The Impact of Information on Supply Chain Oscillations

1
The Impact of Information on Supply Chain
Oscillations

• Ken Dozier David Chang
• Western Research Application Center
• IRMA International , Inc
• Washington D.C.
• May 23, 2006

2
Bio
3
A System of Forces in Organization
Direction
Cooperation
Efficiency
Proficiency
Competition
Concentrat\ion
Innovation
Source The Effective Organization Forces and
Form, Sloan Management Review, Henry Mintzberg,
McGill University 1991
4
Make Sell vs Sense Respond
Chart SourceCorporate Information Systems and
Management, Applegate, 2000
5
Theoretical Environment
Seven Organizational Change Propositions
Framework, Framing the Domains of IT
Management Zmud 2002
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
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

11
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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Applications of statistical physics to economics

• Quasistatic phenomena
• Approach Constrained maximization of
  microstates corresponding to a macrostate
• Applications to date unit cost of production
  productivity
• Time-dependent phenomena
• Approach normal mode analysis
• Current application supply chain oscillations

13
Quasi-static
Comparison of Statistical Formalism in Physics
and Economics Variable Physics Economics Sta
te (i) Hamiltonian eigenfunction Production
site Energy Hamiltonian 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 Te
chnology Example Electric field x
charge Knowledge Entropy (randomness) - ?F / ?T
kBß2?F/?b
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Quasi-static
Comparison of U.S. economic census cumulative
number of companies vs shipments/company (blue
diamond points) in LACMSA in 1992 and the
statistical physics cumulative distribution curve
(square pink points) with ß 0.167 per 106
15
Productivity Ratio (97/92) of the statistical
parameters

• Company size Large Intermediate
  Small
• IT rank 59 70 81
• 0.86 1.0
  0.90
• E(1000s) 0.78
  0.98 1.08
• /company 0.91 1.0 1.21
• Sh (million) 1.53 1.24
  1.42
• Sh/E (1000) 1.66 1.34
  1.35
• ß 1.11 0.90 0.99
• Findings
• Sectors with large companies spend a larger
  percentage on IT.
• Largest increases in shipments are in large
  small company sectors.
• Small companies increased in size while large
  companies decreased.
• Number of large and small companies decreased by
  10.
• Employment decreased 20 in large companies, but
  increased 8 in small companies.
• Largest productivity occurred in large companies.

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Oscillations in Supply Chains

• 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

17
IRMA 2006 Objectives

• To show with a simple product-flow model of a
  supply chain that universal information exchange
• Changes the character of oscillations from those
  of nearest neighbor information exchange
• Causes an increase in the damping of oscillations

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Local Exchange of Information

• Instead of designating each level in the chain
  by a discrete label n
• the position in a chain was designated by a
  continuum variable x.
• Flow of production units through each position in
  the chain was designated by a velocity variable
  v.
• A differential distribution function f(x,v,t)dxdv
  denotes the number of production units in the
  intervals dx and dv at x and v at time t.
• ?f/ ?t ?fdx/dt/ ?x ?fdv/dt/ ?v
  0 1
• A thermodynamic force F that gives the rate at
  which v changes in time, this equation can be
  rewritten
• ?f/ ?t ?fv/?x ?fF/ ?v 0 2

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Nearest neighbor information exchange

• This becomes Vlasov-like equation for f(x,v,t)
• ?f/?t v?f/?x F?f/?v 0 5
• This is the equation for collisionless plasmas
• When the inventory of the level below the level
  of interest is less than normal, the production
  rate (v) will be diminished because of the
  smaller number of production units being
  introduced to that level. At the same time, when
  the inventory of the level above the level of
  interest is larger than normal, the production
  rate will also be diminished because the upper
  level will demand less input so that it can
  catch up in its production through-put. Both
  effects give production rate changes proportional
  to the gradient of n. It is resonable also that
  the fractional changes are related rather than
  the changes themselves, since deviations are
  always made from the inventories at hand.
• ?f/?t v?f/?x - 2?v2(1/n)(dn/dx) ?f/?v 0 13

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Nearest neighbor dispersion relation

• Perturbed distribution
• f(x,v,t) f0(v) f1(v) exp-i(?t kx) 15
• -i(?-kv)f1 - ik 2?v2(1/no)n1?fo/?v 0
  16b
• f1 -2?k(1/no) ?dvf1(v) v2?fo/?v(?-kv)-1 17
  
• This leads to the dispersion relation between ?
  and k
• 1 2?k (1/no) ?dvv2?fo/?v(?-kv)-1 0 18
• Principal and imaginary parts
• ?dvv2?fo/?v(?-kv)-1 PP?dvv2?fo/?v
• (?-kv)-1 - ip(?/k)2(1/k)?fo(?/k) /?v 19

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Nearest neighbor dispersion relation (cont)

• Solving for ?
• ? 4?kVo 1
• (1/n0)ip(4?Vo )2?fo(4?Vo ) /?v 23
• Significance
• f0(v) peaked around V0, ?f0(4?V0 ) / ?v lt0.
• Oscillation resembles a sound-like wave
• Oscillation exhibits small Landau damping that
  is because of distance of phase velocity from Vo

22
Universal information exchange

• Introduce an information exchange potential F
• ?2F/?x2 - C/no?dv f(x,v,t) 24
• from which the thermodynamic force F is obtained
• F - ?F/?x 25
• This reduces to the former results for nearest
  neighbor interactions when we choose
• C ?Vo2 / l2 29

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Universal information exchange dynamic equations

• Introduction of potential into Vlasov equation
• ?f/?t v?f/?x - ?F/?x ?f/?v 0 31
• Perturbation in distribution function caused by F
• f1 -kF1?fo /?v (?-kv) -1 33
• Self-consistency condition
• F1 (1/k2) ?Vo2 /nol2 ?dv f1(v) 34

24
Dispersion relation for universal information
exchange

• ? kVo ?1/2(Vo/l) 1 i p?Vo2/(2k2l2no)?fo/
  ?v 42
• where ?f0/?v is evaluated at
• v ?/k Vo (?1/2Vo/kl) 43
• Significance
• Oscillations resemble plasma oscillations
• Oscillations always exhibit Landau damping. This
  changes the form of the supply chain oscillation
  and in suppression of the resulting oscillation

25
Conclusions
Washington DC

• Supply chain oscillations can be described by a
  simple flow model of product through chain
• Flow model shows that
• Character of oscillation changes from sound-like
  to plasma-like when information exchange becomes
  universal rather than just between nearest
  neighbors
• Damping of oscillation can be large when
  information exchange becomes universal

26
Future Work

• Create a simulation that allows the study of
  various IT architectures on the optimization
  issues of supply chain management
• kdozier_at_usc.edu
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