Outline of Research Activities Dmytro Matsypura Presentation at MKIDS Mini-Workshop September 10, 2003 Virtual Center for Supernetworks

Research Interests Modeling and analysis of complex decision-making on network systems Specific focus on global issues Global transportation networks Global telecommunication networks Global supply chain networks Risk issues

Motivation (Global Supply Chains) Growing competition brought new challenges Supply chains have become increasingly globalized Addressing risk issues is more important then ever SARS Terrorist threats

Motivation (Global Supply Chains) Success can not rely solely on improving the efficiency of internal operations Collaboration can build the foundation for a competitive advantage The principal effect of B2B commerce is in the creation of more profitable supply chain networks

Motivation (E-Commerce) The Net and e-business now is a vital part of commerce The Commerce Dept. estimates: retail e-commerce accounted for $45 billion in sales in 2002, up 11% from the prior year in the first quarter of 2003, online retail sales jumped to $11.9 billion, 30% from the first quarter of 2002, while total retail sales grew just 4.4% in this same period Last year, Intel generated 85% of its orders -- some $22.8 billion worth -- online

Supernetwork

Research Papers Dynamics of Global Supply Chain Supernetworks (GSCS) Anna Nagurney, Jose Cruz, and Dmytro Matsypura, 2002 Global Supply Chain Supernetworks with Random Demands (GSCSwRD) Anna Nagurney and Dmytro Matsypura, 2003 Dynamics of Global Supply Chain Supernetworks with E-Commerce (GSCSwE) Jose Cruz and Dmytro Matsypura, 2003

Decision-Making Setting Supply chain networks Three distinct types of decision-makers Optimizing Agents Multiple countries Multiple currencies Homogeneous product

Our Unique Perspective Dynamics of GSCS Manufacturer-retailer-demand_market Elastic demand GSCSwRD Manufacturer-distributor-retailer Random demand e-commerce Dynamics of GSCSwE Manufacturer-retailer-demand_market Elastic demand e-commerce

Notable features: It handles as many countries, manufacturers, retailers, and demand markets as mandated by the specific application It predicts the equilibrium product shipments and also the equilibrium prices Retailers may be physical or virtual The transaction costs need not be symmetric It allows for the analysis of the equilibrium product flows and prices as well as the disequilibrium dynamics Dynamics of Global Supply Chain Supernetworks

The Supernetwork Structure

The Optimization Problem for the Manufacturer

The Optimization Problem for the Retailer

The Optimality Conditions at the Demand Market and

The Equilibrium Conditions Governing the Global Supply Chain Network

Global Supply Chain Supernetworks with Random Demands Another class of decision-maker: Distributor Retailers can trade with Manufacturers through Distributors as well as directly through e-links Retailers are facing random demand Retailers bear all the risk associated with random demand

Global Supply Chain Supernetwork with Random Demands

The Optimization Problem of the Manufacturer

The Optimization Problem of the Distributor

The Optimization Problem of the Retailer

Market Equilibrium Conditions

Dynamics of Global Supply Chain Supernetworks with E-Commerce Back to manufacturer-retailer-demand_market schema Allow for B2C electronic transactions Elastic demand

Global Supply Chain Supernetwork with E-Commerce

Dynamics of Global Supply Chain Supernetworks with E-Commerce The VI formulation is somewhat similar to previously discussed Yet it is different for it allows for B2C e-commerce Our main interest: behavior of the system in time

Dynamics Demand market price dynamics: The rate of change of the price is equal to the difference between the demand for the product and the amount of product actually available at the particular market

Dynamics The product shipments retailer demand_market: The rate of change of the product shipment is equal to the price consumers are willing to pay minus the price of a retailer and various transaction costs

Dynamics The prices at the retailers: The rate of change of the clearing price is equal to the difference between the amount of product shipped in and out

Dynamics The product shipments manufacturer retailer: The rate of change of the product shipment is equal to the clearing price minus production and transaction costs

Dynamics The product shipments manufacturer demand_market: The rate of change of the product shipment is equal to the price consumers are willing to pay minus production and transaction costs

Results The non-classical projected dynamical system Describes the dynamic evolution of the product flows and prices Describes the dynamic interactions among the product flows and prices The set of stationary points coincides with the set of solutions to the variational inequality problem

The Algorithms General Iterative Scheme Modified Projection Method We seek to determine x* 2 K ½ R n, such that h F(x * ) T, x-x* i¸ 0, 8 x 2 K where F:K ! R n, continuously differentiable K is convex, compact and closed set Assume there exist smooth g(x,y):K £ K ! R n, such that: (i) g(x,x)=F(x), 8 x 2 K, (ii) for every fixed x,y 2 K, n £ n matrix r x g(x,y) is symmetric and positive definite

The Algorithms General Iterative Scheme Modified Projection Method Step 0: Initialization Set X 0 2 K. Let k = 1 Step 1: Construction & Computation Compute X k by solving the VI subproblem: h g( X k, X k –1 ) T, X – X k i¸ 0, 8 X 2 K. Step 2: Convergence Verification If |X k – X k-1 | · ,  > 0, a prespecified tolerance, then stop; else, set k=k+1, and go to Step 1.

The Algorithms General Iterative Scheme Modified Projection Method Step 0: Initialization Set X 0 2 K. Let k = 1 and let  be a scalar such that 0 <  < 1/L, where L is the Lipschitz constant Step 1: Computation Compute Y k by solving the VI subproblem: h Y k + F(X k –1 ) – X k –1, X – Y k i¸ 0, 8 X 2 K. Step 2: Adaptation Compute X k by solving the VI subproblem: h X k + F(Y k-1 ) – X k–1, X – X k i¸ 0; 8 X 2 K. Step 3: Convergence Verification If |X k – X k-1 | · ,  > 0, a prespecified tolerance, then stop; else, set k = k + 1, and go to Step 1.

Summary We have developed a general framework for Modeling Analysis Computation of solutions to Global Supply Chain Supernetworks Proposed a dynamic adjustment process Established stability of the network systems under certain conditions

Future Research The framework we utilize can be adjusted and applied to the developing of the theory of knowledge supernetworks Our algorithms can be used for conducting qualitative analysis sensitivity analysis perturbation analysis of knowledge-intensive organizations

Questions? Comments?