Metode Pengambilan Keputusan

Multi-Criteria Decision Analysis and Multi-Objective Optimization

at the Delft University of Technology, Faculty of Mathematics and Informatics

Freerk A. Lootsma

Delft University of Technology, Faculty of Mathematics and Informatics

Mekelweg 4, 2628 CD Delft, The Netherlands.

Tel. +31.15.278-5093. Fax +31.15.278-7255

Multi-Criteria Decision Analysis (MCDA) and Multi-Objective Optimization (MOO) have been investigated in our faculty since the early eighties. The research started with three different studies: the nomination procedures in a university, the evaluation of non-linear programming software, and the evaluation of alternative energy-research proposals. The decision makers, who usually had a strong background in science and technology, always questioned the scale sensitivity, the dependence on the units of measurement, the dependence on the method employed, and the rank preservation of the final scores. Hence, we altered the original AHP, the method which we originally employed. With the Multiplicative AHP so obtained we carried out several strategic-planning projects in close cooperation with the Energy Study Centre, North-Holland, under the auspices of the Ministry of Economic Affairs. In the late eighties we were also engaged in contract research commissioned by the Directorate-General XII (Science and Technology) of the European Community, Brussels, and by Schlumberger Research Laboratory, Paris.

A generous grant of the Delft University Research Committee (MCDA project TWI 90-06) supplied the financial means for a large-scale project with a challenging goal: the development of robust MCDA methods for the allocation of scarce resources to the competing decision alternatives. In the nineties we have been concerned with the following issues:

· Scaling of human judgement via geometric scales for the Multiplicative AHP and via arithmetic scales for the Additive AHP and SMART. The scales are based upon studies in acoustic and visual perception.

  • Comparative studies of well-known cardinal MCDA methods (SMART, the AHP) and an ordinal method (ELECTRE) under compatible input conditions, that is, within an explicit and uniform model for the context of the decision problem.
  • The power game in groups modelled via the assignment of power coefficients to the decision makers. This yields the basis for weighted voting via the AHP and SMART.
  • The vagueness of human judgement and the development of fuzzy versions of the AHP and SMART.
  • The assignment of weights in MOO in order to find an acceptable compromise, either via minimization of the weighted Chebychev distance with respect to the ideal vector, or via maximization of the weighted geometric mean of the objective functions.
  • The reduction of conflicts via the pairwise comparison of concessions in negotiations between two or more parties.
  • The tools for communication with groups of decision makers. In the eighties we worked with questionnaires so that the decision makers could leisurely answer the questions and return the responses via the mail. In the nineties we used electronic brainstorming and voting in the Group Decision Room of the Faculty for Systems Engineering and Policy Analysis.
  • Resource allocation to competing decision alternatives, the goal of the MCDA project. This study, initiated in a project with the European Community, led us to the solution of distribution problems under the principles of fairness and equity. Several publications are under preparation now. The key concept is the desired-ratio matrix. In principle, there is such a matrix under each distribution criterion.

In the early nineties Leo Rog developed the REMBRANDT system for MCDA (Ratio Estimation in Magnitudes or deci-Bells to Rate Alternatives which are Non-dominaTed) as an amalgamation of the Multiplicative AHP and SMART. This has been our tool in many projects. The preference ratios can be expressed in their original magnitudes on a geometric scale or in orders of magnitude on an arithmetic scale. Thus, we applied logarithmic coding, a mode of operation which is common in psycho-physics, see the decibel scale in acoustics. REMBRANDT has been designed for group decision making, with power coefficients assigned to the respective members.

In the field of MCDA there are at least three competing schools: (1) the axiomatic school around Multi-Attribute Utility Theory, (2) the school around the AHP, and (3) the French school around ELECTRE. Some of our papers appeared to be controversial because they questioned the fundamentals of the AHP (the scale, the calculation of impact scores and final scores) and ELECTRE (the setting of thresholds, the basic idea of constructivism). The confrontations slowed down the publication of our manuscripts but they kept our ideas under a healthy pressure.

In our projects we also encountered strong resistance. In Brussels, for instance, because we proposed to model the power game between the member states of the European Community via weighted voting. This was unfeasible in the late eighties but in certain cases it is possible now. There are even barriers against MCDA in the MCDA community itself. Other projects, however, were encouraging. High-ranking officials of the Ministry of Public Health came to the Group Decision Room in order to evaluate the current diseases on the basis of seriousness, a multi-dimensional concept which plays an important role in any public-health policy. The results of the sessions contributed significantly to the Policy Document “Healthy and Well” submitted to Parliament in 1995.

Key publications

1. Barzilai, J., and Lootsma, F.A., “Power Relations and Group Aggregation in the Multiplicative AHP and SMART”. Journal of Multi-Criteria Decision Analysis 6, 155 – 165, 1996.

2. Boender, C.G.E., Graan, J.G. de, and Lootsma, F.A., “Multi-Criteria Decision Analysis with Fuzzy Pairwise Comparisons”. Fuzzy Sets and Systems 29, 133 – 143, 1989.

3. Bots, P., Kok, M., Lootsma, F.A., and Rog, L., “Schools on Islands, a Journal as a Ferry”. Journal of Multi-Criteria Decision Analysis 3, 123 – 129, 1993.

4. Gennip, C.E.G. van, Hulshof, J.A.M., and Lootsma, F.A., “A Multi-Criteria Evaluation of Diseases in a Study for Public-Health Planning”. European Journal of Operational Research 99, 236 – 240, 1997.

5. Honert, R.C. van den, and Lootsma, F.A., “Group Preference Aggregation in the Multiplicative AHP: the Model of the Group Decision Process and Pareto Optimality”. European Journal of Operational Research 96, 363 – 370, 1996.

6. Lootsma, F.A., “Fuzzy Logic for Planning and Decision Making”. Kluwer Academic Publishers, Boston/London/Dordrecht, 1997.

7. Lootsma, F.A., Athan, T.W., and Papalambros, P.Y., “Controlling the Search for a Compromise Solution in Multi-Objective Optimization”. Engineering Optimization 25, 65 – 81, 1995.

8. Lootsma, F.A., Mensch, T.C.A., and Vos, F., “Multi-Criteria Analysis and Budget Reallocation in Long-Term Research Planning”. European Journal of Operational Research 47, 293 – 305, 1990.

9. Lootsma, F.A., Ramanathan, R., and Schuijt, H., “Fairness and Equity via Concepts of Multi-Criteria Decision Analysis”. To appear in T.J. Stewart and R.C. van den Honert (eds.), Proceedings of the Cape Town MCDM Conference, Springer, Berlin, 1998.

10. Lootsma, F.A., Rog, L., and Kok, M., “Choice of Working Languages in a European Working Group for Multi-Criteria Decision Aid”. Journal of Information Science and Technology 2, 170 – 176, 1993.

11. Lootsma, F.A. and Schuijt, H., “The Multiplicative AHP, SMART, and ELECTRE in a Common Context”. Journal of Multi-Criteria Decision Analysis 6, 185 – 196, 1997.

12. Lootsma, F.A., Sluys, J.M., and Wang, S.Y., “Pairwise Comparison of Concessions in Negotiation Processes”. Journal of Group Decision and Negotiation 3, 121 – 131, 1994.

13. Triantaphyllou, E., Lootsma, F.A., Pardalos, P., and Mann, S.H., “On the Evaluation and Application of Different Scales for Quantifying Pairwise Comparisons in Fuzzy Sets”. Journal of Multi-Criteria Decision Analysis 3, 133 – 155, 1994

A DSS FOR COOPERATIVE MULTIPLE CRITERIA GROUP DECISION MAKING

Tung Bui
Matthias Jarke
Working Paper Series
STERN #IS-84-45
Center for Digital Economy Research
Stem School of Business
Working Paper IS-84-45
A DSS for Cooperative Multiple Criteria
Group Decision Making
?turg Bui and Matthias Jarke
Graduate School of Business Administration
New Ybrk University

ABSTRACT

Many decisions in organizations are made, or at least prepared, by multiple cooperating ecision makers. A distributed DSS architecture is presented that connects multiple individual DSS to a group DSS. The group decisionmaking process is supported by contentoriented methods based on extensions of multiple criteria decision  aking methods, as well s by process-oriented techniques using a computerized conferencing system. A prototype f the system is operational on a personal computer configuration

Introduction

The problem of collective decision making has been extensively investigated by numerous researchers. Most of this work could be classified into two main streams of research. The first approach focuses on the content of the problem, attempting to find an optimal or satisfactory solution given certain social or group constraints, or objectives Studies by Arrow (1951), Nash (1950), Harsanyi (1955), and von Neumann and Morgenstern (1953) are classical illustrations of this approach. By contrast, the second approach is process-oriented. It is based on the observation that the group goes through certain phases in the group decision making process, and on the belief that there could be an ordered way to effectively deal with these phases Behavioral studies of Bales and Strodtbeck (1951), Chamberlain and Kuhn (1965), Walton and McKensie (19651, and Warr (1973) are some of the well-known research devoted to this process-oriented approach

More recently, a third approach to group problem solving has emerged from the decision support system technology. Stohr (1981), Carlson and Sutton (19?4), and Holloway and Mantey (1976) present examples of decision support systems that involve multiple decision makers However, it remains unclear that such DSSs can support group problem solving, since they mostly deal with the pooled type of group decision making
which is only a minimal form of collective decision making.

This paper describes, evaluates, and discusses the potential of a cooperative group decision support system (CGDSS) that uses a multiple criteria decision model as a vehicle to integrate approaches developed in conventional single user DSS and in computerized conferencing systems (CCS). The CGDSS is motivated by some previous work that (1) advocates extensions of DSS to support not only the choice phase of the decision making process, but also the intelligence and design phases (Bui, 1984), and (2) suggests the use of a multiple criteria decision model as a vehicle to expand the DSS framework to organizational group decision making (Bui and Jarke, 1984).

Bearing in mind that the group decision making process is substantially more difficult than the single person decision process, this paper does not attempt to get into the already large number of theoretical discussions.

Rather, it demonstrates that with the aid of a CGDSS the decision makers can alternately use quantitative and behavioral group decision methods to effectively resolve group decision problems, or at least reduce the chances of the decision breakdowns often observed in collective decision situations Specifically, an integrating framework based on an extension of a discrete multiple criteria decision method, the ELEC7’RE method (Roy, 1968) is presented that links (1) a conventional DSS model component that includes time series models, explicative models, and simulation models (Bui, 19821, (2) two computerized prvcess- oriented p u p decision methods, ie. the delphi meGod and the nominal group technique (Van de Ven and Delbecq, 1974), and (3) a simple computerized conferencing system that supports group
communication.

A DSS for Cooperative Group
Decision Making

GROUP DECISION MAKING: Terminology and Typology

A collective decision making process can be viewed as a decision situation in which there are two or more persons, each of which are characterized by their own perceptions, attitudes, motivations, and personalities, who recognize the existence of a common problem and attempt to reach a collective decision.

One can observe three broad types of group decision making: a single decision maker within a collective decision environment, non- cooperative decision making, and cooperative decision making.

In the first type of group decision making, a particular decision maker ultimately makes the decision and assumes responsibility for his/her line of action. However, the decision can be regarded as a collective one because of the existence of the dense network of influences that surrounds this single decision maker. In fact, other participants in the decision maker’s organization can either support or act against the decision-Thus, the idenflication and analysis of the behaviors and attitudes of other people, indirectly involved in the decision making process, should be analyzed.

In the situation of non-cooperative decision making, the decision makers play the mle of antagonists or disputants. Conflict and competition are common forms of noncooperative decision making. While the former represents a situation in which disputants seek to hurt their opponents for their interests, the latter is characterized by the fact that each competitor is an action candidate, and is trying to outperfom others.

Finally, in a cooperative environment, the decision makers attempt to reach a common decision in a friendly and trusting manner, and to share the responsibility. Consensus, negotiation, voting schemes, and even recourse to a third party to dissolve differences, are examples of this type of group decision making.

The Cooperative Collective Decision Environment

The CGDSS presented in this paper operates in the third type of group decision making environment. In particular, it attempts to support the following decision situation:

1. There are multiple users or decision makers who share an equal weight in the decision making process. The assumption of equal weight excludes, among other things, the hierarchically distributed decision situation, as found, for example, in transportation planning (Edelstein and Mehyk, 1982; Jarke, 1982).

2. The decision makers interact in a cooperative manner and in a trusting environment For further simplification, there is no attempt to cheat, to seek coalition within a sub-group, and no third party intervention.

3. The group shares the same set of feasible decision alternatives (e.g., products, actions, strategies, etc.). These alternatives are subject to a selection of one or more alternatives, or to a ranking according to a given set of criteria. The selected alternatives are called the decision outcome.

4. Each decision maker has his or her own objectives that reflect a prion’ values and aspiration levels. Objectives are concretely expressed by criteria or attributes that are discrete and ordinally measurable. Due to individual differences, individual decision outcome-as opposed to the collective decision outcome of the group-often differs from one decision
maker to the other.

Design Issues for Group Decision Support Approaches

Bales and Strodtbeck (1951) were among the first who observed five main types of functional problems during a group decision making process:

1. Problem of orientation. The decision makers often ignore or are uncertain about some of the relevant facts. They seek information, orientation, or confirmation.

2. Problem of evaluation. The decision makers-because of their personalities and of the nature of the problem-have different values and interests. They need a frameworkto analyze the problem and express their wishes and feelings.

3. Problem of control. Each decision maker within the group may end up with a different decision outcome. They seek exchanges of points of view and directions to reach consensus.

4. Problem of tension management. The frequencies of both negative and positive reactions tend to increase during the group decision making process seeks to improve understanding, increase compliance, reduce tension, and avoid member withdrawal.

5. Problem of integration. The group seeks solidarity during the group problem solvingprocess and collective endorsement of the final agreement.

While the problem of evaluation (type 2) often remains the most frequent activity during a decision making process, the problem of orientation (type 1) is typically prevalent at the beginning, whereas the problems of control (type 3), tension-management (type 4), and integration (type 5) and more frequent towards the end of the process.

The decomposition of problems into five types suggests a division of tasks within the group DSS functions. The rationale of such a division of tasks is two fold. First, despite the efforts of the content-oriented DSS technology to help decision makers structure their initially unstructured problems, some unstructured part will remain This partial ‘unstructurability’ is due to uncertainty, fuzziness, ignorance, and inability to quantitatively measure the complesity of decision situations and the decision maker’s preferences (Stohr, 1981). Second, the same efforts to resolve a group decision problem are rendered more difficult by human irrationality and emotionality when dealing with group interaction (Pruit, 1981). It is then necessary to search for some processoriented methods that can support the unstructured part left by the content-oriented DSS, as well as for some communication system that collects, coordinates, and disseminates information within the group.

There is no doubt that defining the boundaries of structurable
and unstructwable problems is difficult It is also difficult to determine whether a process-oriented approach or a content-oriented approach is best suited to solve a particular decision problem. However, since type (2) is likely to be structwable, it could be practically handled by content-oriented methods. Meanwhile, types (I), (3), (4), and (5) that are less or not structurable could probably be best taken care of by process-oriented methods.

The Functions of CGDSS in Group Decision Making

CGDSS provides support for both the decision maker who is a member of the group and for the group itself. From the point of view of the member of the group, the individual DSS offers two levels of support: (i) generalized decision support for individual decision making, and (ii) negotiation advisory support for assisting the individual in negotiating with other decision makers of the group.

From the point of view of the group, the group DSS assures three main functions: (i) automatic selection of appropriate group decision technique(s), unless the group overrides this procedure, (ii) computation and explanation of a group decision, and (iii) suggestions for a discussion of individual differences or for a redefinition of the problem if attempts to reach consensus fail.

It is worth noting that, according to the design of CGDSS, only individual users interact with the system the group as a whole is not a user of the DSS (see Figure 1).

The CGDSS System Architecture

Figure 1 describes the system architecture of a cooperative
group decision support system currently operational in a prototype version at New York University. The architecture is based on the assumption of the following hardware configuration:

  • Decision makers have their individual DSS installed in their familiar working environment that includes a terminal or a local desktop computer system
  • Each terminal or local computer that hosts the ‘individual DSS’ is linked to a computer network. Linked to the network operating system (NOS) that provides communication facilities and data transfers, a groupDSS supports the p u p decision activities.

The CGDSS software package is composed of two independent but interrelated modules. the individual DSS and the group DSS. In each individual DSS, the CGDSS user interface component is a menu-driven program package that allows the decision maker to access the model management system (MMS) , the database management system (DBMS), and the computerized conferencing system (CCS) interface that, in turn, will connect to the group CCS upon request.

The CCS makes it possible for the decision maker to structure, store, and process written communications among the group. The MMS provides a user-oriented milieu for understanding, selecting, retrieving, and operating the decision models stored in the content oriented model bank (COMB) and the multiple criteria decision model bank (MCDMB). The purpose of the
COMB is to provide each individual decision maker with a large set of models to deal with a variety of decision problems. These models can be classified into three broad functional classes: simulation models (e.g., Monte Carlo simulation), explicative models (e.g., linear programming, financial models), and time series models (e.g., regression models, smoothing techniques).


The multiple criteria decision models stored in the MCDMB fall into three main categories: namely, MCDM for selecting (ie., to choose one and only one ‘best’ alternative among many), MCDM for ranking (ie., all alternatives are good but they are ranked according to the decision maker’s objectives or needs), and MCDM for sorting (ie., some alternatives are good, and the remaining are not) (Roy, 1971).

In the group DSS, a simple CCS allows the participants of the group to share a group process-oriented model base (GPOMB) and a group MCDM base (GMCDMB). The GPOMB contains two main facilities: a stsuctured CCS that currently includes the delphi and the nominal group technique and a free-discussion CCS that supports informal types of communications among decision makers. The GMCDMB is linked to the individual MCDM via the network operating system On the request of the decision maker, via the individual MCDMB, the group MCDM computes or updates group results and stores them in the group DBMS. The latter feature ensures that decision makers can freely use their individual DSS before committing to are opinion.

The Role of Electre in the CGDSS

As of this writing, the content-oriented MCDM methods implemented in the group DSS as well as in each of the individual DSS are based on the method ELEC’IRE (Roy, 1968), extended by the authors to a group decision making situation This section discusses the rationale of the use of ELECTRE in the CGDSS and provides a comprehensive description of the method ELECTRE has been selected for three reasons

  • Multiple criteria decision methods, in general, have proven useful in useful in supporting decision making (Keen, 1977; Zeleny, 1982);
  • ELECTRE: is conceptually robust, and easy to learn and use. It has proven its usefulness in aiding a number of ill-defined decision situations sucessfully (Pasquier, et aL, 1979; Heidel and Duckstein, 1983);
  • ELECTRE does not require full information on the decision maker’s preferences and assessment of alternatives, and hence, gives more autonomy and control to the decision maker (Crama and Hansen, 1982). This peculiarity makes it easier to expand the algorithm to resolve group decision making.

The Electre Method for Individual Decision-making: Basic Concepts

ELECTRE is characterized by circumventing the problem of incomplete comparability of alternatives through its concept of outranking relations. Problem and solutions are outlined below. There are number of things that make it difficult for a
decision maker to exhaustively compare all known alternatives. First, the decision maker often cannot compare some alternatives due to uncertainty associated with the measurements and evaluations. Second, the decision maker may be unwilling to compare two alternatives because they are incomparable (e.g., option ai is better than option ak by some criteria, whereas ak is better than ai by some other criteria). The notion of indifference in utility theory does not reflect this incomparability (Roy, 1971). Last but not least, the ill-structuredness and occasional inconsistency of the decision maker’s preferences are serious obstacles to enforcing the complete comparability of alternatives (Saaty, 1980).

The concept of outranking relations seeks to compare decision alternatives only when the decision maker’s preferences are well defined In other words, ai outranks ak when the information obtained from the decision maker’s preferences safely justifies the proposition that ai is at least as good as ak.

The outranking relation can be explained by two further concepts, the presence of concordance, (ie., for a sufficiently
important subset of evaluation criteria, ai is at least weakly preferred to ak), and the absence of discordance, ie., among the criteria for which ak is preferred to ai there is no significant discordant preference that would strongly oppose any form of preference of ai over ak).

Annually, there are a large number of faculty candidates among whom only a few will receive an offer. The selection process has been supported for some time by the use of an informal CCS facility. We expect the following advantages from using the group DSS in the process, as illustrated in Figure 2:

1. The large number of candidates and criteria often leads to confusion, sometimes creating fast, irrational decisions The ELECTRE approach should help rationalize this process and offer each decision maker a structured way to express his or her opinions

2. It has been a general rule that a very strong individual discordance concerning a particular candidate has a strong impact on the group decision Unlike other OR models, the group MCDM outlined earlier supports this practice.

3. However, the use of MCDM alone would be insufficient. The right column of Figure 2 demonstsates the importance of formal and informal CCS coxnmunication, in particular, for transforming the goal space by providing additional information. Conversely, when attempts to obtain concessions from the decision makerfs) fail, conflicts should be dissolved

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