viterbi school of engineering technology transfer center temporal and focal optimization of...

Viterbi School of Engineering Technology Transfer CenterViterbi School of Engineering Technology Transfer Center

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


Bio


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


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)



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


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


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


Background 1: Thermodynamics of technology transfer (T2S 2004 Albany conference: Dozier & Chang)

• 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

Technology Transfer


Statistical physics approach and resulting Boltzmann distribution for output vs unit production costs (T2S-04)

Problem [simplest case]

Given: Total output N of sectorTotal costs of production for sector CUnit costs c(i) of production at sites i within sector

Find: Most likely distribution of outputs n(i) within sector

Approach:

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)

n(i) [ lnW + {N-Σn(i)} +β{C-Σc(i)}] =0 [1]

Solution for simplest casen(i) = P exp{-βc(i)} [Maxwell-Boltzmann distribution] [2]

where the parameters characterizing the sector are:P is a “productivity factor” for the sectorβ is an “inverse temperature” or “bureaucratic factor”

Technology Transfer


Task 1. Comparison of Statistical Formalism in Physics and in Economics

Variable Physics Economics

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 TechnologyExample Electric field x charge Knowledge

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

Technology Transfer : Quasi-static


Total cost of production

C = ∑ C(ξ;i) exp [-β(C(ξ;i) – F(ξ ))] [1]

Conservation law for Technology Transfer (TS2 2004)

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

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

Technology Transfer : Quasi-static


0

500

1000

1500

2000

2500

3000

3500

4000

0 10 20 30 40 50 60

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

Technology Transfer: Quasi-static


Technology Transfer

• 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

Background 2: Oscillations in supply chains(Dozier & Chang, CITSA 05 conference proceedings)


Development of a simple model for normal modes in a supply chain (CITSA 05)

• Assumed oscillations in supply chain inventories of the form exp(it)

• Obtained a simple form for normal modes for uniform processing times

• Derived dispersion relation giving dependence of oscillation frequency on form of normal mode

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[i2pn/N] [2]

• Normal mode dispersion relation

= (2/T) sin(p/N) where p is any integer [3]

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”

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

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 - (v)2 ∂N/∂x [4]

where the dispersion in flow velocities is given by

(v)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]

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]

Technology Transfer


Resulting approximate equations for Fourier components

First order equations

i (-kV0)N1(,k) + N0 ikV1(,k) = 0 [1]

i N0 ( -kV0)V1(,k) = -ik (v)2N1(,k) + F1(,k) [2]

Second order equation for flow velocity

∂V2(0,0)/ ∂t = ddk(ik/N02) (-kV0)2 times

[(-kV0)2 – k2 (v)2] -2 F1(- ,k) F1(- ,k)

[3]

Technology Transfer


Treatment of singularities

• Note that singularities occur in the solutions of the first order equations at

(-kV0)2 – k2 (v)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 = 2i f(n)(z0)/n!

[See, e.g., Chang Phys. Fluids 7, 1980-1986 (1964)]

Technology Transfer


Resulting quasilinear equation for average flow velocity

∂V2(0,0)/∂t =

/(N02v) dk(1/k) times

[ F1(-k(V0- v, -k)F1(k(V0- v),k) – (-k(V0+ v, -k)F1(k(V0+v),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

Technology Transfer


Conclusions

1. Optimization of technology transfer policies for a supply chain depends on understanding the chain’s naturally occurring oscillations

2. 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

3. Future work should include data gathering to calibrate the relevant generalized technology transfer force that impacts the flow velocities (production rates)


Moral

Technology transfer practitioners can learn from surfers

viterbi school of engineering technology transfer center temporal and focal optimization of...

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