International Financial
Networks and Global Supply
Chains
Jose Cruz
Presentation at MKIDS
Mini-Workshop
September 10, 2003
Virtual Center for
Supernetworks
My Research
My general area is complex decision making on
network systems with a specific focus on global
issues.
I am especially interested in international
financial networks with intermediaries and
electronic transactions, and global supply chain
networks.
The methodological tools that I utilize are:
variational inequalities, dynamical systems,
network theory, multicriteria decision-making,
and optimization.
Publications
Nagurney, A. and J. Cruz (2003), “International Financial
Networks with Electronic transactions," in Innovations in
Financial and Economic Networks, A. Nagurney, editor,
Edward Elgar Publishers, Cheltenham, England.
Nagurney, A., J. Cruz and D. Matsypura (2003), “Dynamics
of Global Supply Chain Supernetworks," Mathematical and
Computer Modelling, 37, 963-983.
Nagurney, A. and J. Cruz, (2002), “International Financial
Networks with Intermediation: Modeling, Analysis, and
Computations," to appear in Computational Management
Science; http://supernet.som.umass.edu
Nagurney, A., K. Ke, J. Cruz, K. Hancock and F. Southworth
(2002), “Dynamics of Supply Chains: A Multilevel
(Logistical/Informational/Financial) Network Perspective,”
Environment & Planning B, 29, 795-818.
Publications
Nagurney, A., J. Cruz and J. Dong (2003), “Global Supply
Chain Networks and Risk Management “;
http://supernet.som.umass.edu
Nagurney, A. and J. Cruz (2003), “ Dynamics of
International Financial Networks with Risk Management “;
http://supernet.som.umass.edu
Nagurney, A., J. Cruz, J. Dong and D. Zhang (2003), “Supply
Chain Networks, Electronic Commerce, and Supply Side
and Demand Side Risk”; http://supernet.som.umass.edu
Background for International
Financial Networks and Global
Supply Chains
Advances in telecommunications, including the
adoption of the Internet by businesses,
consumers, and financial institutions have had
an enormous effect on financial services and
options available for financial transactions.
Distribution channels have been transformed, new
types of services and products introduced.
Electronic commerce (e-commerce) through the
Internet has allowed for new connections not
previously possible.
Motivation
Growing competition and emphasis on efficiency
and cost reduction, as well as the satisfaction
of consumer demands, have brought new
challenges for businesses in the global
marketplace.
Business to Business eCommerce is estimated to
reach over $3 trillion by the end 2003.
Business to Consumer transactions are
forecasted to soar to $184 billion by 2004.
Background
At the same time that businesses increasingly
globalized, the world environment has become
filled with uncertainty.
For example, recently, the threat of illness in the
form of SARS (see Engardio et al. (2003)) has
disrupted supply chains, as have terrorist
threats (cf. Sheffi (2001)).
There is an increase need for the development of
Optimal Knowledge network.
The approach That we have utilized for the
study of International Financial Networks and
Global Supply Chains is the concept of
Supernetworks; see the book by Nagurney
and Dong (2002).
Supernetworks: A New Paradigm
Supernetworks
Supernetworks may be comprised of such networks
as transportation, telecommunication, logistical,
and/or financial networks.
They may be multilevel as when they formalize the
study of supply chain networks or multitiered as
in the case of financial networks with
intermediation.
Decision-makers may be faced with multiple
criteria; thus, the study of supernetworks also
includes the study of multicriteria decisionmaking.
Applications of Supernetworks
• Telecommuting/Commuting DecisionMaking
• Teleshopping/Shopping Decision-Making
• Supply Chain Networks with Electronic
Commerce
• Financial Networks with Electronic
Transactions.
A Supernetwork Framework for
International Financial Networks
The Supernetwork Structure of a
Global Supply Chain Networks
Characteristics of the Models
The International Financial Networks
and Global Supply Chains Models :
• handles multiple tiers of multicriteria decisionmakers on multiple levels of networks in
order to represent not only the abstraction
of the decisions but also competition,
cooperation, and interrelationships;
• handles as many countries, currencies, source
agents/manufactures, intermediaries/
distributors/Retailers, and demand markets
as mandated by the specific application;
• considers two modes of transactions: physical
and electronic;
• risk will be an explicit criterion to be
minimized with appropriate associated
weights selected by the decision-makers in
order that they may trade-off this criterion
versus others;
• includes uncertainty into the underlying
production, demand, and cost functions;
• predicts not only the equilibrium flows but also
the equilibrium prices as as well for the study
of the disequilibrium dynamics;
The International Financial Network
Model
Multicriteria Optimization Problem for
Source Agent i in Country l
The Multicriteria DecisionMaking Problem for
Intermediary j
subject to:
K
H
L
2
 
k 1 h 1 l 1 m 1
I
L
H
2
ykhj lˆm   x iljhm , ykhj lˆm  0, x iljhm  0
i 1 lˆ 1 h 1 m 1
The Consumers at the Demand
Markets and their Equilibrium
Conditions
Variational Inequality Formulation
Theorem: The equilibrium conditions governing the
international financial network with intermediation are
equivalent to the solution of the variational inequality given
by: determine (x1*; x2*;y*; *; *3 )K, satisfying:
The Dynamic Adjustment Process
• Demand Market Price Dynamics
We assume that the rate of change of the price, is equal
to the difference between the demand for the financial
product at the demand market and the amount of the
product actually available at that particular market.
The Dynamic Adjustment
Process
• The Dynamics of the Financial Products between
the Intermediaries and the Demand Markets
The rate of change of the financial flow, in turn, is
assumed to be equal to the difference between the price
the consumers are willing to pay for the financial
product at the demand market minus the price charged
and the various transaction costs and the weighted
marginal risk associated with the transaction.
The Dynamic Adjustment
Process
• The Dynamics of the Prices at the Intermediaries
The prices at the intermediaries, whether they are
physical or virtual, must reflect supply and demand
conditions as well. we propose the following dynamic
adjustment for every intermediary j:
The Dynamic Adjustment
Process
• The Dynamics of the Financial Flows from the
Source Agents
we denote the rate of change of the vector of financial
flows from source agent il by xil and noting that the best
realizable direction for the financial flows from source
agent il must include the constraints, we have that:
The Dynamic Adjustment
Process
• The Projected Dynamical System
Consider now a dynamical system in which the demand
market prices, the financial flows between
intermediaries and the demand markets, the prices at
the intermediaries and the financial flows from the
source agents evolve according to the rules presented
above.
then the dynamic model described above can be
rewritten as a projected dynamical system defined by
the following initial value problem:
Global Supply Chain Network
and Risk Management
• Manufacturers and distributors are
multicriteria decision-makers, and
concerned with both profit maximization
and risk minimization.
• Retailers, in turn, are faced with random
demands for the product.
The Global Supply Chain Network
Multicriteria Decision-Making
Problem for a Manufacturer
The Multicriteria DecisionMaking Problem for a Distributor
The Retailer Optimization
Problem
After taking expectation it becomes:
The Equilibrium Conditions of the
Global Supply Chain
Determine (Q1*; Q2*;Q3*; *; *3 )K, satisfying:
Additional Theoretical Results
for both Models
We have established:
• Existence of the solution of the VI
• Uniqueness of the solution of the VI
• Convergence of the Algorithms
The Algorithms
The algorithms that we propose are:
• The Modified Projection Method
(For Global Supply Chain model)
• Euler-type method, which is induced
by the general iterative scheme of
Dupuis and Nagurney [1993]. This is
discrete time algorithm and serve as
approximations to the continuous time
trajectories generated by the dynamic
models.
The notable feature of these algorithms is that
they resolve the VI subproblems into network
optimization problems with special structure
that can be solved exactly in closed form.
Summary and Conclusions
• We developed a framework for the modeling,
analysis, and computation of solutions to
international financial and global supply chains
problems in the presence of electronic
transactions and risk. The framework makes
use of the supernetwork concept.
• The framework allows for the handling of as
many countries, decision-makers and as many
currencies as needed.
Future Research
Knowledge
Supernetworks
Supply Chain
Networks
New Theory
Financial
Networks
Applications
Visualization
Computational
Methods
A Knowledge Supernetwork
A Knowledge Supernetwork
•
•
•
•
•
conceptualization,
modeling,
qualitative analysis,
and solution of
dynamic complex business processes
under risk and uncertainty.
Thank you!
The full text of the papers can be found
under Download Articles at:
http://supernet.som.umass.edu