Multi-criteria Decision Making (MCDM) Techniques in Planning

Multi-criteria Decision Making(MCDM) Techniques in

Planning..

BRYAN H. MASSAM

Department ofGeography, York University, 4700 Keele Street,North York, Ontario M3J IP3, Canada

PERGAMON PRESSOXFORD . NEW YORK . BEIJING . FRANKFURT

SAO PAULO' SYDNEY· TOKYO· TORONTO

JPP 30:1-A

This monograph dedicated to my parents Florence and Richard

Progressin Planning, Vol. 30, pp. 1-84, 1988.Printed in Great Britain. All rights reserved.

Contents

Abstract

Acknowledgements

1. Overview of Literature1.1. Introduction1.2. MCDM and Related Fields1.3. MADM, MODM, MAUT, PCT1.4. Toward a Generic Planning Problem

0305-9006/38 $0.00+.51.Copyright © 1983 Pergamon Press pic

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2. Components of MCDM Problems2.1. Introduction2.2. The Three Components: Plans. Criteria, Interest Grou;2.3. Scores and Impact Values2.4. Standardization ofRaw Data2.5. Benchmarks and Ideal Plans2.6. Errors in the Estimation ofScores and Impacts2.7. Dealing with Criteria2.8. Summary

3. Survey of MCDM Techniques3.1. Introduction3.2. Lexicographic Ordering Methods (LOM)3.3. Graphical Approaches3.4. Consensus Maximization Approaches

3.4.1. Borda-Kendall method3.4.2. Toward an axiomatic approach3.4.3. Cook and Sieford distance method3.4.4. Some problem areas

3.5. Additive Models3.6. Concordance Methods3.7. Conclusions

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4 Progress in Planning

4. Selected Practical Problems4.1. Introduction4.2. Site Selection Problems

4.2.1. The location ofhealth centres in Zambia4.2.2. The fire station location problem in North York. Canada

4.3. Route Alignment Problems4.3.1. Motorway in France(Bourges-Montlucon)4.3.2. Interstate highway in Georgia, U.S.A.

4.4. Priority Rating Problems4.4.1. Paris subway station renovations4.4.2. Ontario transportationprojects

4.5. Conclusions

S. Planning and MCDM Techniques

Bibliography

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Abstract

This monograph provides an introduction, a review and a critique of multi-criteriatechniques as used in the resolution of planning problems. It argues that thetechniques allow information on planning goals and objectives to be converted intoevaluation criteria and to be brought into a framework that incorporates the opinionsof interest groups. A review of the literature suggests that multi-criteria decision making(MCDM) techniques have been developed mainly in operations research, though socialpsychology, regional science and business management also offer useful contributions.With the continuing interest among planners on evaluation techniques it is appropriatethat the MCDM work be closely scrutinized to inform debates on improvements toplanning processes.

In order to discuss the utility of the techniques for planners a generic planningproblem (GPP) is defined. This involves the evaluation of options, using multiplecriteria and different opinions of interested parties. Alternative objectives are alsoconsidered. The basic features of the major classes of MCDM techniques are discussedwithin the framework of the GPP and the fundamental assumptions and datarequirements of the techniques are outlined in non-technical language.

To give a better understanding of the role of the techniques in planning a set ofempirical case studies is included. Three types of problem are considered, first, the siteselection problem, second, the route alignment problem and third the priority ratingproblem given a large number of options and a fixed budget. In conclusion the authorargues that recognition of the complexity of the milieu within which planning occursmeans that the search for an ideal formal MCDM technique to solve planningproblems is a chimera, but their role in helping to enlighten and organize choiceamong planning options is important. Also included are criteria for judging anMCDM technique and comments on the thorny issue of determining what is meant bythe quality of planning.

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Acknowledgements

Some twenty years ago I worked in La Direction Scientifique of SEMA-METRA inParis and it was there that I met Bernard Roy and was introduced to multi-criteriadecision-making techniques. During the intervening years I have followed with greatinterest the attempts which have been made to refine and apply the techniques topractical planning problems. Particularly I have been concerned about the lack ofcontact among theoreticians and practitioners, and this has provided the mainincentive for this monograph, namely to try to bridge the gap between these twosolitudes.

lowe a number of debts of gratitude for help in the preparation of this manuscript.I will not try to enumerate the precise amounts lowe other than to say a sincere thankyou for the hospitality, informal chats, detailed comments, advice, criticisms,references and encouragement that was offered to me. My thanks extend to colleaguesand friends in Australia, Canada, France, Israel and the United Kingdom and includein alphabetical order, Colin Adrian, Ian Askew, Wade Cook, Derek Diamond, BarryGarner, Andrew Karski, Nurit Kliot, Mal Logan, Toni Logan, Lionel Lawrence,Virginia Maclaren, Jean Marchet, Brian McLoughlin, Jim Micak, Bernard Roy, ArieShachar, Jean Siskos, Ian Skelton, Bob Snowdon, Stanley Waterman and Don Webb.

Also, I am particularly grateful to the Planning Group under James Balfour, at M.M. Dillon (consulting engineers, planners, environmental scientists), Toronto, Canada,for our discussions regarding the use of MCDM techniques.

I alone bear responsibility for the contents of this monograph, the opinions and theconclusions.

Partial financial support was provided by the Social Sciences and HumanitiesResearch Council of Canada, and the Joint Program in Transportation of TheUniversity of Toronto and York University and the Faculty of Arts, York University,this is gratefully acknowledged.

Florence Davies and Agnes Fraser typed the manuscript and the figures were drawnby the staff in the Cartographic Laboratory at York University - many thanks.

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CHAPTER 1

Overview of Literature

1.1. INTRODUCTION

This monograph provides an introduction, a review and criticisms of a selection ofmulti-criteria techniques. The focus of attention is on the utility of the techniques asthey serve to help in the resolution of planning problems. In general we suggest thatthe techniques allow infonpation on planning goals and objectives to be convertedinto evaluation criteria and to be brought into a framework that incorporates theopinions of interest groups. The overall purpose is to improve the quality of planning;we will address the problem of defining what is meant by the quality of planning in alater section. For the purposes of this monograph we will refer to the techniques asMulti-Criteria Decision Making (MCDM) techniques. A review of the literaturesuggests that to a large extent they have been developed in operations research, thoughother fields including social psychology, regional science and business managementoffer useful contributions. An extensive list of 92 journals reporting this type of workhas been compiled by Hwang and Yoon (1981), however, probably only a smallpercentage of these journals will be closely familiar to planners.

It was in 1972 that the first international conference on MCDM was held andZeleny (1984) suggests that it was at this meeting, which was convened at theUniversity of South Carolina, the new, previously-unorganized, field of MCDM wasofficially launched. A summary of the papers presented at this conference is containedin the book: Multiple Criteria Decision Making, which was edited by Cochrane andZeleny (1973). The decennial MCDM meeting was held under the auspices andsponsorship of the American Association for the Advancement of Science inWashington, D.C. The field is growing and gaining support from many quarters as isclear from even a casual glance at the 1700 references on MCDM listed in Zeleny's(1984) edited sourcebook on the subject, and perusal of the two Special Issues onMultiple-Criteria Decision Making which were published in 1986 in the EuropeanJournal of Operational Research. In a review article Vincke (1986) documentsconvincing evidence to support his claim that MCDM research has been one of thefastest growing areas of Operational Research in Europe during the last fifteen years.

This monograph is organized into five chapters. The first one will set the scene forunderstanding why MCDM techniques may have a role to play in planning activities.We will cast the net broadly here to offer general statements about planning problemsand offer specific comments on the development of the fields which have given rise to

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MCDM techniques. We will seek to identify a generic planning problem within thecontext of a planning process recognizing that most planning processes are conflictresolution situations of one sort or another. Given that one of the aims of thismonograph is to demonstrate the practical use of the techniques, we wish to avoidproviding a generic problem which is too vague or abstract.

The second chapter will include basic descriptions of the data requirements and theunderlying principles used in MCDM techniques. We will also provide a checklistwhich can help judge the worth and utility of a technique. While the application of thischecklist can be changed to suit particular planning problems we envisage that theitems included will cover most cases. In Chapter 3 we will focus on a discussion of aselection of MCDM techniques. We will avoid esoteric details of algorithms whichmay detract the reader's attention from obtaining an appreciation of the basicprinciples and assumptions of the techniques. However, some detail must be providedso that the analyst, planner, or interested decision-maker is not left with just a list ofreferences without appropriate operational definitions or practical applications. It is inChapter 4 that a small set of empirical planning problems will be treated using selectedMCDM techniques. The problems will be selected to demonstrate the variety of actualplanning problems which are covered by the generic planning problem. In the finalchapter we will offer an assessment of the MCDM techniques as they could or shouldbe used in planning, and given that many share a concern with improving planning wemust tackle the question of judging how successfully a particular planning processoperates. This topic will form part of Chapter 5.

1.2. MCDM AND RELATED FIELDS

The study of MCDM is closely related to other topics, for example, Multi-AttributeDecision Making (MADM), Multi-Attribute Utility Theory (MAUT), Multi-ObjectiveDecision Making (MODM) and Public Choice Theory (PCT). Authors who havereported on these topics include Keeney and Raiffa (1976); Zeleny (1975); Thiriez andZionts (1976); Bell et al. (1977); Nijkamp (1979); Nijkamp and Spronk (1981); Rietveld(1980); Hwang and Yoon (1981); French et al. (1983); Voogd (1983); Linstone (1984)and Fandel and Spronk (1985). Nijkamp and Spronk (1981) suggest somewhatoptimistically that, "multicriteria analysis appears to be becoming a new mode ofthinking for decision-making, planning theory, choice analysis and conflictmanagement," however they add the important caveat; "it occurs too often that thosedesigning new techniques ... are hardly aware of the varying needs and desires of thepotential users of these techniques" (p. 1.). Bell et al. (1977) admit that "the analyticaltools that were developed to aid decision makers facing complex problems originallyaddressed only single-objective problems ... the artificiality and restrictiveness of thatapproach for most real world problems has led to the development of various methods

Multi-criteria Decision Making 11

for handling multiple objective problems". A note of caution and realism has beenadded by Batty in his article in Rationality and Planning edited by Breheny and Hooper(1985). Batty indicates that formal rationality models may be too restrictive in dealingwith complexity for they tend to impose order where there may be no order. This is aview shared by Radford (1980). He is critical of the use of formal decision analysisapproaches for tackling plan evaluation problems and he argues that neither of thetwo most important approaches to organization decision-making, namely the rationalcomprehensive style or the incremental approach is entirely satisfactory. It seems toRadford that the mixed scanning approach propounded by Etzioni (1967) embodies afundamentally new idea, for instead of regarding the conceptualization of a decisionproblem as given in terms of alternatives and outcomes, it views this conceptualizationas an active process engaged in by decision-makers. Perhaps this can be stated moreforcefully as the consensus-building approach. This of course recognizes that complexdecision problems of plan generation, evaluation and selection do involve problems ofdesigning and judging alternatives, but Radford (1986) argues this takes place withinthe context of long-term strategies and shorter-term tactics. With this in mind he hasattempted to elaborate on a strategic-tactical model which could be applied to planevaluation, selection and implementation exercises.

In the 1970s decision analysis was offered as the rational way to tackle a wholerange of choice problems. Bell et al. (1977) suggested that "the aim of decision analysisis to decompose a problem into two parts: one to indicate the probabilities of differentpossible consequences of each alternative and the other to evaluate the desirability ofthose consequences". This seems a perfectly reasonable and sensible way to proceed aslong as all the necessary data can be obtained and there is agreement among all partiesregarding the alternatives and their consequences. Rarely are these demandingconditions satisfied. At this point we should remind ourselves of some of Hardin'swork (1984) on the Tragedy of the Commons problem. He argues that while technicalsolutions to choice problems may always be welcome it is clear that there is a class ofreal problems which can be defined as "no technical solution problems". This is oftenthe situation in planning in which individual or group interests compete with those ofthe whole society or collectivity. The dilemma these conflicts pose is taken up byHollis et al. (1985) and others and we discuss it later in this chapter.

It seems clear that the distinctions among the four areas, MODM, MADM, MAUTand PCT, while conceptually significant, are probably less important when weconsider that they are all related to the generic planning problem. This problem can becharacterised initially as follows:

Given a set of alternate plans, each characterised by a set of assessments for selected criteria, and aset of interest groups whose opinions regarding the selection of criteria and the assessments have tobe considered, provide an appropriate procedure to define the attractiveness of the alternate planswith a view to identifying the best one.

Later we will look at the two sub-problems which are contained within this large oneand then we will restate the above problem as a single generic planning problem(GPP). At this stage we will avoid the thorny tasks first, of offering formal definitionsof the terms in the statement, and second, placing the problem into the broader socio-


political context of a society. Both of these items will be taken up later. We suggestthat many practical planning problems can be accommodated by the GPP and thus itshould be appealing to practitioners who are less concerned with the esotericcharacteristics of each of the four related areas. Comments on each of the four areasare provided further on in this chapter. Ideally we would like to offer a format for aplanning process which would allow all these approaches to be integrated, howeverthis is probably an unrealistic goal, therefore it seems more appropriate to restrictattention to providing suitable descriptions of the principles of MCDM techniques sothat clients can make judicious selections to suit their particular purposes.

At the outset it shouldlbe made clear that we do not intend to argue that aparticular technique exists which will provide the definitive solution to a planningproblem, and that this solution must be implemented. We do however subscribe to theview that the process of organizing information as an integral part of a technique canserve as a valuable part of a planning exercise. While a technique might offer insightsregarding the information; the interpretation of the results depends upon the valuesand attitudes of those who examine the technical results. Keeney (1981) makes thiscase very clearly:

There is no such thing as an objective value free analysis. Furthermore, anyone who purports toconduct such an analysis is professionally very naive, stretching the truth, or using definitions ofobjective and value free which are quite different from those commonly in use.

He goes on to add that a logical systems analytical framework is needed that makesexplicit the necessary professional and value judgments. The element in the planningprocess which is lacking is the ability to integrate.

What has been lacking is not information but a framework to integrate and incorporate it with thevalues of the decision makers to examine the overall implications of each alternate [plan].

It could be contested that it is indeed information which is lacking, because without itthe planning process is piecemeal.

The credibility and legitimacy of MCDM techniques will surely be enhanced if thebasic principles are clearly understood by planners and those who may be affected byplanning decisions and if these principles accord with the wishes of the planners andsociety. In this monograph we wish to highlight the basic principles and offer someguidelines which could serve to help in the application of the techniques to tacklespecific problems. Greater emphasis will be placed on identifying the basic principleswhich planners should be aware of when applying the techniques and less emphasiswill be given to discussing the technical details. Also we will focus attention on thosetechniques which appear to have practical appeal because the data requirements arereasonable, the internal logic appears comprehensible and the results likely to offerinsight to complement professional judgement and intuition. These points will beelaborated on later when we provide a checklist for assessing the worth of anyparticular technique.

The so-called quantitative revolution in the social sciences of the 1960s spawnedapplications of formal numerical, algebraic, geometrical, statistical and systemictechniques to a variety of planning problems (Lee, 1973; Krueckeberg and Silvers,


1974; Bernstein and Mellon, 1978; Wilson, 1974; Wilson and Kirkby, 1975; Batty andHutchinson, 1983). In toto this gave rise to a movement which encouraged the use ofmathematics. However, there seems to be some confusion on this score, for while it isthe case that some of the tools used by mathematicians were cited as being useful,there have been very few applications of specific axioms, theorems and formal proofsto planning problems.

In order to place the MCDM techniques into a broader quantitative framework wecan identify three types of work which characterise formal numerical approaches.

(1) Models using inferential or descriptive statistics.(2) Models based on systems analysis or mathematical programming.(3) Models based on data base management techniques and information systems.

Elements from all of these could well form part of MCDM techniques and it isassumed that the student of MCDM will have some knowledge of these threeimportant areas.

Some have argued that the technocratic approach to plan evaluation (Self, 1975) islimiting as it tends to reduce choice problems to naive data sets without explicitappreciation of political values and the role of interest groups. Perhaps more damningcomment is offered by others who believe that the technocratic thrust blinds us to thereal problems of society which can best be understood by examining social structures,the role of states, politics, legislative instruments and modes of production. Let us notfall into the trap of building a fence around the MCDM techniques, rather we ask thequestion: can we use such techniques to help in the provision of commentary onmatters relating to effectiveness, efficiency and equity as they relate to planning modesand the outcomes of planning practices.

In a very useful review by Healey (1986) of the recent writings of David Harvey, shedraws attention to comments contained in Harvey's The Urbanisation of Capital (1985)which show "how planners are drawn into the task of managing change in the builtenvironment in order to facilitate production, circulation, exchange and consumption.In doing so, they are caught in the crossfire of the conflicts inherent within andbetween these processes. He [Harvey] highlights the significance of the concepts ofsocial balance, planning for people's welfare, and open decision-making as necessarysupports to interventions which have to be seen as legitimate to diverse and conflictinginterests". Healey goes on to argue that "Harvey demolishes the Aunt Sallies of manycritics of planners as narrowly technocratic, evangelistic bureaucrats, mere lackeys ofcapitalism, or naive social engineers". To substantiate this view the followingquotation is used.

. . .the fusion of technical understandings with a necessary ideology produces a complex mix withinthe planning fraternity of capacity to understand and to intervene in a realistic and advantageousway and capacity to repress, co-opt and integrate in a way that appears justifiable and legitimate(Harvey, 1985, p. 178).

At best we hope that the techniques we discuss will help clarify particular planningproblems by assisting decision-makers, analysts and the public to define feasiblealternate solutions, and to evaluate these as systematically as possible in order to seekan acceptable solution for implementation. This approach firmly places the techniques


into the context of a continuous heuristic planning process which involves theidentification of needs and resources as well as political realities of allocation choices.While it is not our purpose to elaborate on the complex milieu within which planningoccurs, it is clear that one of the pressing problems in the profession has arisenbecause of the gap between the work of theoreticians and practitioners. Therefore oneof the purposes of this monograph is to describe basic features of MCDM techniques,encourage theoretical improvements, and to demonstrate to practitioners that thesetechniques may assist in the search for solutions to their specific planning problems.Thus we hope to try to bridge the gap, or at least put in place some connecting linkswhich can be reinforced later. We argue for complementarity of action withoutprejudice regarding the merits of either theoretical or practical work. As the state-ofthe-art of techniques changes, so student and professional planners need to beinformed, and those who try to make improvements need to be aware of the problemsof applying the existing techniques. The pursuit of scholarly goals demands that wecontinue to seek new ways of defining and solving problems, and society canlegitimately ask that advances and benefits of new ideas be incorporated intoorganizations, such as local governments or planning agencies. Certainly in the privatesector, techniques are scrutinized to assess their contributions to the improvement ofthe effectiveness or efficiency of the organization, as well as the competitive edge ofthe firm. Obviously a planning company must be concerned with the costs and benefitsof using a new technique and the possible effects on their business. In the public sectorthe planning and implementing bodies will look at the techniques with a view tojudging their contributions to enhancing the effectiveness and efficiency of theplanning process, also consideration will possibly be given to questions of equity, andunder certain circumstances to expediency. For these reasons we suggest that it istimely that students and practising planners enhance their awareness of some recentadvances in these new techniques. It is clear that the techniques while they mayeliminate spurious conclusions, speed up the planning process, and involve opinions ofa variety of interest groups, they do not necessarily avoid conflicts among proponentsand opponents of plans. Neither are the techniques abstractly objective; the task ofmaking the techniques operational demands that opinions, preferences and choices beexpressed. This exercise of expression may assist in the elucidation of otherwise vagueand nebulous elements which intuitively some may argue should be a part of theplanning process. The implementation of a plan, the adoption by users, the decision topostpone action involve choices and possibly negotiations, arbitration and the use ofthe law. The MCDM techniques have little or no direct role in this phase of theplanning process, though they may serve in any monitoring exercise. Only occasionallyhowever is on-going monitoring of a plan's performance a major feature of theplanning process. This is perhaps particularly true in the case of the public sector withrespect to urban plans for example. It is probably much less the case when we turn tocorporate planning and this is hardly surprising given the nature of public and privateenterprises. Whereas the former typically involves many interest groups, and a numberof objectives, the latter may have a narrow set of interest groups, possibly just themanagement board or the investors and a restricted set of objectives, all focusing uponprofitability for instance.

·Multi-criteria Decision Making 15

1.3. MADM, MODM, MAUT, PCT

If the planning problem is to evaluate a finite feasible set of known alternatives andto select the best one, given that each alternative is characterised by scores for a set ofattributes, then this is generally known as the MADM problem. However, if theproblem is to define the set of alternatives given a series of objectives which act asconstraints and/or goals, and then to find the best one, this is usually referred to asthe MODM problem. It is this latter problem which typically is tackled usingmathematical programming. As Zeleny (1984) has recently noted:

Operational sciences (operations research, management science, decision science, systems analysis)have devoted most of their history to problems characterised by a single, aggregate criterion ofchoice. They dealt with problems of measurement and search in connection with simple problems oflimited practical interest. All decisions, public and private, individual and collective, are characterisedby multiple, apparently conflicting criteria .... In very few problems of interest we find a single,preemptively important criterion of choice. Individuals and their organizations face multipleobjectives, attributes, goals and criteria, .... Decision makers, in public and private institutions aswell as in the government, have to learn to work with multiple and parallel criteria of choice ...(p. xii).

Both MADM and MODM conventionally begin by assuming a single decisionmaker, or at least a unified set of opinions, regarding the relative importance of theattributes, objectives and goals. Clearly the process of estimating the scores andmeasuring impacts is fraught with difficulties, and perhaps the best we can do is toassign some probability values. If this approach is adopted then the problem can berecast as one which seeks to evaluate the expected utilities of the alternatives and to tryto identify the alternative with the highest expected utility value and define this as thebest one. This is usually referred to as the MAUT problem. It has been extensivelydescribed by two of its proponents, Keeney and Raiffa (1976), as an appropriate wayof aiding in a decision process. Vincke (1986) suggests that MAUT is "the privilegedapproach of American researchers in multicriteria analysis but is much less used inEurope, except by the economists for whom utility theory is a classical tool". Wemight further remark that the French and Dutch schools have placed considerableemphasis on MODM and MADM research.

It is clear that the major thrust of most researchers who have tackled these threeclasses of problem is to provide an enlightened approach to decision-making. RecentlyMidgley and Piachaud (1984) offer the view that:

Although it is recognized that planning techniques [such as MCDM techniques] have manylimitations ... , we believe that they are helpful aids to policy-making which enhance objectivity andefficiency. To reject their use is to legitimise Machiavellian tendencies and traditionalism inorganisational politics and to deny the need for greater rationality in decision-making (p. 6).

While we need not subscribe to their view that rejection of techniques suggests supportfor Machiavellian approaches we do believe that the development of open decisionmaking processes which use information rigorously may help to lead to expeditiousplanning and the avoidance of planning disasters. As Hall (1980) has pointed out thestory of planning disasters, while they make fascinating journalism, should also leadtowards improved planning, and it is with this in mind that the latter part of Hall's


book is devoted to a review of procedures which may be able to accommodateuncertainty regarding outcomes, as well as handling the varied interests of parties whoare involved in a planning process.

The fourth area referred to earlier is Public Choice Theory (PCT); this examines thegeneral problem of finding appropriate ways to incorporate the views and opinions ofindividuals, about alternatives, into a constitution which seeks to maximize thesatisfaction of the collectivity. While it can be demonstrated that the ideal constitutionis a chimera, we recognize that opinions of different interest groups have to beincorporated into the planning process. The dilemma facing those who seek to provideappropriate ways to tackle public choice problems stems from the results whichanalysts have provided. Put simply, we find that for certain classes of choice problemthe cooperative approach among interest groups will yield the best overall outcome,yet such cooperation appears to be an anathema to man as a social creature if selfinterest or even so-called enlightened self-interest dominated. This point is neatlysummarised by Hollis et al. (1985).

Ever since the collective action problem was first identified theorists have been puzzled by theparadox that recommending the apparently rational course of action leaves people worse off thanthey need be .... The collective action problem belongs to a wider set of decision problems in whichthe dominant choice leaves individuals worse off than they need be.

So troubling is this result that Hollis and his colleagues argue "that to explain howcollective actions problems are solved is one of the greatest challenges to socialscience". In a recent article in Scientific American, Blair and Pollak (1983) review thecontributions of Arrow and his analytical work on the search for an ideal constitutionto provide the best choice for society while taking into account the views ofindividuals. The results are well known so only a brief summary is offered here. Blairand Pollak note that:

Three widely shared objectives - collective rationality, decisiveness and equality of power - standin irreconcilable conflict ... there is little comfort here for those designing ideal procedures forcollective choice. Nevertheless, every society must make collective choices and devise votingprocedures, however imperfect they may be.

We cannot shy away from trying to make evaluations of alternate plans, and whilevery few jurisdictions attempt to offer any kind of formal voting procedure to elicitopinions on particular plans, most jurisdictions have, in place, processes which involvepublic participation. This may occur informally by pressure groups and the media forexample, or via the courts or other formal bodies empowered to solicit opinions andrender judgement. Arbitration, negotiations and bargaining as well as the use oflegally enforced sanctions often characterise part of the process of plan evaluation andimplementation. Surprisingly there appear to be very few attempts to incorporate thecosts of implementation into the formal plan evaluation exercise. A naive effort hasbeen made by Schlager (1968) who suggested that the evaluation should include asimple probability factor to estimate the chances of a plan being acceptable. Othermore detailed efforts have been made by Wolpert and his students at the University ofPennsylvania in the early 1970s [see for example Mumphrey et al. (1971)]. Theyattempted to develop a procedure to identify the least-cost implementation plan taking


into account the fact that a facility package should consider not only physical costsbut also the short-run placation costs and long-run welfare distributional effects. It isclear that the utility of MCDM techniques can be enhanced if the cost ofimplementation of the alternatives is incorporated into the evaluation process.

One of the rare articles which has attempted to link formal plan evaluationprocedures with the broader social choice environment is provided by Sagar (1981).He looks specifically at Lichfield's Planning Balance Sheet (PBS) method and theGoals Achievement Matrix (GAM) procedure of Hill within the context of localparticipatory planning. Sagar (1981) claims that "the Planning Balance Sheet and theGoals Achievement Matrix have become established as the foremost challenges tocost-benefit analysis in the social evaluation of planning alternatives". We can suggestthat PBS and GAM are closely related to MCDM techniques and that their successaugurs well for the future use of a variety of similar techniques. However, Sagar alsonotes that: "A disadvantage of the multi-objective decision methods ... in relation toparticipatory planning is their mathematical form and rather complicatedalgorithms ... [also] ... relatively little attention has so far been paid in theirdevelopment to situations involving groups of decision makers" (Sagar, 1981, p. 427).It is hoped that this monograph will contribute to the efforts of those who wish to seecloser cooperation between theoreticians who develop MCDM approaches and thosewho are faced with the task of generating and evaluating plans, offering comments onmitigation, compensation and the like, and ultimately making executive decisions as towhich plan to implement.

In the early seventies de Neufville and Marks (1974) anticipated " ... a grandsynthesis of the approaches [formal multi objective methods and the like] into a bodyof procedures that will enable the planner or designer to analyse the options available,and to present relevant information about the choices open to the interested groups,and to suggest areas of possible compromise on a choice" (p. 303). With specificreference to transportation planning Hutchinson (1974) claimed that:

It seems that if any real progress is to be made in evaluation, then the basis of the method should besome consistent theory of democratic group decisions (p. 293).

Hill (1977) clearly recognized this as is evident from the following quotation:

The challenge is to find a way to enable interested and affected publics to enter the planning processat the stages of objective formulation, generation of alternatives, and plan evaluation (p. 202).

Some ten years after these exhortations of Hill and others, Voogd (1983) reportedthat: "There are only a few empirical applications known in urban and regionalplanning which bear some resemblance to the ideas [formal multi-criteria evaluation]elaborated in this book" (p. 237). Innovations in planning technology may be slow,but unless current practises can be systematically compared to alternate modes whichmay include MCDM techniques, there is little chance of change in the status quo ofthe two solitudes - practitioners and theoreticians.

JPP 30:1-8


1.4. TOWARD A GENERIC PLANNING PROBLEM

One of the basic features of many urban planning exercises is the generation ofalternate solutions. This is the starting point for our work, for without alternatives wehave no reason for undertaking any evaluation or assessment. However there is ofcourse the opportunity to provide an assessment of the status quo and possibly thegeneration of normative plans using an optimization procedure for example. Whilethere are a number of different ways of generating alternate plans, fundamentally wecan identify proactive and reactive modes of behaviour. Some may deny that an urbanproblem exists and insist that the status quo is the desired alternative, others mayargue for a particular plan and these proponents may stimulate reactions from interestgroups who previously were not motivated to offer any suggestions. The political,economic and social context within which planning occurs, determines whether greateror lesser emphasis is placed on soliciting the views of interest groups who may wish toreact to a proponent, also to the encouragement to offer plans by more than oneproponent or by directing a proponent to generate a particular plan which will beimplemented. These various degrees of deliberation and debate focus on the attentionwhich a community places on the desirability of building a consensus regarding urbanplanning ventures. In the interests of encouraging open debate, while designing anexpeditious process, attempts have been made by many jurisdictions to publiciseplanning options and allow public hearings prior to issuing a permit for developmentand construction. Appeal processes are typically part of the planning environment.

The necessity of decision-making stems from the fact that a conflict exists and aprerequisite for choice is that two or more alternatives must be judged and compared.For urban planning this clearly suggests that more than one plan is available and thatevaluation and judgement of the merits is called for in order to move towards aninformed opinion. It may also be the case that a vital part of this judgementalevaluation exercise is to attempt to build a consensus and seek public approval for aplanrying scheme. The search for such approval may be quite informal and certainlynot necessarily involve a vote or referendum, it may also be in a form which willdisarm or at least neutralise or satisfy those who felt aggrieved by a proponent'sinitiative. Compensation practises, mitigation devices and compulsory purchase ordersall form part of the milieu within which much planning occurs. Such is the nature ofurban planning in democratic societies.

Perusal of the vast literature on MCDM clearly indicates that the techniques haverarely been viewed within the context of this broader decision-making framework ashas been noted earlieL A large number of the articles on MCDM deal with technicalaspects, however, we should recall that one of the reasons for the identification,codification and organization of the literature on MCDM is to help those who arefaced with making difficult choices. While MCDM techniques fall squarely into thegeneral area of decision analysis they tend to have been developed in vacuo, and apartfrom planning practice.

Let us now turn our attention to two of the more formal and precise statementswhich are derived from the initial statement of the generic planning problem whichwas posed earlier without forgetting the caveat regarding the need to link the


techniques to the broader planning process. We will begin with the plan selectionproblem which can be envisaged as one of selecting the best alternate plan from asmall finite set of feasible alternatives given an evaluation of each alternative on a setof criteria. The set of alternatives can, of course, include the status quo option.Stewart (1979) has summarized this typical planning problem in the following way:

The problem facing the decision maker is thus to select an alternative such that the collection ofcriteria values (jSk, j = 1,2, ... N) is preferable to that of any other alternative.Where Sk is the utility, attractiveness or score for plan k given a set of N criteria.

A similar problem exists in the social choice literature and it has been stated asfollows by Cook and Seiford (1978):

Consider the problem in which each member of a committee provides an ordinal ranking of a setof ... projects. Anyone member's ranking is considered equal in importance to the ranking preferredby any other member. The problem is to determine a compromise or consensus ranking that bestagrees with all the committee's ranking.

It has been shown (Massam, 1984; Rietveld, 1984) that the structure of this problemis similar to the multi-criteria evaluation problem. These two problems can becombined to form a multi-criteria social choice problem. This problem is anelaboration in slightly more formal terms of the one offered earlier, and we can referto this as the generic planning problem (GPP).

Given a set of M plans, and for each an evaluation on a set of N criteria, for a set of G interestgroups, classify the M plans in such a way as to identify their relative attractiveness so that agreementamong the interest groups is maximized.

Rietveld (1984) indicates that in the case of the public choice problem nothing isknown about the relative importance of individuals (note that Cook and Seifordassume equality is the norm), whereas for the evaluation problem some informationon the relative importance of criteria is generally available. In fact it appears to bevery difficult to derive any good formal definitions of satisfactory weights for criteria,as interest groups clearly have their preferred weighting schemes which reflect theirpreferences and priorities only in terms of the final outcome. A discussion onstrategies for handling the weighting problems for criteria is given in Chapter 2.According to Sagar (1981) it can be shown that ex ante weighting of attributes andgoals has logical weaknesses which follow from assumptions of rational choice underuncertainty. Who would willingly agree on a set of weights ex ante and risk that theirpreferred alternative was replaced by another which they perceived to haveinappropriate consequences? It is probably preferable for the planning process toinclude meaningful participation of interest groups in order to attempt to build aconsensus regarding a preferred plan. Conflicts cannot always be avoided, thereforethey must be managed. Amrhein (1985) has noted that "MCDM problems arise whena decision-making process involves the simultaneous evaluation of multiple conflictingobjectives". Clearly criteria and objectives are closely related. Specifically we wouldargue that planning goals (general statements of intent) be converted into objectives(precisely defined areas of concern), and these in turn be formulated as clearly,


comprehensively and unambiguously as possible, as a set of evaluation criteria.Bracken (1981) puts the matter of plan evaluation squarely:

Evaluation can be regarded as the cornerstone of attempting to improve the quality of planningactivities and policies, and will involve making explicit value judgements about the worth ofparticular policies.

and Hatry (1972) offers a plea for careful measurement when he claims that "withoutadequate measurement, so-called evaluations are likely to be little more than publicrelations stories by the sponsors and of minimal practical use".

It is necessary to consider the merits of plans using criteria which clearly relate toplanning goals, and not to base the evaluation only on readily accessible data, but weshould not adopt superior attitudes and assume that numbers present some absolutetruth. At least let us recognize that they are open to different interpretation as regardstheir significance and importance for a particular individual or group at a specificpoint in time.

With all these general points behind us let us now begin to look specifically at theelements of MCDM techniques as they can be used to tackle the generic planningproblem outlined at the end of this chapter.

CHAPTER 2

Components of MCDM Problems

2.1. INTRODUCTION

It is clear from an examination of the generic planning problem that was discussedat the end of Chapter I that there are three major components which must beconsidered. These components are: the alternate plans; the criteria which are used toevaluate the plans; and the interest groups. We will begin this chapter by focusing onthese three components and consider the ways they can be combined as a set ofmatrices. This will lead into a discussion on the scores and values in each matrix, anda review of selected procedures for standardizing these scores. The rationale for suchan exercise will also be given. At this stage we will introduce the notion of benchmarkplans; also we will stress the need to recognize that errors are likely to occur in theestimation of the scores.

One of the areas of concern for those using MCDM techniques rests with theproblem of deciding how to deal with the criteria. Should they be ordered from mostto least important? Should they be weighted? If so, then what rules should be used toderive the order or to assign the weights? These and related questions focusing on thetreatment of criteria will be dealt with in a separate section of this chapter. Finally wewill offer a checklist of criteria which can be applied to assess the utility of a particulartechnique. It should be noted that the emphasis in this chapter is on the generalprinciples of the techniques. In Chapter 3 we will turn our attention to consideralternate strategies for analysing the information in the matrices. These strategies arethe MCDM techniques and we will select a variety of these to show the different wayswhich can be used, remembering that the basic purpose of the exercise is to assist inthe process of generating, evaluating and classifying alternate plans so that a preferredone can be identified. While we take as our starting point a finite set of alternate plans,there is no reason why this set cannot be re-defined in the course of the planningprocess, in fact this is probably a most desirable feature of a process in whichconsensus-building and open participation are critical elements. The techniques werefer to in Chapter 3 are far from an exhaustive list, however we argue that thosewhich are included are suitably representative. For example there are many MCDMtechniques which use an additive approach to deal with scores in order to derive autility value for a particular alternative plan. We will select examples from this body ofwork rather than deal with each variation on this general theme. It should be noted

21


that we specifically exclude those techniques which are based upon formalmathematical optimization procedures, for example, linear or goal-programming.Such techniques fall into the MODM category and require explicit formulation ofconstraints and objectives as equations prior to their application. In Chapter 4 we willexamine a set of case studies to show how the general principles laid out in Chapters 2and 3 can be made operational.

2.2. THE THREE COMPONENTS: PLANS, CRITERIA, INTEREST GROUPS

Let us consider a set of M alternate plans PI' P2, ••• PM, a set of N criteria Ch

C2 , ••• CN and a set ofL interest groups G h G 2 , ••• Gr. These three components can becombined and presented as a series of matrices as shown in Fig. 1. These matrices aresometimes referred to as evaluation tables, options tables or impact or achievementmatrices; terms such as priority matrix and appraisal matrix have been used by Voogd(1983) to describe matrices 2 and 3 respectively. The terms 'exact value matrix' and'preference matrix' have been used to describe matrix 1 (Massam, 1980, p. 255). Thelatter suggests that the data in the matrix have been derived from a technicalassessment without any direct consideration of the views of the interest groups,whereas the information in the former matrix give an indication of the importance ofthe data from the perspective of an interest group. We might distinguish between theseviews by using terms such as magnitude of impact and importance of impact. Thecriteria conventionally focus on economic, social and environmental factors, howeverthis list could be extended to include mitigation measures and implementationdifficulties. The plans may represent alternate locations for a particular type of landuse or a facility, or different strategies for tackling a particular problem. Clearly thealternatives are dictated by the specific problem under investigation. The interestgroups may be composed of producers, operators and consumers as suggested byLichfield (1970) or proponents, opponents and others, or in any other way to representfairly cohesive publics who may have shared interests and concerns. Hill (1968) refersto them as incidence groups in his Goals Achievement Matrix procedure. Again it isthe specific problem and the social milieu, as well as the scale of the enterprise whichwill dictate the definitions of the groups.

Prior to the analysis of each matrix it is necessary to determine the scores, these areshown as jSi (score for plan i for criterion)), jSI (score for criterion) for interest group1) and iSI (score for plan i for interest group 1). A superscript t could be added to eachof these, for example jS:, to indicate the score during a certain time period or at aparticular point in time. This is an important dimension when plans are assessed interms of their long-term and short-term effects. It should also be recognized that theinformation shown on these matrices can be combined into a single table or diagram.Three examples of this are shown in Fig. 2.

Attempts to analyse the three-dimension matrix shown in Fig. 2 have been offeredby Massam (1986), and Jaakson (1984) has used the second type of matrix in hisapplication of an MCDM technique called Planning Assistance Through Technical


Evaluation of Relevance Numbers, (PATTERN). This second matrix is referred to as arelevance matrix.

Obviously there are several variations which can be made to these basic ways fordescribing the three components. We will not explore these in detail, just two exampleswill be given. In the PATTERN technique the information in the relevance matrix isused to derive an adjusted relevance matrix of the style shown in Fig. 3. The purpose isto reduce the information in the initial matrix to a set of single number scores ofattractiveness or utility, and on the basis of these scores determine the best plan. Thissimplistic approach has limited appeal to analysts or planners because it tends toobscure measurement and estimation problems relating to commensuration, it also

1 P, P2 · Pi • PM

C,

C2

C·j S i

J

cN

2 I, 1 2 • II · I L

C,

c2•

j S Icj

cN

3 I, 12 · II • I L

P,

P2

Piis I

PM

jSj score for plan i for criterion j

JSI score for criterion j for interest group I

i SI score for plan i for interest group I

FIG. 1. Matrices derived from three components.


limits the incorporation of differing views on the magnitude and importance of theimpacts as well as hindering the debate on implementation of each proposed plan.Such a debate usually considers an assessment of mitigation and compensation

1 Pi • PM

C1C2

IICj 1 L

is!CN j I

2 CRITERIA INTEREST GROUPS PLANS

C1 11 12 • II • I L P1 P2 • P; . PM

C2

Cj•CN

3 P1 P2· Pi • PM

•Cj•

•

•

FIG. 2. Combinations of three components.


PM1 1 12 • I( • I L

FIG. 3. Adjusted relevance matrix.

measures. The single number approach has been referred to as a Grand Index methodby McAllister (1980) and he asserts that:

... the use of a grand index in evaluations should be abandoned. True, it does represent a neattechnical solution to the age-old evaluation dilemma of making trade-offs between the many, diverseimpacts of complex public actions [but] ... our knowledge of what determines the welfare of societyis entirely too weak to reduce it to a mathematical equation, which all grand index methods implycan be done .... A major reason against the use of grand index schemes is that they short-circuit thecitizen participation process (p. 264). '

Lootsma et al. (1986) offer a novel way to try to identify clusters of similar opinionsamong the interest groups. A summary is given in Fig. 4. Pair-wise comparisons ofcriteria by each interest group yield a set of prefe~encescores which range from +4 to-4 and these data are used in a cluster analysis to try to identify groupings among theinterest groups. The overall grouping which is indicated by the dotted line in Fig. 4can be considered as an indication of the general preferences for the full set ofopinions. Formal measures to indicate the consistency of the opinions can be used andwhile this may appear to enhance objectivity it is hardly likely that they will be ofgreat use in resolving conflicts among the interest groups. Lootsma et al. (1986)conclude that "the main objective of our pilot exercise was to introduce to themembers of the Dutch Energy Research Council the use of multi-criterion decisionanalysis as a discussion model that highlights the points of agreement anddisagreement amongst them, so that they can concentrate on the latter in order toreach a compromise". Seen within this broader framework the method they proposeappears to be useful.

Let us now consider three other types of matrix for describing relationships amongthe components. These are shown in Fig. 5 and they can be described as pair-wisecomparison matrices as the cells in each matrix refer to pairs of plans, criteria orinterest groups. We can envisage in the first case a series of such matrices for theplans, each being offered by a particular interest group. The scores in such a matrixare conventionally measures of similarity or difference. Saaty (1980) has done much topromote this approach. These can be expressed as measures of dominance - more of


FIRST CRITERION 1 m

INTEREST GROUPS

• • I, • • • I L SECOND CRITERION

DENDOGRAM

linking similarprofi les forinterest groups

as bI

yyI

I

score for interest group I. for pair-wisecomparison of criterion a with criterion b

The sca Ie for the score ranges from+4 when a is strongly preferred to b,owhen a is similar to b. to

- 4 when b is strong Iy preferred to a

FIG. 4. Classification of interest groups.

this later. A similar approach can be adopted to handle the second matrix which dealswith the criteria, again a series of matrices could be derived each to represent the viewsof a particular interest group. In the case of the third matrix we have the problem ofdeciding who should provide the scores? Hardly the interest groups, however if theplanner's client is a government agency and the planning problem is one of tackling apublic facility location problem, for example to find a suitable location for a wastedisposal unit, then the planner might seek to identify the possible coalitions andconflicting groups of interested parties in such an issue. Possibly the governmentalagency is primarily concerned with building a consensus and therefore requiresinformation on the strength of opinions and estimates of the similarities anddifferences of these opinions regarding siting options. The planner may be able toidentify shared concerns among the interest groups as well as points of sharp contrastand confrontation. Such information can be of considerable importance to the

MUlti-criteria Decision Making 27

2 C, c2 • Cj • CN

C,

c 2

3 I, 12 • II • I L

I,12•

•

FIG. 5. Pair-wise comparison matrices of three components.

government agency as it seeks to find an appropriate solution to this public choiceproblem.

Among the three components it is clear that the most important one is the set ofinterest groups, for it is from this set that the need for a proposed plan is generated,one or more options may be offered and opposition may arise, also one group may becharged with bringing about a final settlement. We can identify three types of interestgroups. First, those who express the need for a planning exercise or who recognize anopportunity for development - the proponents. Second, those whose lives will beaffected by the actions of the proponents, and third, those who have the legitimateresponsibility for mediation, arbitration or sanctioning the actions of the proponentsor opponents. This third group may also have the implicit authority to protect thosewho do not overtly support or object to a specific plan. For example, their concernmay be to enhance the public good. These three types of interest group may each tryto assess the range of planning options available, as well as the criteria which they feelreflect suitable indices to make judgments on the relative merits of the options given


their particular objectives. As well, it is clear that the interest groups will seek tounderstand the views of each other and to estimate ways to ensure particularoutcomes. It is the recognition of this that has led Radford (1986) to move away fromformal methods for analysing the matrices of the style presented in Figs 1,2 and 3 andto seek a more general bargaining-negotiating framework to handle the conflicts. Wedo not contest the validity of this, rather we argue that the MCDM techniques weoffer could possibly be incorporated by the interest groups into the strategic-tacticalmodel framework he has proposed. We do however strongly oppose the view that planevaluation and selection can be reduced to a simple matrix and this can be analysedusing a procedure such as PATTERN or a dendogram to yield the preferred result. Itis vital that the MCDM techniques be incorporated into the planning process.

This first stage which involves the organization of information as a set of matricesprovides a useful framework for handling the debate on the identification of options,criteria and interest groups. Perhaps no further formal analysis of the information inthese matrices is undertaken in the plan evaluation process and the debate on therelative merits of each option is undertaken within a bargaining framework in whicheach of the interest groups seeks to present its case as forcefully as possible, whileavoiding unsatisfactory outcomes and recognizing that delay has a price. If, however,detailed analysis of the options is seen to be an important part of the planning processthen we must look further at these matrices and consider how the scores in each onecan be derived and used.

2.3. SCORES AND IMPACT VALUES

Once it is decided that a particular matrix is to be examined the next task is toobtain scores for the cells. In this section brief comments on the four major types ofmeasurement scales for such scores will be given. We will then consider the problem ofstandardizing these scores so that the values are commensurate. Basically thedisadvantage of this approach is that the units of measurement - costs, jobs, noiselevels etc., which probably have fairly clear meaning and significance for an interestgroup, are converted into dimensionless units which do not have a specific attribute.On the other hand, by converting all the different sorts of impacts onto a standardscale there is some legitimacy in accumulating the scores to give a single value. If thestandardization procedure allows all the scores to be converted to a single scale andthis scale is in monetary units, for example dollars or sterling, then the final score foreach plan potentially has significance for the interest groups. This assumes that thisunit - dollars or sterling - is the critical variable on which decisions are based. Anattempt to adopt this approach was incorporated into part of the analysis of theRoskill Commission in its assessment of alternate sites for a third airport for London.Hall (1980) discusses this in some detail. One of the impact tables accumulates thescores for a set of criteria for each of the sites. This approach was roundly criticized bySelf (1975) among others and clearly it did not stand up to close scrutiny, especiallywhen other non-monetary criteria were included and also when the status quo optionwas assessed, the opportunity costs considered as well as the distributional effects of


costs and benefits. So overall, while we might try to standardize scores in order tomake the criteria commensurate, it would be naive to suppose that simple arithmeticoperation on the new numbers will yield the right or even acceptable solution. Whatwe might hope for perhaps is that the standardization procedure can yield valueswhich we can then use in a classification exercise and add to this a series of sensitivitytests. It is this latter operation which is a vital part of using MCDM techniques.

The four measurement scales which can be used for the scores in the matrices are:(i) ratio,

(ii) interval,(iii) ordinal,(iv) nominal.

The characteristics of each of these are discussed in standard texts and the details willnot be repeated here. See for example Voogd (1985).

The ratio scale contains most information, as a basic point of departure, an origin isgiven and the magnitude of the measurement units; the nominal scale providescategorical information, and as such it is hard to use for comparative purposes.Recently there has developed a more concerted effort to develop a body of literatureon the analysis of categorical data, but as yet it has hardly been linked to the MCDMtechniques. A mistake frequently made in the analysis of a matrix is to assume that anordinal scale has the same properties as an interval scale. This point has beenforcefully made by Nowlan (1975) and the case is reviewed in Massam (1980). As ageneral rule, whenever numbers are placed in a matrix a declaration of the scaleshould be made so that all ambiguities are avoided and precision is stressed. Ordinalscales are frequently used by planners and care must be taken to ensure that simplearithmetic operations are not conducted using such scales. The rationale for this restson the notion that the ordinal scale does not give details of the magnitude ofdifferences; ratio and interval scales contain such information. We should also avoidusing geometrical approaches for analysing ordinal data, for example it is notlegitimate to draw a graph and claim that the data on the axes have only ordinalproperties. There have been attempts to introduce the idea of a fuzzy boundary whichdefines the edge of a measurement scale (Siskos and Hubert, 1983) and Brans et al.(1986) have attempted to examine systematically the intensity of preferences as theyrelate to the comparison of pairs of plans for a particular criterion. This work is inmany ways a restatement of the assertion that a particular score may have errorsassociated with it and it should be better characterised by upper and lower limits. Thisis an important idea from a practical standpoint and one which should and can beincorporated into MCDM techniques within the framework of sensitivity orrobustness tests.

The assignment of an impact score to a particular cell may lead us to believe that weare objective and that our personal biases are removed. To some extent this is true,however we should acknowledge that while the magnitude of an impact may beassessed with some objectivity, depending upon the instrument, the importance of thisimpact is directly related to the opinions, perceptions or the expectations of theinterest groups. A further complication is added for some impacts because the physicalintensity can be perceived differently from the psychological intensity, yet it may be


the former that produces damage to our health. For example, plan A may generate 10decibels more noise on a sound meter than plan B, the physical energy is ten times asgreat yet subjectively the difference only appears to be twice the amount. A 20 decibelincrease produces one hundred times more energy but only a four-fold increase inperceived loudness. As ear damage is related to the physical intensity levels we shouldbe wary of using perceived intensities, yet it is these which cause psychologicalannoyance. Great care is needed to examine the nature of the impacts; simplerecording of numbers without supplementary explanations may lead to spuriousconclusions. Yet again we stress the need to deal carefully with magnitudes andimportance as separate, but related issues. A plan to destroy 50 oak trees may be seenas most unacceptable if these are the only trees in the region, on the other handremoval of 50 such trees from a large forest may be of little consequence. A relatedaspect concerns the marginal effects of increasing the level of the impacts. This pointunderlies the rationale for using a function-form to transform basic scores, that is theraw data, into standard scores. The term function-form is used by Brown and Valenti(1983) and Hammond et al. (1980). Keeney and Nair (1977, Chap. 14) use the termsingle-attribute function and Gardiner and Edwards (1975) refer to this as a valuecurve. We will discuss this in Section 2.4 under the heading of a transformationfunction.

In summary we. can envisage that the jS; values from matrix 1 on Fig. 1 arepresented as raw data, for example financial costs (long-term, short-term), numbers ofjobs etc. and ideally we would hope that interval data are available for each criterion.With respect to the jSI and iSI scores perhaps the best we can hope for is a set of datain the form of ranks. Conceptually it is possible to derive ratio values for jSI and is! byasking each interest group to place each criterion or plan onto a scale ranging from 0to 10, for example, or by the division of 100 points among the competing plans orcriteria. This is often referred to as Metfessel allocation (Solomon and Haynes, 1984;Rowe and Pierce, 1982b).

In the case of the matrices in Fig. 5 the score in each cell refers to the degree ofsimilarity. For example we could use a ratio scale from 1 to 9 following the ideas ofSaaty (1980). A value of 1 indicates that the comparison of the two plans, criteria orinterest groups are identical, whereas a value of 9 indicates that one of the pair is"absolutely more important", and following Saaty a score of 3 indicates "weakly moreimportant", 5 suggests "strongly more important" and 7 "very strongly moreimportant". Saaty has proposed that the similarity scores can be summarised in theform of a positive reciprocal matrix of the style shown in Fig. 6. In this example theplans are compared. Obviously the values on the principal diagonal are 1'so Withrespect to the comparison between PI and P2, a value of 9 indicates that PI is"absolutely more important" than P2, the reciprocal value of 1/9 is placed in the cell(P2 , PI); plan i is "weakly more important" than PI and the reciprocal value of 1/3 isplaced in the cell (PI' Pi)' Plans 1 and M are identical, hence the values of 1 in cells(PM, PI) and PI' PM)' If the information regarding the pair-wise comparisons can besummarised in a positive reciprocal matrix then Saaty argued that an ordering of theplans (referring to Fig. 6) could be derived. In technical language the principaleigenvector is used to indicate the relative importance of the plans. Cook (1986a) has

P, P2 • Pi

P, 9 1;3

P2 %

•

Pi 3


PM

FIG. 6. Sample positive reciprocal matrix.

suggested that there is room for improvement in this method and refers to thetechnical contributions on the use of such eigenvector approaches by Cogger and Yu(1985) and Johnson et al. (1979). From the planning perspective, while it seemsappropriate to seek values for the cells it is not clear about the level of confidence thatcan be placed in the eigenvector results as a procedure for determining the relativeimportance of the plans and hence an ordering. Research continues on this problem asdoes other work by Cook et al. (1985) on binary matrices under the general topic oftournaments. This work assumes that a 1 or a 0 in a cell indicates a clear preferencefor a plan in a pair-wise comparison.

Another approach for describing similarities for the matrices shown in Fig. 5 is toassign values to each cell which represent proximity measures, without any indicationof dominance among the pair-wise comparisons. For example using a matrix for planswe might try to assign interval values ranging from 0 to 1 as indicators of similarity,with a value of 0 indicating that the distance or difference between the two partners ina pair is 0, hence the partners are identical. A value of 1 suggests maximum difference.If correlation coefficients between the pairs of plans are used then a value of 1indicates the pair is identical and as the value approaches 0 so the difference getslarger. If similarities are described using this type of data then a symmetrical distancematrix of the type shown in Fig. 7 is produced. This matrix refers to pair-wisecomparisons of plans and suggests that plans 1 and 2 are identical whereas i and 1 arevery different and the difference between M and 1 is less pronounced. If the data arepresented in this form then the matrix can be analysed using a multi-dimension scalingmethod. A good survey of this literature is given by Golledge and Rushton (1972). Theend product of the analysis is a map of the plans showing their relative positions.Examples of typical one- and two-dimension maps for five plans are shown in Fig. 8and empirical examples in Massam (1980, Chap. 6).

In order to interpret such a map it is necessary to assign labels to the axes or theends of the scales, or to incorporate plans with known characteristics into the analysis,such plans are referred to as benchmarks. The strategy of using such benchmarks is auseful one whenever a classification exercise is undertaken. Details of benchmarkplans are given in a later section of this chapter and an example of a two-dimensionmap is presented in Section 3.6 of Chapter 3.


P, P2 • Pi • PM

P, 0 0 0.5

P2 0

•

Pi 0

•

PM 0.5 0

FIG. 7. Symmetrical distance matrix.

ONE DIMENSION P4+

TWO DIMENSION

FIG. 8. Typical one- and two-dimension maps.

2.4. STANDARDIZATION OF RAW DATA

The basic reason for standardizing data rests with the argument that thestandardized values will give an indication of the underlying structure in theinformation. For example we might choose to calculate Z scores given a set ofobservations for a criterion for a set of plans with the view that we want to use someunderlying statistical properties in our analysis. This approach has been used. by Smith(1977) for classifying census tracts using socio-economic variables with a view todetermining the social well-being of residents of each tract. However, such anapproach lacks validity unless we are confident that the basic distribution of values forthe particular criterion is normally distributed. Also, from a practical perspective if wehave only a few plans, for example five, then the exercise of calculating Z scores lacks


credibility. If we wish to combine values for a set of criteria then it 'is necessary thatthe scales be commensurate and thus frequently raw data are standardized to achievethis end. We should recognize however that there are many ways of standardizing rawscores and in this section we will summarise the five basic approaches. Karski (1985)has referred to the fourteen methods proposed by Langley (1974) in his work for theDepartment of the Environment (U.K.) on evaluation techniques which could be usedin the preparation of structure plans. It appears that this large number is generatedfrom using slight variations on the maximum and minimum values used in some of thecalculations. The first four can be presented as simple formulae whereas the fifth issomewhat different because the method of converting the raw scores depends upon theshape of the transformation function. This will be discussed separately.

Let us consider a set of five plans (A, B, C, D, E) and a single criterion - jobscreated. The results of the four standardization procedures are given in Table 1.

TABLE 1. Results of four standardization procedures

Raw Data 2 3 4

PlanA 18 0.12 0.24 0.20 0.21B 30 0.21 0.40 0.35 0.35C 20 0.14 0.27 0.22 0.24D 4 0.03 0.05 0.00 0.04E 74 0.50 1.00 1.00 0.87

The procedures in Table 1 are summarised below. While we note that the relativepositions of the plans remain unchanged the differences between plans depend uponthe standardization procedure. This is shown in Fig. 9. Hence if the classificationprocedure relies on this information then potentially the final results, namely theordering of the alternate plans, is subject to the particular standardization routinewhich is adopted. Such an example is provided by the discordance index which is partof ELECTRE, an overranking method developed in France. Comments on this areprovided in Section 3.6 of Chapter 3.

1. Raw score

! all scores

2. Raw score

Max score

3. Raw score - min score

Max score - min score

4. Raw score

-J ! (raw score)2

JPP JO:I-C

B CA D. I0

E B CA D.. . I

B CA D. . .B CA D

•• 4

B CA D.

E


RAW DATANumber of jobs 1~

E

E3 +-4-----------------+-----i

E2 t-I-------------------------t

4

FIG. 9. Standardized value scales.

The maximum values in procedures 2 and 3 can be set by using hypothetical orpractically acceptable levels. We need not use the maximum value from the raw scores.The fourth procedure tends to put greater emphasis on the larger values and henceextends the scale in comparison to the results using procedure 1. The second procedurealways gives a value of 1.0 for the highest level and procedure 3 scales all theobservations between zero and unity. It should be noted that for the job creationcriterion a high value increases the attractiveness of a plan, whereas if constructioncosts were used the reverse would be the case. If this is the situation then thestandardized scores have to be adjusted accordingly by subtracting them from 1.0 forexample.

The fifth procedure which involves a transformation function converts the rawscores into a scale that can range from zero to unity, this scale has been called aconstant worth scale, or a subjective scale or a utility scale, and the raw scores scale isoften known as the objective scale. An example of a transformation function using thejob creation criterion data is shown in Fig. 10.

The particular function shown in Fig. 10 as a solid line suggests that while thecreation of 74 jobs yields the maximum utility value of 1.0, there is hardly a decreasein utility until we drop below 20 jobs, when there is a sudden decline towards zero. Analternate function could be a straight line as shown in Fig. 10 by the dashed line.Analysts who have used transformation functions as part of an MCDM techniquerecognize that this allows considerable flexibility and has greater intuitive appeal inderiving the utility values than one of the four standardization procedures offeredearlier. Particularly this transformation function strategy which pays attention tomarginal changes in the raw scores and their corresponding effects on the worth of aplan. It may be that there is a limiting value for a criterion and once this is reached aplan which is characterised by this value ceased to be a feasible alternative - hencethe utility is zero. This can be reflected on the transformation curve. Some possibleshapes for these curves have been offered by Hammond et al. (1980) and Brown andValenti (1983). A survey of some typical curves is offered in Fig. 11. Possible examplesfor a, b, c and d for Fig. 11 are population of a wild life species, a natural resource,


1.0

FIG. 10. A transformation function.

74 Numberof jobs

1.0 (a) 1.0 (b)

0"----------INCREASING

0"------------INCREASING

oL---------.:::::::..-INCREASING

1.0 (c)

2 3 4

1.0 Cd)

Modified after Brown and Valenti (1983)

FIG. 11. Samples of transformation functions.


annual population growth and average student-teacher ratio. Obviously each planningexercise dictates the precise criteria which must be considered. Brown and Valenti(1983) have argued that there are basically two ways to determine the shape of thesecurves. First, by direct specification and second, as a result of questioning arepresentative of an interest group in order to determine points of indifference on thecurves and hence the shape of the function. While theoretically appealing it is likelythat for practical purposes it is difficult to obtain meaningful results to hypotheticaltrade-off questions. Keeney and Nair (1977) elaborate on the way of obtaining theform of these curves for a set of criteria for a practical planning problem.

2.5. BENCHMARKS AND IDEAL PLANS

The matrices given in Fig. 1 and Fig. 2 which focus attention on the plans, begins byidentifying M feasible alternatives. This is the set {PI' P2, Pi, PM}' The generic planningproblem seeks to find a classification of these plans in order to identify their relativeattractiveness and one way of doing this is to compare the alternatives to a givenstandard. It is this standard which we can refer to as a benchmark plan. There are anumber of different ways that we can approach the problem by defining thisbenchmark plan and the four most common ones are:

(i) status quo option plan,(ii) ideal best plan,

(iii) hypothetical worst plan,(iv) plan of minimum satisfaction.To illustrate these let us consider an impact matrix of the style shown in Table 2

using two criteria and a set of six feasible alternatives. The characteristics of the fourbenchmark plans are included to give a (10 X 2) matrix as presented in Table 2.

TABLE 2. Sample impact matrix with benchmarks

PI P2 PJ p. P, P6 ii iii iv

Costs 106$ C 1 30 26 42 16 19 17 0 16 42 35No. jobs created C2 14 18 10 20 11 13 0 20 10 15

The plan iv has been defined by a budget constraint of $35 million and the need to create at least 15 jobs.

The matrix in Table 2 suggests that while the status quo option involves no financialoutlay in the form of construction costs we also have no generation of employment.The characteristics of the ideal best and hypothetical worst options are derived fromthe existing data in the matrix, and the values for the minimum satisfaction plan aredefined by considering the available budget, the goals and objectives of the planningexercise and taking into account norms and standards. Hence constraints andexpectations can be used to characterise this plan. We suggest that the exercise ofproducing these benchmark plans or norms may help in the interpretation of thevalues in the matrix. Certainly if we resort to the use of multi-dimension scaling, for


example, then if we include benchmark plans into the classification we may be in amuch stronger position to interpret the results. Consider two classifications of fiveplans as shown in Fig. 12.

It is clear from Map 2 in Fig. 12 that Pz is closest to the ideal best plan and probablythe most acceptable of the five options. It is impossible to draw such a conclusionfrom an examination of Map 1 in Fig. 12. Benchmark plans can be defined by eachinterest group and similarities and differences can be identified. A practical example ofa planning problem which uses benchmark options to interpret two-dimension maps isgiven in Massam (1980, Chap. 6).

2

• ii

FIG. 12. Two classifications of five plans.

2.6. ERRORS IN THE ESTIMATION OF SCORES AND IMPACTS

In Hall's (1980) overview of some recent great planning disasters he pays particularattention to the fact that underestimation of costs and overestimation of benefits arethe major factors which have contributed enormously to the disasters. Explicitrecognition of possible errors associated with the values in the matrices may help toreduce the incidence of planning mistakes. Having said this we must try to face up tothe problem of determining the errors, and perhaps the most satisfactory approach isby using a series of sensitivity tests each assuming a different amount of error. Forexample we might produce a classification of the plans using information in a matrixof the style shown in Fig. 1 under the assumption that the estimates for the impactscores 08;) were perfectly accurate. Next we could modify these estimates by a givenamount and examine the new classification. Estimates for the errors could be offeredby technical analysis or examination of past experiences, another approach is to makearbitrary adjustments in order to identify the maximum amount of error which wouldbe needed in order to change a classification radically. This type of approach looks atthe robustness of the classification. It might be the case that a small change in thescore for a particular criterion could alter the relative attractiveness of the plans quitedramatically. In other cases it could be that considerable variations in the scoresconsistently produce the same classification. This point is clearly illustrated withrespect to the analysis of an impact matrix which involved three interest groups, threeplans and five criteria (Massam, 1986) for a specific set of data regarding the


evaluation of alternate marina facilities for a lake near Ottawa, Canada. A variety ofdifferent scores produced the same ordering of the plans. The message is clear, namelywhenever an MCDM technique is used to analyse a set of data it is necessary toconduct a series of analyses to take account of possible error in the scores and values.

2.7. DEALING WITH CRITERIA

In the last section we made a case for sensitivity tests to deal with possible errorsassociated with scores and impact values, and in this section we can continue theargument by suggesting that we should also undertake sensitivity tests for the criteria.At the outset of a planning problem we may be able to define a long list of criteriawhich will encompass all the possible goals and objectives of the various interestgroups. However before we can apply a particular MCDM technique it may benecessary to organize the criteria in a particular way. There are three basic strategiesfor handling criteria. First, by assuming they are all of equal importance, hence thelength of the list determines those criteria that will be considered in the analysis.Second, by ordering the criteria from most to least important, and third, by assigningweights to the criteria to indicate their relative importance. A variation on the secondmethod is to divide the complete set of criteria into groups and possibly order thesegroups according to their importance.

One method for determining the weights for criteria is to use Saaty's (1980) positivereciprocal matrix approach from the set of pair-wise comparisons. Another method isoffered by Keeney and Nair (1977). They start by deriving an order for the criteriausing the opinions of an interest group and then they seek to identify the trade-offsamong hypothetical values for pairs of criteria to identify indifference levels. Whilesuch an approach is logical and can yield values which allow weights to be assigned tothe criteria we should remind ourselves that we are asking interest groups or theirrepresentatives to make a priori statements about hypothetical levels for criteria and assuch we might feel that the results of such questioning lack credibility. Roy andBouyssou (1986) have critically examined this approach and specifically they have reexamined the data used by Keeney and Nair using an overranking method (ELECTREIII). While both approaches give the same best plan, the classifications of the set of thenine alternatives using six criteria vary quite dramatically. Both procedures concur onthe worst two plans. Sagar's point about ex ante weights for criteria that was reportedin Chapter 1 is worth bearing in mind, for who would willingly participate in thesearch for weights without knowing the outcome of this participation. In summary weargue that alternate ways of treating criteria using the three basic strategies within ageneral sensitivity framework provides probably the most balanced approach. We cantake this a step further and suggest that a series of scenarios be described eachcharacterised by a particular set of criteria or ordering of criteria. For each scenariothe planning options could be assessed and comparisons among the results made. Itmay occur that different interest groups have unique orderings of criteria and differentcombinations of criteria, yet in the final analysis some of the planning options appearconsistently as among the most preferred. Sensitivity tests may identify such patterns.


2.8. SUMMARY

Before we apply a particular MCDM technique it is appropriate that we have abasic understanding ~f the three major components of the generic planning problemand also a clear definition of the purpose of the exercise. The construction of matricesof the style shown in Figs 1 and 2 may contribute in this regard. The next step is toexamine the scores and values in the matrices and characteristics of the constraintsregarding the planning options as well as alternate ways of dealing with the evaluationcriteria. Perhaps the most satisfactory approach to handle most of the issues relatingto these is within the framework of a set of sensitivity tests. Again we are arguing thatno single MCDM technique should be proposed to generate the right answer, ratherthat the techniques should be selected to help in the classification of the threecomponents, the generation and evaluation of the options and consideration of theimplementation aspects. Finally we propose a list of criteria which could be used toassess a particular MCDM technique. Precise definitions of each criterion will not begiven though it is hoped that they will assist in a critical discussion of the techniques.The list is not ordered and the criteria are presented as a set of questions.

(1) Can the technique be readily incorporated into the existing or an acceptableplanning process?

(2) Are the required data available?(3) Will the technique assist in consensus-building and expedite debate?(4) Can sensitivity tests be conducted?(5) Is the internal logic of the technique acceptable?(6) Can the results be displayed and explained to non-experts?(7) Is the technique comprehensible to planners?(8) Does the technique require sophisticated computer software or hardware?(9) Is the technique expensive to implement?

(10) Can the technique be used to teach, complement or improve professionaljudgement and intuition?

Finally, perhaps the single question which overrides all others: does the techniqueappear to justify the time and effort involved?

CHAPTER 3

Survey of MCDM Techniques

3.1. INTRODUCTION

In this chapter we will focus attention on a selection of MCDM techniques whichcan be used to analyse the information in the matrices discussed in Chapter 2. Theoverall purpose of the analysis will be to deal with the generic planning problem thatwas posed at the end of Chapter 1. Essentially this requires that the alternate plans beclassified and that this classification should be based upon the opinions of interestgroups regarding the evaluation criteria. Obviously these criteria must be developedfrom the goals and objectives of the planning exercise. For the classification to be ofuse it is necessary that it be presented in such a way as to reflect the relativeattractiveness of the plans. This can be achieved by comparing alternatives to thestatus quo or to benchmark options. We should also stress that the classificationexercise should include sensitivity tests, for example to examine the consequenceswhich might result from possible errors in estimating the values for the evaluationcriteria. In general terms we will describe selected MCDM techniques whilerecognizing that these techniques only help organize information which must beincluded within a broader planning process.

The MCDM techniques that we will consider can be arranged into five types asfollows:

(1) Lexicographic ordering methods.(2) Graphical approaches.(3) Consensus maximization approaches.(4) Additive models.(5) Concordance methods.

Each of these will be treated separately.

3.2. LEXICOGRAPHIC ORDERING METHODS (LOM)

An introduction to LOM is given in Massam (1980) and basically these methodsassume that the criteria can be ordered from most to least important. The plans whichsatisfy the first criterion are then judged with respect to the second criterion and ifmore than two plans satisfy this criterion a third one is used and so on down the listuntil just one plan is identified. It is this plan which is offered as the most satisfactory.

40


It should be noted that a unique solution is not guaranteed. In its basic form thisprocedure does not allow any trade-off among criteria, in technical terms this issometimes referred to as a non-compensatory approach. If a single plan scores highlyand above all others on the most important criterion, then it would be identified as thebest and no matter how well other plans performed for the other criteria or how badlythis first plan performed for the other criteria, there could be no modification. Themethod seeks to identify a single best plan. At first glance we might believe that a noncompensatory approach is generally an unacceptable one in planning as compromisesand trade-offs appear to characterise many planning choice problems. However, forsome planning problems precise explicit constraints do exist and options which do notsatisfy these have to be excluded. It might be the case that such an approachdetermines that no feasible planning solution exists given a particular constraint andthis means that the search exercise either stops, or the constraint has to be relaxed.Perhaps the classic example of this in current planning applies to the search for sitesfor the storage of radioactive waste material. Possibly there is consensus that such sitesmust be confined to geological areas with at least a certain thickness of a particulartype of rock, and yet be at least a minimum distance from densely populated areaswhile not being further than a certain maximum distance from the sources whichgenerate the waste. Clearly other criteria are involved in this problem, but if we restrictattention to just these three the feasible sites are likely to depend upon the precisedefinitions of rock thickness, distance to populated areas and distance to source. Thoseinvolved in the search for appropriate sites must decide if there are clear definitions ofthese criteria which must be satisfied and if these criteria can be orderedlexicographically, or if trade-offs are possible.

The cartographic sieve-mapping and overlay approaches of McHarg (1969), ofteninvolve constraint mapping and as such are a type of LaM. Regions or districts maybe excluded from consideration as possible locations for a facility if they containarchaeological remains for example, no matter how attractive they are with respect toother criteria. Other similar approaches are provided by the conjunctive anddisjunctive models. While the former uses the principle that an alternative is rejected ifthe score for a particular criterion does not reach a minimum standard, the latterselects an alternative on the achievement of the highest score for a selected criterion.Details of these models are given in Massam (1980), Hwang and Yoon (1981), andSolomon and Haynes (1984). In general, in order to pose a planning problem inlexicographic terms it is vital to have a clear strong consensus on the importance of asmall number of criteria which must be satisfied, prior to the consideration of othercriteria which may be traded one against another. Such consensus may be built aroundhealth concerns, especially with respect to pollution levels, or around cultural valuesand the protection of national heritage. The exigencies of economic development andjob creation may however militate against the formation of rigid consensus and lead toa relaxation of the firm initial conditions attached to the criteria.

An alternative way of posing the lexicographic problem may be to try to order theinterest groups rather than the criteria, and to see if particular plans emerge whichsatisfy the highly ranked target groups. For many planning problems target groupscan be defined as those which specifically should be helped by a plan, these groups


could head the list. In summary a lexicographic framework may assist in focusing adebate on the ordering of the evaluation criteria and establishing the firmness ofopinions regarding critical levels for the criteria. However unfortunately, lexicographicordering does not produce a classification of all the feasible plans and not all theinformation for the full set of criteria is necessarily used. In the process of comparingplans for a particular criterion it is possible to take account of measurement errorsassociated with the estimates for the impacts. For example, a threshold value can bedefined which must be exceeded before one plan is rated more attractive than another.By altering the threshold values for each criterion we can judge if the same planconsistently appears as the most attractive. This exercise of examining the stability ofthe solution is a sensitivity test. A further type of sensitivity test can be undertaken bychanging the ordering of the criteria. An example of this is given in Massam andAskew (1982) for a problem involving the evaluation of twenty-four policies using aset of five criteria.

3.3. GRAPHICAL APPROACHES

Information on alternate plans for a set of criteria can be summarised in graphicalform in a variety of ways. Perhaps the most simple is to draw a set of graphs for pairsof criteria and to plot the alternate plans together with benchmark options. This graphcan be used to identify those plans which are among the best. An example of this isshown in Fig. 13.

The set of plans {PI' Ps, P3} in Fig. 13 is superior to {Pz, P4 } and can be referred toas "efficient" plans using the language of economics. The possibility frontier joinssuch alternate plans. The five alternatives available to the decision maker are shown inFig. 13, and clearly two seem to be unattractive. In order to compare the threeefficient solutions we need to know the way in which the decision-maker trades off C l

against Cz• If we can identify the shape of the indifference curve for these two criteria,then we may be able to determine the best alternative. An elaboration of this approach

c,

BEST

° P,\

" oP4\\\0-

-t P5 ------- -- oP3

BEST

FIG. 13. Graphical presentation of five plans using two criteria (raw scores).


is given in many economics and policy texts, for example, Stokey and Zeckhauser(1978). Theoretically elegant and potentially able to handle many criteria within ananalytical framework this approach has considerable intellectual appeal, howeverproblems relating to the determination of the shape of indifference curves for practicalchoice problems militate against its widespread adoption in plan evaluation andselection. Also there are difficulties of incorporating several interest groups anduncertainties regarding the selection of criteria and the determination of the predictedimpacts.

In Fig. 13 the benchmark is given by minimizing the values for the two criteria,however, potentially three other combinations may be feasible for an ideal benchmark;the full set of four benchmarks is listed below:

Benchmark C1 C2

1 min min2 min max3 max min4 max max

The selection of the efficient plans obviously depends upon the definition of thebenchmark and its position on the graph. The particular problem will dictate theappropriate definition, we should also note the other types of benchmarks that couldbe used as discussed in Chapter: 2. One further point should be stressed, namely thatprior to constructing a graph it is mandatory to ,have interval or ratio data.

At first glance at Fig. 13 we might believe that P5 is the preferred plan as it appearsclosest to the best benchmark. We cannot support this unless we know that the criteriaare measured on commensurate scales: If we wish to adopt this approach then wecould standardize the criteria scores and the benchmark scores, then measure thedistance between each plan and a benchmark and use these distance measures toclassify the alternatives. This approach has been called Technique for OrderedPreference by Similarity to Ideal Solution (TOPSIS). It is discussed in some detail inHwang and Yoon (1981). The distance between a particular plan and a benchmark isgiven by the general Minkowski distance measure:

where Pi is plan i, and Pb is the benchmark plan, and each plan is characterised by Ncriteria. The value for criterion} for plan i is Cij and for the benchmark it is Cbj. Thescores obviously must be commensurate and hence the raw data have to bestandardized. It is also assumed that all the N criteria are equally important. Clearlythis list of criteria could be modified in the course of a set of sensitivity tests. If we setp = 1 then the distance is sometimes called the rectangular distance or manhattanmetric, ifp = 2 the straight-line distance is calculated. Modifications to this approach


could be made to reflect the fact that different interest groups may have differentdefinitions of the benchmark plan. Also alternate constrained plans could be definedas benchmarks, following the ideas presented in Chapter 2. We should note that thedistance which we calculate is a dimensionless number and as such it is difficult tointerpret. However, if under a variety of alternate schemes, using different benchmarksand different sets of criteria, some plans consistently head the list we can be fairlyconfident they are among the best ones. Equally, if the same group of plansconsistently appears at the bottom of the list then these plans are clearly the leastattractive. Of course different scenarios may give rise to different groups of plansappearing at the top of the list. To be aware of these conflicts may help in thenegotiation process which needs to consider the implementation of a plan. Potentiallya benchmark plan which is the easiest to implement could be defined and thealternatives compared to this one. In summary, while it is most unlikely that TOPSISor one of the variations on this theme could be used to solve a planning problem, it ispossible that the general strategy of comparing alternatives to a benchmark may helpin the debate and search for a preferred plan. Szidarovszky and Duckstein (1986) drawattention to the fact that "many of the multi objective decision making techniqueswhich have been developed make use of a geometrical definition of the 'best' solution.By this phrase, it is meant that the decision maker would like either to minimize thedistance from some 'ideal' or 'goal' point or to maximize the distance from some'pessimistic' or 'status quo' alternative". They develop a technique called RHOD anda dynamic variation entitled DYRHOD and apply it within the framework of MODMto a specific planning problem in the Bakony Transdanubian region of Hungary. Theproblem concerns the selection of water management policies to allow bauxite miningto proceed over a ten-year period. Three conflicting objectives involving mining, watersupply and recharge for the thermal spas of Budapest are identified. The approachthey offer complements the static one offered by TOPSIS.

The Minkowski distance measure defined earlier can be used to compare pairs ofplanning options. However, because the measure is a dimensionless number it is hardto know how to interpret its significance. One approach which can be used is toconsider that errors are associated with each criterion and then to calculate thedistance between pairs of plans in the presence and absence of such errors. It mayappear in the latter case that a particular pair of plans generate a distance measurewhich becomes very small when errors are included. This clearly raises the necessity toacknowledge that errors will almost certainly exist when values or scores are assignedto impacts for the criteria.

In Chapter 2 brief comments were offered on the use of multi-dimension scaling andits application to produce 'maps' of alternate plans. It was stressed that theinterpretation of such maps can be greatly assisted if benchmark plans are includedand more specifically the distance between the benchmark and each plan can becalculated as in the TOPSIS approach. The attractiveness of the plans decreases as thedistance to the best benchmark increases. If the distance is calculated from a multidimension map, then the same general Minkowski distance formula as noted abovecan be used, except that N refers to the number of dimensions of the map. For a twodimension map of the style shown in Fig. 12, N = 2, and if the straight-line distance is


required p is set to 2; thus the distance is calculated using Pythagoras's theorem. Anexample of this is given in Section 3.6.

3.4. CONSENSUS MAXIMIZATION APPROACHES

Almost two hundred years ago Borda (1781) and Condorcet (1786) began the formalsearch for a procedure to aggregate individual preferences for a set of alternatives intoa group consensus. While their concern was to consider a set of alternate candidates inan electoral process the generality of their problem is immediately apparent for it liesat the heart of Public Choice Theory, as was pointed out in Chapter 1. There havebeen a number of useful reviews of this literature, for example, Fishburn (1971, 1974),Richelson (1978) and Cook and Kress (1984). One of the most prolific contemporaryworkers who is tackling the consensus problem using formal approaches is Cook andwe will draw on his results. In order to provide some organization to this literature wewill arrange the material under four headings which will allow us to move from theearliest simplistic approaches to more recent analytical work which is based on anaxiomatic approach. We will also examine one of the basic algorithms and indicatesome problem areas. The four headings are:

(1) Borda-Kendall method.(2) Toward an axiomatic approach.(3) Cook and Sieford distance method.(4) Some problem areas.

3.4.1. Borda-Kendall method

If we have information on a set of alternate plans presented as an ordered set ofpreferences for interest groups as shown on matrix 1 in Fig. 1, then one way ofderiving the consensus ranking of the plans is to sum the 'ranks' assigned to each planby each interest group. It is implicit in this procedure that the ordering of thepreferences is an interval scale of integers from 1 to M, if there are M plans. The term'rank' is often used though strictly speaking we should not use it as we are conductingarithmetic operations with the numbers and assuming that the scale in fact hascardinal properties. Cook and Sieford (1982) claim that Kendall (1962) was the first tostudy this ordering problem within a statistical framework using the notion of anestimation for the true ordering on the basis of the individual estimates provided bythe separate interest groups. Intuitively this is not too satisfactory as each group is infact concerned only with its own view and hence the idea that all groups have acommon goal lacks credibility. Kendall's solution to the ordering problem is to use thesum of the 'ranks'. This is the same approach offered by Borda and hence thisprocedure now bears the title, the Borda-Kendall (B-K) method. It is widely usedbecause of its basic simplicity yet because it appeared to be ad hoc and lacking a solidtheoretical foundation it has not enjoyed great respect among analysts. Critics havesuggested that the preferred approach for deriving a consensus should satisfy the basic


axioms of social choice theory as enunciated by Arrow (1951). One of Arrow's axiomsdeals with pair-wise determination and this requires that society's ranking of any pairof alternate plans depend only on the individuals' rankings of these two alternatives.The wayan individual rates another alternative should not bias the comparison of thetwo under consideration. This axiom is sometimes referred to as the irrelevantalternative axiom. Unfortunately this axiom is not satisfied by the simple rankingprocedure that sums scores and determines the attractiveness of a plan on the basis ofthe scores. This is illustrated below for three interest groups II> 12 and 13 and three .plans PI' P2 and P3• Let us examine the following preference structure:

1st 2nd 3rd (priority order)

and the assignment of 3 points for 1st, 2 for 2nd and 1 for 3rd positions yields finalscores of 6 for PI> P2 and P3; suggesting that society's view is that all the plans areequally attractive. However if we consider that for II the preference order is changedto P1>P3>P2, from PI>P2>P3, then the final scores are: PI = 6; P2 = 5; P3 = 7. Henceby only changing the positions of P2 and P3 for one individual we have effectivelyaltered the way in which s~ciety views PI and P2 , for this time PI is not equal to P2•

Cook and Sieford (1982) note that the B-K method is least satisfactory if tied ranksoccur in the original set of preferences and they offer a modification called theminimum variance (MV) approach which they argue is appropriate for handling ties.In essence the MV approach uses the principle from statistics that the sample meanminimizes the square of the deviations. This work represents an extension of the ideasoffered by Kemeny and Snell (1962) who proposed that the preference orders beconsidered as a set of distance measures. Explicit in this approach is the notion thatthe scale and the rankings have interval properties, and specifically the distancebetween a pair of adjacent ranks is constant. Cook and Sieford (1978) note that:

The problem is to determine a compromise or consensus ranking that best agrees with allthe ... rankings [of the interest groups]. Implicit in this statement ... is the existence of a measure ofagreement or disagreement between rankings.

It is this search for an appropriate measure which prompted a number of efforts byBogart (1973, 1975) among others to turn to an axiomatic approach.

3.4.2. Toward an axiomatic approach

This work is based on the view that the distance measure between rankings, if it is tobe appropriate, should satisfy a series of axioms, each of which appears to bereasonable. These axioms refer more specifically to measure theory, and work remainsto be done on the precise comparison of these axioms to those developed within thecontext of social choice theory. We will not elaborate on the axioms here, the details


are given in a paper by Cook and Sieford (1978), though we should note that theyfound that the axioms were consistent and they identified a distance function which isunique. This is a most satisfactory theoretical result and we would hope that itprovides a firm basis for the solution of some practical problems, however the axiomsrelating to the distanct measure are not exactly the same kinds of social choice axiomswhich Arrow proposed, so we are left with only a partial solution to the consensusproblem.

3.4.3. Cook and Sieford distance method

Let us now consider the consensus problem more explicitly by examining the Cookand Sieford distance measure and the sample data they used. They examine a matrixof the style shown in Table 3.

TABLE 3. Ordered preference matrix: 10 interest groups: 5 plans [after Cookand Sieford (1978, 1984)]

I, 12 I, I. Is 16 17 18 I. 110

PI I 4 3 1 2 1 4 1 3 3P2 4 3 2 4 5 4 1 3 1 4P, 3 1 5 2 4 3 5 4 5 2p. 5 5 4 5 1 2 3 2 4 1Ps 2 2 1 3 3 5 2 5 2 5

II - 110: interest groups; PI - Ps: alternate plans; 1,2, ... 5: orderedpreferences, 1 is best.

The data in Table 3 can be converted into a square (5X5) distance matrix in thefollowing way. The distance, dll , in the matrix is given by:

and

and

dll =11-11 +14-11 +13-11 + +13-11 = 13

d21 =14-11+13-11+12-11+ +14-11= 21

d55 =12-51+12-51+11-51+.·· +15-51= 20

to give the following matrix as shown in Table 4.

TABLE 4. Distance matrix: using Table 3 [after Cookand Sieford (1978, 1984)]

1321242220

1115161612

1111121412

1711121416

2719161820


Table 4 can be used in an assignment algorithm to find the total distance associatedwith any ordering of the five plans, and hence we can try to find the ordering whichgives the smallest distance. The distance matrix can be viewed as an assignment matrixas shown in Table 5.

TABLE 5. Asignment matrix [after Cook and Sieford (1978, 1984)]

Priorities2 3 4 5

Plans I *(13)2 *(11)3 *(12)4 *(18)5 *(12)

* indicates the priority or position of each plan, the values inparentheses .are taken from Table 4.

The order of the plans shown in Table 5 from most to least preferred is P" Ps, P2,

P3, P4 and the total distance for this order is 66. This is the minimum value; howeverthis is not a unique order. The following order P" Ps, P3, P2 , P4 is also given by Cookand Sieford as having a distance value of 66. The order P" Ps, P2 , P4 , P3 is given usingconcordance analysis (this approach is discussed in Section 3.6) and this too has avalue of 66. Any other order has a larger value therefore Cook and Sieford concludethat the consensus or compromise ordering is given by the minimum distanceassignment. This is conventionally referred to as the median ranking.

3.4.4. Some problem areas

In this section we will focus on just two problems. First we will consider the meritsof the median ranking and suggest that while it gives an optimum solution to thedistance-minimizing type of consensus problem it is less satisfactory if we examine theresults in terms of the opinions of the interest groups. This is an important practicalmatter if we are concerned with finding the plan which is acceptable to a majority ofthe interest groups. Second we will note that the results using a distance measure arelikely to be treated sceptically as the consensus measure is a dimensionless number andthe distance techniques appear to be at arm's length to a planning process whichtypically involves estimation of preferences as merely starting points in a framework ofbargaining and negotiation.

The orders PI' Ps, P3, P2 , P4 and PI' Ps, P2 , P4 , P3 identified earlier contain thefollowing pair-wise comparisons as shown in Table 6.


TABLE 6. Pair-wise comparisons and agreements

PI> Ps 6/10PI> P3 8/10PI> P, 6/10PI> p. 7/10Ps > P3 SilOPs> P, SIlOPs > p. 6/10P3 > P, 6/10P3 > p. 3/10P, > p. 6/10

PI>Ps 6/10PI >P, 6/10PI >p. 7/10

58 PI >P3 8/1060

- Ps>P, SilO -100 Ps>p. 6/10 100

PS >P3 SIlOP,>P. 6/10P,>P3 4/10p.> P3 7/10

To examine the data in Table 6 to see the extent to which they agree with the originalinformation in the matrix shown in Table 3, we need to consider the number ofinterest groups who accept the proposed ordering given by the median rankingmethod. These are shown as proportions in Table 6. It is clear that the order PI' P5, P2,

P4, P3 agrees more closely with the original set of opinions. In fact out of the 100 pairwise comparisons 60% agree with this order while 58% agree with the alternate ordereven though both orders have the same distance value of 66. The dilemma that thisposes for the practitioner is to decide if the distance approach should be used andwhich of the two solutions should be recommended. If our interest is to identify thetop one, or two alternatives, the distance approach may be satisfactory, however, for acomplete ordering of the alternatives it seems to be less satisfactory than an approachusing concordance analysis.

The second point is to stress that the preference orders, as stated in Table 3, do notreflect variations in strength of preferences by interest groups or firmness of opinionsor possible errors which interest groups are prepared to acknowledge. Before we coulduse a distance-type approach to tackle a practical problem it would be necessary toadd these dimensions to the original data, as we must seek to build a dynamic planevaluation methodology and one which allows preferences to evolve as newinformation becomes available, in the form of mitigation measures or incentives, forexample. The static rigid nature of the consensus problem formation is likely tomilitate against its acceptance by those who are tackling planning problems, not leastof all because the assumption that all interest groups have the same importance israrely found. Finally we can note that for the data used by Cook and Sieford,concordance analysis identifies the ordering of the five plans which not only has thelowest distance value, but also has the highest level of agreement with the opinions ofthe ten interest groups.

3.5. ADDITIVE MODELS

Perhaps the largest single collection of MCDM techniques are subsumed under thisheading. In general the additive models (often referred to as compensatory models),seek to reduce the plan evaluation and selection problem to one in which each of the

JPP 30:1-D


alternate plans is eIassified using a single score which represents the attractiveness orutility of a plan. The selection of a preferred plan is based upon these scores. Hwangand Yoon (1981, p. 99) suggest that the "simple additive weighting (SAW) method isprobably the best known and very widely used method of MADM". While we mightcontest the legitimacy of using a simple additive function for combining impacts inorder to obtain a single value for each alternate plan it has been argued by Hwang andYoon (1981, p. 103) that "theory, simulation computations, and experience all suggestthat the SAW method yields extremely close approximations to very much morecomplicated non-linear forms, while remaining far easier to use and understand".

An interesting review of the errors which can be associated with the use of SAWmodels is given by Rowe and Pierce (1982b). They use hypothetical data and introduceerrors of known types and magnitudes in an attempt to determine "in a general waythe sensitivity of the weighting summation decision model to some of the classes oferror to which it is subject". For those who rely on the use of SAW to tackle a planselection problem it is most important that clear recognition of the potential errors beincorporated into the study, and specifically that sensitivity tests be run as part of theanalysis. Solomon and Haynes (1984) also conclude that while there are a variety ofmodels for accumulating impacts into a final score, "the use of the simple weightingsummation model is probably justified." It is this use of a formal single dimensionlessnumber ~hich causes considerable problems for anyone who wishes to use the resultsand participate in a debate which involves compromises, trade-offs and a discussion ofimpacts in terms of jobs, houses, costs, environmental damage and the like. Theaggregation of impacts across a wide range of variables is worrying to practisingplanners. Some argue that the worth of a particular plan is not a simple additivefunction of the worth of the various components or even a readily identifiablemultiplicative function, for that matter. This is stressed in a paper by Roy andBouyssou (1986). In philosophical terms we are reminded of the debate propoundedby Moore in Principia Ethica when he argued that "the worth of what he termed anorganic whole bears no regular proportion to the sum of the values of its parts". Inparticular, "the value of a whole must not be assumed to be the same as the sum of thevalues of its parts" (Rosenbaum, 1975, p. 127). Yet this concern does not seem tohinder the development of the additive models. However, we can observe that thereappears to be limited dialogue between theoreticians and practitioners in this area.One or two notable examples of cooperation should be mentioned, for example, thework of Keeney (1972) and the examples provided by Edwards (1971), and in Chapter1 we have already referred to Jaakson's (1984) work using PATTERN, one of thesimplest of the additive models.

We should further note that if we wish to defend the use of a simple additive modelthe following two conditions should be satisfied. First, that preferences for, or thetrade-off for pairs of criteria, for example Cr and Cs should be preferentiallyindependent of fixed levels for any other criteria, for example Ct. Second, that Cr, forexample, should be utility independent of the other criteria. Intuitively these conditionsare appealing however very rarely are they verified prior to the application of anadditive model. One case of verification is given by Keeney and Nair (1977) in theirstudy on the use of a set of six criteria for evaluating nine alternate sites for a nuclear


power plant in the Pacific northwest of the U.S.A. They use the MAUT approach. Theverification of the two conditions depends upon the confidence we can attach toopinions regarding the trade-offs among criteria at hypothetical levels. These types ofquestions are obviously not easy to pose in manageable practical ways to the variousinterest groups.

A caveat could be included here if we draw attention to multiplicative models whichexplicitly seek to accumulate the scores for individual criteria in such a way as to takeaccount of cumulative effects which are greater than the sum of the individual criteriavalues. An example of this work is given by Keeney and Nair (1977). They develop aformal methodology to establish if a multiplicative model is appropriate, then toestablish the parameters for the model in a particular situation. The intellectual beautyof this approach contrasts with its practicality, first in seeking the sympathy ofplanners for its adoption, and second to elicit the appropriate answers to hypotheticalchoice questions to determine the values for the parameters. Rowe and Pierce (1982a)draw attention to the fact that those who are asked to describe indifference levels ortrade-offs may not have great confidence in their ability to make the necessaryjudgements. They draw this conclusion after interviewing knowledgeable panelmembers with respect to a specific power plant site selection project on Long Island,New York. Let us recall Sagar's comments referred to earlier, namely that individualsare unlikely to attach importance to a particular set of weights for individual criteriawithout an appreciation of the significance of their opinions on the final outcome. It isthe outcome which is of prime importance to an interest group, not the parametervalues of a multiplicative or additive model or criteria weights per se. Roy andBouyssou (1986) have analysed the data of Keeney and Nair (1977) using aconcordance method (ELECTRE III). Of the nine available sites for the facility allagree on the best one and the two least favoured, however the relative attractiveness ofthe full set of alternatives depends upon the method used. Roy and Bouyssou (1986)draw attention to the different underlying principles of MAUT and ELECTRE III,specifically the nature of the compensatory features of the impacts on the set of sixcriteria. The ELECTRE III method is only partially compensatory in contrast toMAUT. It is concluded from this particular analysis that:

... these inevitable disagreements do not imply that decision-aid [MCDM techniques] is useless butsimply that a single problem may have several valid responses. Given that two different decision-aidmodels cannot be implemented in the same decision process, the decision-maker must be conscious ofthe qualitative choices implied by the different models - often conveying the analysts' own ethicalchoices - before coming to personal conclusions on the choice to be made. In this domain, the manydifferent approaches reflect in our view the complexity of the researcher's task much more than ascientific weakness (Roy and Bouyssou, 1986, p. 214).

The expected utility models developed in the field of MAUT fall into the additivemodel category. The use of an expected value criterion (EVC) for judging the worth ofa particular plan can be criticised on the grounds that the alternate plans are presentedjust once for evaluation. Radford (1980) puts the point succinctly as follows:

[EVC is] Generally agreed to be appropriate in decision problems that are repeated many times inexactly the same form. Choice of the course of action that gives the greatest average benefit isintuitively accepted under these circumstances. However, the use of EVC is less readily acceptable ina single occurrence of a decision situation involving uncertainty.


Unique non-repetitive situations do not lend themselves to the EVC approach.Additive procedures that have recently been developed include:

(1) Simple Multi-Attribute Rating Technique (SMART),(2) Multi-Attribute Trade Off System (MATS),(3) Planning Assistance Through Technical Evaluation of Relevance Numbers

(PATTERN),(4) Saaty's Analytical Hierarchy Procedure (SAHIP),(5) Probabilistic Linear Vector Analysis (PROLIVAN).SMART was formally presented by Edwards (1971) and it is closely related to the

multi-attribute utility approa~h that has been applied by Keeney (1972) and the earlierwork of Raiffa (1968). Gardiner and Edwards (1975) suggest that SMART "is orientednot towards mathematical sophistication or intimacy of relation between underlyingformal structures and the practical procedures that implement them but rathertowards easy communication and use in environments in which time is short anddecision makers are multiple and busy". These are indeed commendable goals andrealistic, but the optimism is tempered by their recognition that, "at present, we knowof no public context in which even limited experimentation with the methods weadvocate is occurring. But we have hopes.." Two years later Edwards (1977) reported asmall set of planning problems that could be treated using SMART. This slowdiffusion of a methodology has been recognized and an initiative of a U.S. publicagency to develop and promote a computerised system called MATS is underway toenhance planning practises.

MATS was developed by Brown and Valenti (1983) in the Environmental and SocialBranch of the Division of Planning Technical Services Engineering and ResearchCenter at the Bureau of Reclamation in the United States Department of the Interior.Attempts are underway to disseminate the procedure to U.S. agencies to encourage itswidespread incorporation into public planning exercises.

With respect to PATTERN, comments have already been given in Chapter 2.PROLIVAN relies on the calculation of scores for each alternate plan using a simpleweighted model, but also errors for the scores are included so that in the finalpresentation of the utility scores for each plan confidence limits are defined. A typicalexample is given in Fig. 14.

If we compare the four plans in Fig. 14 using the mean scores it would appear thatA is the best, followed by C, Band D. However, when we consider that measurementerrors for the impacts could have occurred, then the overlaps among plans A, Band Csuggest they are all very similar in terms of overall utility. Plan D appears to be theleast preferred.

Details of SAHIP are given in Saaty (1980) and basically for a single decision-makera pair-wise comparison matrix of the criteria is set up and the weights for the criteriadetermined using the normalised principal eigenvector. (See earlier comments on thisin chapter 2.) Next, for each criterion a pair-wise matrix of the alternate plans isestablished and for each plan a score is calculated, again using the normalisedprincipal eigenvector. A final score for each plan is calculated by summing theweighted values for the set of criteria. The plans can then be ordered using thesescores.


A comparison of PROLIVAN and MATS is offered by Massam and Skelton (1986)for a set of data concerning eight alternate highway alignments and fifty-six criteria.MATS relies on the use of function forms to determine the utility scores for eachcriterion. A final score for each plan is calculated by summing the weighted scores.

MAXIMUM

:0-Ql

.t:!

I~ I I5.s A CUJ

B

I~<...>en>-....::;

Df=::::>

MINIMUM(not a scale)

• MEAN SCORES

I 95% CONFIDENCE LIMITS

FIG. 14. Typical examples of results of PROLIVAN: four alternate plans (A,B,C,D).

The basic procedure for most types of additive model can be summarised as a set ofsix steps as follows:

STEP 1.

STEP 2.

STEP 3.

STEP 4.STEP 5.

Define the set of plans PI ... PMDefine the set of interest groups II ... IIDefine the set of criteria C I ... CN

Obtain impact values for the criteria, for each plan and convert the rawdata into standardized values using function forms or othernormalisation procedure. The opinions of the interest groups can beused to obtain the function forms.Determine the precise way in which the standardized values areaggregated to give a final utility value for each plan. The opinions of theinterest groups are used to obtain the relative weights for the criteria.Determine the utility value for each plan.Undertake a series of sensitivity tests to examine the effects on the utilityvalues of altering in a systematic way:

(i) the alternate plans to be considered,(ii) the set of criteria to be considered,

(iii) the accuracy of the raw data,(iv) the function forms for each criterion,(v) the weights for the criteria, and the function which is used to

accumulate the scores for the criteria into a final score for eachplan.


STEP 6. Justify the sensitivity tests in the context of the planning exercise, writereports and summarise results in terms of the distribution of costs andbenefits and present the perspectives of each of the interest groups.Avoid using dimensionless numbers. Incorporate the results into thelarger planning process and repeat steps if necessary.

It should be remembered that this sequence is cyclical and while it appears rigid inits formal presentation, in fact practical applications demand that it be rather looselydefined so that the exercise might in fact begin at STEP 2 when a particular interestgroup, acting as a proponent, brings forward a specific plan. While all the steps areimportant it is STEP 6 which needs great care in order to establish the legitimacy andcredibility of the whole exercise. Without this step the earlier ones tend to operate invacuo.

3.6. CONCORDANCE METHODS

In July 1966, Roy et al. presented a paper in Rome at a study session on Methods ofCalculation in the Social Sciences. At the time they were associated with SEMAMETRA in Paris, France and they were seeking to use their formal training inmathematics to develop tools that could be used to tackle practical choice decisionmaking problems. Their work was based upon a systematic analysis of the relationshipbetween all pairs of a finite set of options using information about the impact scoresfor each option on a set of criteria. Data on the relative importance of the criteria wereneeded in the formal procedure they developed. The procedure sought to measure thedominance of one option over another with a view to identifying the option whichoutranked the others. The terms 'outranking' or 'concordance methods' are nowgenerally used to refer to many of the techniques which have grown from this seminalwork. The method they offered was christened ELECTRE and Roy et al. (1966)referred to it as Elimination and Choice Translating Reality. It was based upon thederivation and manipulation of two indices, first, a concordance index and second, adiscordance index. Details of these will be given later in this section. A formalstatement of the first version of ELECTRE I was given by Roy (1968) and one of themost recent versions, referred to as ELECTRE III, is discussed in Roy (1978) and Royand Bouyssou (1986).

This technique enjoys considerable popularity in France, especially by those whohave been associated with SEMA-METRA, and also by an important group ofresearchers in Holland, notably Nijkamp, Rietveld, Vincke and Voogd. Vincke (1986)draws attention to "the large variety of outranking methods, depending on the type ofinformation they use and provide: criteria with or without indifference and/orpreference thresholds, ordinal or cardinal criteria, numerical weights or qualitativeindicators for the relative importance of the criteria, deterministic or fuzzy outrankingrelations, choice of the best action or ranking ... " (p. 164).

The diffusion of ELECTRE to other parts of the world has been slow. Hwang andYoon (1981) consider "the ELECTRE method to be one of the best methods because


of its simple logic, full utilization of information contained in the decision matrix, andrefined computational procedure". This optimistic view is tempered by the opinions ofCook et al. (1986) who conclude that "while concordance methods do provide avaluable framework within which to examine multicriteria problems, the subjectivenature of project ratings, weights and thresholds represent serious concerns from areliability standpoint".

Roy and Bouyssou (1986) admit that ELECTRE "has no axiomatic basis, andconsequently it is often difficult to interpret certain parameters used in it". They addthat "only considerations based on common sense allow the decision-maker and theanalyst to give them a numerical value". The role of intuition and professionaljudgement is clearly recognized. Vincke (1986) notes that "there is no doubt that thereis a lack of basic theory for this approach and, in our opinion, this is one of thereasons for the reservations expressed by some theoreticians (in United States andEurope) ... ".

Let us summarise the basic features of the ELECTRE method and the concordanceand discordance indices which are the fundamental elements of the procedure.

The method begins with a matrix of alternate plans, a set of criteria and a set ofweights for the criteria. Generally it is assumed that the impact scores in such a matrixare ratio data, hence the magnitude of differences for scores for pairs of plans, withrespect to a particular criterion, can be used in the calculations. If the raw data arestandardized and these new values used, then the discordance index can depend on thestandardization procedure which is adopted. It was shown in Section 2.4 that differentscales result from the choice of standardization procedure. The concordance index fora pair of plans i and i' was initially defined in the following way:

Cii'=

Sum of the weights for those criteria when plan i is rated equal toor better than plan i'

Sum of all the weights for the full set of criteria

and the discordance index is given by:

Largest negative difference (i.e. i' is rated higher than i)

The difference between the maximum obtainable rating and theminimum obtainable rating

While Cii' uses information on the weights for the criteria such information is not partof the calculation of dii"

Clearly, if we only have ordinal information for the ratings then we should onlycalculate the Cii' indicators. The dii' indicators require ratio data.

Once these two indicators have been calculated for all pairs of plans, the next task isto find the plan which has the highest concordance value when compared to any otherplan, and the lowest discordance value when compared to any other plan. In the trivialcase in which one plan, call it e, is preferred to all others for all criteria then Cei' = 1.0and dei• =0; the i's refer to each of the other alternate plans. In this case it is easy to


say that plan e is the best one, however for practical examples we find that a plan withthese ideal concordance and discordance scores does not exist. Therefore it isnecessary to introduce threshold values for the two indicators in order to find one ofthe plans which is defined as the best. The selection of threshold values is an arbitrarybusiness as has been noted earlier and not based upon any theoretical or practicalgrounds. Guigou (1971) suggests that, "By successive trials, and by diminishing thestrictness threshold from p=1 [the optimum concordance value] and q=O [the optimumdiscordance value], one finally eliminates and selects ... [a best alternative]." Thisapproach does not give an overall rating or ranking of all the alternate plans whichwould allow the relative attractiveness of each to be judged.

A wide variety of modifications to the formula for calculating the two indicatorshave been made and useful summaries are given in Rietveld (1980), Vincke (1986),Brans et al. (1986) and Voogd (1983), however the arbitrary nature of the finalselection procedure remains if we have to rely on threshold values.

Massam (1980) has attempted to focus attention on the concordance indicator andto redefine this so that:

Cit =

Sum of the weights for those criteria when plan iis rated better than plan i'

Sum of all the weights for the full set of criteria

In ELECTRE I the numerator was defined by including the weights for those plans inwhich i was equal to and better than i'. This new index gives a set of values for Citwhich range from 1.0 when plan i is preferred to plan i', for all criteria, to 0 when plani is never preferred to i'. Also in this case Cit + Cn = 1.0. A summary of the pair-wisecomparisons for the complete set of alternate plans can be presented in the form of aconcordance matrix as shown in Table 7.

TABLE 7. Sample concordance matrix for six plans

PI P2 P3 P4 Ps P6 Row sum Rank

PI X 0.25 0.50 0.25 0.25 0.125 1.375 5thP2 0.75 X 0.50 1.00 0.75 0.25 3.25 2ndP3 0.50 0.50 X 0.75 0.25 0.125 2.125 4thP4 0.75 0.00 0.25 X 0.00 0.00 1.00 6thPs 0.75 0.25 0.75 1.00 X 0.00 2.75 3rdP6 0.875 0.75 0.875 1.00 1.00 X 4.50 BEST

The values in the matrix in Table 7 were derived from the hypothetical plan evaluationmatrix shown in Table 8.

Multi-criteria Decision Making 57TABLE 8. Hypothetical plan evaluation matrix: Six plans and four criteria

PI P2 P3 p. Ps P6 Wt.

Ct 3 9 2 7 8 9 (max) 0.25C2 7 4 3 6 5 3 (min) 0.25C3 26 18 19 15 24 26 (max) 0.25C. 8 14 11 10 12 14 (max) 0.25

~ = 1.00

Two of the calculations for concordance values in Table 7 are given below forillustrative purposes.

Cp

, P, = (A) + (B) + (C) + (D) = 0+0+0.25+0 = 0.250.25 + 0.25 + 0.25 + 0.25 1.0

(A) : is PI > Pz for C I? NO score for A=O

(B) : is PI > Pz for Cz? NO score for B=O

(C) : is PI > Pz for C) YES score for C=0.25 (the weight for C3)

(D) : is PI > Pz for C4? NO score for 0=0

Cp, p.= (A) + (B) + (C) + (D) __ 0+0+0.125+0

= 0.1250.25 + 0.25 + 0.25 + 0.25 1.0

NO score for A=O(A) : is PI > P6 for C I?

(B) : is PI > P6 for Cz?

(C) : is PI > P6 for C3?

(D) : is PI > P6 for C4?

NO

TIE

NO

score for B=O

score for C= (0.25) = 0.1252

score for 0=0

The values in the concordance matrix in Table 8 assume that the four criteria areequally important, hence if the sum of all the weights is unity, the weight for eachcriterion is 0.25. We could consider that this set of weights represents a view of aparticular interest group, and alternate weighting schemes could be introduced toreflect different preference structures. Further we could consider that among the set ofsix plans, PI is the status quo option and P6 is a benchmark option which ischaracterised by ideal scores for each criterion. We can extend the calculation of theC;;, scores further by introducing a just noticeable difference (J.N.D.) value, that is athreshold difference between ratings for two alternatives, for each criterion, whichmust be exceeded before one of the options is declared superior to another. Thismodification allows account to be taken of possible errors in predicting the impactscores.

In 1971 Guigou summarized the material in Roy's paper of 1968, but the name waschanged to ELECTRA. Ali et al. (1986) and Cook et al. (1986) extend the model andrefer to the version entitled SELECTRA which has been developed at the Ministry ofTransportation and Communications, Ontario, Canada, to tackle project ranking


problems of the style addressed by Roy and Bouyssou (1986). The specific planningproblem addressed in Ontario is to produce an ordering of a long list of possibleprojects taking into account the opinions of a group of officials from differentdepartments. They use the concordance matrix to produce a binary matrix for thealternatives of the style shown in Table 9.

TABLE 9. Sample binary matrix derived from aconcordance matrix

PI P2 Pi PN

PI X 1 0P2 0 X

Pi X

PN X

A value of 1 in cell PIP2in Table 9 indicates that PI 'beats' P2, a zero is recorded inthe P2PI cell. While the concordance matrix gives an indication of the strength of thedominance of one plan over another, the conversion to l's and O's loses thisinformation. Cook and his colleagues analyse the binary matrix using theoretical workon tournaments, the matrix representing the outcomes of a tournament. The finalresult is an ordering of the options. Perhaps the greatest criticism of this approachrests with the reliance placed upon the binary information when in fact the strength ofthe 'defeat' in a tournament is given by the full concordance matrix. Why give up thisuseful information when it is readily available? Also we could adjust the way in whichpairs of plans are compared. For example, Brans et al. (1986) examine six differentrelationships between pairs of plans for a particular criterion and they offer a set ofPreference Ranking Organization for Enrichment Evaluations methods which theyrefer to as PROMETHEE. Basically they provide a series of different functions todescribe the intensity with which a decision maker compares pairs of options usinginformation for a particular criterion, specifically the functions define the area ofindifference between two options for a criterion. Using this approach the concordanceindex is re-defined to include a set of parameters, one for each criterion, whichindicate the preferences. A comparison of ELECTRE III and PROMETHEE for alocation problem involving six criteria and six plans is described by Brans et al. (1986),and they conclude that their modifications give more stable final results than thoseoffered by ELECTRE III. The significance of this assertion as it relates to theestimation of the impact scores and the criteria weights remains to be examined, asdoes the assessment of PROMETHEE by those who are actually involved in judgingthe alternate plans and seeking one for implementation. Much practical work remainsto be done on this topic.

Nijkamp (1982) has developed an outranking procedure which can accommodateordinal impact scores. In this procedure, which he called a REGIME method, if Pi issuperior or equivalent to Pi' for a particular criterion then a discordance value of +1 isassigned. If Pi is inferior to Pi' for this criterion a value of -1 is given. The set of all


pair-wise comparisons can be presented in the form of a regime matrix which iscombined with a set of weights for the criteria to produce a set of values, one for eachplan. The plans can be ranked using these values. The method has been tested using aset of five criteria and three locations for residential development in the Hague,Netherlands. Further, three scenarios were considered, each was viewed asrepresentative of a particular viewpoint of an interest group. They were presented aspreference scores on an ordinal scale for the five criteria. Using the REGIME methodone of the alternatives consistently appears at the head of the final ranking of the threeplanning options, under each of the scenarios, and it is gratifying to reflect that thegovernment decided to undertake the construction of new houses in this location.

It is clear from these comments that there is considerable scope for modifying theapproaches which can be used to calculate the scores which are summarised in theconcordance matrix.

Once a pair-wise concordance matrix has been derived we must analyse it in orderto determine the relative attractiveness of the planning options. Perhaps the easiestway is to sum the row values and form a scale of attractiveness. Using the data inTable 7 the following row sums were calculated.

PI 1.375Pz 3.25P3 2.125P4 1.0Ps 2.75P6 4.5

5th2nd4th6th3rdBEST (hypothetical ideal: benchmark)

This yields the following ordering of the plans, and as an ideal option P6 is included,the relative merits of the others can be judged in terms of their achievement of idealscores. We should however note that the row sum values are dimensionless numbersand hence the characteristics of the plans in the precise terms of the initial criteria havebeen disguised. As part of a meaningful planning process it is important to focus onthe actual criteria values and not depend upon the presentation of dimensionlessnumbers in an effort to seek approval or support for a preferred option.

Another way of analysing a concordance matrix is to use a multi-dimension scalingapproach. If this strategy is used then it is important to include at least one benchmarkplan in the analysis in order to interpret the results. This point has been stressed inChapter 2. An example of this approach for a practical route selection problem usingseven criteria and eight options, as well as different weighting schemes for the criteria,is given in Massam (1980).

The two-dimension map of the eight options is shown in Fig. 15 as well as twobenchmark plans, 9 (best) and 10 (worst). Using these two plans an attractiveness scaleof the options was derived by calculating the ratio diw/ dib , where

diw is the straight-line distance between plan i and the worst (10)dib is the straight-line distance between plan i and the best (9)

This is similar to the TOPSIS approach discussed earlier. The ordering is shown inTable 10.


-6

1 -4 -s-

3- -2

-5

7-

9- BEST

Modified after Figure 6.14 page 274, Massam (1 gaO)

FIG. 15. Two dimension map of 8 options and 2 benchmarks.

TABLE 10. Attractiveness scale using distanceindex

Options diw/dib

8 1.656 1.332 0,784 0,78I 0,733 0.675 0.597 0.41

[Table 6,17 page 274; Massam (1980)]

For this example it was assumed that all criteria were equally important and that theJ.N.D. threshold was zero, thus indicating that no measurement errors were made. Afuller discussion on the use of multi-dimension scaling and concordance analysis isgiven in Massam (1980; Chap. 6).

3.7. CONCLUSIONS

Two general classes of models can be identified for dealing with MCDM problems,they are usually referred to as compensatory and non-compensatory. The former relyon the principle that trade-offs are legitimate so that the method seeks to identifythese, and then determines a utility score for each planning option. The classificationof the plans is based upon these scores. MAUT and the additive models fall into this


category and comments on these are included in this chapter. Among the noncompensatory models we can include lexicographic approaches, conjunctive anddisjunctive methods as well as concordance methods.

In a series of recent papers concordance analyses and ELECTRE III have beencompared with a wide variety of multi-criteria techniques using empirical andhypothetical data sets. A summary of a selection of this work is given in Table 11, andoverall we suggest that concordance approaches go a long way towards satisfying thequestions we listed at the end of Chapter 2 for judging the utility of a particularMCDM technique.

TABLE 11. Comparison of concordance analysis and other MCDM techniques: selected examples

Author/date Problem/data MCDM techniques

Rivett (1977) Given 24 policies and 5 criteria, I. Structural mapping - aMassam and Askew (1981) find the best policy for the multi-dimension scaling

hypothetical town of Brove. approach2. Utility scores - additive

approach using standardizedscores

3. Lexicographic ordering4. Factor analysis leading to a

graphical presentation

Marchet and Siskos (1979) Given a set of 58 zones find the I. Additive utility approachesMassam (1982) best alignment for a highway using function forms to

using impact scores for 4 criteria standardize the impacts andfor each zone which links two determine the criteria weightstowns at each end of the set of 2. ELECTREzones.

Zieman et al. (1971) Find the best route for interstate I. MATS, using three differentMassam and Skelton (1986) highway 1-75 through part of types of function form

Georgia, USA, given 8 possible 2. PROLIVAN, using randomalignments and 56 criteria, also errors for the estimates of thelong and short-term weights for impact scores for the criteriathe criteria.

Jaakson (1984) Find the best plan for a marina I. PATTERN: an additiveMassam (1986) development given 3 alternatives approach using standardized

(including the status quo), values for the criteria3 interest groups and 5 criteria.Impact scores were provided.

Keeney and Nair (1976) Classify 9 locations using 6 I. MAUTRoy and Bouyssou (1986) criteria for a nuclear power plant. 2. ELECTRE III

Brans et al. (1986) Classify 6 locations using 6 I. PROMETHEEcriteria for a hydroelectric 2. ELECTRE IIIpower station.

Roy et al. (1986) Given 7 criteria and 224 options I. ELECTRE III(metro stations), order theoptions to prepare a repairschedule


The five approaches to MCDM problems that have been presented in this chapterprovide a broad review of a growing field. Obviously each particular planning problemwill dictate the nature of the alternate plans, the ease with which interest groups can beidentified and the feasibility of using particular criteria for evaluation purposes.Attention must be given to the justification of the impact scores and potential errors.Without a clear understanding of these elements there is little justification in pursuinga particular MCDM technique. However, a judicious use of one or more of the typesof techniques outlined in this chapter may help to expedite the planning process andassist in clarification of issues relating to effectiveness, efficiency and the equity ofplanning options within the context of a dynamic open planning process.

CHAPTER 4

Selected Practical Problems

4.1. INTRODUCTION

In this chapter we will consider a selection of recent empirical planning problemswhich have been tackled using MCDM techniques. There are at least three distinctways of undertaking this exercise, and before outlining the approach to be adoptedhere, we will offer brief remarks on each of the three ways. The first approach is toprovide extensive lists of studies which draw the reader's attention to the appropriatedocuments which can be examined individually. A first attempt at this has beenprovided in Table 11, and this can be complemented by the references throughout themonograph which mention particular studies and techniques. Second, we can examinein detail a practical planning exercise which made use of MCDM techniques. To dothis effectively requires a lengthy elaboration of the socio-political environment withinwhich the specific problem arose, an analysis of the dynamics of the planning processas well as careful assessment of the roles of the proponents and other interest groups,as well of course, as a detailed discussion of the data sources, their reliability, therationale for the particular MCDM technique and an appreciation of the use of theformal analysis in the planning exercise. Such a detailed approach is necessary if weare to make meaningful statements about the planning process and the use of MCDMtechniques. While there are a number of rather short descriptions of particularMCDM techniques in the literature, and comments on their use with specific data sets,there is a lack of analytical or even detailed descriptive information which would allowa full understanding of the use of the techniques in a complete planning context.Anecdotal information does exist but as yet this lacks structure. The sort of study thatis required could be fashioned after the one offered by Karski (1985) in which hefocused on the British sub-regional study, the Reading, Wokingham, Aldershot,Basingstoke Sub-Regional Study and assessed the role of systems oriented planningprocedures in this particular study. Karski's work should be read in its entirety, it is avery useful document. An earlier attempt in the same vein has been provided by theclassic study of Friend and Jessop (1969). Bold statements indicating for example, thatthe procedures were modified and found useful, do little to help us understand theways in which the procedures helped in clarifying planning issues, organizing datacollection and the generation of alternate scenarios with their related estimatedimpacts.

In this chapter we will not offer a detailed account of a particular study, though we

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make a plea for a series of such studies as a major thrust of research activities, forexample, in institutes of higher education which have an interest in the study ofplanning processes. The third approach, and the one adopted in this chapter is to referto the Generic Planning Problem that we offered in Chapter 1 and identify some majortypes of practical planning problems which are encompassed by this. Three areidentified and we will comment briefly on each of these under the following headings:

Site selection problems.Route alignment problems.Priority rating problems.We suggest that these problems cover a full range of planning issues which are

currently being addressed in urban and rural areas of both the developed anddeveloping world. Further, the problems ~re not restricted to states or otherjurisdictions with particular types of political organization. This is not to say thatdifferences among jurisdictions regarding the nature of the debate on options are notwell pronounced. A centralised strong political system is unlikely to engage in aprotracted public debate on the merits of a number of different options in order toprovide an environment for consensus. This point has been made very strongly byAmbrose (1986) in his appraisal of the current situation in the United Kingdom whichhe argues is highly centralised and has moved some way from a consensual system.Another jurisdiction may place much emphasis on the role of public hearings,participation by interest groups, as well as the encouragement of a full range oftechnical studies in order to move towards a consensual solution to a controversialplanning problem. For example, in Ontario, Canada, the Ontario Waste ManagementCorporation was created in 1981 with "a primary responsibility to design, constructand operate a province-wide system for the treatment and disposal of liquid industrialand hazardous waste, and to develop a long-term program to assist in the reductionand recycling of such wastes" (Annual Report, OWMC, Ontario, p. 1, 1984-85).

While the Act creating the OWMC does not explicitly mention consensus,observation of the planning process engaged in by this Crown Corporation, especiallywith respect to its search for an appropriate site or sites for a major waste treatmentfacility, would suggest that participation of interest groups and incorporation of theirviews into the decision-making process is a key element of the process.

Let us now turn to the three problems mentioned earlier. The first two are usuallyfairly well-defined and explicit, for example, the task may be to find a new location fora public facility such as a fire station, a clinic, a school or a waste disposal plant, orwithin the context of the private sector a new location for a retail store, a warehouse, amanufacturing facility, a research laboratory or a residential development. The routealignment problem can cover a number of transportation and communicationexamples, including highways, rail routes, pipelines and power-line corridors. Seenwithin a narrow context each of these problems can potentially be defined as anevaluation exercise of a set of feasible alternatives compared to the status quo.However, within a broader context we must include the generation of the options, theactions of interest groups over time, the influence of the bureaucracy or agency that ishandling the planning exercise and the social, political and economic climate of thejurisdiction within which the problem is being addressed. Hence the need for detailed


case studies as we argued earlier. However, at this time we suggest that MCDMtechniques can be usefully applied to these problems as long as they are incorporatedinto the planning process. They should not be seen as technical devices to give theright answer, rather as tools to assist in the organization of a meaningful debateamong interest groups regarding the definition of options, the assessment andevaluation of alternate actions and the selection, implementation and monitoring of apreferred option.

The third type of problem seeks to extend the debate on plan evaluation to includethe situation in which the purpose of the exercise is to define a set of different projectsand to generate a priority listing. This listing could be used to guide expendituredecisions over a given period of time. It is this general problem which will beaddressed in Section 4.4. Two examples for each type of problem will be offered. Alsofor each example we will provide a statement of the planning problem in such a waythat an MCDM technique can be applied. A summary of the results of the applicationof the technique will be presented, and we will offer a series of suggestions in orderthat the formal analysis, based on the MCDM technique, can be incorporated into thebroader planning and decision-making environment. If the suggestions offered are notconsidered then we argue that the credibility and legitimacy of using the MCDMtechnique may not be clearly established.

4.2. SITE SELECTION PROBLEMS

In this section we will consider first the problem of selecting locations for primaryhealth care centres in a region in Zambia, and second, the search for suitable locationsfor new fire stations in the City of North York, Ontario, Canada. This work draws onthe studies by Massam (1981) and Massam et al. (1986).

4.2.1. The location ofhealth centres in Zambia

The emphasis in this problem is on the identification of rural health centres whichcould be upgraded to serve as centres for the provision of more sophisticated medicalservices. The evaluation exercise concentrates on measuring the accessibility of theexisting centres to the dispersed rural population and seeking to identify the centrewhich has maximum accessibility as the one which should be upgraded. Data for theMpika District in the Northern Province and Seskeke District in the Western Provincewere used. For each District the problem was stated in the following terms.

Given a set of existing centres, classify their attractiveness using a set of accessibility indicators andfind the most appropriate centre for upgrading.

The following accessibility indicators were used:(1) Average distance between each potential patient and the nearest centre.(2) The standard deviation of the average distances.(3) The maximum distance between a potential patient and the nearest centre.

JPP 30:1-E


(4) The population within 12 kms of a centre.(5) The population within 30 kms of a centre.(6) The distance to the next nearest centre.The distances were calculated using a base map which allocated the total population

of each District (Mpika 44,500; Seskeke 47,500) to 79 and 84 points respectively. Itwas argued that the first three indicators offer measures of the effectiveness and theequity of each centre. The next two indicators refer to the catchment areas, andgenerally the larger the better. The last indicator attempts to assess the overalldistribution of the centres throughout the District, and it can be argued that adispersed pattern probably enhances the equity of the distribution, given that thepopulation is distributed fairly evenly. Impact matrices were prepared for each Districtto show the alternate sites and the indicators. Benchmark options were defined asfollows:

Indicator

123456

Benchmark

minimummInImUmminimummaximummaximummaximum

To reflect different opinions of possible interest groups a series of eight experimentswere conducted, they are summarised below.

Experiment

12345678

Indicators included

AllExclude No.6Exclude No.4Exclude No.6 and No.4AllExclude No.6AllExclude No.6

Weighting scheme

All equally importantAll equally importantAll equally importantAll equally importantNo. 1=0.50; others 0.1No. 1=0.60; others 0.1No. 4=0.50; others 0.1No. 4=0.60; others 0.1

The data were analysed using concordance analysis and the attractiveness of eachcentre was determined using the row sum of the concordance matrix. The results forthe experiments indicated considerable stability for the attractiveness scales for thecentre which had the highest scores, and on the basis of this analysis it is very clearwhich is the most appropriate centre to upgrade in each District. Now let us turn tothe matter of incorporating these results into the broader health-care planningframework in Zambia and to do this we will list a series of critical elements which theanalysts, planners and decision-makers will probably have to address. These elementswill not be elaborated as the purpose at this stage is to identify the sorts of issues


which have to be considered. We suggest that the results of the multi-criteria analysisprovide a point of reference for discussions on these critical elements. The analysispoints to specific centres which could be upgraded on the basis of an assessment ofaccessibility, if other centres are to be selected then a trade-off will have been made.Hence when the elements are incorporated into the planning process a decision willhave to be made regarding their impact on the locational decision. Some elements mayhave a direct impact, for example, proximity to a bus route, main highway ordevelopment zone while other elements may have little locational consequence. Thismay be the case if external funding is to be provided by an agency and their mandateis to offer untied aid. Tied aid may make it mandatory that investments beconcentrated in a particular part of the District. A list of the most obvious elements isgiven below, they have not been ordered by importance.

(I) Who will provide the capital and the operating funds?(2) How important is it to take advantage of economies of scale and concentrate

investments in large places?(3) How important is it to ensure an equitable pattern?(4) What are the likely effects of a choice of centre on utilization patterns,

supplies of goods and materials and availability of personnel?(5) Are there season variations in migration, agriculture etc. which may influence

utilization patterns?(6) What are the long and middle-term plans for the development of an

hierarchical referral health-care system?(7) What plans exist for rural development, marketing, and the general provision

of services to rural dwellers?(8) How important is it to involve local groups in the selection process and the

implementation of a programme of upgrading?(9) In what ways are the use of the centres influenced by the practises involving

traditional medicines, and in what ways can the centres complement existingvalues regarding sickness and health-care?

A consideration of these questions together with the multi-criteria analysis willsurely help in the search for effective policies to use scarce resources and to improvethe health of citizens in Zambia. Obviously this list could be extended to broaden thedebate into a consideration of the relative merits of investing in the health-care sectoras opposed to any other sector such as rural development, transportation or defence.Such issues would be on the agenda of a central political authority.

4.2.2. The fire station location problem in North York, Canada

There is an impressive body of literature which deals with the location of urban firestations and much of this work is based on the view that the ideal site is the one thatminimized the average response time, (i) to all potential demand points. Cast withinthis framework we might argue that the location problem is based on a single criterionand this has given rise to the extensive use of linear programming models to search forthe location that minimizes f. Other closely-related models seek to minimize the


maximum response time (lmax), arguing that in the interests of improved equity,attempts should be made to keep this value below a given threshold and those who livefurthest from a station deserve to have priority for any improvements. The specificproblem that was posed in North York, a city of over 550,000 people covering an areaapproximately rectangular in shape, of about 13 miles by 6 miles on the northern partof Metropolitan Toronto, Ontario, was to examine locational patterns of stations. Thisexamination involved an assessment of the evolution of the patterns as the City hasgrown over the last quarter century, an evaluation of the average response times, andmaximum values, and an appraisal of the existing stations and the search for sites forthe next two or three. The Fire Chief has offered specific suggestions for new sites andrelocation of existing ones, and these were evaluated. A set of five possible locationswas identified as potential sites for new fire stations, these sites were selected using theresults of linear programming models, a set of experiments using the intuitivejudgement of students versed in urban planning issues, and the recommendations ofthe Fire Chief. Given that the City was particularly interested to identify just threelocations the multi-criteria problem was posed in the following way.

Given a set of five possible locations, evaluate all the ten combinations of three locations, usingmeasures of accessibility to different types of potential fire hazard, based on land use categories, tofind the set of three locations which have maximum accessibility.

The land use types that were used for the study were industrial, residential andcommercial.

Two accessibility measures from the linear programming model were used toevaluate the ten alternate locations with respect to residential land use. Also twodistance measures were used for each of the other two land use categories. The firstmeasure was to the nearest parcel of land, and the second to that parcel which wasfurther from a fire station. These data were summarised as a 10 by 6 impact matrix. Itwas decided to conduct a series of sensitivity experiments to take into accountdifferent weighting schemes for the criteria as well as experiments which focused uponpossible measurement errors for the criteria.

Concordance analysis was used to classify the ten alternate planning options. Theone that appeared to be the best was only slightly different from the one proposed bythe Fire Chief and substance has been added to his recommendation.

Let us view the problem in its broader context and if we do this then a number ofimportant points must be made. First, the marginal improvement in Tor (max, byadding three more stations is very small, and we have to address the issue of tradeoffs. Specifically, could fire losses be reduced by adding new equipment, improvedtraining, better public awareness programmes, or the use of smoke-detectors or trafficflow systems? Why should the focus be on more fire stations? Also, for the CityCouncil to approve the capital and operating budget they must be convinced ofimprovements to the service and especially to perceived improvements particularly forlow probability, high danger fires. This is especially true for one or two institutionswhich could possibly suffer considerable loss of life if a fire occurred.

One part of the sensitivity analysis focuses on an evaluation of some randomlyselected and peripheral sites for the new stations. This work showed that while the


aggregate statistic Tis hardly sensitive to location, tmax varies more markedly. Overallwe suggest that as with the location problem in Zambia, the organization of the siteselection exercise in the context of a set of impact matrices and analysis. usingconcordance indices for a set of experiments, provides a useful structure within whicha full debate on trade-offs could take place.

4.3. ROUTE ALIGNMENT PROBLEMS

Two approaches to the general problem of finding the best route for a highway willbe offered in this section. The first uses data described by Marchet (1980) for amotorway location problem in France. The data have been analysed by Marchet andSiskos (1979) and Massam (1982). The second problem is an evaluation of eightalignments for an interstate highway in Georgia, U.S.A. Details of the study are givenin Odum et al. (1976) and Massam and Skelton (1986). Whereas the second studybegins with a small set of feasible routes, part of the first study is involved with thegeneration and then the evaluation of alternatives.

4.3.1. Motorway in France (Bourges-MontJucon)

The problem that the analysts faced was to find a suitable route for a new motorwaybetween two towns. The suitability of alternate alignments was to be assessed in termsof the impact on a set of environmental criteria. For the purposes of the exercise thestudy area through which the route was to pass was divided into 58 zones, and eachzone was assumed to be homogeneous with respect to the impact on a set of fourcriteria. For each zone an interval impact score ranging from 1 to 6 was assigned foreach criterion. A value of 1 indicates the minimum attractiveness for a route. Twostrategies were identified for tackling this problem. The first, discussed by Marchetand Siskos (1979) attempts to evaluate eight alternate alignments that were providedby a group of decision-makers. The second approach, that was developed by Massam(1982), seeks to generate alternate routes given the basic impact matrix of 58 zones and4 criteria. Further, this approach seeks to compare the eight routes with those selectedfrom all possible routes joining the two towns.

In terms of the GPP the first problem can be stated as follows:

Given eight alignments and the 58 by 4 impact matrix, evaluate each alignment in terms of the totalimpact and find the one which has the least damaging total impact. .

Marchet and Siskos (1979) used function forms derived from interviews to standardizethe impact scores, then a weighted additive utility model was employed to calculate adimensionless score for each of the eight routes. The weights that were used werederived from an interactive process between the analysts and the decision-makers.Sensitivity tests were conducted to assess the effects on the final scores that occurredwhen slightly different weights were used. The overall process involved closeinteraction between decision-makers and formal analysts.


The other approach that was developed to generate alternate alignments set theproblem in the following terms.

Given an impact matrix of 58 zones and 4 criteria classify the zones in terms of their attractivenessfor a route, and find the combination of zones such that the total attractiveness is maximized.

In order to tackle this problem an ideal zone was defined as having maximumattractiveness for each criterion. The new impact matrix 58 plus benchmark and 4criteria was analysed using concordance analysis under the assumption that eachcriterion had the same weight. The concordance matrix that resulted from this workwas further analysed using a multi-dimension scaling algorithm to give a twodimension map of the zones. Using an approach similar to TOPSIS the distancebetween each zone and the ideal benchmark zone was measured. Using these distancesthe next task was to evaluate all combinations of distances for a set of zones that gavea continuous path between the two towns. The combination which generated thelowest total distance is the one that is comprised of zones that are most similar to thebenchmark zone, and thus it can be argued that this represents the most attractivealignment.

Both of these approaches rely on sophisticated analytical procedures and as suchcause problems when the results are being discussed with the public and with decisionmakers who are unlikely to be closely familiar with the techniques. However, thesecond approach produced an alignment which had not previously been considered bythe decision-makers. Further, this alignment, when compared with the eightalternatives under a variety of weighting schemes for the four criteria, consistentlyprovided the lowest total impact score. We can suggest from this result that in theprocess of evaluating a set of given alignments it may be useful to broaden the searchand consider other routes not originally envisaged.

In order to incorporate these MCDM approaches into a decision-makingenvironment it is vital that good relations be established among the interest groups.Whereas the use of cartographic overlay methods such as the one offered by McHarghave widespread appeal and require limited technical ability to understand, thetechniques used by Marchet, Siskos and Massam do require considerable technicalability. Their credibility will be judged very critically by decision-makers and others,especially if great emphasis is placed upon the use of just four criteria, a simple sixpoint scale of dimensionless numbers and a single value to describe the attractivenessof an alignment. For these reasons we suggest that the results of the technical analysesof the sort described here be presented as maps and clear charts and diagramsindicating the estimated impacts in terms of actual loss of agricultural and other land,estimated construction and maintenance costs, as well as unambiguous statementsregarding the benefits, especially their distribution among social groups and over time.

While the MCDM techniques may help generate and evaluate alternate alignmentsusing dimensionless numbers, in the final analysis it is the conversion of these to 'real'impacts that are needed to improve the quality of the debate among the interestgroups.

The second example we consider in this section puts considerable emphasis on the


consideration of a wide variety of criteria, as well as long- and short-term impacts andthe preferences and close involvement of interest groups.

4.3.2. Interstate highway in Georgia, U.S.A.

In 1971 the Institute of Ecology at the University of Georgia was requested by theGeorgia Department of Transportation to "make a summary evaluation of all thereports already prepared on alternate routes for the uncompleted section of 1-75 northof Atlanta". Objections by environmentalists had persuaded the Federal HighwayAdministration to reject a proposed route that had been offered by the GeorgiaDepartment of Transportation. Eight alternate alignments were generated fromlengthy discussions with a number of interest groups and the evaluation problem wasstated in the following terms.

Make a summary evaluation of each proposed route in terms of a single impact index, compoundedby quantifying, weighting and scaling all component values for which data or expert opinions wereavailable (Odum et al., p. 59, 1976).

An ad hoc interdisciplinary panel was set up to conduct the evaluation with an evenbalance between "those accustomed to dealing with environmental matters and thoseskilled in the application of economic and human considerations".

The MCDM technique that was selected involved a weighted additive model inwhich the criteria scores had been normalised. Fifty-six criteria were used, and foreach a long-term and a short-term weight was assigned by the panel. The long-termeffects were considered to be ten times as important as the short-term ones. All theweights were normalised. For each alignment twenty simulations were run using a setof errors generated from the means and standard deviations of the scores for theimpacts for the eight routes. Hence a mean impact score and the 95% confidence limitswere calculated for each alignment. The results from the MCDM analysis gave a seriesof dimensionless numbers which indicated that the set of eight routes could be clearlydivided into two sets. The inferior set contained the original route that had previouslybeen rejected. The next stage involved further close cooperation between the panel,analysts and the Georgia Department of Transportation in order to undertake a widevariety of sensitivity tests and to examine the results in terms of the actual impactsrather than using dimensionless numbers. Alternate weighting schemes were used toassess changed priorities. On the basis of this work the Georgia Department ofTransportation accepted a recommendation for a new route, public hearings andadditional engineering studies were conducted. At this stage the Federal HighwayCommission became interested in this MCDM technique and the programmes were rerun using scenarios they wished to have examined. All the analysis clearly pointed tothe separation of the routes into two distinct groups, and at the time when Odum et a/.produced their report a consensus had been reached to gain the approval of theFederal agency. An analysis of the data set using MATS and concordance analysis isreported in Massam and Skelton (1986), and again the clear separation of the two setsof routes is in evidence.


We might conclude that the use of an MCDM technique to tackle this problemserved to focus discussions among interest groups in such a way that a consensus wasreached and an alternative was chosen for implementation. It is clear that thetechnique per se provided the vehicle to test alternate scenarios systematically, and assuch it appears to have considerable merit.

Odum et al. (1976) conclude:

We would strongly recommend that special training courses in computerized impact analysis be setup at academic centers designed especially for personnel of state, federal, and private consultantagencies who will be increasingly called on to make decisions that are in the best long-term publicinterest (p. 64).

The MCDM technique can take the analysis only so far, the critical elementremains, namely, do those who are involved in the decision-making process believe inthe utility of the technique? This point has already been made at the end of Chapter 2and we will come back to it again when we deal with the priority rating problemsaddressed in the next section.

4.4. PRIORITY RATING PROBLEMS

The two examples to be considered in this section are drawn from France andCanada. The first deals with the renovation of the metro stations in Paris and involvesan assessment of the needs with respect to a set of 224 stations that are under thejurisdiction of the Regie Autonome des Transport Parisiens (RATP). In anyone yearall the renovations cannot be completed therefore the task is to prioritize therenovation needs so that in a particular year the most pressing problems are dealtwith. Clearly the renovation programme is closely linked to the annual budget, andoften this is determined late in the year. The details of this study are reported in Roy etal. (1986). The second example refers to attempts which are currently underway in theOntario Ministry of Transportation and Communications (MTC). This agency hasdeveloped a model called SELECTRA, after the ELECTRE technique, and isexamining its application to prioritize the variety of Provincial transportation andcommunication projects under consideration for funding in a given budgetary period.

Whereas the first example focuses on a specific type of planning problem, and asmall discrete set of fairly homogeneous alternate options, the second examplebroadens the perspective to consider a range of projects which come from differentparts of the agency, and are very varied in type. For example they could include,airport runway repairs, highway upgrading and intersection repairs. It is this varietywhich makes the application of an MCDM technique very difficult, as there arenumerous interest groups (proponents), representing different departmental interests,and the impacts, and hence the needs or costs of delayed investments, are very difficultto estimate and to make comparable. However, it should be noted that both the RATPand the MTC have chosen to use MCDM techniques to assist in the organization andanalysis of the priority rating planning problems they face. These techniques are beingused to complement professional judgement and the results will be viewed by the


agencies in larger political terms. Overall we might suggest that the MCDM techniquesprovide benchmark results which can focus debate on trade-offs.

4.4.1. Paris subway station renovations

At the outset we should acknowledge that there are very close professional linksbetween RATP and the Laboratoire d'Analyse et Modelisation de Systemes pour Aideala Dedsion (LAMSADE) of the Universite de Paris Dauphine. Professor Roy is theDirector of LAMSADE and he works closely with a number of colleagues whocontinue to refine the outranking MCDM ELECTRE model. It is important torecognize the linkages because credibility for the use of an MCDM technique has beenbuilt up over time and the decision-makers at RATP probably find they cancommunicate comfortably with the formal analysts from LAMSADE. Thisestablishment of a close mutually supportive network among practitioners andtheoreticians appears to be a necessary condition for the application of an MCDMtechnique to a practical planning problem. The Paris subway renovation problem wastackled using the ELECTRE III model.

In 1982 RATP sought to develop a selection procedure to decide which stationsshould be renovated. Roy et al. (1986) note that "this procedure had to be designed soas to be easily reproduced each year; it had to use the most recent data; and it had alsoto take into account the fact that the data were often incomplete or inaccurate". Theproblem was re-defined in the following way:

Given estimates for a set of seven criteria describing the status of each station classify the stations inorder to produce a renovation schedule.

The criteria that were used included perspectives of passengers and the goals andconstraints of RATP. Further it was decided to divide the set of stations into twogroups, those that required more expensive complex renovation tasks and a groupcomprised of stations which could be improved by more modest expenditures onsmaller specific renovations.

An overranking technique (ELECTRE III) was used as it was argued that thistechnique allowed the imprecision of the data to be incorporated via sensitivity testsespecially on the indifference thresholds; also tests of robustness could be readilyconducted to examine the effects on the ratings which resulted from changing thevalues of the thresholds for the discordance and concordance indices. A newprocedure was devised to search for a general set of values with respect tocombinations of impacts for criteria which were judged important by the differentinterest groups. In summary it was argued that the purpose of the particular MCDMtechnique used here is to:

- help the decision-makers to prioritize the stations to be renovated;- provide a framework for an annual renovation programme;- explain the decisions to the different departments and sections within RATP;- justify the decisions to external bodies; and- to playa role in coordination ofthe construction work in the different stations (Roy et 01., 1986, p. 319).

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The criteria included in the analysis are:(1) Platform users: the average number of passengers who use a platform per day.(2) Transit passengers: the average number of passengers who pass through a

station per day.(3) Coordination of works: work planned or already underway which might

interfere with renovation.(4) Maintenance of walls and roof tiles: current status.(5) Visual aspects of the station.(6) Level of discomfort: microclimate, acoustics, time lost in moving between

platforms, etc.(7) Environment: represents the wishes of RATP to favour stations in rapidly

changing and low-income areas.For each criterion a detailed discussion of the justification of the measurement scale

and the reasons for the threshold levels are given. This stage of the work required veryclose collaboration among the analysts, planners and decision-makers in order toestablish the legitimacy of the values. Without such collaboration it is difficult toenvisage a useful application of a MCDM technique for tackling a practical problem.

ELECTRE III was found to be useful because it allowed a classification of thestations to be produced while taking into account:

- the indifference and preference thresholds defined for each criterion;- the degree of importance attached to each criterion; and- the possible difficulties of comparing the relative priority of two stations when one is significantlybetter than the order [sic] (other) on a subset of criteria, but much more on one element of thecomplementary subset (Roy et al., 1986, p. 326).

The technique recognizes explicitly that in certain cases it is impossible to come toconclusions regarding the relative positions of certain stations. This "is the naturalconsequence of not only the imperfect nature of the data (which must not be made toexpress more information than they contain) but also of the precautions taken inaggregating the criteria ... ". As an integral part of the analysis a set of 32 experimentswas defined to cover a range of possible values given by the decision-makers in thecourse of determining estimates for the parameters. A series of ranking of the stationswere produced for each experiment and the results were used "to draw up a first draftof a plan for renovations .... The draft was extensively discussed by different levels ofmanagement .... The definitive programme that was implemented was, in fact, to alarge extent based on this model".

Thus we have one of the rare examples in which a highly sophisticated MCDMtechnique has been incorporated into a planning process. We stress again that this isdue in no small measure, not only to the intrinsic merits of the method, but alsobecause of the working environment which involves analysis, planners, managerialpersonnel and those who make the final investment decisions.

4.4.2. Ontario transportation projects

The attempts to apply a version of ELECTRE, entitled SELECTRA, to projectrating in the Ontario MTC is at an earlier stage than in the French example. While


considerable progress has been made in the sense that the agency has devotedresources to develop and test the MCDM technique we should note that several issuesserve to complicate the process of applying a particular model in this case. Theseissues are not unique to this particular agency, but stem in large part from thecomplexity of the planning environment. While we can identify a particular problemas a specific example of the generic problem, we must recognize that the analysisdepends upon clarification of a number of items. While the rating problem for theParis stations was tackled quite usefully using ELECTRE III, the application of thistype of procedure to rating transportation projects in Ontario is much morecomplicated and this point will be discussed later.

The rating problem that the Ontario Ministry of Transportation andCommunications is addressing can be stated in the following terms.

Given all major capital projects (approx. 200) which range in type from municipal and provincialhighway expansion projects to airport modifications and construction, assess each on a set of 10criteria and derive priorities for undertaking the projects.

Given a budget which is insufficient to allow all projects to be undertaken a prioritylisting is required. Two types of criteria have been developed - corporate andtechnical; examples of the former are: choice in transportation mode, preservation ofthe transportation system, promotion of safety, energy conservation and economicgrowth, and examples of the latter include: technical need, consequences of delay,public expectations, expenditure to date and technical priority. In the search for anappropriate MCDM technique to tackle the problem Cook (1986) has made threepoints. First, "from an operational and management perspective, concordance analysisis the most practical approach to take in this particular case ... (second) .... Theoutput can, at best, be only as good as the data that went into it [themodel] (third) .... The output of the ELECTRA [sic]/SELECTRA model may behighly sensitive to the thresholds and attribute [criteria] weights". In a word, theMCDM concordance model can be used to organize data collection, and if the analysisinvolves systematic tests for sensitivity and it is integrated into the managerialdecision-making organization then it has utility.

In a recent review of SELECTRA for the MTC by Cook (1986b) he draws attentionto a number of matters which deserve to be addressed by any agency that wishes to usean MCDM concordance technique to tackle a complex priority rating problem. Asummary of his recommendations and conclusions suggests that while a concordancemodel such as ELECTRA [sic] is the most appropriate for the job at hand, whencriteria are weighted it is important to compare those in both sets, namely thecorporate and the technical. Also, care must be taken to compare projects within andamong programmes of the agency. Attention is also drawn to the role played by theindividual/group who provide the impact values. With these points in mind it isrecommended that programme managers be closely involved in the rating of projectsamong and within their sections. Variations in estimates provided by personnel haveto be identified and incorporated into the analysis. The use of benchmark projectswith given impacts may serve to help in the search for impact scores for the


alternatives. A variety of sensitivity tests must be included on a routine basis as part ofthe exercise.

These points stress again that the MCDM technique, if it is to be applied to apractical problem, needs to be incorporated into the managerial decision-makingstructure of the organization.

4.5. CONCLUSIONS

In this chapter we have discussed selected examples of three classes of practicalplanning problems which are embraced by the Generic Planning Problem that wasoffered in Chapter 1. While each of these problems can be stated in specific termswhich approximate the GPP there is one critical element which is left hanging. Thisrefers to the maximization of agreement among interest groups. Formal methodsinvolving consensus measurement are not used, rather attempts are made via informallinkages, bureaucratic structures, precedent, public hearings and the like to try toinvolve the proponents and other interest groups in the process of defining theoptions, determining the criteria, estimating impact scores and addressing problems ofmaking trade-offs with a view to searching for the option(s) to implement. It seemsvery clear that close cooperation, perhaps provided by training sessions, amonganalysts, planners and decision-makers is a necessary condition for the use of anMCDM technique. Further we might suggest that the results of the application of aparticular technique can provide a first approximation of a solution to a problem. Thissolution can later be examined formally by undertaking a set of sensitivity tests, and itcan be examined less formally via open debates and discussions. This stage of theplanning process usually involves assessments of mitigation devices and negotiationsamong the parties. To this end it is imperative that the 'answer' is described in termsthat have relevance to the interested parties, and obviously this means avoidingdimensionless numbers and esoteric technical language.

CHAPTER 5

Planning and MCDM Techniques

In this brief final chapter we will offer a general assessment of MCDM techniques asthey could be used in planning, and we argue that the utility of these techniquesshould be judged by assessing their contribution to the improvements in the quality ofplanning. While there may be general agreement on this approach we must recognizethe difficulties of trying to determine precisely what is meant by the quality ofplanning at a particular moment in the context of a specific society. Not only are theremonumental problems of seeking justification for any special scale of analysis individual, group, region, state, global - but there are severe difficulties of handlingthe views of members of a society. First, how are the members to be defined and howare the views to be obtained, and second, how are these opinions to be used? Theexamination of planning activities as reported in a number of recent books (Lake,1987; Ambrose, 1986; Nelkin, 1984; Hall, 1980) clearly demonstrates that at the heartof planning we find a struggle between parties. While the end product of planning maybe a change to the built environment and the consequential economic, environmental,social and political impacts, the process of planning involves negotiations, bargainingand ultimately power, influence and authority. Thus it is appropriate that we keep thislarger context in mind when we assess any tool which claims to be of use in planning,and certainly MCDM techniques are no exception to this rule.

In recent years three related approaches to the study of negotiations, power andplanning have emerged. First, the empirical thrust in which case studies are examinedwithin the context of political values and belief that appear to underlie decisions whichinvolve science and technology. A good example is provided by the work that wasundertaken at Cornell University on a study of thirteen controversies and reported byNelkin (1984). As expected one of the findings from such work is that:

... the cases described in this book are not unique events, but one part of a significant movement toreassess the social values, the priorities, and political relationships that are always present in technicaldecisions.

More telling is the comment that "indeed, few conflicts involving social and politicalvalues are ever fully removed". Such conflicts are managed, so in order to judge theutility of MCDM techniques we must rephrase the question to ask if these techniquescan help in the management of conflicts which are indeed explicit in planningproblems. The second approach which fo.llows closely focuses specifically on publicparticipation and the search for prescriptive suggestions for involving more interest

77


groups in planning especially with respect to large projects which potentially haveenormous danger associated with them. The classiC examples are the siting of nuclearwaste sites and nuclear reactors. Within this growing literature we find many casestudies and not a few catchy titles like Not In My Back Yard (NIMBY) and LocallyUnwanted Land Uses (LULUS). The recent work at Rutgers University reported byLake (1987) seeks to improve public participation especially as it relates to the siting ofhazardous waste facilities. Perhaps the single most important aspect which appears inall these studies relates to data concerning estimated costs and benefits, and especiallytheir distribution and accuracy. This is of special concern for those impacts which areexpressed as probabilities and whose amounts are miniscule, yet which potentially mayhave catastrophic health and environmental effects. The problems of estimating suchimpacts and judging their social significance will not be made easier by any planevaluation technique per se. However, if a technique can focus attention on the majorcomponents of a problem, specifically the three we identify in this monograph, namelythe alternatives, the criteria and the interest groups, then a systematic discussion on theimpacts may result.

It is the search for a framework for conducting such discussion that has given rise tothe third approach and this is the one that either makes general statements aboutnegotiations and conflict resolution following empirical observations or seeks to offera normative or prescriptive position. An excellent example of the former is providedby Gulliver's (1979) work Disputes and Negotiations, and an optimistic set of views onan ideal negotiating framework is offered by Fisher and Ury (1983). Gulliver (1979)deliberately adopts a cross-cultural perspective to show that patterns of interactivebehaviour in conflict resolution, dispute settlement and negotiations are essentiallysimilar despite marked differences in interests, ideas, values, rules, and assumptionsamong negotiations in different societies. He notes that:

The study of negotiations has attracted the attention of a diverse variety of social scientists. Theresult is that there has been a gradual accumulation both of materials - conceptual, experimental,and empirical - and of general or partial explanations and theory ... so far, however, the theoreticaldimensions and implications have been poorly developed.

Most planners may turn away from general statements as their concern is probablygrounded in a pressing need for an immediate approach to deal with a uniqueplanning problem. To this end they may resort to the method of principled negotiation(PN) which has been developed as part of the Harvard Negotiation Project andreported by Fisher and Ury (1983) under the title: Getting to Yes. They argue that PNseeks "to decide issues on their merits rather than through a haggling process focussedon what each side says it will and won't do: It suggests that you look for mutual gainswhenever possible, and that where your interests conflict, you should insist that theresult be based on some fair standards independent of the will of either side". Wecould of course criticize the naivete of such an implicit view of negotiations but if wetake PN at face value it is clear that it may help resolve differences, and seen withinthe context of planning we therefore need a clear exposition of the alternatives underreview, the evaluation criteria and the interested parties, as well of course as theimpact values.


Overall we suggest that by structuring a planning problem in terms of the threecomponents (P's: C's: I's) and impact scores we can go someway to providing a usefulframe of reference for negotiations.

If we now turn to the GPP we should note that alternate formulations for theobjective can be offered to replace the one initially suggested in Chapter 1. As astarting point we might define the objective as to "maximize agreement among theinterest groups", but other options can include:

"minimize the long-term social costs","maximize the long-term social benefits","maximize the long-term net benefits",

or less formally we might suggest"seek to build a consensus among the interest groups","seek to protect minority opinions".For practical planning problems all of these objectives have to be defined in the

context of the specific issues as well as the political and social milieu. However, twothings are clear, first, that a formal definition of the objective rarely if ever will allowthe problem to be solved just using an MCDM technique. We may be able to provideneat technical solutions to well-defined plan evaluation exercises but unless we canimplement the 'solutions' the exercise is sterile from a practical point of view. Second,in an effort to focus the attention of decision-makers on specifics it is useful to offer adefinition of an objective for the GPP so that operational terms can be discussed. Forexample, what do we mean by long-term? Precisely which costs and benefits must betaken into account? How much opposition can be tolerated before a consensus breaksdown? The formulation of a planning problem in the style of a GPP and the use ofMCDM techniques may assist in debating some of these questions. Attention may alsobe focused on the ease with which a possible plan may be implemented and the costs ofdelayed decisions. Both of these aspects enter into the planning process.

At various points in this monograph we have made specific recommendationsregarding the utility of MCDM techniques. In this chapter it is our intention to repeatfour of the major ones and not to present an exhaustive list. First, the conclusionsfrom any analysis using an MCDM technique should be offered in terms of 'real'impacts, not dimensionless single indices for a preferred alternative. Second, therelative attractiveness of options vis-a.-vis an ideal and the status quo provides usefulreference information for debate and decisions. Third, explicit recognition of errorsshould be incorporated into the analyses. Fourth, in order to build up an appropriateenvironment for the legitimate use of MCDM techniques it is necessary to offertraining sessions and to arrange for the exchange of personnel among thoseinstitutions, agencies and firms where theoreticians, decision-makers and practitionerstend to cluster in isolation.

Finally, if indeed it is the case as suggested by Fisher and Dry (1983) that "standardstrategies for negotiation often leave people dissatisfied, worn out, or alienated", it istime to seek better ways and perhaps these can take advantage of the GPP structureoffered here together with MCDM techniques. Such an approach may help in themanagement of conflicts and uncertainty which are an intrinsic part of planning, whilehelping to preserve respect for minority opinions and the need to improve the human


condition. For when all is said and done we are planning for ourselves as individualsand for the survival of our species. It is in all our interests to improve planningpractises and to continue the debate on the quality of planning.

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Multi-criteria Decision Making (MCDM) Techniques in Planning

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