On the Use of a Multicriteria Decision Aiding Tool for the Evaluation of Comfort

Abstract

In this paper we present a real word application of multicriteria decision aiding for the evaluation of high speed trains comfort from passengers’s point of view. Our study is used as a feasibility analysis for the introduction of multicriteria tools in the SNCF. Our approach concerns different steps of a decision aiding procedure. We firstly define the complex notion of comfort and propose to use a hierarchical model for its representation. We then present in more detail the seating comfort by assigning value scales to its components. Our problem being a sorting problem and our data being very heterogeneous, we decide to use the ELECTRE TRI method for the aggregation of the components. The article presents how the decision parameters, such as thresholds, weights and limit profiles, of ELECTRE TRI are selected and conclude with three fictitious assignment examples.

Appendices

Appendix 1

For more details, see Roberts (1979).

A scale (or measurement scale) is a couple formed by a set of numbers, called echelon, used to code an information relative to objects. There exist different types of scales:

Ordinal scale: An ordinal scale is a measurement scale that assigns values to objects based on their ranking with respect to one another. It defines a total preorder of objects (objects are ranked from the worst one to the best one and there can be more than one objects in one ranking level). The scale values themselves have a total order; qualitative nouns may be used like “bad”,“medium”,“good”, etc. If numbers are used they are only relevant up to strictly monotonically increasing transformations. For instance one can define an ordinal scale for global comfort with five echelons: very comfortable, comfortable, normal, not bad and very bad and put numbers like “5” for very comfortable, “3” for comfortable, etc.

Interval scale: On interval measurement scales, one unit on the scale represents the same magnitude on the trait or characteristic being measured across the whole range of the scale. For instance, if pleasure were measured on an interval scale, then a difference between a score of “10” and a score of “11” would represent the same difference in pleasure as would a difference between a score of “50” and a score of “51”. Interval scales do not have a “true” zero point and therefore it is not possible to make statements about how many times higher one score is than another. For the pleasure scale, it would not be valid to say that a person with a score of “30” was twice as pleased as a person with a score of “15”. Hence if f is a representation for an interval scale, all the other acceptable representations will be in form of α f +β. A classical example of an interval scale is the Fahrenheit scale for temperature. Equal differences on this scale represent equal differences in temperature, but a temperature of 30^∘ is not twice as warm as one of 15^∘.

Ratio scale: A ratio measurement scale is a scale in which a certain distance along the scale means the same thing no matter where on the scale you are, and where “0” on the scale represents the absence of the thing being measured. Thus a “4” on such a scale implies twice as much of the thing being measured as a “2.” Hence if f is a representation of a ratio scale, all the other acceptable representations will be in form of α f. A classical example of a ratio scale is the metric scale for distance.

Appendix 2: General Presentation of Electre TRI

The general procedure of ELECTRE TRI has two consecutive steps:

• construction of a binary relation establishing how alternatives are compared to the boundaries of classes,

• exploitation (through assignment procedures) of the binary relation in order to assign each alternative to a specific class.

We present first of all the first step consisting in comparing alternatives to profiles representing the frontiers between ordered categories. We will note by X the set of objects to be classified (for instance suppliers’ offers), $X =\{ x_{1},x_{2},\ldots,x_{n}\}$, and by $A =\{ a_{0},a_{2},\ldots,a_{m}\}$ the set of limit profiles. Let us denote by $C =\{ C_{1},C_{2},\ldots,C_{m}\}$ the set of classes, the class C ₁ being the worst one and C _m the best one etc. If we have m classes, we will have m + 1 limit profiles where a ₀ (resp. a _m ) represents a fictive profile having the worst (resp. the best) evaluation on each criterion while a limit profile a _i , $i \in \{ 1,2,\ldots,m - 1\}$, represents the frontier between the classes C _i and C _i+1. The comparison between two elements x and y (x may represent an object and y a limit profile or the inverse) is done by an outranking relation denoted by S. The affirmation xSy (or S(x, y)) means that “the element x is at least as good as the element y” and is calculated using two indices, the Concordance and the Discordance index. One can find different, more or less refined, definition of such indices in the literature but all of them are based on the same following idea:

• Concordance index: shows if there is a sufficiently strong majority of criteria in favor of the outranking relation;

• Discordance index: shows if there is at least one criterion “strongly opposed” to the outranking relation (in such a case we say that the criterion has a veto for the outranking relation).

In the following we note C(S(x, y)) (resp. D(S(x, y))) in order to say that there is a concordance (resp. discordance) for the outranking S(x, y). Hence the relation S(x, y) is verified if there is concordance but not discordance:

$$\displaystyle{\mathit{xSy}\ \text{if and only if}\ C(S(x,y))\ \text{and not}\ D(S(x,y))}$$

We will present in the following a classical formula of concordance and discordance indices. An interested reader can find more detailed explanations on the subject in Roy (1996); Roy and Bouyssou (1993). The calculation of these indices makes use of different parameters such as importance weight of a criterion, indifference threshold, veto threshold and majority threshold.

$$\displaystyle\begin{array}{rcl} C(x,y)\;\Longleftrightarrow\;\frac{\sum _{j\in J_{\mathit{xy}}}w_{j}} {\sum _{j}w_{j}} \geq \gamma,\ \ & &{}\end{array}$$

(16.1)

$$\displaystyle\begin{array}{rcl} D(x,y)\;\Longleftrightarrow\;\exists j: g_{j}(y) - g_{j}(x) > v_{j}& &{}\end{array}$$

(16.2)

where:

• g _j is a real valued function representing the evaluation of alternatives with respect to the criterion c _j (to be maximized);

• w _j is a non negative coefficient which represents the importance of the criterion c _j ;

• J _xy represents the set of criteria for which x is at least as good as y; more precisely, $J_{\mathit{xy}} =\{ j: g_{j}(y) - g_{j}(x) \leq q_{j}\}$ where q _j is the indifference threshold associated to criterion c _j ;

• γ is a majority threshold;

• v _j is a veto threshold on criterion c _j ;

The majority threshold represents the minimum percentage of criteria (weighted according to their importance) needed in order to have a concordance. The veto threshold is used for the discordance index and represents for each criteria the threshold for which a difference of evaluation on this criterion becomes problematic for the construction of the outranking relation. The indifference threshold represents the maximum tolerated difference between evaluations of two objects x and y in order to say that x and y are indifferent. In what follows, we will assume, without any loss of generality, that preferences increase with the value on each criterion.

It is easy to see that comparing two objects x and y, four situations may appear:

• xSy and not ySx: we say that “x is preferred to y”;

• not xSy and ySx: we say that “y is preferred to x”;

• xSy and ySx: we say that “x and y are indifferent”;

• not xSy and not ySx: we say that “x and y” can not be compared;

The last case shows that the outranking relation is not necessary a complete relation, this relation does not satisfy any special property other than reflexivity.

After the construction of all comparisons between alternatives and profiles, the exploitation procedure begins. The role of the exploitation procedure is to analyze the way which an alternative x compares to subsequent profiles in order to determine the class to which x should be assigned. ELECTRE TRI proposes two different assignment procedures:

• the pessimistic assignment procedure:

  • i. compare x successively to limit profiles a _i , for $i \in \{ p,p - 1,\ldots,0\}$,

  • ii. a _h being the first profile such that xSa _h , assign x to class C _h+1.

  If a _h−1 and a _h denote the lower and upper profile of the category C _h , the pessimistic procedure assigns alternative a to the highest class C _h such that x outranks a _h−1, i.e., xSa _h−1.

• the optimistic assignment procedure:

  • i. compare x successively to a _i , for $i \in \{ 1,2,\ldots,p\}$,

  • ii. a _h being the first profile such that a _hSx and not xSa _h (i.e. x is preferred to a _h ), assign x to class C _h .

  The optimistic procedure assigns x to the lowest class C _h for which the upper profile a _h is preferred to x.

The ideas that ground the two assignment procedures being different, these assignment procedures might assign some alternatives to different classes. The difference is basically related to the partial nature of the outranking relation, more precisely:

• when the evaluation of an alternative is between the two profiles of a class on each criterion, then both procedures assign this alternative to this class,

• a divergence exists among the results of the two assignment procedures only when an alternative is incomparable to one or several profiles; in such a case the pessimistic assignment rule assigns the alternative to a lower class than the optimistic one.

Editors’ Comments on “On the Use of a Multicriteria Decision Aiding Tool for the Evaluation of Comfort”

Özturk, Tsoukiàs, and Guerrand address an evaluation problem in the context of an important activity in many organizations: procurement. This chapter starts by presenting the problem definition and formulation stages (see Chap. 2), and then describes the definition and application of an aggregation procedure to a particular subproblem within a large project. This work illustrates the sorting problematic based on a variant of the ELECTRE TRI method (see Chap. 4, Sect. 4.4.4). In this case, ELECTRE TRI is used to evaluate alternatives according to a specific axis of evaluation, corresponding to one high-level criterion among other criteria. It therefore describes how the evaluation of a single (top-level) criterion can originate further aggregation problems concerning different aspects that need to be taken into account concerning that criterion, which in turn can be further decomposed in a hierarchical structure.

The French railways company SNCF, the client of this study, needs to evaluate the comfort of trains not only to select suppliers but also to define specifications in calls for tenders. The objective of the intervention was to improve a simplistic evaluation method used by the client, using comfort evaluation as a case study to demonstrate the value of a thorough MCDA study.

The decision process involved directly many actors: experts in decision aiding (the analysts), an expert in psycholinguistics, and company experts from the comfort and acquisition departments. Actors involved indirectly were the train passengers, whose voice was heard.

Several stages can be identified in this intervention: analysis of passenger survey data, definition of the evaluation criteria, definition of parameter values of the model, and application of the model. Among different dimensions of comfort, this chapter focusses on the passenger experience on the train. The hierarchy of criteria was developed based on a content analysis of passenger survey answers about what they value in terms of comfort, as well as on previous knowledge of the client organization. There were five top-level criteria which are subdivided into many more elementary attributes of the train. It is interesting to note that the same type of content analysis was used to define the criteria weights, under the assumption that aspects mentioned more often would correspond to higher importance for the passengers, instead of following a typical elicitation process. The analysts deemed these weights were acceptable and they set the remaining parameters of the evaluation model. This weight elicitation could be improved by performing new surveys based on the final list of criteria, possibly based on choosing among alternatives as often is the case in transportation research (Hensher 1994; Louviere 1988). Nevertheless, in their conclusions the authors warn that an implementation of this tool will require dealing with divergent opinions and performing sensitivity analysis.

The authors opted for a sorting problem statement because they intended to evaluate the intrinsic merit of potential offers in a call for tenders from the comfort viewpoint. This means they did not intend to select the most comfortable option, or to rank the options in terms of comfort. Actually, the chosen method, ELECTRE TRI, was used as a means to obtain a qualitative scale (this is a common use for ELECTRE TRI, see e.g., André and Roy 2007). ELECTRE TRI was the chosen aggregation method, using a simplified outranking relation which is slightly different from the one used in Chap. 15 in this book. The choice of ELECTRE TRI, besides fitting the sorting problem statement, is also justified for being a noncompensatory method, not requiring the definition of substitution rates among the criteria. ELECTRE TRI also presents the advantage of allowing the use of veto thresholds. Such thresholds can be used to prevent that an offer which is very bad in one of the subcriteria reaches a high category, which is a quite realistic requirement when we are dealing with comfort assessment. For most lower levels in the hierarchy, ELECTRE TRI was again used to aggregate subcriteria, but in some simpler cases a weighted sum was used.

As an illustration, the authors evaluate a set of alternatives consisting of three fictitious offers (confidentiality agreements do not allow presenting the true alternatives). These examples are characterized by a list of their characteristics in the comfort-related attributes, and are then sorted into their respective categories. Such categories correspond to qualitative grades that can be taken into account for a global evaluation of each offer considering other dimensions besides comfort.

The tangible results of this decision process were the definition of a criteria hierarchy and the characterization of an ELECTRE TRI sorting model—using inputs from the passengers—for building a global comfort scale. Concerning intangible results, the client understood the methodology as being useful, wishing to use it again in the future, and to extend it to other evaluation problems.

As for the relevance of this chapter, it demonstrates how the evaluation of alternatives under a single criterion (in this case comfort) can be in itself a complex MCDA problem. It also illustrates that the list of criteria does not necessarily have to be elicited from the client. Other stakeholders, in this case the train passengers, can be the source of the criteria list and contribute to the inclusion of aspects that might otherwise not be valued.