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

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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
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Make Sell vs Sense Respond
Chart SourceCorporate 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
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
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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
• RD 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

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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 Wn(i) be the number of possible ways that
  a set of outputs n(i) can be realized.
• Maximize Wn(i) subject to given constraints N,
  C, and c(i)
• d/dn(i) lnW ?N-Sn(i) ßC-Sc(i)
  0 1
• Solution for simplest case
• n(i) P exp-ßc(i) Maxwell-Boltzmann
  distribution 2
• where the parameters characterizing the sector
  are
• P is a productivity factor for the sector
• ß is an inverse temperature or bureaucratic
  factor

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Technology Transfer Quasi-static
Task 1. Comparison of Statistical Formalism in
Physics and in Economics Variable Physics Eco
nomics State (i) Hamiltonian
eigenfunction Production site Energy Hamiltoni
an eigenvalue Ei Unit prod. cost
Ci Occupation number Number in state Ni
Output Ni exp-ßCißF Partition function Z
?exp-(1/kBT)Ei ?exp-ßCi Free energy F kBT
lnZ (1/ß) lnZ Generalized force f?
?F/?? ?F/?? Example Pressure Technology Ex
ample Electric field x charge Knowledge Entropy
(randomness) - ?F / ?T kBß2?F/?b
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Technology Transfer Quasi-static
Conservation law for Technology Transfer (TS2
2004)
Total cost of production C ? C(?i) exp
-ß(C(?i) F(? )) 1
Effect of a change d? in a parameter ? in the
system and a change dß In bureaucratic factor
dC - ltf? gt d? ß d2F/ dßd? d? d2ßF/
dß2 dß 2
which can be rewritten
dC - ltf? gt d? TdS 3
Significance First term on the RHS
describes lowering of unit cost of production.
Second term on RHS describes increase in
entropy (temperature)
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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 ß 0.167 per 106
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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

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

• 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

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Resulting normal modes in a supply chain with
uniform processing times (CITSA 05)
Technology Transfer

• Supply chain normal mode equation
• y(n-1) 2y(n) y(n1) (?T)2 y(n)
  0 1
• Normal mode form for N companies in chain
• y(p(n) expi2?pn/N 2
• Normal mode dispersion relation
• ? ? (2/T) sin(?p/N) where p is any
  integer 3

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Implications of normal modes (CITSA-05)
Technology Transfer

• 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

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Fluid flow model of a supply chain rationale
Technology Transfer

• 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

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Basic fluid flow equations
Technology Transfer

• 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

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Expand quantities through second order and
Fourier analyze
Technology Transfer

• 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) gt N(x,t), V(x,t), F1(x,t) 4

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Resulting approximate equations for Fourier
components
Technology Transfer

• 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

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Treatment of singularities
Technology Transfer

• 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)n1 2pi f(n)(z0)/n!
• See, e.g., Chang Phys. Fluids 7, 1980-1986
  (1964)

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Resulting quasilinear equation for average flow
velocity
Technology Transfer

• ?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(V0Dv),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

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Conclusions

• Optimization of technology transfer policies for
  a supply chain depends on understanding the
  chains 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)

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Moral

• Technology transfer practitioners can learn from
  surfers