Virtual Center for Supernetworks
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Transcript of Virtual Center for Supernetworks
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Outline of Research Activities
Dmytro Matsypura Presentation at MKIDS
Mini-Workshop September 10, 2003
Virtual Center for
Supernetworks
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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
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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
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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
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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
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Supernetwork
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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
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Decision-Making Setting
Supply chain networksThree distinct types of decision-makersOptimizing AgentsMultiple countriesMultiple currenciesHomogeneous product
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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
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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
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The Supernetwork Structure
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The Optimization Problem for the Manufacturer
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The Optimization Problem for the Retailer
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The Optimality Conditions at the Demand Market
and
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The Equilibrium Conditions Governing the Global Supply Chain Network
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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
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Global Supply Chain Supernetwork with Random Demands
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The Optimization Problem of the Manufacturer
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The Optimization Problem of the Distributor
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The Optimization Problem of the Retailer
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Market Equilibrium Conditions
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Dynamics of Global Supply Chain Supernetworks with E-Commerce
Back to manufacturer-retailer-demand_market schema
Allow for B2C electronic transactions
Elastic demand
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Global Supply Chain Supernetwork with E-Commerce
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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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.
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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
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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
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Questions? Comments?
http://supernet.som.umass.edu