Virtual Center for Supernetworks

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 issuesGlobal transportation networksGlobal 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

SARSTerrorist 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 commerceThe Commerce Dept. estimates:

retail e-commerce accounted for $45 billion in sales in 2002, up 11% from the prior yearin 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 networksThree distinct types of decision-makersOptimizing AgentsMultiple countriesMultiple currenciesHomogeneous 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 applicationIt predicts the equilibrium product shipments and also the equilibrium pricesRetailers may be physical or virtualThe transaction costs need not be symmetricIt 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 K½ Rn, such thath F(x*)T, x-x*i¸ 0, 8 x2 K

where F:K! Rn, continuously differentiableK is convex, compact and closed set

Assume there exist smooth g(x,y):K£K! Rn, such that:

(i) g(x,x)=F(x), 8 x2 K,(ii) for every fixed x,y2 K, n£n matrix rxg(x,y) is

symmetric and positive definite

The Algorithms

General Iterative Scheme

Modified Projection Method

Step 0: InitializationSet X02 K. Let k = 1

Step 1: Construction & ComputationCompute Xk by solving the VI subproblem:

hg( Xk, Xk –1)T, X – Xki¸ 0, 8 X2 K.

Step 2: Convergence VerificationIf |Xk – Xk-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 X02 K. Let k = 1 and let be a scalar such that 0 < < 1/L, where L is the Lipschitz constant

Step 1: ComputationCompute Yk by solving the VI subproblem:

h Yk + F(Xk –1) – Xk –1, X – Yki¸ 0, 8 X2 K.Step 2: AdaptationCompute Xk by solving the VI subproblem:

h Xk + F(Yk-1) – Xk–1, X – Xki¸ 0; 8 X2 K.Step 3: Convergence VerificationIf |Xk – Xk-1|·, > 0, a prespecified tolerance,

then stop; else, set k = k + 1, and go to Step 1.

Summary

We have developed a general framework forModelingAnalysisComputation

of solutions to Global Supply Chain SupernetworksProposed a dynamic adjustment processEstablished 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 supernetworksOur algorithms can be used for conducting

qualitative analysis sensitivity analysis perturbation analysis

of knowledge-intensive organizations

Questions? Comments?

http://supernet.som.umass.edu