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, Nagurney, A. and J. Cruz, (2002), “International Financial Networks with Intermediation: Modeling, Analysis, and Computations," to appear in Computational Management Science; 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,

Publications Nagurney, A., J. Cruz and J. Dong (2003), “Global Supply Chain Networks and Risk Management “; Nagurney, A. and J. Cruz (2003), “ Dynamics of International Financial Networks with Risk Management “; Nagurney, A., J. Cruz, J. Dong and D. Zhang (2003), “Supply Chain Networks, Electronic Commerce, and Supply Side and Demand Side Risk”;

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 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 decision- making.

Applications of Supernetworks Telecommuting/Commuting Decision- Making 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

The International Financial Networks and Global Supply Chains Models : handles multiple tiers of multicriteria decision- makers 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; Characteristics of the Models

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;

Multicriteria Optimization Problem for Source Agent i in Country l The International Financial Network Model

The Multicriteria Decision- Making Problem for Intermediary j subject to:

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 (x 1 *; x 2 *;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. 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 x il 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 Decision- Making Problem for a Distributor

The Retailer Optimization Problem After taking expectation it becomes:

The Equilibrium Conditions of the Global Supply Chain Determine (Q 1 *; Q 2 *;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 Supply Chain Networks Financial Networks Knowledge Supernetworks New TheoryApplicationsComputational Methods Visualization

A Knowledge Supernetwork

conceptualization, modeling, qualitative analysis, and solution of dynamic complex business processes under risk and uncertainty.

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