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    Computers & Operations Research 33 (2006) 1831

    www.elsevier.com/locate/cor

    A problem structuring front end for a multiple criteria decisionsupport system

    Ralph Scheubreina,, Stanley Ziontsb

    aUniversity of Hohenheim, Business Administration Institute (510A), 70593 Stuttgart, Germanyb

    State University of New York at Buffalo, School of Management, Buffalo, NY 14260-4000, USA

    Available online 6 July 2004

    Abstract

    Structuring a problem is a key part of decision making. For multiple criteria decision problems, defining the

    criteria is an important element of the structuring process. To provide a decision maker with a general instrument

    for identifying relevant criteria, two methods representing different approaches were empirically evaluated. This

    evaluation showed that Kellys repertory grid technique in particular has several useful features. Accordingly, the

    repertory grid technique was adapted to build a problem structuring front end for the aspiration-level interactive

    method proposed by Lotfi, Stewart, and Zionts. 2004 Elsevier Ltd. All rights reserved.

    Keywords: Aspiration-level interactive method (AIM); Repertory grid technique; Problem structuring; Multiple criteria

    decision making (MCDM)

    1. Introduction

    Problem-solving activities pervade all aspects of human life. Solving a problem generally involves

    making one or more decisions. The resources invested in the problem-solving effort depend on various

    factors. Relevant to this article in particular is the perceived importance and the complexity of the problemunder consideration.

    One aspect of complexity is how much problem information is available. In [1] this amount of in-formation is used to provide a classification into the three broad classes: well-structured problems,

    Corresponding author.

    E-mail address: [email protected](R. Scheubrein)

    0305-0548/$ - see front matter 2004 Elsevier Ltd. All rights reserved.

    doi:10.1016/j.cor.2004.05.014

    http://www.elsevier.com/locate/cormailto:[email protected]:[email protected]://www.elsevier.com/locate/cor
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    Table 1

    Decision matrix with alternatives xi , criteria cj, and outcomes yi,j

    Criteriac1 c2 cjx1 y1,1 y1,2 y1,j

    Alternatives x2 y2,1 y2,2 y2,j...

    ......

    . . ....

    xi yi,1 yi,2 yi,j

    semi-structured problems, and ill-structured problems. A well-structured problem is understood and anappropriate solution procedure may be formulated. In contrast, an ill-structured problem must be defined

    in order to solve it. A semi-structured problem is in between these two extremes; i.e., some aspects of theproblem are well-structured whereas others are not. In order to solve complex problems many processeshave been proposed (see, e.g., [2] for a survey). Such processes may be interpreted as a means of graduallytransforming an ill- or semi-structured problem into a well-structured one. This is achieved by gathering

    relevant information, organizing it according to a specific scheme, and evaluating it accordingly.In many real life problems, choosing between possible courses of action may be difficult because it

    requires balancing several factors. Multiple criteria decision making (MCDM) deals with situations inwhich the decision maker has several conflicting objectives (see, e.g., [3] for a recent survey). There isgenerally no perfect alternative, and a good compromise must be identified.

    Methods for supporting MCDM can be divided into two broad classes [4], namely into approaches formultiple objective decisionmaking (MODM) [5] and for multiple attribute decision making (MADM)[6]. In MODM the alternatives are often defined implicitly, e.g., by the restrictions of a mathematical

    program. For MODM problems the decision maker must come up with or design the most preferredalternative by assigning values to decision variables. For MADM problems, the decision maker must

    choose from a set of alternatives that is typically defined explicitly. Of course not all the alternatives maybe known a priori. In other words, the decision maker selects a most preferred alternative. For MADMin a deterministic context, a central data structure is the decision matrix (see Table 1). In this matrix the

    i alternatives xi X, the j criteria cj C, and their outcomes yi,j := cj(xi ) are recorded.If the decision matrix is known, the dominance relation on the alternatives can be identified. An

    alternative is said to dominate another if the first alternative is at least as good as the second in every

    criterion and strictly better in at least one criterion. Alternatives which are not dominated by any other

    alternative are called nondominated alternatives.A main concern of MCDM is how to structure a decision problem [7]. With respect to the decision

    matrix, an ill-structured problem may be characterized by the fact that some alternatives, criteria andperhaps also outcomes are unknown. To structure the problem, these elements of a decision matrix have

    to be determined as part of the decision making process.Under the umbrella term Soft OR, many problem structuring procedures have been developed (see,

    e.g., [7] for a survey). Such approaches to problem structuring are often extended procedures, emphasizing

    the creativity of a group of people, and are typically organized by a facilitator or a decision analyst. Inthat literature, the recommendation is often given to concentrate first on the criteria and then to define

    the alternatives. A typical MCDM-related example is Keeneys value-focused thinking [8]. He argues

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    that decision making should always start by focusing on the criteria even if some alternatives seem to beobvious ([9, p. 537] values first principle).

    For decisions with a strategic impact (e.g., the case presented in [9, p. 538543]) an extensive effort

    seems to be justified. Many decisions in an organization are made on a much lower, operational levelwhere fewer resources are available. Therefore it seems interesting to check whether the values firstprinciple is also appropriate for an operational decision situation.

    Accordingly, a field study on operational decision making of students was carried out. In the followingsection, the first phase of the field study, which evaluates two methods of supporting problem structuring,

    is described. Next, the acceptance of a multiple criteria decision support system, which implements theaspiration-level interactive method (AIM) [10], is tested. The result of the second phase of the fieldstudy is presented in the third section. In the fourth section a decision support system which integrates a

    problem structuring approach and the aspiration-level interactive method is presented. The evaluation ofthat system represents the third phase of the field study. A brief summary in the fifth section concludes

    the article.

    2. Evaluation of two methods for problem structuring

    Decisions can be broadly classified into strategic, tactical, and operational depending on their overallimpact. Strategic decisions are higher-level and longer-term, whereas operational are lower-level and

    short term. Tactical decisions are in between. An operational decision situation usually has the followingcharacteristics:

    The decision is de facto made by one person. The time to make the decision is limited and is relatively short.

    No external analysts are usually involved because of time and money restrictions.

    For operational decisions, a decision maker might be interested in a systematic procedure to elicit relevant

    criteria. As a basis for creating and evaluating an appropriate procedure, a field study was conducted. Thefield study consisted of three phases:

    Phase 1: Evaluation of two methods which represent opposing problem structuring methodologies. Phase 2: Evaluation of a multiple criteria decision support system without a problem structuring front

    end.

    Phase 3: Evaluation of an integrative system which is based on the conclusions from the previousphases.

    The subjects participating in the field study were students of a university business school. Table 2 sum-marizes the demographic data of these participants.

    In order to mimic an operational decision situation, the subjects were asked to prepare a typicaldecision problem which they were currently facing. The rationale is that the students should be activelyand seriously involved in the decision problem.

    The problem most often presented was choosing a car to purchase (22% of all problems in this phaseof the field study). Other problems included choosing a graduate school, choosing a major, taking a leave

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    Table 2

    Demographic data of the study participants

    Subjects 37 (56% female, 44% male)

    Age Minimum Mean (Std. Dev.) Maximum

    18 23.7 (6.07) 44

    Year Freshman Sophomore Junior Senior

    12% 9% 55% 24%

    Nationality US Other

    84% 16%

    of absence from their studies (or not), deciding on involvement in university club activities, moving toa new location, deciding where to go and how to travel during a school holiday, choosing a watch topurchase, and choosing a snowmobile to purchase. In accordance with a typical decision situation on an

    operational level, all the discussed problems had a single decision maker.For those students who had inappropriate problems (e.g., not enough data or incomplete information),

    the default problem of selecting a cell phone contract was used. The data of this case study was based on

    actual plans of six cell phone companies operating in the Buffalo, NewYork area. The data was condensedinto a decision matrix having 22 alternatives and 17 criteria. This decision problem was used by 28% of

    the students during the first phase of the study. Taking into account both the necessary investment and thelong-term effect of the decision, 67% of the problems discussed during this phase can be characterizedas operational decisions for a student whereas the other problems are more tactical or strategic.

    Each subject was supported by a facilitator who directed the subject to work according to one of the twomethods under consideration. The facilitator avoided acting as a decision analyst who would have triedto help structure and solve the decision problem. This role of the facilitator reflects that for an operational

    decision, normally no external analysts can be involved.In order to simulate a time restriction, each subject was instructed to work on the problem for one

    hour. Within this time limit, the subject was asked to structure the problem by articulating the availablealternatives, the relevant criteria, and the respective outcomes. Once this data was provided, the facilitatorgenerated the decision matrix. Next, the facilitator identified the nondominated alternatives. Working on

    a decision problem was stopped after 75 minutes, even if the problem structuring process had not beencompleted.

    The focus of the first phase of the field study was the comparison of two different methods of elicitingthe alternatives and the criteria, namely the KepnerTregoe approach and the repertory grid technique.

    The KepnerTregoe [11] approach for management decisions can be characterized as criteria-oriented,

    following the values first principle. This approach originally consists of two phases: problem analysis anddecision making. The problem analysis phase is not considered here in more detail, because the subjectsparticipating in the field study had already identified their problems. The decision making phase consists

    of seven stages (see [2, p. 336342] for details):

    (1) Establish objectives.

    (2) Classify objectives into must and want requirements.

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    Table 3

    Typical layout of a repertory grid

    Constructs Elements Contrasts( = 1) E1 E2 . . . Ei ( = 5)

    C1 C1C2 C2...

    ...

    Cj

    Cj

    (3) Develop alternatives.(4) Compare alternatives using the objectives.

    (5) Make tentative selection.(6) Evaluate adverse consequences.

    (7) Choose and implement the best alternative.

    In contrast, the repertory grid technique can be characterized as an alternative-oriented method. It wasdeveloped by Kelly [12] in the context of the theory of personal constructs in the field of psychology.The theory has its origin in the need to understand and map an individuals thinking process. Giving a

    complete overview of the theory is beyond the scope of this article. The essence relevant to this article isthat an individuals expectations may be considered as a finite set of personal constructs which the personuses to evaluate a particular phenomenon. Each construct is bipolar; i.e., a constructcontrast pair forms

    a dimension for assessing a phenomenon.

    As a means of operationalizing the personal construct theory, the repertory grid technique is intendedto allow an individual to exhibit his idiosyncratic constructs with a minimum of interviewer bias. The

    repertory grid technique has been used in a variety of business contexts reflecting the flexibility of thisprocedure (see [13,14] for surveys). In the context of MCDM, in [15] a procedure based on the repertory

    grid technique is used to assess the importance of criteria.While there are various modifications of the repertory grid technique, three phases are typical [16]:

    (1) Identification of the elements of the considered phenomenon.

    (2) Elicitation of the distinguishing constructs.(3) Construction of a grid using the evaluation of the elements and the constructs.

    To elicit the constructs, the triad method is commonly used. The interviewee is confronted with threeelements and asked to consider ways in which two are alike but different or opposite from the third (see,e.g., [17] for details).

    Table 3 shows the typical layout of a repertory grid (adapted from [14, p. 40]). First elements under

    consideration are recorded in the header of the grid. Then, using the triad method, a construct is elicited.The two poles of each construct are written on the left side and the right side, respectively. If an elementmatches the left-side pole it is rated with 1; if it matches the pole on the right side it is rated with 5. If an

    element falls in between then a rating in the range from 2 to 4 is given.For each subject in the first phase of the study, the facilitator used either the KepnerTregoe approach or

    the repertory grid technique. The subject then tried to structure the problem using the method introduced.

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    Table 4

    Comparison of elicitation methods

    KepnerTregoe Repertory gridCriteria elicited Minimum 7 3

    Maximum 8 7

    Mean 7.7 6

    Alternatives elicited Minimum 2 3

    Maximum 5 7

    Mean 3.7 5.5

    Time restriction met 33% 87%

    The facilitator supported the subject only in questions related to the method but not in structuring theproblem. Table 4 shows the result of this experiment.

    On average, when using the KepnerTregoe approach, the subjects identified more criteria; whereaswhen using the repertory grid technique, the subjects generated more alternatives. This reflects the se-quence of activities of the methods; i.e., a higher output was generated by the subjects in the earlier stages

    of each method.One important difference between the two methods is the time required. When using the repertory grid

    technique it was almost always possible to complete the problem structuring process within the giventime frame, whereas when using the KepnerTregoe approach, in only 33% of the experiments the subjectwas able to complete the problem structuring process within the given time frame.

    Based on the above result, it appears that the repertory grid technique is preferable if tight deadlinesmust be met. The decision to implement the repertory grid technique as the problem structuring methodfor a multiple criteria decision support system was made. The methodology of this decision support

    system is presented in the next section.

    3. The Aspiration-level interactive method

    AIM [10] is an MADM approach intended to help identify the most preferred alternative in a decisionmatrix. The basic idea of AIM is that a decision maker explores the efficient frontier by interactively

    adjusting levels of aspiration and obtaining feedback. For each aspiration level, the system gives the

    nearest nondominated solution, as well as a ranking of alternatives, based on a metric constructed usingthe current levels of aspiration.

    The approach used in AIM can be easily adapted to various contexts (see [18, Chapter 10] for somecases studies). In [19] AIM is used to support the selection of strategic initiatives of a Balanced Scorecard.

    Ref. [20] compares AIM and the conjoint analysis for predicting consumer choices.While the original AIM software provides various functions for supporting a decision maker (see [10]

    for details), the process basically consists of four steps as depicted in Fig. 1.

    First, the decision maker defines active alternatives. Next the decision maker has to specify the criteria.Basically, three criteria function types are supported: maximizing, minimizing, and target (see Fig. 2).The

    decision maker can also choose a qualitative criterion which is a maximizing criterion with a five-point

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    Fig. 1. Decision process supported by AIM (straight process of ExcelAIM).

    Fig. 2. Criteria function types.

    scale: i.e., an outcome is rated as awful, poor, fair, great, or superb. For each criterion, the

    decision maker can specify up to four parameters to express his perception of the value of an outcome.With the definition of the alternatives and criteria, the system can set up a decision matrix and the

    decision maker enters the outcomes during the third phase.

    Finally, the decision maker interactively explores the efficient frontier by adjusting levels of aspiration.The system supports this adjustment by providing various feedback information on the so-called basicdisplay. Based on the current levels of aspiration, the system reports the proportion of alternatives that

    satisfy the level with respect to each criterion individually and to all criteria when considered together.In addition, the basic display shows the nondominated alternative having the minimum distance from the

    current aspiration level. Also, the system can compute a ranking of alternatives using a metric based onthe current aspiration levels (see [10] for details).

    Using information provided in the basic display, the decision maker adjusts the levels of aspiration until

    he finds an acceptable compromise in the set of alternatives. Fig. 3 shows an example of this decisionprocess for a problem with two minimizing criteria. In this example, the decision maker starts at thenadir point in the upper right corner. He then adjusts his levels of aspiration six times until he finds an

    alternative which he views as the best compromise. The numbered positions on the right side of Fig. 3

    are the levels of aspiration chosen in each iteration.The decision maker cannot select a level of aspiration arbitrarily but has to choose an achievable level

    for each criterion. As shown on the right side of Fig. 3 the levels of aspiration can only be set at gridintersections. The idea is that the selected levels of aspiration are always related to alternatives. In addition

    to this interactive adjustment procedure, AIM has other procedures included (see [10] for details).AIM was implemented as a DOS-based application some years ago [10]. For the field study it was

    reimplemented in Microsoft Excel 2002, which is part of Office XP. This new implementation is named

    ExcelAIM. In this system, the data is stored in standard Excel worksheets, while the functions for theinteractive adjustment procedure are implemented in the programming language Visual Basic for

    Applications which is integrated in the Microsoft Office product family. The source code of ExcelAIM

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    Fig. 3. Example of adjusting the levels of aspiration.

    has a size of 250 KB, while a complete workbook requires about 1 MB. One of the main advantages of

    an application based on a spreadsheet package is that today many end-users are sufficiently computerliterate to be able to modify the application according to their specific needs (see [21] for an empiricalstudy). Additionally, spreadsheet applications can often be integrated easily in a working environment.

    In particular, recent versions of Excel provide functions for accessing data stored in XML-format andin HTML-format (see [22, Chapter 27] for implementation details). This feature is useful for a decision

    support system in a business context because a lot of information is today accessible in this way bothin the companys intranet and the Internet. In addition to this spreadsheet implementation an Internetversion is currently under development (see http://www.scheubrein.com/webaim/).

    ExcelAIM implements twodecisionprocesses, namely the straight processand the standard process.The straight process of ExcelAIM basically implements the AIM approach as presented above (see Fig.1). This process can be used if all data necessary for the decision matrix is available and the decision

    maker can proceed to directly solve his problem.In the second phase of the field study, all subjects were asked to use the straight process of ExcelAIM

    to select a cell phone contract from the prepared case study. As soon as the subjects had made the decisionusing ExcelAIM, they completed a questionnaire. This questionnaire was inspired by the one used in [23]to evaluate commercial multiple criteria decision support systems.

    The subjects were asked to answer the following questions on a five-point scale, for which one pointindicates the worst rating and five points the best rating.

    (1) How demanding is it to get the program running?(2) How easy is it to use the program?(3) How comprehensible is the process?

    (4) How reasonable is the process?(5) Did you learn much about the decision problem?(6) How easy is it to tell the system what is relevant in making the decision?

    (7) How strong is your confidence in the process?(8) How strong is your confidence in the result of the process?

    (9) How user-friendly is this program?

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    Table 5

    Evaluation of ExcelAIMs straight process

    Question Minimum Mean (Std. Dev.) Maximum1 3 4.2 (0.83) 5

    2 3 4.2 (0.73) 5

    3 2 3.9 (1.04) 5

    4 3 4.0 (0.82) 5

    5 2 3.4 (0.87) 4

    6 2 3.9 (1.12) 5

    7 3 4.3 (0.75) 5

    8 4 4.4 (0.51) 5

    9 2 3.8 (1.07) 5

    10 2 4.0 (1.00) 5

    11 2 4.2 (0.93) 5

    12 2 3.8 (1.14) 5

    Overall 2 4.0 (0.27) 5

    (10) How useful is this system for supporting decision making?(11) How satisfied are you with this methodology for decision making?

    (12) Would you make the recommendation to a friend to use the system for this decision problem?

    These questions cover a broad range of aspects which influence the acceptance of a decision supportsystem. In particular, there is one group of questions related to the implementation of the software, one

    group about the methodological approach to supporting the decision making, and a third group concerningthe realization of the approach in the software under consideration. Table 5 summarizes the results of thesubjects assessments.

    Overall, the mean assessment of all questions is 4.0 (with a standard deviation of only 0.27), whichindicates a high acceptance of both the approach and the implementation. The subjects had a very highlevel of confidence in the result of the decision making process (see question 8 in Table 5).

    In addition to the straight process, ExcelAIM also supports a second process. The details of that processand its assessment by the subjects are presented in the next section.

    4. Problem structuring and decision making with ExcelAIM

    ExcelAIMs standard process is an extension of the straight process discussed earlier. The standardprocess helps the decision maker identify criteria that are relevant by using the repertory grid technique.Fig. 4 shows the steps of this process.

    Fig. 4. Standard process of ExcelAIM.

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    Table 6

    Example of the temporary decision matrix after the elicitation of three criteria using the triad method

    c1 c2 c3

    x1 1 0 0 1

    x2 1 1 1 1

    x3 1 1 1 3

    x4 0 1 1 2

    x5 0 0 0 0

    x6 0 0 0 0

    Table 7

    Example of the temporary decision matrix after the elicitation of an additional criterion using the paired comparison method

    c1 c2 c3 c4

    x1 1 0 0 0 1

    x2 1 1 1 0 1

    x3 1 1 1 0 3

    x4 0 1 1 0 2

    x5 0 0 0 1 1

    x6 0 0 0 1 1

    First the alternatives and criteria are elicited. As a starting point the decision maker has to provide at

    least three alternatives. Next the triad method of the repertory grid technique is used to differentiate thealternatives. The decision maker selects three alternatives and inputs a criterion in which two are similar(i.e., both are rated either as good or as bad) and one is the opposite. This input is stored by the

    system in a temporary decision matrix. For each assessment of type good, an outcome of 1 is stored;for each assessment of type bad, an outcome of1 is stored. For each alternative that is not an element

    of the triad that produced the criterion, an outcome of 0 is stored. The rationale for these values is that thedecision maker probably selects extreme alternatives to define a criterion and therefore the value 0 is usedto approximate the outcomes of the probably non-extreme alternatives. Table 6 shows an example with

    six alternatives and three criteria. In this example the first criterion c1 was elicited with the triad x1 (ratedgood), x2 (rated bad), and x3 (rated bad). The second and third criterion is created similarly inthis example. This elicitation using the triad method continues as long as the decision maker can identify

    additional criteria.

    Next, the system computes the sums of the columns in the temporary decision matrix (last column inTable 6). If two alternatives are having a comparable overall score, the system presents this pair to thedecision maker and asks if they can already be differentiated using the available criteria, or if an additionalcriterion is required. In the example in Table 6 the first pair presented to the decision maker would be x5and x6. Table 7 shows the temporary decision table after the decision maker has provided a new criterionc4 and rated the alternative x5 as good and the alternative x6 as bad with respect to that new criterion.Again this elicitation continues as long as the decision maker can identify such pairs of alternatives.

    To conclude the first step of the standard process, the system searches the temporary decision matrixfor alternatives which score either extremely well or extremely poorly. Suppose an alternative is rather

    poor. The decision maker is asked if such an alternative is really poor in so many criteria, or if there exist

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    Fig. 5. ExcelAIMs basic display.

    criteria for which the alternative performs well. Posing this question might lead to the elicitation of anadditional criterion. In the example in Table 7 the first alternative presented to the decision maker by thesystem would be x3. The decision maker would then be asked if there exists any criteria by which x3would be judged as good.

    In the second step of the standard process the definition of the criteria is put into more concrete terms(see Fig. 2 in the previous section). For each criterion the decision maker selects a type (i.e., maximizing,

    target, or minimizing) and provides the parameters (i.e., range of feasibility, and indifference thresholds).

    Next, the outcomes are recorded and ExcelAIM computes the feasible and the nondominated alter-natives. Based on this analysis, the decision maker can refine the set of criteria and their parameters.This analysis can also be a reason to add a new criterion if an obviously good alternative is found to bedominated. If the final decision is the selection of exactly one alternative, then the decision maker has the

    option of instructing the system to exclude all dominated alternatives from further consideration.Finally, the decision maker uses the basic display of ExcelAIM to adjust his levels of aspiration (see

    Fig. 5). The basic display shows the current levels of aspiration and provides a button for each criterion

    to raise or lower that criterion to the next better or worse level, respectively.The basic display also provides a ranking of alternatives based on the Tchebycheff distance measure

    constructed from the given levels of aspiration. The algorithm used assures that only a nondominated

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    Table 8

    Evaluation of ExcelAIMs standard process

    Question Minimum Mean (Std. Dev.) Change Maximum1 3 4.5 (0.84) +0.3 5

    2 4 4.7 (0.52) +0.4 5

    3 4 4.2 (0.41) +0.2 5

    4 4 4.5 (0.55) +0.5 5

    5 3 4.3 (0.82) +0.9 5

    6 3 4.0 (0.89) +0.1 5

    7 2 4.0 (1.10) 0.3 5

    8 4 4.5 (0.55) +0.1 5

    9 3 4.3 (0.82) +0.5 5

    10 4 4.5 (0.55) +0.5 5

    11 4 4.7 (0.52) +0.4 5

    12 2 4.0 (1.10) +0.2 5

    Time needed 4 4.5 (0.55) n.a. 5

    Overall 2 4.3 (0.25) +0.3 5

    alternative can get the best rank. Let aj denote the level of aspiration currently set for criterion cj. Letthe function vj map an outcome onto the interval [0,1] according to the function type of criterion cj(see Fig. 2). Then the distance of alternative x to the current levels of aspiration is defined by d(x) :=

    maxj |vj(cj(x))vj(aj)|. Based on this distance measure, the following algorithm computes the rankingof the alternatives.

    (1) Empty the ranking.(2) Let X X be the set of all feasible alternatives ofX.

    (3) Let X X be the set of all nondominated alternatives of X.(4) Let x := arg minxX (d(x)).(5) Put the alternative x on the best rank which is still free.

    (6) Let X := X\{x}.(7) IfX = go to step 3.

    ExcelAIM does not prescribe the presented sequence of steps for decision making (see Fig. 4). Instead,the decision maker can jump back and forth adding, modifying, or deleting alternatives and criteria.The subjects in the study consistently used this feature of ExcelAIM often. Our interpretation is thatthe subjects used feedback provided by ExcelAIM to iteratively capture the important aspects of their

    problem.The intention of the final phase of the field study was to compare ExcelAIMs standard process to its

    straight process. Therefore the case study and the questions which were already presented in the previous

    section were used again. Additionally, the subjects were asked if a decision could be made in a reasonableamount of time with the system (question time needed). Table 8 summarizes the results of the subjects

    assessments and relates them to the data presented in Table 5.

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    In eleven out of twelve issues, ExcelAIMs standard process was rated better than its straight process.The only issue in which it was rated worse is the confidence in the process (see question 7). In fact, in thestandard process ExcelAIM actively queries the decision maker according to the repertory grid execution

    schema; i.e., primarily the system has control over the process. In contrast, in the straight process thedecision maker controls the system by setting up the decision matrix. Letting the decision maker do thesetup manually probably leads to a higher degree of confidence in the process.

    The greatest improvement in the rating concerned the insight in the problem gathered when using thesystem (see question 5). It seems that the subjects regarded the repertory grid technique as a very useful

    instrument in this respect.

    5. Conclusion

    In this article a field study about structuring multiple criteria problems on an operational level ispresented. Such decision problems are characterized by the fact that few resources in terms of time andmoney are available. The study has led to the implementation of the decision support system ExcelAIM.ExcelAIM combines the repertory grid technique with the aspiration-level interactive method (AIM).

    The underlying mathematics are easy to understand even for non-expertsa feature that is crucial for theacceptance of a decision support system in a business environment.

    References

    [1] Keen PGW, Morton MSS. Decision support systemsan organizational perspective. Reading, MA: Addison-Wesley;

    1978.

    [2] VanGundy AB. Techniques of structured problem solving. New York: Van Nostrand Reinhold; 1988.[3] HabenichtW,Scheubrein B, ScheubreinR. Multiplecriteria decision making. In: Derigs U, editor.Theme 6.5 Optimization

    and Operations Research of the Encyclopedia of Life Support Systems (EOLSS). Developed under the auspices of the

    UNESCO. Oxford, UK: Eolss Publishers; 2002. http://www.eolss.net.

    [4] Korhonen P, Moskowitz H, Wallenius J. Multiple criteria decision supporta review. European Journal of Operational

    Research 1992;63:36175.

    [5] Hwang C-L, Masud ASM. Multiple objective decision makingmethods and applications. Berlin: Springer; 1979.

    [6] Hwang C-L, Yoon KP. Multiple attribute decision makingmethods and applications. Berlin: Springer; 1981.

    [7] Belton V, Stewart TJ. Multiple criteria decision analysisan integrated approach. Boston: Kluwer; 2002.

    [8] Keeney RL.Value-focused thinkinga path to creative decision making. Cambridge, MA: Harvard University Press; 1992.

    [9] Keeney RL. Value-focused thinkingidentifying decision opportunities and creating alternatives. European Journal of

    Operational Research 1996;92(3):53749.

    [10] Lotfi V, Stewart TJ, Zionts S. An aspiration-level interactive model for multiple criteria decision making. Computers &Operations Research 1992;19(7):67181.

    [11] Kepner CH, Tregoe BB. The rational manager. Princeton, NJ: Princeton Research Press; 1976.

    [12] Kelly GA. The psychology of personal constructs. New York: Norton; 1955.

    [13] Jankowicz A. Applications of personal construct theory in business practice. In: Neimeyer G, Neimeyer R., editors.

    Advances in personal construct psychology, vol. 1. New York: JAI Press; 1990. pp. 25788.

    [14] StewartV, StewartA. Business application of repertory grid. London: McGraw-Hill; 1981 http://www.enquirewithin.co.nz/

    BUSAPP/business.htm.

    [15] Rogers M, Bruen M. A new system for weighting environmental criteria for use within ELECTRE III. European Journal

    of Operational Research 1998;107:55263.

    [16] Gammack JG, Stephens RA. Repertory grid technique in constructive interaction. In: Cassell CM, Symon G., editors.

    Qualitative methods in organizational research: a practical guide. London: Sage Publications; 1994. pp. 7290.

  • 7/27/2019 0 a Problem Structuring Front End for a Multiple Criteria Decision Support System

    14/14

    R. Scheubrein, S. Zionts / Computers & Operations Research 33 (2006) 18 31 31

    [17] Easterby-Smith M, Thorpe R, Holman D. Using repertory grids in management. Journal of European Industrial Training

    1996;20(3):330.

    [18] Olson DL. Decision aids for selection problems. New York: Springer; 1996.

    [19] Scheubrein R, Bossert B. An internet system to apply the balanced scorecard concept to supply chain management.In: Kksalan M, Zionts S., editors. Multiple criteria decision making in the new millenium. Berlin: Springer; 2001.

    pp. 34857.

    [20] Angur M, Lotfi V. A comparison of aspiration level interactive method (AIM) and conjoint analysis in multiple criteria

    decision making. In: Karwan MH, Spronk J, Wallenius J., editors. Essays in decision makinga volume in honour of

    Stanley Zionts. Berlin: Springer; 1997. pp. 6073.

    [21] Leon L, Przasnyski Z, Seal KC. Spreadsheets and OR/MS models: an end-user perspective. Interfaces 1996;26(2):92104.

    [22] Albright SC. VBA for modelersdeveloping decision support systems with microsoft excel. Pacific Grove, CA: Duxbury;

    2001.

    [23] Zapatero EG, Smith CH, Weistroffer HR. Evaluating multiple-attribute decision support systems. Journal of MultiCriteria

    Decision Analysis 1997;6:20114.