Download My Research - The 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 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
Dynamics of Global Supply Chain
Supernetworks
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
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 that
h F(x*)T, x-x*i¸ 0, 8 x2 K
where F:K! Rn, continuously differentiable
K 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: Initialization
Set X02 K. Let k = 1
Step 1: Construction & Computation
Compute Xk by solving the VI subproblem:
hg( Xk, Xk –1)T, X – Xki¸ 0, 8 X2 K.
Step 2: Convergence Verification
If |Xk – Xk-1|·e, e > 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 a be a scalar such
that 0 < a < 1/L, where L is the Lipschitz
constant
Step 1: Computation
Compute Yk by solving the VI subproblem:
h Yk + aF(Xk –1) – Xk –1, X – Yki¸ 0, 8 X2 K.
Step 2: Adaptation
Compute Xk by solving the VI subproblem:
h Xk + aF(Yk-1) – Xk–1, X – Xki¸ 0; 8 X2 K.
Step 3: Convergence Verification
If |Xk – Xk-1|·e, e > 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?
http://supernet.som.umass.edu