Western Research Application Center (WESRAC) Ken Dozier & David Chang Western Research Application Center HICSS 2007 Hawaii International Conference on System Sciences May 23, 2006 January 3-6, 2007 Hilton Waikoloa Village Resort Waikoloa, Big Island Hawaii The Impact of Information Technology on the Temporal Optimization of Supply Chain Performance

Western Research Application Center (WESRAC) Bio - Ken

Western Research Application Center (WESRAC) Bio - David

Western Research Application Center (WESRAC) 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

Western Research Application Center (WESRAC) TruthKnowledgeBelief Universal No Debate Effect Social Converge on debate Cause Personal Diverge on debate Cause Source: “Ten Philosophical Mistakes”, Mortimer J. Adler 1985 Source: “Design Research in the Technology of Information Systems: Truth or Dare.”, Purao, S. (2002). What is Knowledge ? Ontology Epistemology Axiology

Western Research Application Center (WESRAC) Design Research Source:Takeda, H.. "Modeling Design Processes." AI Magazine, Winter: Awareness Slides Abduction Deduction Conclusion 43-46

Western Research Application Center (WESRAC) Business Takes on Many Forms Efficiency Direction Proficiency Competition Concentration Innovation Cooperation Source: “The Effective Organization: Forces and Form”, Sloan Management Review, Henry Mintzberg, McGill University 1991

Western Research Application Center (WESRAC) 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

Western Research Application Center (WESRAC) Temporal Oscillations (Firms) Source: Gus Koehler, University of Southern California Department of Policy and Planning, 2002

Western Research Application Center (WESRAC) System Dynamic Common Modes of Interaction Between Positive and Negative Feedback Source: System Dynamics, John Sterman, 2000

Western Research Application Center (WESRAC) 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

Western Research Application Center (WESRAC) 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

Western Research Application Center (WESRAC) The Beer Game Steady state at 4 cases per week. Beer Game Demo Densmore, O. June 2004 Wilensky, U. (1999). NetLogo. Center for Connected Learning and Computer-Based Modeling. Northwestern University, Evanston, IL

Western Research Application Center (WESRAC) Connectivity Model Developed by Dr. Nathan B. Forrester of A.T. Kearney, Atlanta, 2000

Western Research Application Center (WESRAC) The Beer Game - Not Sharing The system after only a single change from 4 to 8 case. Wilensky, U. (1999). NetLogo. Center for Connected Learning and Computer-Based Modeling. Northwestern University, Evanston, IL Beer Game Demo Densmore, O. June 2004

Western Research Application Center (WESRAC) The Beer Game - Sharing Knowledge sharing, Wilensky, U. (1999). NetLogo. Center for Connected Learning and Computer-Based Modeling. Northwestern University, Evanston, IL Beer Game Demo Densmore, O. June 2004

Western Research Application Center (WESRAC) Government Dynamics Source: Gus Koehler, University of Southern California Department of Policy and Planning, 2002

Western Research Application Center (WESRAC) Supply Chain Dynamics Source: Gus Koehler, University of Southern California Department of Policy and Planning, 2002

Western Research Application Center (WESRAC) Complex System Dynamics Source: Gus Koehler, University of Southern California Department of Policy and Planning, 2002

Western Research Application Center (WESRAC) 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 R&D costs –Self-consistency check provided by distribution functions

Western Research Application Center (WESRAC) 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.plasmawaves instabilities Source: University of Oulu, FInland

Western Research Application Center (WESRAC) Stratification 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 High β Low β

Western Research Application Center (WESRAC) JITTA Investigated the β bureaucratic factor and it’s 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

Western Research Application Center (WESRAC) 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 = per $106 Maxwell Boltzman Distribution Confirmation

Western Research Application Center (WESRAC) 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, 11 th International Conference on Cybernetics and Information Technologies, Systems and Applications

Western Research Application Center (WESRAC) Discrete Supply Chain NN-1N+1 Start with a simple “Daisy Chain” topology with discrete label N Nth stage receives information from (N-1) stage and delivers to (N+1) Simple Static Analysis Similar to Sound Waves in a Solid

Western Research Application Center (WESRAC) 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 =MA=dv/dt [2]

Western Research Application Center (WESRAC) 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 β is the “bureaucratic factor” (inverse of operating temperature T) Provide Partition Function Z = Σ exp[-βC(i)]] [3]

Western Research Application Center (WESRAC) Parametric Force From the partition function Z we can determine the associated free energy F where Z = exp [-βF] Statistical Physics formalism provides the framework to assign a force to variations of any parameter ξ We therefore have f (ξ) = ∂ F/ ∂ξ We simply assume that F = α f (ξ) [6] Where f (ξ) could represent change induced by government incentives Or f (ξ) could be change induced by a prime contractor’s new requirement

Western Research Application Center (WESRAC) 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 +[∂f F ] / ∂v = 0[8]

Western Research Application Center (WESRAC) 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.

Western Research Application Center (WESRAC) 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 = F 1 - ∂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 - (  v) 2 ∂N/∂x [19] –This implies that the change in velocity flow is impacted by the primary forcing function and the interacting gradients

Western Research Application Center (WESRAC) 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

Western Research Application Center (WESRAC) Normal Mode Expansions Density Variations – N(x,t) = N 0 + N 1 (x,t) [20] Velocity Variations –V(x,t) = V 0 + V 1 (x,t) [21] Substituting [20] and [21] into –∂N/∂t + ∂[NV]/∂x = 0 [14] –∂V/∂t +V ∂V/∂x = F 1 - (  v) 2 ∂N/∂x [19] ∂N 1 /∂t + V 0 ∂N 1 /∂x + N 0 ∂V 1 /∂x = 0 [ 22] ∂V 1 /∂t +V 0 ∂V 1 /∂x = F 1 (x,t) – (∆v) 2 ∂N 1 /∂x [23]

Western Research Application Center (WESRAC) First Order Oscillations N 1 (x,t) = N 1 (x) exp(iωt) [24] V 1 (x,t) = V 1 (x) exp(iωt) [25] Given ∂N 1 /∂t + V 0 ∂N 1 /∂x + N 0 ∂V 1 /∂x = 0 [22] ∂V 1 /∂t +V 0 ∂V 1 /∂x = F 1 (x,t) – (∆v) 2 ∂N 1 /∂x [23] Since coefficients are independent of x, the normal mode equations can be expressed in terms of wave number N 1 (x) = N 1 exp(ikx) [26] V 1 (x) = V 1 (x) exp(ikx) [27]

Western Research Application Center (WESRAC) Propagating Waves N 1 (x,t) = N 1 exp[i(ωt-kx)] [28] V 1 (x,t) = V 1 exp[i(ωt-kx)] [29] Using these forms ∂N 1 /∂t + V 0 ∂N 1 /∂x + N 0 ∂V 1 /∂x = 0 [22] ∂V 1 /∂t +V 0 ∂V 1 /∂x = F 1 (x,t) – (∆v) 2 ∂N 1 /∂x [23] Becomes i(ω-kV 0 )N 1 +N 0 ikV 1 = 0 [30] iN 0 (ω-kV 0 )V 1 =- ik(∆v) 2 N 1 [31]

Western Research Application Center (WESRAC) Two Solutions In order to have none zero values of N 1 and V 1 (ω-kV 0 ) 2 = k 2 (∆v) 2 [32] Equation [32] has two solutions ω + =k (V 0 +∆v) [33] A propagating supply chain wave that has a velocity equal to the sum of the steady state velocity V 0 plus the dispersion velocity ∆v ω - = k (V 0 -∆v) [34] A propagating supply chain wave that has a velocity equal to the difference of the steady state velocity V 0 minus the dispersion velocity ∆v Dozier, Chang previous work limited either V 0 or ∆v to be zero

Western Research Application Center (WESRAC) 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

Western Research Application Center (WESRAC) Fourier F 1 (x,t) = (1/2π)∫∫dωdkF 1 (ω,k)exp[i(ωt-kx)] [35] Where F 1 (ω,k) = (1/2π)∫∫dxdt F 1 (x,t)exp[-i(ωt-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) = V 0 + V 1 (x,t) + V 2 (x,t) [37] Substituting into [19] ∂V/∂t +V ∂V/∂x = F 1 - (  v) 2 ∂N/∂x solving for V 2 (x,t) N 0 ( ∂ V 2 / ∂ t + V 0 ∂ V 2 / ∂ x) + N 1 ( ∂ V 1 / ∂ t +V 0 ∂ V 1 / ∂ x) + N 0 V 1 ∂ V 1 / ∂ x = -(∆v) 2 ∂N 2 /∂x [38]

Western Research Application Center (WESRAC) Convolution Using convolution for the product terms ∫∫dxdtexp[-i(ωt-kx)] f(x,t)g(x,t) = ∫∫dΩdΚf(-Ω+ω,Κ+κ)g(Ω,Κ) [39] Where f(Ω,Κ) = ∫∫dxdt exp[(-i(Ωt-Κx)]f(x,t) [40] g(Ω,Κ) = ∫∫dxdt exp[(-i(Ωt-Κx)]g(x,t) [41] Interest in net change in V 2 changes that don’t average 0, V 2 (w=0,k=0) requires we know N 1 and V 1

Western Research Application Center (WESRAC) New Normal Modes i(ω-kV 0 )N 1 +N 0 ikV 1 = 0 [30] i(ω-kV 0 )N 1 (ω,k) + N 0 ikV 1 (ω,k) = 0 [42] iN 0 (ω-kV 0 )V 1 =- ik(∆v) 2 N 1 [31] iN 0 (ω-kV 0 )V 1 (ω,k) =- ik(∆v) 2 N 1 (ω,k) + F 1 (ω,k) [43] Solutions N 1 (ω,k) = -ik F 1 (ω,k)[(ω-kV 0 ) 2 – k 2 (∆v) 2 ] -1 [44] V 1 (ω,k) = -i{F 1 (ω,k)/ N 0 }(ω-kV 0 )[(ω-kV 0 ) 2 -k 2 (∆v) 2 ] -1 [45]

Western Research Application Center (WESRAC) Landau Acceleration Substitution into ω=0,k=0 components of the Fourier transform N 0 ( ∂ V 2 / ∂ t + V 0 ∂ V 2 / ∂ x) + N 1 ( ∂ V 1 / ∂ t +V 0 ∂ V 1 / ∂ x) + N 0 V 1 ∂ V 1 / ∂ x = -(∆v) 2 ∂N 2 /∂x [38] becomes ∂V2(0,0)/∂t=∫∫ddk(ik/N 0 2 )(ω-kV 0 ) 2 [ω-kV 0 ) 2 – k 2 (∆v) 2 ] -2 F 1 (-ω,k) F 1 (-ω,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)

Western Research Application Center (WESRAC) Conclusions 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 HICSS 07

Western Research Application Center (WESRAC) 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.

Western Research Application Center (WESRAC) 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 Φ and its universal properties on the ability to constructively adapt the supply chain in real time.

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