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AI Magazine, Winter: 37-48. Awareness Slides 7 -19. Abduction 20-24. Deduction 25-42 ... Model Developed by Dr. Nathan B. Forrester of A.T. Kearney, Atlanta, 2000 ... – PowerPoint PPT presentation

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Title: 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
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