Operations Research Management Science Today - April 2003

<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> - April 2003</I></B></font><BR> <hr size="1"> <img src="cleardot.gif" width=1 height=1 vspace=4 border=0><br> <IMG SRC="art/Int-OR.jpg" WIDTH="468" HEIGHT="183" HSPACE="0" VSPACE="0" BORDER="0" ALT=" "> <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>International OR</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>Thirsting for Consensus</B></FONT><BR> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <FONT SIZE="+1"><I>Multicriteria decision analysis helps clarify water resources planning in South Africa</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 Theodor J. Stewart</B></FONT><br> <hr size="1"> <img src="../cleardot.gif" width=1 height=1 vspace=12 border=0><br>    This paper reflects more than a decade of experience in applying concepts from multicriteria decision analysis (MCDA) to problems of water resource planning in the Republic of South Africa (RSA).<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> The most important starting point is to realize that the RSA is generally a very dry country. This is illustrated to some extent by the rainfall map given in Figure 1. Approximately half of the land area receives less than 400mm (about 15 inches) per annum. The only areas with substantial rainfalls are over the mountain ranges that form the edge of the higher lying, inland plateau areas. Furthermore, what rain does fall is highly seasonal and concentrated into a small number of intense events (as much of the country only receives rainfall in the form of summer thunderstorms). This results in rapid run-off of the water when rainfall occurs, and in a very high interannual variability (coefficients of variation exceeding 35 percent).<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> <IMG SRC="art/Stewart_Fig1A.jpg" WIDTH="465" HEIGHT="297" HSPACE="0" VSPACE="0" BORDER="0" ALT=" "><BR> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=1><B>Figure 1: Mean annual rainfall (in millimeters) across South Africa, taken from Schulze et al, "South African Atlas of Agrohydrology and Climatology." Reprinted with permission.</B></font><BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> There are no large natural lakes in the country and very few permanent rivers. The natural run-off is already very heavily exploited, and few opportunities for additional large storage dams exist. In any case, the government is sensitive to the ecological damage done by such constructions. South Africa, in fact, hosted the secretariat of the World Commission on Dams, which was also chaired by the previous South African Minister of Water Affairs, Kader Asmal.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> On the other hand, water is a critical resource to the social and economic development that the country desperately needs. This has led to increasing conflict between: <UL> <LI> basic human needs and industrial expansion;<BR> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <LI> subsistence needs of developing areas and first world recreation and ecotourism; and<BR> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <LI> balancing all of the above as well as the needs of the natural environment. </UL> A number of these conflicts will be illustrated by the case study on the North East Cape Forests given later.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> With this as a background, about 1990, the University of Cape Town started a first project, funded by the South African Water Research Commission (WRC) and in collaboration with the national Department of Water Affairs and Forestry (DWAF), to explore the potential role for MCDA in water resources planning.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> Initial literature studies revealed a number of applications of MCDA to water resources planning in many parts of the world, which was encouraging. Closer study, however, and first attempts to apply similar approaches in the RSA, led to some disillusionment. Much of the literature concerned the specific problems of the placement, design and operation of large dams, rather than the broader strategic issues facing the South African authorities. These issues relate to the developing of complete management plans for catchment regions in the country, which might include consideration of dam construction, but would also involve decisions around land uses, broad infrastructure development, inter-basin transfers of water, etc. Central to such strategic concerns would be the conflicts indicated above.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> The bulk of the literature at that time assumed a relatively well-defined, multicriteria decision-making structure, often within the context of a multiattribute utility function framework. Common assumptions tended to include the following: <UL> <LI> that alternatives, or available courses of action, were explicit and well-defined;<BR> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <LI> that the criteria could, to a large degree, be associated with well-defined quantitative attributes;<BR> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <LI> that any conflicts between different group interests could be represented by specific criteria; and<BR> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <LI> that there existed clearly identified decision makers whose values could, in principle, be elicited. </UL> The reality in the emerging South African context was different, especially in view of the rapid political changes happening at that time (the early 1990s). There was deep suspicion of technocratic solutions, and an insistence that there should be grassroots involvement of all stakeholders at all stages of policy evaluation. Political decision-makers required that policy recommendations from project teams should already represent a broad consensus of acceptance from the community.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> Some implications of this changing context were the following: <UL> <LI> Policy decisions needed to consider a broad range of developmental issues apart from purely technical engineering issues (such as dam placement and operation). As a result, alternatives tended to be rather fuzzily defined, for example including policy directives such as "decrease exotic forestry by 15 percent," without stating specific sites or timeframes.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <LI> Different stakeholders had widely divergent criteria, sometimes linked in different ways to the same physical attributes (for example, diametrically opposed preferences regarding the occurrence of floods in rivers).<BR> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <LI> Some criteria (such as community quality of life) could not clearly be linked to specific attributes at all, with substantial resistance from stakeholders to further decomposition and/or statement of preferences in terms of quantitative attributes. </UL> It was not long before the realization emerged that the "classical" multicriteria approach (especially in Multiattribute Utility Theory, or MAUT) of decomposition of problems into more-or-less separate stages of value assessment (construction of the preference model) and of analysis (application of the preference model) would not be workable. This led to the evolution of a rather different mode of thought, as described in the next section.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=12 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=3><B>From MAUT to Scenario-Based Planning</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 multicriteria nature of the problem was, if anything, of greater prominence in the newer context. It had to be accepted, however, that many of the criteria were highly qualitative and intangible in nature. It might have been possible for stakeholders to assert that one course of action better satisfied their aspirations than another, but direct links to quantitative physical measurements were often unattainable. On the other hand, it seemed that some form of value measurement approach had the potential to render widely differing perspectives much more comparable in the search for compromise or consensus.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> In wrestling with this situation, we were influenced by work on decision conferencing and "requisite modeling" [e.g., Phillips, 1984] and the associated view of simple multiattribute value models as described by Belton and Stewart [2002]. The basic idea is to define alternatives to just sufficient a level of detail to allow different stakeholders to at least rank order them in terms of desirability according to each identified criterion. This led to what we called Scenario-Based Policy Planning [Stewart and Scott, 1995], an iterative process of consultation and analysis which can be described in the following terms:<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> 1. Initial problem structuring (with various stakeholders) was directed toward identifying criteria of concern, as well as different "policy elements" (i.e., different interventions or actions that may be possible). With each policy element would be associated a range of options (often represented by a small number of nominal levels). From these we could, in principle, construct a (possibly quite large) number of potential "policy scenarios" (i.e., feasible coherent combinations of policy elements). This construction may be formal or informal.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> 2. Available models (hydrological, economic, etc.) are used to compute relevant quantitative consequences ("attributes") related to identified criteria. These are used as a basis for a pre-screening of the policy scenarios, in order to select a small number for detailed evaluation by stakeholder groups. It is important to keep this number small enough (say "7±2"), as such evaluations would often require direct comparisons of the alternatives under consideration. The pre-screening is itself a multiobjective programming problem, but at this stage we shall not digress into details.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> 3. Intensive decision workshops are held with stakeholder groups (separately or together), aimed at evaluating the scenarios presented. These scenarios would be rated according to each criterion identified earlier, by direct holistic judgement and/or by reference to quantitative attributes where relevant. We have guided these evaluations by asking the groups to order policy scenarios on "thermometer scales," as illustrated in Figure 2. Advantages of the use of thermometer scales in this way are that communication between groups of different levels of numeracy are facilitated, and that by emphasizing the gaps between alternatives, we obtain something approximating interval scales of measurement (justifying later weighted additive aggregation).<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> <IMG SRC="art/Stewart_Fig2.jpg" WIDTH="223" HEIGHT="300" HSPACE="0" VSPACE="0" BORDER="0" ALT=" "><BR> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=1><B>Figure 2: Illustration of a "thermometer scale" for comparison of policy alternatives according to a single criterion.</B></font><BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> 4. Any inability to reach reasonable consensus on rating for one particular criterion indicates either a lack of clarity in defining the criterion or a need for more detail in defining scenarios (perhaps introducing additional policy elements). This leads to a refinement of the problem structure, and possibly a re-definition of policy scenarios for further consideration.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> 5. Conventional value measurement approaches can often be used to develop value trees for each interest group, and to do some form of weighted aggregation to achieve a ranking of alternatives from each group's perspective. These can be placed side-by-side for comparison and inter-group communication. Further use of the value function model to aggregate across interests can sometimes generate useful information if the group preferences are not too dissimilar. With or without the highest level aggregation, it is usually clear that certain policy scenario options would need to be eliminated if there is to be any hope of consensus. Typically, the remaining scenarios then need to be extended or replaced by two or three different refinements.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> 6. The process is strongly iterative. Typically, at least three rounds of workshops would need to take place, before two or three policy scenarios with sufficiently broad acceptability emerge.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=12 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=3><B>Case Study: North East Cape Forests</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> Some of the highest rainfalls in the country occur along the eastern escarpment areas, where high mountains separate the eastern coastal plains from the interior plateau areas. Runoff from this rainfall provides for much of the water needs in many surrounding regions.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> Over most of the escarpment the natural ecosystems are based on grasslands (afro-montane grasslands). The country has very little natural forest, but the escarpment areas are well-suited to the cultivation of commercial forestry, based on exotic trees (mainly pines and eucalyptus). The resulting timber industry is economically important, both to the country as a whole and in providing employment locally. However, commercial forestry comes into potential conflict with environmental concerns and with the needs of downstream water users. One of the ironies here is that in South Africa, the planting of exotic trees where they should not be often causes more widespread environmental damage than the clearing of natural forests!<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> We were invited to contribute to the evaluation of a number of possible strategies for the development of such commercial forestry in an area of the northern parts of the Eastern Cape Province. Figure 3 provides an indication of the geographical location of this area.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> <IMG SRC="art/Stewart_Fig3.jpg" WIDTH="465" HEIGHT="494" HSPACE="0" VSPACE="0" BORDER="0" ALT=" "><BR> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=1><B>Figure 3: Commercial forestry areas in the North East Cape</B></font><BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> The background to this case study was that a private company, North East Cape Forests (NECF), had acquired or had options on 75,000 hectares of land over an 80-kilometer stretch of the southern foothills of the Drakensberg Mountains. By the time of the study, NECF had planted about 38,000 hectares of forests (mainly pines), some on old grazing lands, and others on virgin afro-montane grasslands.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> Fuller details of this case are described by Stewart and Joubert [1998]. In brief, however, some of the key issues were the following. <UL> <LI> The company had asserted that the 38,000 hectares was sub-critical, and thus not sustainable economically.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <LI> There were increasing concerns about the need to conserve the rapidly decreasing afro-montane grassland biomes, and this had led to an extensive World Wildlife Fund-sponsored study in the region.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <LI> In terms of the law, any planting of forests required a permit from the National Department of Water Affairs and Forestry (DWAF), who were required to take all aspects of the conflict into consideration. NECF was becoming concerned at the slowness of DWAF in issuing permits. </UL> We were invited by NECF to facilitate workshops, bringing together the various stakeholders. Our original brief was to assist the group to develop decision rules for the issuing of permits, so that decisions could be made more quickly and transparently. As we guided the group to identify the relevant criteria and the impacts of different affore-station policies on these, it rapidly became clear that it made no sense to talk of decision rules for individual permit allocations without first developing a regional affore-station plan (thus foreshadowing the National Water Act of 1998, as described in the next section).<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> Once the permit allocation problem was seen in the context of a regional plan, the entire process quickly became an application of SBPP as previously described. Another two decision planning workshops were to take place, involving NECF, DWAF, national and provincial nature conservation groups, local councils (concerned with socio-economic development, and in one case represented directly by the mayor), and hydrologists (concerned with downstream water users). It turned out to be possible to involve all stakeholders in a single workshop setting, which assisted greatly in improving levels of understanding between groups.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> Initially, the key policy elements were identified as the extent of land to be covered by commercial forestry (ranging between 38,000 and 70,000 hectares), and the mode of processing to be undertaken (i.e., saw mills; a centralized pulp mill or transport of logs to other regions). This led to the definition of six policy scenarios, including the status quo.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> At the next workshop, two of the six scenarios were eliminated. In the process of evaluating options against the criteria, it became evident that greater detail would be needed regarding the location as well as the extent of areas to be afforested. Without such specifications, it was clear that consensus on rankings even within single criteria could not be achieved. As a result, a further policy element was identified, so that any expansion of areas under forestry would be permitted either <I>with</I> or <I>without</I> restrictions on developments in areas of high biodiversity or endemicity, as determined by a team of environmental specialists.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> With this further policy element and the consequently enhanced set of policy scenarios, the final workshop did in fact reach a broad consensus on the most desirable option (maximum extension of forestry, subject to conservation restrictions, with a single pulp mill in the area). This conclusion was subjected to extensive sensitivity analysis of the value function models. This analysis revealed the effective tradeoffs between conservation and economic goals (i.e., by how much profits would have to be reduced by the imposition of the land use restrictions, before the indicated solution would change).<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> The results of these workshops and the associated decision analysis were not binding on DWAF. Nevertheless, many of the participants in the workshops were involved in the final permit allocations that did not differ greatly from the above conclusions.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=12 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=3><B>The National Water Act of 1998</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 continuing application of the simple multicriteria decision analysis embodied in the SBPP process received a boost from the promulgation of a new National Water Act (Act 36 of 1998). An important aspect of this act was that it mandated the involvement of affected communities in the development of regional water development plans and in classifying of rivers by conservation status. Furthermore, the act required that in the exploitation of national water resources, a number of factors had to be taken into account, including basic human needs, redressing past discrimination, social and economic development, environmental protection and human safety.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> These requirements of the Act implied the need for mechanisms to involve all sectors of the community in strategic planning of water resources and to take into account a wide diversity of interests ("criteria"). The use of MCDA terminology became widespread in discussions on water resources planning, and there was a recognition in some quarters (e.g., management of the Water Research Commission, as expressed at project steering committee meetings) that our earlier work had largely anticipated the requirements of the Act.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> On the other hand, the promulgation of the Act also provided new challenges to the implementation of MCDA. These included: <UL> <LI> The need to adapt the scenario based policy planning concepts to the development of performance indices (e.g., of river quality or conservation status) rather than to evaluate specific policy actions directly. The SBPP mode of thinking did, however, provide a means by which such indices could be made operationally meaningful and placed in a realistic context.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <LI> The need for greater interaction and collaborative work with other disciplines involved in water resources planning, such as resource economists, as part of multidisciplinary teams in the spirit of early OR. </UL> An important advantage of the MCDA-based approach is that it avoids the need for an explicit reduction of all costs and benefits to monetary scales. In societies in which there is an extremely large gap between rich and poor, and in which some communities still exist in a subsistence-farming context, serious questions must be raised concerning the validity of such reductionism. There is a substantial potential for bias against the poor, in the sense that the rich may be prepared to pay more for luxuries than the total disposable incomes of the poor have available for necessities. Comparisons of alternatives directly in terms of each criterion can be carried out on a "level playing field."<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> On the other hand, the implementation of MCDA does generate implied trade-offs between naturally financial criteria and the more qualitative, less tangible concerns of society. Such trade-offs are frequently found to be highly nonlinear, varying sometimes by orders of magnitude across ranges of possible outcomes. The trade-offs generated in this way may be compared with other forms of contingent valuation say, and used as a check on absurd conclusions.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> Since the implementation of the new Act, we have been involved in a number of further studies, including an evaluation of water supply and demand options for the City of Cape Town (our first major involvement in an urban, rather than rural, water resource planning exercise), and land use planning for catchments in the KwaZulu-Natal Province.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=12 border=0><br> <FONT face="verdana, arial, helvetica" SIZE=3><B>Some 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> Reflecting back on the experiences of the last decade or more of involvement with water resource planning in South Africa, we believe that the use of MCDA in this context has demonstrated a number of valuable advantages. Our approach has been based primarily upon value measurement, but many of the advantages derive more from the formal structuring in MCDA terms, so that similar benefits may accrue from using other methods of MCDA [Belton and Stewart, 2002].<BR> <img src="../cleardot.gif" width=1 height=1 vspace=6 border=0><br> These advantages include the following: <UL> <LI> MCDA provides a mechanism and a level playing field for involving all stakeholders, from a wide variety of backgrounds and cultures, in the process of water resource planning.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <LI> MCDA provides a means whereby qualitative and quantitative criteria can receive equal attention, without the necessity for reduction to monetary scales.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <LI> MCDA identifies the level of detail that is or is not necessary in defining strategic options, in order to allow groups to reach consensus.<BR> <img src="../cleardot.gif" width=1 height=1 vspace=2 border=0><br> <LI> MCDA reveals where major conflicts may hinder the achievement of consensus, and is essentially constructive in developing newer policy scenarios in this case. </UL> Although this work has been carried out primarily within the context of water resources planning, there is every reason to believe that SBPP process can contribute to other natural resource planning problems, especially where there are wide divergences between stakeholder groups.<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> V. Belton and T.J. Stewart, 2002, "Multiple Criteria Decision Analysis  An Integrated Approach," Kluwer Academic Publishers, Boston. <LI> L.D. Phillips, 1984, "A theory of requisite decision models," <I>Acta Psychologica,</I> Vol. 56, pgs. 29-48. <LI> R.E. Schulze, M. Maharaj, S.D. Lynch, B.J. Howe and B. Melvil-Thomson, 1997, "South African Atlas of Agrohydrology and  Climatology," University of Natal, Pietermaritzburg <LI> T.J. Stewart and L. Scott, 1995, "A scenario-based framework for multicriteria decision analysis in water resources planning," <I>Water Resources Research,</I> Vol. 31, pgs. 2,835  2,843. <LI> T.J. Stewart and A. Joubert, 1998, "Conflicts between conservation goals and land use for exotic forest plantations in South Africa," in E. Beinat and P. Nijkamp, editors, "Multicriteria Analysis for Land Use Management," pgs. 17  31, Kluwer Academic Publishers, Dordrecht.</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><B>Theodor J. Stewart</B> is a professor in the Department of Statistical Sciences, University of Cape Town, South Africa.</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</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 © 2003 by <A HREF="http://www.informs.org/" target="_new">the Institute for Operations Research and the Management Sciences</a>. 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