SupernetworksSupernetworks:: Decision-Making in the Decision-Making in the

2121stst Century Century

Anna NagurneyJohn F. Smith Memorial Professor

andDirector

The Virtual Center for SupernetworksUniversity of Massachusetts - Amherst

Brown University - March 15, 2005

The Virtual Center forSupernetworks

http://supernet.som.umass.edu

Funding for reseach provided by:

National Science Foundation

AT&T Foundation

John F. Smith MemorialFund - University ofMassachusetts at Amherst

Outline• Introduction• Background• Reality of Today’s Networks• A New Paradigm• New Tools• Some Successes• Novel Applications• New Directions• New Challenges, Results, and

Opportunities• Summary and Conclusions

We are in a New Era of Decision-MakingCharacterized by:

• complex interactions among decision-makers in organizations;

• alternative and at times conflictingcriteria used in decision-making;

• global reach of many decisions;• high impact of many decisions;• increasing risk and uncertainty, and• the importance of dynamics and

realizing a fast and sound response toevolving events.

The complexity of today's decision-makingenvironments in organizations requires thedevelopment and harnessing ofappropriate and rigorous scientific andengineering tools which must be based oninformation technology since only suchtechnology provides one with the speedand accuracy needed to model complexinteractions and to optimize accordingly.

The New Era is Network-Based with theInternet providing critical infrastructurealong with transportation/logisticalnetworks as well as othertelecommunication networks andenergy networks.

No longer are networks independent ofone another but critically linked withmajor questions arising regardingdecision-making and appropriatemanagement tools.

Indeed, the events of 9/11 coupled withthe recent computer worm and virusesalong with the biggest blackout in UShistory demonstrate irrevocably that wemust as a nation harness the best andmost powerful methodologies for themodeling, analysis, and solution ofcomplex decision-making problems.

We at the Isenberg School ofManagement have established theVirtual Center for Supernetworks, whichalong with the SupernetworksLaboratory for Computation andVisualization, serves as a resource forresearchers, educators, andpractitioners.

The center emphasizes the importance ofnetwork systems, their modeling, andanalysis, and simultaneously expandsupon scientific network tools fordecision-making.

The center team is multidisciplinary andmulticultural and at present consists ofdoctoral students from three differentcountries.

The center supports undergraduates inresearch since they are our future andprovide new and fresh perspectives.

Center associates from different academicinstitutions and industry work closelywith the center director and studentassociates.

The Supernetwork Team2004-2005

Background

Throughout history, networks have servedas the foundation for connecting humansto one another and their activities.

• Roads were laid, bridges built, andwaterways crossed so that humans, bethey on foot, on animal, or vehicle couldtraverse physical distance throughtransportation. The airways wereconquered through flight.

• Communications were conducted usingthe available means of the period, fromsmoke signals, drum beats, and pigeons,to the telegraph, telephone, andcomputer networks of today.

Importance of Networks to theEconomy and the Nation

• US consumers, businesses, andgovernments spend about $950 billionon transportation annually (US DOT).

• Corporate buyers spend about $517.6billion on telecommunications annually(Purchasing).

• Energy expenditures in the UnitedStates are about $515.8 billion a year(US Dept. of Commerce).

Information technology hastransformed the ways in whichindividuals work, travel, and conducttheir daily activities, with profoundimplications for existing and futurenetworks.

The decision-making process itself hasbeen altered due to the addition ofalternatives and options which were notpossible or even feasible.

The boundaries for decision-makinghave been redrawn as individuals cannow work from home or purchaseproducts from work.

We live in an era in which thefreedom to choose is weightedby the immensity of choices andpossibilities:

• Where should one live?

• Where should one work? Andwhen?

• How should one travel? Orcommunicate? And with whom?

• Where should one shop? And how?

Not only has individual decision-makingbeen transformed in this new era butorganizations have as well.

How do we capture in a scientific mannercooperation vs. competition and theramifications, centralized control vs.decentralized control, and differentcriteria in decision-making?

Moreover, what are the results on theflows on the networks be they in theform of vehicles, messages, products,and/or services, as well as financial?

Who wins and who loses?

Classical NetworksNetwork System Nodes Links FlowsTransportat ionUrban Intersections, Roads Autos

Homes,Places of Work

Air Airports Airline Routes PlanesRail Railyards Railroad Track TrainsManufacturing Distribution Points, Routes Parts,and Logist ics Processing Points Assembly Line ProductsCommunicat ion Computers Cables Messages

Satellites Radio MessagesPhone Exchanges Cables, Voice,

Microwaves VideoEnergy Pumping Stations Pipelines Water

Plants Pipelines Gas, Oil

Transportation science has historically beenthe discipline that has pushed thefrontiers in terms of methodologicaldevelopments for such problems (whichare often large-scale) beginning with thework of Beckmann, McGuire, and Winsten(1956).

Dafermos (1980) later showed that thetraffic network equilibrium conditions asformulated by Smith (1979) were a finite-dimensional variational inequality andthen utilized the theory to establish bothexistence and uniqueness results of theequilibrium traffic flow pattern as well asto propose an algorithm withconvergence results.

Finite-dimensional variational inequalitytheory has been applied to-date to thewide range of equilibrium problems notedabove, as well as to game theoreticproblems, such as oligopolistic marketequilibrium problems, and to generaleconomic equilibrium problems (see, e.g.,Nagurney (1993) and the referencestherein).

Reality of Today’sNetworks

Characteristics of Today's Networks:• large-scale nature and complexity of

network topology;• congestion;• alternative behavior of users of the

network, which may lead to paradoxicalphenomena;

• the interactions among networksthemselves such as in transportationversus telecommunications networks;

• policies surrounding networks todaymay have a major impact not onlyeconomically but also socially,politically, and security-wise.

Large-Scale Nature and Complexity

• Chicago's Regional TransportationNetwork has 12,982 nodes, 39,018links, and 2,297,945 origin/destinationpairs.

• AT&T's domestic network has 100,000origin/destination pairs. In the detailgraph applications in which nodes arephone numbers and edges are calls,there are 300 million nodes and 4 billionedges.

Congestion

• In the case of transportation networksin the United States alone, congestionresults in $100 billion in lostproductivity, whereas the figure inEurope is estimated to be $150 billion.

• In terms of the Internet, the FCCreports that the volume of traffic isdoubling every 100 days, which isremarkable given that telephone traffichas typically increased only by about 5percent a year.

System-Optimization versusUser-Optimization

In transportation networks, travelersselect their routes of travel from anorigin to a destination so as to minimizetheir own travel cost or travel time,which although optimal from anindividual's perspective (user-optimization) may not be optimal froma societal one (system-optimization)where one has control over the flows onthe network.

The Braess’ Paradox

Assume a network with a singleO/D pair (1,4) . There are 2paths available to travelers:p1=(a,c) and p2=(b,d).

For a travel demand of 6, theequilibrium path flows arexp1

* = xp2* = 3 and

The equilibrium path travel costis Cp1

= Cp2= 83.

32

1

4

a

c

b

d

ca(fa)=10 fa cb(fb) = fb+50

cc(fc) = fc+50 cd(fd) = 10fd

Adding a LinkIncreased Travel Cost for All!

Adding a new link creates a newpath p3=(a,e,d).

The original flow distributionpattern is no longer anequilibrium pattern, since at thislevel of flow the cost on path p3,Cp3=70.

The new equilibrium flow patternnetwork is xp1

* = xp2* = xp3

*=2.The equilibrium path travel costs:Cp1 = Cp2 = Cp3

= 92.

32

1

4

a

c

b

d

e

ce(fe) = fe + 10

This phenomenon is also relevant totelecommunications networks and,in particular, to the Internet whichis another example of anoncooperative network.

Recently, we have discoveredparadoxes in networks with zeroemission links such astelecommmunication networks:

• The addition of a zero emission linkmay result in an increase in totalemissions with no change in demand!

• A decrease in demand on a networkwith a zero emission link may result inan increase in total emissions!

One must incorporate the networktopology, the relevant cost and demandstructure, as well as the behavior of theusers of the network(s) into anynetwork-based policy!

These paradoxes further illustrate theinterconnectivity among distinctnetwork systems and that they cannotbe studied simply in isolation!!!

A New Paradigm

Supernetworks: A New Paradigm

Supernetworks• Supernetworks may be comprised of such

networks as transportation,telecommunication, logistical, and/orfinancial networks.

• They may be multilevel as when theyformalize the study of supply chainnetworks or multitiered as in the case offinancial networks with intermediation.

• Decision-makers may be faced withmultiple criteria; thus, the study ofsupernetworks also includes the study ofmulticriteria decision-making.

New Tools

The tools that we have been using inour supernetworks research include:

• network theory• optimization theory• game theory• variational inequality theory and• projected dynamical systems theory

(which we have been instrumental indeveloping)

• network visualization tools.

SupernetworksSupernetworks

Computer ScienceComputer Science

ManagementManagementScienceScience

EngineeringEngineering

EconomicsEconomicsand Financeand Finance

A Multidisciplinary Paradigm

We are interested not only in addressingtopological issues in terms ofconnectivity but in predicting thevarious flows on the networks whetherphysical or abstract subject to humandecision-making under the associatedconstraints, be they budget, time,security, risk, and/or cost-related.

Some Successes

• We were the first the lay down thetheoretical foundations for dynamicalsystems with constraints (calledprojected dynamical systems) whichallows for the qualitative analysis ofsuch systems including stability analysisalong with discrete-time algorithms.

• The applications that we have studiedrange from dynamic transportationnetworks to global supply chains andinternational financial networks with riskmanagement.

• We were the first to quantify and modeldecision-making on multitiered networksas well as multilevel networks (alongwith the dynamics).

• We have made fundamental extensionsto multicriteria decision-making onnetworks with mutiple decision-makers.

• We have demonstrated through severaldistinct network systems how risk andstochastic components could be directlyincorporated into a variational inequalityframework.

Novel Applications

Applications of Supernetworks• Telecommuting/Commuting Decision-

Making

• Teleshopping/Shopping Decision-Making

• Supply Chain Networks with ElectronicCommerce

• Financial Networks with ElectronicTransactions

• Reverse Supply Chains with E-Cycling

• Knowledge Networks

• Energy Networks/Power Grids

A Supernetwork Conceptualization ofCommuting versus Telecommuting

A Supernetwork Framework forTeleshopping versus Shopping

The Supernetwork Structure of aSupply Chain Network

International Financial Networkswith Electronic Transactions

The 4-Tiered E-Cycling Network

The Electric PowerSupply Chain Network

New Directions

The knowledge supernetwork theorythat we are developing ismultidimensional in scope andconceptualizes and abstracts complexdynamic business processes and theiroutcomes as multitiered and multilevelnetworks on which multicriteria decision-makers interact, both competitively andcooperatively, and the effects of theirdecisions may affect a variety of flows .

A Knowledge Supernetwork

2

1

3 4

n

2

1

3 4

n2

1

3 4

n

Knowledge Product 1

Knowledge Product 2

Knowledge Product k

Supernetworks IntegratingSocial Networks

The models explicitly consider the role thatrelationship levels play in other networksystems and include multicriteria decision-making with individual weights for thecriteria such as:

–maximization of profit–minimization of risk–maximization of relationship value.

Supernetworks IntegratingSocial Networks

Decision-makers in the network can decideabout the relationship levels [0,1] thatthey want to establish.

Establishing relationship levels incurs somecosts.

Higher relationship levels–Reduce transaction costs–Reduce risk–Have some additional value

(relationship value).

Supernetwork Structure: IntegratedSupply Chain/Social Network System

Supernetwork Structure:Integrated Financial/Social

Network System

Supernetworks IntegratingSocial Networks

Dynamic evolution of:

• Product transactions/financial flows andassociated prices on the supply chainnetwork/financial network withintermediation

• Relationship levels on the socialnetwork

Computational Procedure

We use the Euler Method to solve theVariational Inequality (VI) problems andto track the dynamic trajectoriesassociated with the projected dynamicalsystems. The VI is in standard form:

The Euler Method

New Challenges,Results,

andOpportunities

BellagioResearch

Team ResidencyMarch 2004

• We are working with Professors Cojocaruand Daniele on infinite-dimensionalprojected dynamical systems andevolutionary variational inequalities andtheir relationships and unification.

• This allows us to model dynamic networksover different time scales.

• In addition, there are ties with evolutionarygame theory.

A Pictorial of theDouble-Layered Dynamics

Summary and

Conclusions

We have described the realities surroundingnetworks today and the challenges andcomplexities posed for their analysis andstudy.

We have argued for new paradigms tocapture decision-making in theInformation Age.

We have focused on the concept ofsupernetworks and have discussed avariety of applications.

There has never been a more exciting time tobe doing research in operations research /management science.

It is this discipline that is instrumental inbuilding bridges with economics, finance,computer science as well as different fieldsof engineering.

Operations researchers / managementscientists have the technical expertise aswell as the application-based practical know-how to truly make a difference in this world.

Thank you!

For more information, seehttp://supernet.som.umass.edu

The Virtual Center for Supernetworks