Operations Research Management Science - October 2001 - Resource Allocation

<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> - October 2001</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>Resource Allocation</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>The Art of Science</B></FONT><BR> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <FONT SIZE="+1"><B><I>National transplant system: What's fair and what's possible?</I></B></FONT><BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=2><B>By Tom Koch</B></FONT><br> <hr size="1"> <img src="../cleardot.gif" width=1 height=1 vspace=12 border=0><br>   The art of the science isn't in the solution to a problem but in its definition. How an issue is perceived largely determines the data that is collected, the method of its analysis, and thus the conclusions that result. It is therefore surprising that few experts take the time to critically question the appropriate scale of the problem or the perspective that results from its application. Defining the scale and perspective of address is perhaps the critical determinant when addressing problems of allocation and distribution.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> I learned my lesson in the late 1990s while studying the U.S. system of graft organ distribution  the way in which transplantable human organs are distributed across the United States. My goals, like those of the U.S. agencies involved in transplantation, were equality, efficiency and optimality. These are, after all, the goals of the system itself, ones enshrined in law  the National Organ Transplant Act of 1984 (NOTA) [1] and in the writings of officials involved in transplant services [2].<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> A national system, I thought. The scale is self-evident: if not the entire United States  including Alaska and Hawaii  then at least the "lower 48" continental states. And so I attempted to develop a linear model (using LINDO) of the U.S. system of organ distribution that simultaneously would decrease wastage of donor organs (up to a third of those donated, depending on organ type and donor location) while assuring as equitable a distribution as possible. This model took the supply of organs as a given and tried to maximize its usage. It thus obscured the links between organ supply and distributive inequalities, between the limits of service and its potential effect on the greater system.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> If my program was a failure, it was in good company. The Department of Health and Human Services (DHHS), the United Network for Organ Sharing (UNOS) and a group of National Institute of Medicine (NIM) experts all made the same mistake. We all focused reflexively on one or another limited scale, that of the nation or of the administrative region. What we should have asked first was at what scales can organ distribution and supply be best understood.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=12 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=3><B>The 'Transplant Dilemma'</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> Since the first successful human organ transplant in 1954  a kidney donated by identical twin Ronald Herrick to his brother Richard  the focus has been on the organ donor as well as the recipient. After all, without a voluntary donor there will be no recipient. "At the conclusion of our last preoperative discussion," transplant surgeon Thomas Murray recalled years later, "the donor [Ronald Herrick] asked whether the hospital would be responsible for his health care for the rest of his life if he decided to donate his kidney" [3].<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> From the start, encouraging voluntary donation has been a critical goal of transplant professionals. Typically, however, experts have assumed donor organ supply and distribution to be wholly separate issues. The former is about "giving" and "beneficence," while the latter is about efficiency and maximization in a situation where scarcity rules. From the start, organ demand has consistently exceeded the available supply. At present, more than 50,000 U.S. citizens await a suitable donor organ and, in any year, perhaps one-third of those waiting for an organ transplant will receive it. In a nutshell, this is the "organ transplant dilemma" [4].<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> The general issues of limited supply and efficient distribution were first considered in the 1980s when Congress ordered a study to determine how best to secure transplantable organs while achieving equity and efficiency in a system of national organ distribution [5]. Since that time equality of treatment has been argued as a practical goal  one designed to encourage donation  as well as a political principle reflecting broader ethical and political concerns. Efficiency has been seen as a necessary objective if maximum use of available organs is to be achieved.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> As a result of that report, the United Network for Organ Sharing (UNOS) was created as the official OPTN (organ provider and transportation network) to administer the U.S. transplant program under the general supervision of the Department of Health and Human Services. The UNOS system divided the nation into 11 regions for administrative ease and distributive efficiency. These regions included wide disparities in population density, areal size and the number of transplant services available to citizens. They did reflect, however, historical U.S. regional designations and appeared to serve a general principle that in matching organ donor and recipient, closer is better.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> Proximity makes sense. Organs are a rapidly perishable commodity. Through the 1990s, hearts and lungs survived at most four to five hours outside a living host; livers survived 10 to 12 hours. Each transplantable organ has a distinct "ischemia rate" defining the rate of degradation for an organ outside a host. This creates a practical barrier to distanced organ sharing and a practical rationale for advancing organ sharing between people within a limited region, if not the same hospital or city.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> Through the mid-1990s, most experts were pleased with the UNOS system. Indeed, some argued it was a model of the just and efficient distribution of limited health resources. "No part of the health care system has done more to resolve questions of justice than transplantation" [6]. In the mid-1990s, however, that assumption was questioned by a series of issues involving both allocation  who is deemed eligible to receive an organ  and organ distribution [7].<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> In 1998, DHHS Secretary Donna Shalala informed Congress the UNOS system was inequitable. "In some areas of our nation," she said, "patients wait five times longer or more for an organ than in other areas. Less visible but more important are the resulting inequities in who receives organs. Where waiting times are shortest, organs may go to patients who are less ill; while at the same moment, in areas where patients wait longer, organs often are not offered to patients with greater medical need" [8].<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> The answer, she concluded, was to change from a regional to a national system of organ distribution. In this new system eligible patients would be prioritized on a "sickest first" basis irrespective of geographical location. For its part, UNOS defended the regional system as not only generally fair and efficient but also as one encouraging voluntary donation. A national perspective would diminish voluntary giving, its officials warned, by distancing potential donors from local (or near-by) transplant sites [9]. Researchers at the National Institute of Medicine (NIM) were asked to review the problem. They concluded the regional system, while equitable, was not optimal. A national system of distribution utilizing population-based catchment areas  a region-by- population size approach  would best serve the country's transplant needs [10].<BR> <img src="../cleardot.gif" width=1 height=1 vspace=12 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=3><B>Scale and Perspective</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> DHHS Secretary Shalala's concerns were based on demonstrable regional inequalities in a national system. Based in part on the work of simulation modeler Alan Pritsker [11], UNOS used the regional perspective as a means of increasing the efficiency of a national system. The focus of the first was on equality among potential organ recipients nationwide; the latter sought to maximize distributive efficiency across the national system. For their part, NIM experts took a similar perspective by recommending that population-based catchment areas replace historical regional assignments.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> My analysis considered the potential relations between supply and demand, location and equality, at a range of scales. This admittedly novel approach was facilitated by the use of Geographic Information Systems (GIS) tools. As a class, these mapping programs use spreadsheets to store, manipulate and organize data applicable at a range of scales that can be projected onto a mapped representation of the world [12]. In this case, GIS permitted a multi-scale analysis involving data on hospital transplant performance, the urban environments that sustain them, the states in which they are located, the UNOS regions themselves, the nation at large, and finally, international data as well. <BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> The ability to consider transplantation at a range of scales simultaneously, and through a range of data sets, suggested inequality was far more embedded in the system than others or I had previously believed. Further, equality and efficiency in transplantation supply and distribution could not be separated from a range of locational, economic and ethnic attributes. Perhaps just as important, I discovered that social and locational inequalities appeared to adversely effect organ donation as well.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=12 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=3><B>Inequalities</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> Because of different ischemia rates for different organs  and different issues of urgency in their collection  I focused in this work only on hearts and heart transplants. In this article I illustrate my argument with data from 1996, the same data used by UNOS and DHHS in their 1998 disagreements over how best to distribute organs. <BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> Illustration 1 presents one way to consider inequalities in heart transplantation at the scale of the UNOS region as it existing in the late 1990s. Using Mean Waiting Time  a measure of time waiting for patients in later stages of heart failure  regional inequalities were determined through an equation weighted by regional populations. By this measure, patients might wait 10 times longer for a viable heart in some regions than in others. Surprisingly, regions with smaller populations  Regions One and Six  seemed to do better than more densely populated areas (Regions Two, Five and Nine, for example). That the former regions had relatively few transplant centres per capita, while the latter populations were far better served made these results even more inexplicable. What was going on? <BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> <IMG SRC="art/koch1.jpg" WIDTH="400" HEIGHT="250" BORDER="0" ALT="Illustration 1 resource allocation organ transplants"><br> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=1><B>Illustration 1 </B></FONT><BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> Illustration 2  the number of heart transplants performed per state  gives the answer. Many states have no transplant program at all. Their citizens must travel outside the state  often hundreds of miles  for service. Because the largest transplant centres are in major cities (Los Angeles, New York, etc.), patients from under-served states typically must fly to different regions for service. A North Dakotan is far more likely to be listed for a transplant in cities whose hospitals do scores of heart transplants a year (Los Angeles or Chicago, for example) than in the relatively small but proximate transplant hospital in Spokane, Wash. <BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> <IMG SRC="art/koch2.jpg" WIDTH="400" HEIGHT="250" BORDER="0" ALT="Illustration 2 resource allocation organ transplants"><br> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=1><B>Illustration 2</B></FONT><BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> Several problems arise as a result. Not the least of these is the failure to provide equal opportunities of service for all citizens in a national health delivery program. Federal law promises equality of service unconditionally, not "only when it is convenient and profitable." It violates the spirit if not the letter of the law to have no transplant program in more than 20 percent of all state jurisdictions while defining transplantable organs as a "national resource" and transplantation as a national health priority.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> Nor will this problem be resolved by the catchment areas based on population proposed by the NIM experts. A redistricting analysis using GIS techniques  including Thiessen Polygons and a redistricting algorithm based on distance  showed that inequalities in local service would be generally maintained in a national solution using population as a basis for organ distribution algorithms. <BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> At a service level, the failure to serve some state populations locally results in an increased demand for service elsewhere. Transplant hospitals in major cities located in populous states (Los Angeles, New York, Pittsburgh) have longer waiting times in part because they also must minister to populations from under-serviced states. This explains why, in Illustration 1, the areas with greater concentrations of service (Regions Two and Five, for example) have longer mean waiting times by population than those (Regions One and Six, for example) with a large number of non-transplant performing states. Even if local donation rates are good in, say California, the organs received must serve citizens from both the local population and that of under-served states. <BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> Finally, the failure to provide reasonably proximate service for all may effect adversely organ donation while increasing organ wastage. UNOS' argument for regionalization rested, in part, on the assumption people are more likely to donate organs if they know people who are organ recipients and live near a facility where transplantation is an accepted procedure. Inequalities in transplant service mean millions of people in under-served areas will be distanced from this "neighborhood effect." If I'm in North Dakota, my interest in contributing to a program operative in, say, Texas or California (or Chicago) will be lessened as a result.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> Even were this not true, practical difficulties arise effecting organ supply. Even when donors are identified in cities like Bangor, Maine, and Bismark, N.D., their retrieval and distribution may be problematic. The time required to bring in an expert surgical team, retrieve the organ and transport it in a timely fashion to a patient in a waiting service center may be a barrier to donation. Health providers in the largely private U.S. system do not uniformly pay for private jet service, more typically using commercial airlines instead to transport donor organs.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=12 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=3><B>Travel Time/Distance</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 general assumption has been that distance can be overcome through air travel. Persons living in under-served states can access transplant programs through commercial air flights to distant hospitals. While this may be expensive, it is a "cost" of rural living. But is air travel sufficient? An analysis of travel times from cities in under-served states (Bismark, N.D., Billings, Mont., Bangor, Maine, etc.) found the window of opportunity for many persons  and thus for donated organs traveling on commercial airlines  surprisingly restricted.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> Some cities  Bismark, N.D., for example  had few commercial air links capable of carrying patients to a transplant hospital within the four-to-five-hour time frame dictated by a donated heart's ischemia rate (Illustration 3). Scheduled flights were limited both in the number of flights per day and in the time those flights departed. Other cites in the same region  Billings, Mont., for example  had better connections and a broader band of travel opportunities.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> <IMG SRC="art/koch3.jpg" WIDTH="350" HEIGHT="272" BORDER="1" ALT="Illustration 3 resource allocation organ transplants"><br> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=1><B>Illustration 3</B></FONT><BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> Obviously, this impacts not only equality of service but also the ability to collect and use organs that volunteers wish to donate. If a perspective donor in Bismark, N.D., has a fatal accident, he or she must be kept alive until transplant teams can be flown to the local hospital. Commercial schedules make this difficult. Then the transplant team and the retrieved organs must be flown to the hospitals where potential recipients await. Again, the limits of commercial air service make this difficult. The result limits the potential to collect and use hearts from under-served regions, and may discourage donation as well.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> While the travel barrier could be overcome through the frequent use of private jets, their chartering adds an extraordinary expense to a medical procedure costing in excess of $300,000. And even were this supported by all health insurers, the likelihood that North Dakota patients themselves would be offered the same jet service is unlikely. The result would be a system that values the donor organ more than the potential recipient. That impacts negatively on the sense of sharing and community that in theory argues for voluntary donation from all citizens.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=12 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=3><B>Health Care/Race</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 an earlier article in this magazine I argued that general inequalities in health care delivery adversely impacted transplantation [13]. Approximately 15 percent of the U.S. population  more than 44 million people  have no health insurance. These are people who, because they do not have regular health care, are more likely to have chronic conditions that would exclude them as organ donors. Millions more have only minimal health coverage that may provide general coverage but will not cover services like transplantation. Citizens from both groups are therefore largely outside the "national" transplant system.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> Remember Ronald Herrick, the twin who wanted to know if his health care needs would be met if he decided to donate a kidney for his twin brother's health? People who have no expectation of service or equal treatment will, like him, be suspicious of participating as donors in a program that effectively excludes them or their families as potential recipients. Thus inequality of service promises to affect not merely efficiency of service for all, but also supply, exacerbating the chronic organ shortage that has plagued transplantation from the start.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=12 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=3><B>National/International Scales</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 ability to incorporate varying scales of data in a single analysis, and to then add varying types of data to the mix, is a fundamental advantage of a GIS, map-based analysis. It also may offer surprising insights. In considering the problem of under-service in areas in the West and Northeast, for example, only the continental United States is typically considered. But if one adds a map of Canada to the mix, a very different picture occurs. <BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> ILLUSTRATION 4 shows what happens when transplant services are regularized across North America. Using a network of Thiessen polygons based on city location and transplant service cites, an interesting pattern emerges [14]. Several under-served areas in the United States are advantaged by their proximity to Canadian service centers. Alaska  typically left out of continental projections  can be incorporated into the Western Canadian service. Indeed, the additional population of Alaska to that of north central British Columbia and Alberta would create a potentially viable transplant service area in central B.C., improving service to all three jurisdictions.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> <IMG SRC="art/koch4.jpg" WIDTH="333" HEIGHT="250" BORDER="1" ALT="Illustration 4 resource allocation organ transplants"><br> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=1><B>Illustration 4</B></FONT><BR> <img src="../cleardot.gif" width=1 height=1 vspace=12 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=3><B>Conclusions</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> What are the lessons of this work? Scarcity is clearly exacerbated by inequalities in this type of distributive system. More generally, scales of analysis and their resulting perspective are critical. Finally, it is important to remember that no one scale is necessarily sufficient. Several scales  and several perspectives (organ supply, equality and efficiency of distribution, etc.)  may be simultaneously operative.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> GIS-based approaches are helpful, and may be critical for some types of projects. But in the end GIS is simply another tool that facilitates the collection, manipulation and presentation of data. What to collect, how it should be manipulated, and what the final projection will be remains the art of the science, not the science itself.<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> <ol><FONT Size=2> <LI> National Organ Transplant Act, Pub. L. No. 98-507; 98 Stat. 2339 (1984). <LI> See, for example, UNOS' "Principles and objectives of equitable organ allocation," online Oct. 18, 2000, at <A HREF="http://www.unos.org/" target="_new">http://www.unos.org/</A> . <LI> Murray, J. E, "Human organ transplantation: Backgrounds and consequences," <I>Science</I>, Vol. 56, 1992; 1411. <LI> R. N. Ehrle, T. J. Shafer, and K. R. Nelson, "Determination and Referral of Potential Organ Donors and Consent for Organ Donation: Best Practice�A Blueprint for Success," <I>Critical Care Nurse</I>, Vol. 19, No. 2, 1999, pgs. 21-36. <LI> Task Force on Organ Transplantation, "Organ Transplantation: Issues and Recommendations," Washington, D.C.: US Department of Health and Human Services, 1986. <LI> Cohen, B. M. and Grochowski, E, "What Transplantation can teach us about health care reform," <I>New England Journal of Medicine</I> (March 24, 1994), pgs. 858-860. <LI> Koch, T., "The Limits of Principle: Deciding Who Lives and What Dies," Westport, Conn.: Praeger Publishing, 1998. <LI> Shalala, D., "Letter from Secretary of Health and Human Services to members of Congress, February, 1998," online May 15, 1998, <A HREF="http://www.unos.org/newsroom/archive%5Fregs%5Fshalala%5F022698.htm" target="_new">http://www.unos.org/newsroom/archive%5Fregs%5Fshalala%5F022698.htm</A>. <LI> Graham, W., "Letter to UNOS Membership," online April 5, 1998, <A HREF="http://www.unos.org/" target="_new">http://www.unos.org/</A>. <LI> Institute of Medicine Committee on Organ Procurement and Transplant Policy, "Organ Procurement and Transplantation: Assessing Current policies and the Potential Impact of the DHHS Final Rule," Washington, D.C.: National Academy Press, 1999. <LI> Pritsker, Alan, "Life & Death Decisions," <I>OR/MS Today</I>; August 1998, Vol. 25, No. 4, pgs. 21-28 <LI> Koch, T, "Mapping the ORMS World," <I>OR/MS Today</I>, August 1999, Vol. 26. No. 4, pgs. 26-30. <LI> Koch, T, "The Transplant Dilemma," <I>OR/MS Today</I>, February 1999, Vol. 26, No. 1, pgs. 22-29. <LI> Koch, T., "Organ transplants without borders,"<I> National Post</I>, (April 2001) pgs. A 13, 30.</FONT> </OL><BR> <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>Tom Koch, Ph.D., is an adjunct professor of gerontology at Simon Fraser University in Vancouver, a research associate in bioethics at The Hospital for Sick Children in Toronto and a forum associate at the David Lam Centre for International Communications, SFU. His book, "Scarce Goods: Justice, Fairness, and Organ Transplantation" (Praeger Publishing, <A HREF="http://www.greenwood.com">www.greenwood.com</A>), will be released this fall.</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> <FONT face="verdana, arial, helvetica" SIZE=1> <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 � 2001 by <A HREF="http://www.informs.org/" target="_new">the Institute for Operations Research and the Management Sciences</a>. All rights reserved.<br> <img src="../cleardot.gif" width=1 height=1 vspace=3 border=0><br> <img src="../bargrey.gif" width=468 height=1 border=0 alt=" "><br> <b>Lionheart Publishing, Inc.</b><br> 506 Roswell Street, Suite 220, Marietta, GA 30060, USA<br> Phone: 770-431-0867 | Fax: 770-432-6969<br> E-mail: <a href="mailto:lpi@lionhrtpub.com">lpi@lionhrtpub.com</a><br> URL: <A HREF="http://www.lionhrtpub.com" target="_top">http://www.lionhrtpub.com</A><br> <img src="../cleardot.gif" width=1 height=1 vspace=3 border=0><br> <img src="../bargrey.gif" width=468 height=1 border=0 alt=" "><br> Web Site � Copyright 2001 by Lionheart Publishing, Inc. All rights reserved. </td></tr></table> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> </BODY>