Statics and Dynamics of Complex Network Systems: Supply Chain Analysis and Financial Networks with Intermediation

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Statics and Dynamics of Complex Network Systems
Supply Chain Analysis and Financial Networks with
Intermediation

• Ke Ke
• MKIDS Mini-Workshop
• September 10, 2003

The Virtual Center for Supernetworks
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Introduction

• Literature Survey
• Related Publications
• Research Motivation

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Literature Survey

• Supply Chain Analysis
• Nagurney and Dong (2002)
• Nagurney, Dong, and Zhang (2001)
• Nagurney, Loo, Dong, and Zhang (2001)
• Nagurney and Dong (2000)
• Nagurney, Dong, and Mokhatarian (2000, 2001)

• Financial Networks with Intermediation
• Thore (1969, 1980)
• Nagurney, Dong, and Hughes (1992)
• Nagurney and Dong (1995, 1996a, b)

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Related Publications

• Nagurney, Ke, Cruz, Hancock, and Southworth
  (2002)
• Nagurney and Ke (2001a, b)
• Nagurney and Ke (2003)

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Research Motivation

• We propose a multilevel network to capture
  distinct flows, in particular, the logistical,
  informational, and financial flows within the
  same supply chain network system.
• The theoretical framework provides an abstraction
  of decision-making in the case of agents, such as
  firms, consumers, as well as intermediaries, who
  operate in a decentralized fashion on both
  physical and virtual networks, and allows not
  only for the visualization of business processes
  as networks but also for the prediction of
  production volumes and shipments of products,
  prices, as well as, as appropriate information
  and financial flows.

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Research Motivation (Cont.)

• We develop a framework for the modeling,
  analysis, and computation of solutions to
  financial network problems in the presence of
  intermediation.
• Advances in telecommunications have had an
  enormous effect on financial services and the
  options available for financial transactions. We
  then will further to include the electronic
  transaction in the financial network modeling.

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Dynamics of Supply Chains a Multilevel Network
Prospective
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Notations

• m firms with a typical firm denoted by i,
• n retailers with a typical retailer denoted by j,
• o demand markets with a typical demand market
  denoted by k.

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The Demand Market Price Dynamics
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The Dynamics of the Commodity Shipments Between
the Retailers and the Demand Markets
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The Dynamics of the Prices at the Retail Outlets
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The Dynamics of Commodity Shipments BetweenFirms
and Retailers
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The Projected Dynamical System
Let X the shipment and price variables
and F(X)
(Fij, Fjk, Fj, Fk) i1,,m j1,,n k1,,o,
Where
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Then the dynamic model can be rewritten as the
PDS defined by the initial value problem
?K(X, -F(X)), X(0)X0.
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The Equilibrium Point
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Qualitative Properties

• Monotonicity
• Lipschitz continuity
• Existence and uniqueness of a solution to the
  initial value problem
• Stability of the system

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A Discrete Time Algorithm

• Step 0 Initialization
• Step 1 Computation
• Step 2 Convergence verification

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Step 1 Computation
Compute (Q1?, Q2?, , ) ? by
solving the variational inequality
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Financial Networks with Intermediation
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Introduction

• Financial network with intermediation
• consists of
• source of funds
• intermediaries
• consumers of funds
• the flows on the links the allocation of the
  financial instruments

• Multilevel supply chain network
• consists of
• manufacturers
• retailers
• consumer markets
• the flows on the links prices of products

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Introduction (Cont.)

• direction of financial flows from top tier,
  through middle tier, until the bottom tier.
• objective of the decision-makers of first two
  tiers
• profit maximization
• minimization of risks

• direction of financial flows
• bottom up
• objective of the decision-makers of first two
  tiers
• Profit maximization

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The Behavior of Source Agents
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The Optimality Conditions for Source Agents
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The Behavior of Financial Intermediaries
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The Optimality Conditions for All Intermediaries
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The Behavior of Consumers at Demand Markets
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The Optimality Conditions for Demand Markets
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The Equilibrium Conditions
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Qualitative Properties

• Monotonicity
• Existence of a solution to the VI problem
• Uniqueness
• Lipschitz continuity

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The Algorithm
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Financial Networks with Electronic Transactions
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The Network Structure

• electronic transactions
• source agents can transact
• with the intermediaries either physically or
  electronically
• with the consumers in an electronic manner.
• intermediaries transact with the consumers either
  physically or electronically

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Notations

• l the transaction mode
• l1 a physical transaction
• l2 an electronic transaction via the Internet
• All other notations and assumptions remain the
  same as in the previous model.

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The Behavior of Source Agents
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The Optimality Conditions for Source Agents
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The Behavior of Financial Intermediaries
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The Optimality Conditions for All Intermediaries
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The Behavior of Consumers at Demand Markets
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The Optimality Conditions for Demand Markets
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The Equilibrium Conditions
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Qualitative Properties

• Monotonicity
• Existence of a solution to the VI problem
• Uniqueness
• Lipschitz continuity

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The Algorithm

• Step 0 Initialization
• Step 1 Computation
• Step 2 Convergence verification

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Step1 Computation
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Numerical Examples
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Numerical Examples (Cont.)
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Numerical Examples (Cont.)
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Summary

• The dynamic supply chain network model and a
  series of financial equilibrium models are
  developed here. Sufficient progress has already
  been obtained as evidenced from our publications.
• We extend the work in general financial
  equilibrium modeling, analysis, and computation
  in a network framework to include financial
  intermediaries, the underlying dynamics
  associated with the financial flows and prices,
  and the inclusion of electronic transactions. It,
  thus, will incorporate the dimension, lacking in
  financial flow of funds accounts, of the explicit
  dynamic behavior of the various financial agents
  as well as the price dynamics.

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Thank You!
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