Ken Dozier

1
The Impact of Information Technology on the
Temporal Optimization of Supply Chain Performance

• Ken Dozier David Chang
• Western Research Application Center
• HICSS 2007Hawaii International Conference on
  System Sciences May 23, 2006
• January 3-6, 2007
• Hilton Waikoloa Village Resort
• Waikoloa, Big Island
• Hawaii

2
Bio - Ken
3
Bio - David
4
Objectives

• Develop a mathematical artifact that allows
  optimization of supply chain performance and
  reduces production times though Information
  Technology Policies
• Provide the basis for an interactive simulation
  artifact that increases understanding of
  optimization strategies for supply chain
  performance and reduces production times though
  Innovative Information Technology Policies

5
What is Knowledge ?
Truth
Knowledge
Belief
Ontology
Epistemology
Axiology
Universal
Social
Personal
No Debate
Diverge on debate
Converge on debate
Effect
Cause
Cause
Source Ten Philosophical Mistakes, Mortimer J.
Adler 1985 Source Design Research in the
Technology of Information Systems Truth or
Dare., Purao, S. (2002).
6
Design Research
Awareness Slides 7 -19 Abduction 20-24 Deduction
25-42 Conclusion 43-46
SourceTakeda, H.. "Modeling Design Processes."
AI Magazine, Winter 37-48.
7
Business Takes on Many Forms
Direction
Cooperation
Efficiency
Proficiency
Competition
Concentration
Innovation
Source The Effective Organization Forces and
Form, Sloan Management Review, Henry Mintzberg,
McGill University 1991
8
Flow 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
• Negative Feedback Systems with Delays Oscillate
• Phase dependence of oscillations on position in
  chain
• Understanding of Managements Personality Impact
• The sharing of Knowledge has value

9
Temporal Oscillations (Firms)
Source Gus Koehler, University of Southern
California Department of Policy and Planning, 2002
10
System Dynamic
Common Modes of Interaction Between Positive and
Negative Feedback
Source System Dynamics, John Sterman, 2000
11
Exponential Growth

• How thick do you think a paper folded in-half 42
  times would be?
• How thick would it be after 100 folds?

Source System Dynamics, John Sterman, 2000
12
Exponential Growth

• The Answers
• 42 folds 440,000 Km (the distance from the
  earth to the moon.)
• 100 folds 850 trillion times the distance from
  the earth to the sun!

Source System Dynamics, John Sterman, 2000
13
The Beer Game
Steady state at 4 cases per week.
Wilensky, U. (1999). NetLogo. http//ccl.northwest
ern.edu/netlogo. Center for Connected Learning
and Computer-Based Modeling. Northwestern
University, Evanston, IL
Beer Game Demo Densmore, O. June 2004
14
Connectivity
Model Developed by Dr. Nathan B. Forrester of
A.T. Kearney, Atlanta, 2000
15
The Beer Game - Not Sharing
The system after only a single change from 4 to 8
case.
Wilensky, U. (1999). NetLogo. http//ccl.northwest
ern.edu/netlogo. Center for Connected Learning
and Computer-Based Modeling. Northwestern
University, Evanston, IL
Beer Game Demo Densmore, O. June 2004
16
The Beer Game - Sharing
Knowledge sharing,
Wilensky, U. (1999). NetLogo. http//ccl.northwest
ern.edu/netlogo. Center for Connected Learning
and Computer-Based Modeling. Northwestern
University, Evanston, IL
Beer Game Demo Densmore, O. June 2004
17
Government Dynamics
Source Gus Koehler, University of Southern
California Department of Policy and Planning,
2002
18
Supply Chain Dynamics
Source Gus Koehler, University of Southern
California Department of Policy and Planning,
2002
19
Complex System Dynamics
Source Gus Koehler, University of Southern
California Department of Policy and Planning,
2002
20
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

21
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
22
Stratification
Low ß
High ß
Seven Organizational Change Propositions
Framework, Framing the Domains of IT
Management Zmud 2002
23
JITTA

• Investigated the ß bureaucratic factor and its
  inverse organizational temperature T (dispersion)
  
• Investigate the ability of Stratification to
  Differentiate impact of IT Investment on output
  and job creation
• Large firms invest in IT to increase output and
  eliminate jobs
• Small firms invest in IT to increase output and
  expand workforce
• Investigate Partition Function Z, Cumulative
  Distribution Function opened the linkage to
  Statistical Physics
• Dozier-Chang (06) Journal of Information
  Technology Theory and Application

24
Maxwell Boltzman Distribution Confirmation
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
25
CITSA 05

• Wave Phenomena in a Supply Chain
• Approach Constrained maximization of
  microstates corresponding to a macrostate
• Opened the Linkage to Fluid Dynamics
• Best Paper at Session, 11th International
  Conference on Cybernetics and Information
  Technologies, Systems and Applications

26
Discrete Supply Chain

• Start with a simple Daisy Chain topology with
  discrete label N
• Nth stage receives information from (N-1) stage
  and delivers to (N1)
• Simple Static Analysis
• Similar to Sound Waves in a Solid

N
N-1
N1
27
Continuous Supply Chain

• Replace the discrete variable N by a continuous
  variable x.
• Replace difference equations with differential
  equations
• Draw on Fluid Dynamics and Designate a flow rate
  through the supply chain with a velocity
  variable v and a driving force F
• v dx/dt. 1
• F MAdv/dt 2

28
Partition Function

• A quantity that encodes the statistical
  properties of a system.
• It is a function of temperature and other
  parameters. Many of the statistical physics
  variables such as free energy can be expressed in
  terms of the partition function and its
  derivatives.
• Previous statistical physics quasi-static model
  determined that a distribution of unit costs of
  production is Maxwell Boltzman (Dozier Chang 05)
• Where C(i), unit cost of production
• ß is the bureaucratic factor (inverse of
  operating temperature T)
• Provide Partition Function Z S exp-ßC(i) 3

29
Parametric Force

• From the partition function Z we can determine
  the associated free energy F where Z exp -ßF
• Statistical Physics formalism provides the
  framework to assign a force to variations of any
  parameter ?
• We therefore have f (?) ? F/ ??
• We simply assume that F a f(?)
  6
• Where f (?) could represent change induced by
  government incentives
• Or f (?) could be change induced by a prime
  contractors new requirement

30
Distribution Function

• 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 7
• A force F that gives the rate at which v
  changes in time, this equation can be rewritten
• ?f/ ?t ?fv/?x ?fF / ?v 0 8

31
Abduction 3 Vlasov Equation

• This becomes Vlasov-like equation for f(x,v,t)
• ?f/?t v?f/?x F ?f/?v 0 11
• This is the equation for collisionless plasmas
• This is a very useful approximate way to describe
  the dynamics of a plasma and to consider that the
  motions of the plasma particles are governed by
  the applied external fields plus the macroscopic
  average internal fields, smoothed in space and
  time, due to presence and motion of all plasma
  particles.

32
Basic fluid flow equations

• Density is of production units in the
  interval dx at x and time t
• N(x, t) ?dvf(x,v,t)
  12
• Average flow of the production units
• V(x,t) (1/N)?vdvf(x,v,t)
  13
• Density and velocity conservation equations
• ?N/?t ?NV/?x 0 14
• ?V/?t V ?V/?x F1 - ?P/?x
  15
• F 1 is total force per unit dx F 1 dV/dt
• and P is pressure defined by dispersion of
  velocities
• where the dispersion in flow velocities is given
  by
• P ?dv(v-V)2 f(x,v,t)/N(x,t)
  
• Velocity dispersion is independent of x and t
• ?V/?t V ?V/?x F 1 - (Dv)2 ?N/?x
  19
• This implies that the change in velocity flow is
  impacted by the primary forcing function and the
  interacting gradients

33
Supply Chain Normal Modes

• Normal Modes are naturally occurring oscillation
  of a system
• If an external force has the same spatial and
  temporal form as a Normal Mode, amplification can
  occur
• Normal modes are usually obtained by examining
  the perturbations about the steady state

34
Normal Mode Expansions

• Density Variations
• N(x,t) N0 N1(x,t)
  20
• Velocity Variations
• V(x,t) V0 V1(x,t)
  21
• Substituting 20 and 21 into
• ?N/?t ?NV/?x 0 14
• ?V/?t V ?V/?x F 1 - (Dv)2 ?N/?x
  19
• ?N1/?t V0?N1/?x N0?V1/?x 0
  22
• ?V1/?t V0?V1/?x F 1(x,t) (?v)2 ?N1/?x
  23

35
First Order Oscillations

• N1(x,t) N1(x) exp(i?t)
  24
• V1(x,t) V1(x) exp(i?t)
  25
• Given
• ?N1/?t V0?N1/?x N0?V1/?x 0
  22
• ?V1/?t V0?V1/?x F 1(x,t) (?v)2 ?N1/?x
  23
• Since coefficients are independent of x, the
  normal mode equations can be expressed in terms
  of wave number
• N1(x) N1 exp(ikx)
  26
• V1(x) V1(x) exp(ikx)
  27

36
Propagating Waves

• N1(x,t) N1 expi(?t-kx)
  28
• V1(x,t) V1 expi(?t-kx)
  29
• Using these forms
• ?N1/?t V0?N1/?x N0?V1/?x 0
  22
• ?V1/?t V0?V1/?x F 1(x,t) (?v)2 ?N1/?x
  23
• Becomes
• i(?-kV0)N1 N0ikV1 0 30
• iN0 (?-kV0)V1 - ik(?v)2N1
  31

37
Two Solutions

• In order to have none zero values of N1 and V1
• (?-kV0)2 k2(?v)2
  32
• Equation 32 has two solutions
• ? k (V0 ?v)
  33
• A propagating supply chain wave that has a
  velocity equal to the sum of the steady state
  velocity V0 plus the dispersion velocity ?v
• ?- k (V0 -?v)
  34
• A propagating supply chain wave that has a
  velocity equal to the difference of the steady
  state velocity V0 minus the dispersion velocity
  ?v
• Dozier, Chang previous work limited either V0 or
  ?v to be zero

38
Interactions

• It has been demonstrated that a force F 1(x,t)
  can be used to accelerate the rate of production
  in a supply chain
• The force will be most effective when it has a
  component that coincides with the normal mode of
  the supply chain
• This minimizes non destructive interaction
• This resonance effect is best seen when using the
  Fourier decomposition of the Force F

39
Fourier

• F 1(x,t) (1/2p)??d?dkF1(?,k)expi(?t-kx)
  35
• Where F1(?,k) (1/2p)??dxdtF 1(x,t)exp-i(?t-kx)
  36
• Now each component has the form of a propagating
  wave. These waves are the most appropriate
  quantities to interact with the normal modes of
  the supply chain
• We go to a higher order of V(x,t)
• V(x,t) V0 V1(x,t) V2(x,t)
  37
• Substituting into 19 ?V/?t V ?V/?x F 1 -
  (Dv)2 ?N/?x
• solving for V2(x,t)
• N0(?V2/ ?t V0?V2/?x) N1(?V1/ ?t V0?V1/?x)
  N0 V1?V1/?x
• -(?v)2?N2/?x
  38

40
Convolution

• Using convolution for the product terms
• ??dxdtexp-i(?t-kx) f(x,t)g(x,t)
• ??dOd?f(-O?,??)g(O,?) 39
• Where
• f(O,?) ??dxdt exp(-i(Ot-?x)f(x,t) 40
• g(O,?) ??dxdt exp(-i(Ot-?x)g(x,t) 41
• Interest in net change in V2 changes that dont
  average 0, V2 (w0,k0)
• requires we know N1 and V1

41
New Normal Modes

• i(?-kV0)N1 N0ikV1 0
  30
• i(?-kV0)N1(?,k) N0 ikV1(?,k) 0
  42
• iN0 (?-kV0)V1 - ik(?v)2N1
  31
• iN0 (?-kV0)V1(?,k) - ik(?v)2N1(?,k) F1(?,k)
  43
• Solutions
• N1(?,k) -ik F1(?,k)(?-kV0)2 k2 (?v)2 -1
  44
• V1(?,k) -iF1(?,k)/ N0(?-kV0)(?-kV0)2-k2(?v)2
  -1 45

42
Landau Acceleration

• Substitution into ?0,k0 components of the
  Fourier transform
• N0(?V2/ ?t V0?V2/?x) N1(?V1/ ?t V0?V1/?x)
  N0 V1?V1/?x
• -(?v)2?N2/?x 38 becomes
• ?V2(0,0)/?t??ddk(ik/N02)(?-kV0)2?-kV0)2
  k2(?v)2-2 F1(-?,k) F1(-?,k) 46
• This resembles the quasilinear equation that has
  long been used to describe the evolution of
  background distribution of electrons that are
  subjected to Landau acceleration (Drummond and
  Pines( 1962)

43
Conclusions
HICSS 07

• Supply chain oscillations can be described by a
  fluid flow model of production units through a
  supply chain
• There is as normal mode resonance for a supply
  chain
• Any net change in the rate of production in the
  entire supply chain is due to the gradient
  interaction and the resonance of the Fourier
  components from external parametric forces and
  Fourier components of the normal modes of the
  supply chain
• An Information Technology Infrastructure is most
  effective when it provides a capability to time
  the interactions in such a manner as to
  constructively align the component interaction

44
Findings

• A simple daisy chain topology for the IT in a
  supply chain can be extended to allow the
  analysis of the optimal timing for external
  interventions using a fluid dynamics model.
• Fluid-like equations for a simple system describe
  naturally occurring waves that propagate at two
  velocities .
• This model does allow examination of the optimal
  timing for interventions of these propagations
  and parametric forces. Something not possible in
  simulation models to date
• The most effective paramedic interventions will
  be those that use information technologies to
  apply them so as to mimic the naturally occurring
  normal modes of the system.

45
Future Work

• Create a simulation artifact that allows
  understanding of the optimization principles
  necessary to tune the IT architecture to
  facilitate the alignment of external disturbances
  and normal mode interactions cooperative
  production.
• Of particular interest is the minimal amount of
  IT required for positive cooperation
• Expansion of both artifacts to study the effect
  of a Field Effect F and its universal properties
  on the ability to constructively adapt the supply
  chain in real time.

46
Contact Information
For more information, please Visit the Learning
Center
http//wesrac.usc.edu
kdozier_at_usc.edu
Google wesrac Google Ken Dozier