Operations Research Management Science - System Dynamics

<BODY bgcolor="#ffffff" link="cc0000" vlink="cc0000" text="#000000"> <img src="../cleardot.gif" width=1 height=1 vspace=4 border=0><br>   <table border=0 cellspacing=0 cellpadding=0 width=480><tr valign=top> <td width=10><img src="../cleardot.gif" width=1 height=1 hspace=4 border=0></td> <td width=470> <FONT face="verdana, arial, helvetica" SIZE=2><B><I><A HREF="../../ORMS.shtml" TARGET="_top">OR/MS Today</A> - June 2002</I></B></font><BR> <hr size="1"> <img src="cleardot.gif" width=1 height=1 vspace=4 border=0><br> <font face="times new roman, times"> <img src="../cleardot.gif" width=1 height=1 vspace=4 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=2><B>System Dynamics</B></FONT><br> <IMG SRC="../barbluehook.gif" WIDTH="468" HEIGHT="4"><br> <img src="../cleardot.gif" width=1 height=1 vspace=8 border=0><br> <FONT SIZE="+2"><B>System Dynamics</B></FONT><BR> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <FONT SIZE="+1">Tutorial provides a primer on a set of tools and techniques aimed at improving decision-making in integrated value chain.<I></I></FONT><BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=2><B>By Amitava Dutta and Rahul Roy</B></FONT><br> <hr size="1"> <img src="../cleardot.gif" width=1 height=1 vspace=12 border=0><br>    <BLOCKQUOTE><I>"You cannot have a learning organization without a shared vision...A shared vision provides a compass to keep learning on course when stress develops."  Peter Senge</I></BLOCKQUOTE> Some time in the mid-1990s, America Online switched from variable to fixed all-you-can-use pricing for Internet services. The intent was to maintain or increase customer base in the face of fixed price plans introduced by competitors. The immediate consequence, however, was a lot of disgruntled AOL customers facing constant busy signals, unable to log-on. This had major financial consequences for AOL and led to customer retention problems.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> AOL's marketing move did not appear to be coordinated with network operations (there were not enough dial-up modems in place to handle the increased load), suggesting a lack of holistic thinking in arriving at the pricing decision. As competitive pressures force organizations to operate "faster, better, cheaper," their value chains are becoming increasingly more integrated. In an increasingly integrated environment, the mental models on which management decisions are based need to be more holistic than ever due to the tighter coupling among different components of the environment. Therefore, the need for "systems thinking" has never been stronger.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> Moreover, companies need a shared mental model across the organization in order for decision-makers to take consistent and effective action. Without such understanding, policies can have unanticipated side effects, or their intended effects can be diluted or defeated by the reaction of the environment itself to policy actions. System dynamics provides a set of tools and techniques to develop shared mental models of organizational systems, to represent them rigorously, to test their validity through simulation, and to gauge the impact of policy alternatives via sensitivity and what-if types of analyses. Systems dynamics can help companies gain insights into underlying mechanics that determine the behavioral dynamics of organizational systems. This, in turn, can help improve decision-making in today's integrated value chain.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> The first article on system dynamics, written by Jay W. Forrester, appeared in <I>Harvard Business Review</I> in 1959 [3]. In that article, Forrester utilized principles of information-feedback control found in servomechanisms to explain how aggressive advertising by a company could create workload fluctuation on the shop floor. At the time, this approach to modeling management processes was quite novel, but more than that, it introduced the notion that the dynamics of an industrial system arises as a result of its underlying structure. The basic structural element is the feedback loop; the underlying structure refers to the collection of interacting feedback loops comprising the system. This linkage between structure and behavior remains the guiding principle for practitioners of systems dynamics.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> In 1961, Forrester wrote the seminal book titled "Industrial Dynamics" [4] in which he described the methodology of modeling industrial systems with physical flows (personnel, money, material and machinery), their respective accumulations, and information-based, decision-making mechanisms that control the flows to achieve desired accumulation levels. The central theme was that all decisions are made in the information-feedback structure. A study of the feedback structure could therefore provide a good understanding of the system's dynamics.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> The concept was founded on theories of control systems, but there were augmentations to handle non-linearity and intangibles that characterize industrial systems. Modeling elements representing lags, information attenuation and forecasting  processes commonly found in industrial systems  rounded out the methodology.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> The unified framework to model all parts of an organization and their inter-linkages makes systems dynamics well suited for visualizing the organization from a holistic perspective. In the period following publication of the book, the methodology found application in different problems that varied widely in scope (single organization to national and economies), business process (supply chain management, project management, service delivery, IT infrastructure and strategic planning) and business types (manufacturing, service, research and development, health care, insurance, military and government).<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> Roberts[5] and Sterman[6] report several interesting applications made by corporate organizations over the years using systems dynamics. Side by side, the field was enriched with methodological enhancements for modeling and analysis [7]. In 1990, Peter Senge's book, "The Fifth Discipline  The Art and Practice of Learning Organizations"[8], highlighted the connection between system dynamics and systems thinking, and gave fresh impetus to the practice of the field.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> Systems thinking or the idea of viewing an organization as a whole was already well-known due to earlier works of Ludwig Von Bertalaffy, Norbert Wiener, Russel L. Ackhoff and others in the area of cybernetics. The idea was considered important, but its application in management was limited and convenient tools for practicing systems thinking were not readily available. Senge's book established system dynamics as a tool for systems thinking. It also introduced the concept of "System Archetypes," which are generic structures observable in business systems demonstrating qualitatively similar behavior.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> The availability of visual modeling and simulation software also contributed significantly in making the methodology popular. In the early days of system dynamics, the only software available were DYNAMO and DYSMAP, which were compilers that could create object code from model equations. In spite of the power that these compilers provided, the requirement to learn a programming language limited its use among managers. Today there are at least three visual modeling and simulation softwares (STELLA, VENSIM and POWERSIM) available commercially to develop and test systems dynamics models. All of these are comparable in terms of their capability to create the model graphically, simulate the same and perform sensitivity analysis.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=12 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=3><B>The Methodology</B></FONT><BR> <IMG SRC="../barbluehook.gif" WIDTH="468" HEIGHT="4"><br> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> The philosophy of system dynamics modeling is founded on three principles:<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> <B><I>1. Structure determines behavior </I></B> structure here implies the complex inter-linkages among different parts of organization and includes human decision-making processes. An example of this is a supply chain, which involves complex interaction of the components (customer, retailer, wholesaler, distributor, factory, and raw material supplier) through order and material flows and decisions made about these flows.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> <B><I>2. The structure of organizational systems often involves "soft" variables </I></B> e.g. perceptions of quality, user satisfaction, morale, etc. A supply chain structure includes how each agent forms perceptions about the future behavior of its customer. The mental models of people play a crucial role in determining the dynamic behavior of organizational systems.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> <B><I>3. Significant leverage can be obtained from understanding the mental model and changing it.</I></B><BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> Modeling in system dynamics starts with identification of the reference mode behavior  time dependent behavior of one or two important variables of the system, the dynamics of which the model would try to explain.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> The next step involves creating a causal loop diagram, a pictorial representation of the underlying structure that is thought to explain the reference mode behavior. Typically, modelers and subject matter experts will be involved in the process of arriving at a causal loop diagram. In doing so, they have to resolve differences in their individual mental maps and arrive at a shared understanding of the underlying causes of the reference mode behavior. <BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> As explained earlier, structure is made up of stocks and flows that make up important business processes and how these flows are controlled. For example, in a manufacturing firm, business processes center around flow of orders, flow of material, flow of skilled labor, flow of machinery and flow of money. For a health care firm, flow of doctors, health workers, patients and medical equipment are important. Accumulations of these flows depict the state of the firm. Stock of materials determines the level of inventory held by a firm, stock of orders determines the backlog of orders pending with the firm etc.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> By controlling the flows, management tries to achieve a favorable level of accumulation. Thus, the production manager tries to maintain a low level of order backlog so that customers don't experience large delivery delays. The materials manager makes sure that an appropriate level of raw material is maintained on the shop floor so that neither production suffers from shortages nor is there a huge inventory build-up. So while flow determines the state, state also guides the action to change the flow. The causal loop diagram (Figure 1) shows the circular relationship between the flow and the accumulation.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> <IMG SRC="art/systemf1.jpg" WIDTH="252" HEIGHT="252" ALT="Figure 1: Casual loop"><BR> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=1><B>Figure 1: Casual loop.</B></font><BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> On the diagram, each arrow represents a cause and effect relationship. The polarity of the link (+/-) indicates the direction of change that a change in the cause induces in the effect. A positive sign indicates change in the same direction (increase/decrease induces increase/decrease) while a negative sign indicates change in the opposite direction (increase/ decrease induces decrease/increase). The pair of parallel lines on the links indicates time delay between cause and effect. It's easy to see that this structure models situations where management decision controls a flow thereby changing the level of accumulation and so on, giving rise to a sequence of decisions over time that determine the dynamic behavior of the system.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> Depending on the polarities of causal links present, a feedback loop (Figure 2) can generate one of two types of effects  a snowball effect, one in which a change in state generates action that causes a bigger change in the state, or a balancing effect where a change in state generates action to absorb the change. In the parlance of system dynamics, these two loops are termed as reinforcing or balancing loops, respectively.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> <IMG SRC="art/systemf2.jpg" WIDTH="350" HEIGHT="167" ALT="Figure 2: Feedback loop: Reinforcing loop (left) and Balancing loop (right) ."><BR> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=1><B>Figure 2: Feedback loop: Reinforcing loop (left) and Balancing loop (right) .</B></font><BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> A reinforcing loop generates exponential growth behavior. A balancing loop stabilizes the system around a target state. In some cases, depending on loop conditions, a balancing loop can generate oscillations around the target state. In a typical system, the presence of a number of such feedback loops of either type generates the complex dynamics of the system. For illustration we present a firm that is experiencing growth in a particular market. In this example, the firm uses its sales force to get orders from the market. As sales persons get orders, a part of the revenue earned is allotted to support the sales staff salary. As more orders get booked, the company hires more staff. This is a reinforcing loop that pushes for growth in the firm's sales force. However, the stream of orders booked increases the order backlog and progressively pushes production capability to the limit until the delivery delay no longer remains a ratio between order backlog and production rate permitted by capacity. This delay causes deterioration in sales force effectiveness (they find it harder to sell) and reduced orders booked. This balancing loop limits the growth of the firm.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> From of a study of these two loops we can intuitively say that the while the orders received by the firm increases initially, it ultimately reaches stability. Based on this understanding, management can decide to design an appropriate policy by which the firm augments its capacity at appropriate times and continues to grow to the full potential market. By showing the feedback loops, the modeler provides a structural explanation of the mechanics underlying the system's dynamic behavior. The causal links are drawn based on existing theory, results of correlation study or hypotheses about the relationship between cause and effect.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> <IMG SRC="art/systemf3.jpg" WIDTH="350" HEIGHT="190" ALT="Figure 3: Feedback sales loop."><BR> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=1><B>Figure 3: Feedback sales loop.</B></font><BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> In the next step of model building, the stock and flow structure of the system is drawn based on the causal loop diagram (There are technical limitations of determining loop polarity from causal loop diagrams, which are ignored in this overview). The stock and flow structure shows stocks, flow controllers and decision structures within the system. Conserved physical flows connect stocks in the diagram. Information flows drive different physical flows. The stock and flow diagram for the sales system discussed earlier is shown in Figure 4.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> <IMG SRC="art/systemf4.jpg" WIDTH="350" HEIGHT="187" ALT="Figure 4: Stock and flow diagram for sales system."><BR> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=1><B>Figure 4: Stock and flow diagram for sales system.</B></font><BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> The arrows drawn with regulating valves indicate physical flows. Rectangles (Order Backlog, Sales Staff) indicate accumulations or stocks. The valves (Order Bookings, Deliveries, Hiring) on the physical flows control flows in and out of stock. In system dynamics parlance they are termed as flow variables. Circles (Budget Allotted for Sales Force) indicate converters that are used to capture decision rules or perform intermediate computation. Thin arrows represent information flows connecting converters with stocks.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> The stock and flow structure of the system is simply shorthand for the underlying mathematical representation of the system. Each stock is an integration of flows affecting it. For the purpose of simulation this is expressed as a difference equation wherein over a time period "dt," the value of stock changes by "dt" times the net flow into the stock. A flow is expressed as a function of one or more stocks and converters. Each converter represents the decision rule that is dependent on the current state. Associated delays or attenuation, if any, are represented appropriately. Software packages available today are capable of automatically creating the underlying mathematical representation from the graphical stock and flow structure.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> Simulating the system equations over time with assumed initial values for system variables generates the dynamic behavior of the system. At this point elaborate tests are performed to validate the model for adequacy of problem boundary coverage and reproduction of reference mode behavior. A validated model is used for performing different kinds of analysis like sensitivity analysis and what-if analysis to support decision-making about a future course of action. One important analysis involves experimental identification of feedback loops that dominate the dynamics at different points of time. Termed as loop dominance analysis, this provides further insight into the structure of the system and leads to design of policy structures that result in favorable dynamics.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=12 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=3><B>Software Support for System Dynamics Modeling</B></FONT><BR> <IMG SRC="../barbluehook.gif" WIDTH="468" HEIGHT="4"><br> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> The main objective of system dynamics modeling is to capture mental models of the underlying behavior structure of organizational systems. The modeling software available on the market today contributes greatly toward achieving that objective by allowing model builders to concentrate on conceptualizing the system rather than on the technicalities of model building. As of now, we can report availability of three commercial software packages  Powersim (Powersim Corp, Bergen, Norway, <A HREF="http://www.powersim.com" TARGET="_new">http://www.powersim.com</A>), iThink (High Performance Systems Inc., Hanover, NH 03755, <A HREF="http://www.hps-inc.com" TARGET="_new">http://www.hps-inc.com</A>) and Vensim (Ventana Systems Inc., Harvard, MA 01451, <A HREF="http://www.vensim.com" TARGET="_new">http://www.vensim.com</A>). All three provide the following basic capabilities: <UL> <LI> Drawing the model using a GUI interface. <LI> Simulating the same with different values of simulation intervals. <LI> Publishing the results both as table and graph. <LI> Performing sensitivity analysis and publishing comparison of run results.<BR> </UL> Figure 5 shows an example of the user interface for version 7.0 of iThink.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> <IMG SRC="art/systemf5.jpg" WIDTH="350" HEIGHT="116" ALT="Figure 5: iThink interface."><BR> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=1><B>Figure 5: iThink interface.</B></font><BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> The interfaces of other packages look similar with minor differences. Modeling elements from the toolbar are dragged and dropped on the white area to create the structure. For stocks, initial values need to be specified. Decision rules for the flow variables and converters are written by getting into the dialogue box, shown below. A rich set of built-in functions allows representation of most real-life situations. The packages also allow writing the relationship in the form of a graphical function linking the cause and effect variables. The graph can be drawn by clicking on the appropriate point on the plot area. The equations for the variables are written automatically.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> <IMG SRC="art/systemf6.jpg" WIDTH="350" HEIGHT="231" ALT="Figure 6: Flow/Converter input dialog box"><BR> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=1><B>Figure 6: Flow/Converter input dialog box</B></font><BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> <IMG SRC="art/systemf7.jpg" WIDTH="350" HEIGHT="250" ALT="Figure 7: Graphical function input dialog box"><BR> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=1><B>Figure 7: Graphical function input dialog box</B></font><BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> Beyond these basics, each package also provides additional features. iThink, for example, provides a multi-level modeling interface that allows for separating out the user interface, the stock and flow model and the equations into three different levels. The interface level can be used to show an overview of the system, the causal loop diagram and model outputs. The model tracing facility provides an easy way to navigate through the feedback loops and learn about the reasons behind the dynamics. iThink in recent times has been used to build multimedia games meant to give managers an experimental set up for experiential learning. Vensim enforces strict rigor in writing model equations. It provides features for tracing feedback loops. In addition "Causes Tree" and "Uses Tree" features helps in debugging the model. Powersim comes with the powerful feature of adding user written functions. This can become useful in modeling situations where new concepts (e.g. fuzzy logic) need to be incorporated. The latest version of Powersim can build reusable model components that can be plugged in without much difficulty.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> Summarizing, one could say that while the basic capabilities are present in all three packages, the additional features make each one suitable for particular modeling situations.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=12 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=3><B>Forty-Five Years of Growth</B></FONT><BR> <IMG SRC="../barbluehook.gif" WIDTH="468" HEIGHT="4"><br> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> In the 45 years since the appearance of the first article, the use of system dynamics has grown considerably. Every major management-consulting firm has a practice in this area. Sterman [6] reports three interesting business applications of system dynamics undertaken at General Motors, Ingalls Shipbuilding of Pascagula Miss., and Du Pont. At General Motors, the modeling exercise showed how new car leasing policies, intended to increase new car sales, were actually causing a large supply of almost new used cars and cutting into the new car sales. As a result, GM modified its leasing schemes to eliminate short-term leases. Ingalls used a system dynamics model to establish the reasons for project delays and win a legal battle with the U.S. Navy over project cost and time overrun. At Du Pont, system dynamics modeling was used in a learning workshop for changing people's perceptions about the effectiveness of proactive maintenance strategy. The attitudinal change helped Du Pont save significant maintenance costs. The authors have also studied systems dynamics applications involving Internet diffusion in developing countries [1] and network service planning [2].<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> In our view, the ability to conceptualize organizations holistically in systemic terms should be considered an essential skill for managers of the 21st century. For example, the AOL experience cited at the start can be seen as a natural behavior of that system's structure. If you switch from variable to fixed pricing, you may initially attract more customers. But in the absence of network capacity increases, service quality drops, leading to an exodus of existing customers. This negative feedback loop dominates system behavior. Qualitative systems thinking is a first step in that direction, but systems dynamics imparts more rigor into the process. System dynamics, under different names, is taught at many management schools on five continents, sometimes as a full course and sometimes as a part of related courses like business policy, business simulation, process reengineering, etc. The System Dynamics Society (<A HREF="http://www.systemdynamics.org/" TARGET="_new">http://www.systemdynamics.org/</A>), the official forum of system dynamics practitioners the world over, publishes the quarterly journal titled <I>System Dynamics Review</I> and holds annual meeting for exchange of ideas. In addition, application of the methodology regularly gets reported in major management journals. System dynamics is a mature discipline that has necessary tools and techniques to analyze the causes of organizational performance (or lack thereof) and take appropriate management action.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=12 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=3><B>References</B></FONT><BR> <IMG SRC="../barbluehook.gif" WIDTH="468" HEIGHT="4"><br> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <OL> <font size=1> <LI> Dutta A. and R. Roy, 2001, "Internet Diffusion in India: Lessons for Developing Countries," <I>Proceedings of ICIS2001,</I> New Orleans. <LI> Dutta A., 2001, "Business Planning for Network Services: A Systems Thinking Approach," <I>Information Systems Research,</I> Vol. 12, No. 3, pgs. 260-285. <LI> Forrester J. W., 1959, "Advertising: A problem in Industrial Dynamics," <I>Harvard Business Review,</I> Vol. 37, No. 2. <LI> Forrester J. W., 1961, "Industrial Dynamics," Cambridge: MIT Press; currently available from Pegasus Communications: Walthum, Mass. <LI> Roberts E. (ed.), 1978, "Managerial Applications of System Dynamics," Pegasus Communications: Walthum, Mass. <LI> Sterman J. D., 2000, "Business Dynamics: Systems Thinking and Modeling for a Complex World," Irwin McGraw-Hill. <LI> Sastry A. and Sterman J. D.,1993, "Desert Island Dynamics: An Annotated Survey of the Essential System Dynamics Literature," in Zepeda, E. and J. Machuca (eds.), <I>Proceedings of the 1993 International System Dynamics Conference,</I> Albany, N.Y., System Dynamics Society <LI> Senge P., 1990, "The Fifth Discipline: The Art and Practice of the Learning Organization," New York: Doubleday. </font> </OL> <img src="../cleardot.gif" width=1 height=1 vspace=4 border=0><br> <IMG SRC="../barbluehook.gif" WIDTH="468" HEIGHT="4"><br> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=2><I>Amitava Dutta (<A HREF="mailto:adutta@gmu.edu">adutta@gmu.edu</A>) holds the LeRoy Eakin Chair in Electronic Commerce in George Mason University's School of Management. Rahul Roy (<A HREF="mailto:Rahul.roy@uni.edu">Rahul.roy@uni.edu</A>) is an associate professor at the Indian Institute of Management Calcutta. He is currently visiting The University of Northern Iowa.</i><BR>  <img src="../cleardot.gif" width=1 height=1 vspace=5 border=0><br>  <img src="../barblue.gif" width=468 height=1 border=0 alt=" "><br> <img src="../cleardot.gif" width=1 height=1 vspace=8 border=0><br> <font face="verdana, arial, helvetica" size="1"> <CENTER><script type="text/javascript"></script> <script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script></CENTER><br> <img src="../cleardot.gif" width=1 height=1 vspace=8 border=0><br> <LI> <A HREF="tocfr.html" Target="_top"><I>Table of Contents</I></A><br> <img src="../cleardot.gif" width=1 height=1 vspace=4 border=0><br> <LI> <A HREF="../../ORMS.shtml" TARGET="_top"><I>OR/MS Today</I> Home Page</A><br>  <img src="../cleardot.gif" width=1 height=1 vspace=8 border=0><br> <img src="../barblue.gif" width=468 height=1 border=0 alt=" "><br> <b><i>OR/MS Today</i></b> copyright � 2002 by <A HREF="http://www.informs.org/" target="_new">the Institute for Operations Research and the Management Sciences</a>. 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