Title: Ken Dozier
1The 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
2Bio - Ken
3Bio - David
4Objectives
- 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
5What 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).
6Design Research
Awareness Slides 7 -19 Abduction 20-24 Deduction
25-42 Conclusion 43-46
SourceTakeda, H.. "Modeling Design Processes."
AI Magazine, Winter 37-48.
7Business 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
8Flow 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
9Temporal Oscillations (Firms)
Source Gus Koehler, University of Southern
California Department of Policy and Planning, 2002
10System Dynamic
Common Modes of Interaction Between Positive and
Negative Feedback
Source System Dynamics, John Sterman, 2000
11Exponential 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
12Exponential 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
13The 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
14Connectivity
Model Developed by Dr. Nathan B. Forrester of
A.T. Kearney, Atlanta, 2000
15The 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
16The 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
17Government Dynamics
Source Gus Koehler, University of Southern
California Department of Policy and Planning,
2002
18Supply Chain Dynamics
Source Gus Koehler, University of Southern
California Department of Policy and Planning,
2002
19Complex 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
22Stratification
Low ß
High ß
Seven Organizational Change Propositions
Framework, Framing the Domains of IT
Management Zmud 2002
23JITTA
- 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
25CITSA 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
26Discrete 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
27Continuous 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
28Partition 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
29Parametric 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
30Distribution 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
31Abduction 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.
32Basic 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
33Supply 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
34Normal 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
35First 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
36Propagating 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
37Two 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
38Interactions
- 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
39Fourier
- 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
40Convolution
- 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
41New 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
42Landau 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)
43Conclusions
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
44Findings
- 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.
45Future 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.
46Contact Information
For more information, please Visit the Learning
Center
http//wesrac.usc.edu
kdozier_at_usc.edu
Google wesrac Google Ken Dozier