Viterbi School of Engineering The Impact of Information on Supply Chain Oscillations Ken Dozier & David Chang Western Research Application Center IRMA

Viterbi School of Engineering

The Impact of Information The Impact of Information on Supply Chain on Supply Chain

OscillationsOscillations

Ken Dozier & David ChangKen Dozier & David ChangWestern Research Application CenterWestern Research Application Center

IRMA International , IncIRMA International , Inc

Washington D.C.Washington D.C.May 23, 2006May 23, 2006

USC Viterbi School of Engineering

BioBio


A System of Forces in A System of Forces in OrganizationOrganization

Efficiency

Direction

Proficiency

Competition

Concentrat\ion Innovation

Cooperation

Source: “The Effective Organization: Forces and Form”,Sloan Management Review, Henry Mintzberg, McGill University 1991


Make & Sell vs Sense & Make & Sell vs Sense & RespondRespond

Chart Source:“Corporate Information Systems and Management”, Applegate, 2000


Theoretical EnvironmentTheoretical Environment

Seven Organizational Change Propositions Framework, “Framing the Domains of IT Management” Zmud 2002

Business Process Improvement

Business Process Redesign

Business Model Refinement

Business Model Redefinition

Supply-chain Discovery

Supply-chain Expansion

Market Redefinition


Supply Chain (Firm)Supply Chain (Firm)

Source: Gus Koehler, University of Southern California Department of Policy and Planning, 2002


Supply Chain (Government)Supply Chain (Government)



Supply Chain (Framework)Supply Chain (Framework)



Supply Chain (Interactions)Supply Chain (Interactions)



Why statistical physics?Why statistical physics?

► Proven formalism for “seeing the forest past the Proven formalism for “seeing the forest past the trees”trees” Well established in physical and chemical sciencesWell established in physical and chemical sciences Our recent verification with data in economic realmOur recent verification with data in economic realm

► Simple procedure for focusing on macro-parametersSimple procedure for focusing on macro-parameters Most likely distributions obtained by maximizing the Most likely distributions obtained by maximizing the

number of micro-states corresponding to a measurable number of micro-states corresponding to a measurable macro-statemacro-state

Straightforward extension from original focus on energy Straightforward extension from original focus on energy to economic quantitiesto economic quantities

► Unit cost of productionUnit cost of production► ProductivityProductivity► R&D costsR&D costs

Self-consistency check provided by distribution functionsSelf-consistency check provided by distribution functions


Plasma theories Plasma theories

► Advanced Advanced plasmaplasma theories are extremely important theories are extremely important when one tries to explain, for example, the various when one tries to explain, for example, the various waveswaves and and instabilitiesinstabilities found in the plasma found in the plasma environment. Since plasma consist of a very large environment. Since plasma consist of a very large number of interacting particles, in order to provide number of interacting particles, in order to provide a macroscopic description of plasma phenomena it a macroscopic description of plasma phenomena it is appropriate to adopt a is appropriate to adopt a statisticalstatistical approach. This approach. This leads to a great reduction in the amount of leads to a great reduction in the amount of information to be handled. In the information to be handled. In the kinetic theorykinetic theory it it is necessary to know only the is necessary to know only the distribution distribution functionfunction for the system of particles. for the system of particles.

Source: University of Oulu, FInland


Applications of statistical physics to economicsApplications of statistical physics to economics

► Quasistatic phenomenaQuasistatic phenomena

Approach: Constrained maximization of Approach: Constrained maximization of microstates corresponding to a macrostatemicrostates corresponding to a macrostate

Applications to date: unit cost of production Applications to date: unit cost of production & productivity& productivity

► Time-dependent phenomenaTime-dependent phenomena

Approach: normal mode analysis Approach: normal mode analysis Current application: supply chain oscillationsCurrent application: supply chain oscillations


Comparison of Statistical Formalism in Physics and Economics

Variable Physics Economics

State (i) Hamiltonian eigenfunction Production site

Energy Hamiltonian eigenvalue Ei Unit prod. cost Ci

Occupation number Number in state Ni Output Ni = exp[-βCi+βF]

Partition function Z ∑exp[-(1/kBT)Ei] ∑exp[-βCi]

Free energy F kBT lnZ (1/β) lnZ

Generalized force fξ ∂F/∂ξ ∂F/∂ξ

Example Pressure TechnologyExample Electric field x charge Knowledge

Entropy (randomness) - ∂F / ∂T kBβ2∂F/∂

Quasi-staticQuasi-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 β = 0.167 per $106

Quasi-staticQuasi-static

0

500

1000

1500

2000

2500

3000

3500

4000

0 10 20 30 40 50 60


Productivity: Ratio (‘97/’92) of the statistical parametersProductivity: Ratio (‘97/’92) of the statistical parameters

Company size: Company size: Large Large Intermediate Intermediate Small Small

IT rankIT rank 59 59 7070 81 81## 0.86 0.86 1.0 1.0 0.90 0.90E(1000s)E(1000s) 0.78 0.78 0.98 0.98 1.08 1.08#/company#/company 0.91 0.91 1.0 1.0 1.21 1.21Sh ($million)Sh ($million) 1.53 1.53 1.24 1.24 1.42 1.42Sh/E ($1000)Sh/E ($1000) 1.66 1.66 1.34 1.34 1.35 1.35 ββ 1.11 1.11 0.90 0.90 0.99 0.99

Findings:Findings:

Sectors with large companies spend a larger percentage on IT.Sectors with large companies spend a larger percentage on IT.Largest % increases in shipments are in large & small company sectors.Largest % increases in shipments are in large & small company sectors.Small companies increased in size while large companies decreased.Small companies increased in size while large companies decreased.Number of large and small companies decreased by 10%.Number of large and small companies decreased by 10%.Employment decreased 20% in large companies, but increased 8% in small Employment decreased 20% in large companies, but increased 8% in small

companies.companies.Largest productivity occurred in large companies.Largest productivity occurred in large companies.


Oscillations in Supply ChainsOscillations in Supply Chains

► ObservationsObservations Cyclic phenomena in economics ubiquitous & Cyclic phenomena in economics ubiquitous &

disruptivedisruptive Example: Wild oscillations In supply chain Example: Wild oscillations In supply chain

inventoriesinventories► MIT “beer game” simulationMIT “beer game” simulation

Supply chain of only 4 companies for beer Supply chain of only 4 companies for beer production, distribution, and salesproduction, distribution, and sales

► Results of observations and simulationsResults of observations and simulations Oscillations Oscillations Phase dependence of oscillations on position in Phase dependence of oscillations on position in

chainchain Spatial instabilitySpatial instability


IRMA 2006 ObjectivesIRMA 2006 Objectives

►To show with a simple product-flow To show with a simple product-flow model of a supply chain that universal model of a supply chain that universal information exchangeinformation exchange Changes the character of oscillations from Changes the character of oscillations from

those of nearest neighbor information those of nearest neighbor information exchangeexchange

Causes an increase in the damping of Causes an increase in the damping of oscillationsoscillations


Local Exchange of InformationLocal Exchange of Information

► Instead of designating each level in the chain by a discrete label nInstead of designating each level in the chain by a discrete label n the position in a chain was designated by a continuum variable x. the position in a chain was designated by a continuum variable x. Flow of production units through each position in the chain was Flow of production units through each position in the chain was

designated by a velocity variable v. designated by a velocity variable v.

► A differential distribution function f(x,v,t)dxdv denotes the number of 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. production units in the intervals dx and dv at x and v at time t.

► ∂ ∂f/ ∂t + ∂[fdx/dt]/ ∂x + ∂[fdv/dt]/ ∂v = 0f/ ∂t + ∂[fdx/dt]/ ∂x + ∂[fdv/dt]/ ∂v = 0 [1][1]► A thermodynamic force F that gives the rate at which v changes in A thermodynamic force F that gives the rate at which v changes in

time, this equation can be rewritten time, this equation can be rewritten ► ∂ ∂f/ ∂t + ∂[fv]/∂x +[∂fF]/ ∂v = 0f/ ∂t + ∂[fv]/∂x +[∂fF]/ ∂v = 0 [2][2]


Nearest neighbor information exchangeNearest neighbor information exchange

This becomes Vlasov-like equation for f(x,v,t)This becomes Vlasov-like equation for f(x,v,t)∂∂f/∂t + v∂f/∂x + F∂f/∂v = 0f/∂t + v∂f/∂x + F∂f/∂v = 0 [5] [5]

This is the equation for collisionless plasmasThis is the equation for collisionless plasmas

When the inventory of the level below the level of interest is less When the inventory of the level below the level of interest is less than normal, the production rate (v) will be diminished because than normal, the production rate (v) will be diminished because of the smaller number of production units being introduced to of the smaller number of production units being introduced to that level. At the same time, when the inventory of the level that level. At the same time, when the inventory of the level above the level of interest is larger than normal, the production above the level of interest is larger than normal, the production rate will also be diminished because the upper level will rate will also be diminished because the upper level will demand less input so that it can “catch up” in its production demand less input so that it can “catch up” in its production through-put. Both effects give production rate changes through-put. Both effects give production rate changes proportional to the gradient of n. It is resonable also that the proportional to the gradient of n. It is resonable also that the fractional changes are related rather than the changes fractional changes are related rather than the changes themselves, since deviations are always made from the themselves, since deviations are always made from the inventories at hand.inventories at hand.

∂∂f/∂t + v∂f/∂x - 2ξv2(1/n)(dn/dx) ∂f/∂v = 0f/∂t + v∂f/∂x - 2ξv2(1/n)(dn/dx) ∂f/∂v = 0 [13] [13]


Nearest neighbor dispersion relationNearest neighbor dispersion relation

Perturbed distributionPerturbed distribution

f(x,v,t) = ff(x,v,t) = f00(v) + f(v) + f11(v) exp[-i((v) exp[-i(t – kx)]t – kx)][15][15]-i(-i(-kv)f-kv)f11 - ik 2ξv2(1/n - ik 2ξv2(1/noo)n)n11∂f∂foo/∂v = 0 /∂v = 0 [16b][16b]ff11 = -2ξk(1/n = -2ξk(1/noo) ∫dv’f) ∫dv’f11(v’) v2∂f(v’) v2∂foo/∂v(/∂v(-kv)-kv)-1-1 [17][17]

This leads to the dispersion relation between This leads to the dispersion relation between and k and k

1+ 2ξk (1/n1+ 2ξk (1/noo) ∫dvv2∂f) ∫dvv2∂foo/∂v(/∂v(-kv)-kv)-1-1 =0 =0 [18][18]Principal and imaginary partsPrincipal and imaginary parts

∫∫dvv2∂fdvv2∂foo/∂v(/∂v(-kv)-kv)-1-1 = PP∫dvv2∂f = PP∫dvv2∂foo/∂v/∂v ((-kv)-kv)-1-1 - iπ( - iπ(/k)2(1/k)∂f/k)2(1/k)∂foo((/k) /∂v/k) /∂v [19][19]


Nearest neighbor dispersion relation (cont)Nearest neighbor dispersion relation (cont)

Solving for Solving for = 4ξkV= 4ξkVoo [1+ [1+

(1/n(1/n00)iπ(4ξV)iπ(4ξVoo )2∂f )2∂foo(4ξV(4ξVoo ) /∂v] ) /∂v] [23][23]

SignificanceSignificance

ff00(v) peaked around V(v) peaked around V00, ∂f, ∂f00(4ξV(4ξV00 ) / ∂v <0. ) / ∂v <0.

Oscillation resembles a sound-like waveOscillation resembles a sound-like wave

Oscillation exhibits small Landau damping that Oscillation exhibits small Landau damping that is because of distance of phase velocity from is because of distance of phase velocity from VVoo


Universal information exchangeUniversal information exchange

Introduce an Introduce an information exchange potential Φinformation exchange potential Φ

∂ ∂22Φ/∂xΦ/∂x22 = - [C/n = - [C/noo]∫dv f(x,v,t)]∫dv f(x,v,t) [24][24]

from which the thermodynamic force F is obtained from which the thermodynamic force F is obtained

F = - ∂Φ/∂xF = - ∂Φ/∂x [25][25]

This reduces to the former results for nearest This reduces to the former results for nearest neighbor interactions when we chooseneighbor interactions when we choose

C = ξVC = ξVoo22 / / ll22 [29] [29]


Universal information exchange dynamic Universal information exchange dynamic equationsequations

Introduction of potential into Vlasov equationIntroduction of potential into Vlasov equation

∂∂f/∂t + v∂f/∂x - ∂Φ/∂x ∂f/∂v = 0f/∂t + v∂f/∂x - ∂Φ/∂x ∂f/∂v = 0 [31][31]

Perturbation in distribution function caused by Perturbation in distribution function caused by ΦΦ

ff11 = -kΦ = -kΦ11∂f∂foo /∂v ( /∂v (-kv) -kv) -1-1 [33] [33]

Self-consistency conditionSelf-consistency condition

ΦΦ11 = (1/k = (1/k22) [ξV) [ξVoo22 /n /nooll22] ∫dv f] ∫dv f11(v)(v) [34] [34]


Dispersion relation for universal information Dispersion relation for universal information exchangeexchange

≈ ≈ kVkVoo + ξ + ξ1/21/2(V(Voo//ll) [1 + i {πξV) [1 + i {πξVoo22/(2k/(2k22ll22nnoo)}∂f)}∂foo/∂v ]/∂v ] [42][42]

where ∂fwhere ∂f00/∂v is evaluated at /∂v is evaluated at

v = v = /k ≈ V/k ≈ Vo o + (ξ+ (ξ1/21/2VVoo/k/kll)) [43][43]

SignificanceSignificance

Oscillations resemble plasma oscillationsOscillations resemble plasma oscillations

Oscillations always exhibit Landau damping. This Oscillations always exhibit Landau damping. This changes the form of the supply chain oscillation and in changes the form of the supply chain oscillation and in suppression of the resulting oscillationsuppression of the resulting oscillation


ConclusionsConclusions

► Supply chain oscillations can be described by a simple Supply chain oscillations can be described by a simple flow model of product through chainflow model of product through chain

► Flow model shows that Flow model shows that Character of oscillation changes from sound-like to Character of oscillation changes from sound-like to

plasma-like when information exchange becomes plasma-like when information exchange becomes universal rather than just between nearest universal rather than just between nearest neighborsneighbors

Damping of oscillation can be large when Damping of oscillation can be large when information exchange becomes universalinformation exchange becomes universal

Washington DC


Future WorkFuture Work

►Create a simulation that allows the study Create a simulation that allows the study of various IT architectures on the of various IT architectures on the optimization issues of supply chain optimization issues of supply chain managementmanagement

►[email protected]@usc.edu►Visit the Learning CenterVisit the Learning Center►http:wesrac.usc.eduhttp:wesrac.usc.edu►Google wesracGoogle wesrac►Google Ken DozierGoogle Ken Dozier

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Viterbi School of Engineering The Impact of Information on Supply Chain Oscillations Ken Dozier & David Chang Western Research Application Center IRMA