

14. Statistical physics approach and resulting Boltzmann distribution for output vs unit production costs (T2S-04) Technology Transfer Problem [simplest case] Given: Total output N of sector Total costs of production for sector C Unit costs c(i) of production at sites i within sector Find: Most likely distribution of outputs n(i) within sectorApproach: Let W{n(i)} be the number of possible ways that a set of outputs {n(i)} can be realized. Maximize W{n(i)} subject to given constraints N, C, and c(i) d/dn(i) [ lnW + {N-Σn(i)} +β{C-Σc(i)}]=0 [1] Solution for simplest case n(i) = P exp{-βc(i)} [Maxwell-Boltzmann distribution] [2] where the parameters characterizing the sector are: P is a “productivity factor” for the sector β is an “inverse temperature” or “bureaucratic factor”

15. Technology Transfer : Quasi-static Task 1. Comparison of Statistical Formalism in Physics and in Economics VariablePhysicsEconomics State (i) Hamiltonian eigenfunction Production site Energy Hamiltonian eigenvalue Ei Unit prod. cost Ci Occupation number Number in state Ni Output Ni = exp[-βCi+βF] 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 Technology Example Electric field x charge Knowledge Entropy (randomness) - ∂F / ∂T kBβ2∂F/∂b

16. Technology Transfer : Quasi-static Conservation law for Technology Transfer (TS2 2004) Total cost of production C = ∑ C(ξ;i) exp [-β(C(ξ;i) – F(ξ ))] [1] Effect of a change dξ in a parameter ξ in the system and a change dβ In bureaucratic factor dC = - <fξ > dξ + β [d2F/ dβdξ] dξ + [d2[βF]/ dβ2] dβ [2] which can be rewritten dC = - <fξ > dξ + TdS [3] Significance First term on the RHS describes lowering of unit cost of production. Second term on RHS describes increase in entropy (temperature)

17. Technology Transfer: Quasi-static Comparison of U.S. economic census cumulative number of companies vs shipments/company (diamond points) in LACMSA in 1992 and the statistical physics cumulative distribution curve (square points) with β = 0.167 per $106

18. Technology Transfer Background 2: Oscillations in supply chains(Dozier & Chang, CITSA 05 conference proceedings) • Observations • Cyclic phenomena in economics ubiquitous & disruptive • Example: Wild oscillations In supply chain inventories • MIT “beer game” simulation • Supply chain of only 4 companies for beer production, distribution, and sales • Results of observations and simulations • Oscillations • Phase dependence of oscillations on position in chain • Spatial instability

19. Technology Transfer Development of a simple model for normal modes in a supply chain (CITSA 05) • Assumed oscillations in supply chain inventories of the form exp(iwt) • Obtained a simple form for normal modes for uniform processing times • Derived dispersion relation giving dependence of oscillation frequency on form of normal mode

20. Technology Transfer Resulting normal modes in a supply chain with uniform processing times (CITSA 05) • Supply chain normal mode equation y(n-1) – 2y(n) + y(n+1) +(T)2 y(n) = 0 [1] • Normal mode form for N companies in chain y(p:(n) = exp[i2pn/N] [2] • Normal mode dispersion relation  =  (2/T) sin(p/N) where p is any integer [3]

21. Technology Transfer Implications of normal modes (CITSA-05) • Supply chains naturally oscillate at frequencies below and up to inverse of processing times • In agreement with observations • Disturbances in inventories propagate through supply chain at different velocities • Phase velocities increase to saturation as disturbance wavelength decreases • Group velocities decrease as disturbance wavelength decreases • Maximum control exerted by resonant interactions (Landau damping) with propagating waves • Control by “surfing”

22. Technology Transfer Fluid flow model of a supply chain: rationale • In a long supply chain • Discrete levels can be replaced by a continuum of levels • End effects can be ignored • Adding value to a developing product in a chain is like enriching a fluid flowing through a pipeline by adding different colors at various points (levels) • Product components enter supply chain needing value to be added by processing, assembly, etc. • Fluid enters pipeline colorless and needs sequential addition and interaction of colors • Finished product exits supply chain with the desired values added by supply chain manipulations • Fluid exits pipeline with desired rich blend of colors

23. Technology Transfer Basic fluid flow equations Conservation equation for distribution function f(x,v,t) designating density of fluid in phase space consisting of position x in supply chain (pipeline) and flow velocity v at time t ∂f/ ∂t + v ∂f/ ∂x + F ∂f/ ∂v = 0 [1] Density and velocity moments N(x, t) = dvf(x,v,t) & V(x,t) = (1/N)vdvf(x,v,t) [2] Density and velocity conservation equations ∂N/∂t + ∂[NV]/∂x = 0 [3] ∂V/∂t +V ∂V/∂x = F1 - (Dv)2∂N/∂x [4] where the dispersion in flow velocities is given by (Dv)2 = dv(v-V)2 f(x,v,t)/N(x,t)[5] and where the generalized statistical physics force acting to change V is defined by F1 = dV/dt [6]

24. Technology Transfer Expand quantities through second order and Fourier analyze Expansions N(x,t) = N0 + N1(x,t) + N2(x,t) [1] V(x,t) = V0 + V1(x,t) + V2(x,t) [2] Fourier analyze G(,K) =dxdt exp[-i(t-Kx)]G(x,t)[3] where G(x,t) => N(x,t), V(x,t), F1(x,t) [4]

25. Technology Transfer Resulting approximate equations for Fourier components First order equations i (w-kV0)N1(w,k) + N0 ikV1(w,k) = 0 [1] i N0 (w-kV0)V1(w,k) = -ik (Dv)2N1(w,k) + F1(w,k) [2] Second order equation for flow velocity ∂V2(0,0)/ ∂t = dwdk(ik/N02) (w-kV0)2 times [(w-kV0)2 – k2 (Dv)2] -2 F1(- w,k) F1(- w,k) [3]

26. Technology Transfer Treatment of singularities • Note that singularities occur in the solutions of the first order equations at (w-kV0)2 – k2 (Dv)2 = 0[1] • These are the famous Landau (surfing) resonances that define the normal mode frequencies, and can be treated by contour integration around a small half circle around the singularities dz f(z)/(z-z0)n+1 = 2pi f(n)(z0)/n! [See, e.g., Chang Phys. Fluids 7, 1980-1986(1964)]

27. Technology Transfer Resulting quasilinear equation for average flow velocity ∂V2(0,0)/∂t = p/(N02Dv) dk(1/k) times [ F1(-k(V0- Dv, -k)F1(k(V0- Dv),k) – (-k(V0+ Dv, -k)F1(k(V0+Dv),k)] Significance Average flow velocity is most impacted by technology transfer policies that have Fourier components that resonate with the naturally occurring normal modes in the supply chain

28. Conclusions • Optimization of technology transfer policies for a supply chain depends on understanding the chain’s naturally occurring oscillations • To be most effective, the focus of technology transfer should have frequency components in time and in space (level) that resonate with the natural traveling waves in the supply chains • Future work should include data gathering to calibrate the relevant generalized technology transfer force that impacts the flow velocities (production rates)

29. Moral Technology transfer practitioners can learn from surfers