Decision SupportA new method for elicitation of criteria weights in additive models: Flexible and interactive tradeoff
Graphical abstract
Introduction
One of the most relevant issues in using a multicriteria decision model is probably that of evaluating the weights of criteria (or attributes) in the aggregation procedure. This is particularly relevant for aggregation using an additive model. In practice, this aggregation procedure is the most commonly found in a multicriteria decision model (Spliet & Tervonen, 2014), for instance when selecting suppliers (Xia & Wu, 2007), or planning of metro extension lines (Hurson & Siskos, 2014). The additive model can be applied under some basic assumptions covered by many earlier studies (Fishburn, 1967, Keeney, 1972, Keeney, 1992, Keeney and Raiffa, 1976). Stewart´s survey on multicriteria methods shows some useful characteristics for an additive model (Stewart, 1992). A more recent survey considers eliciting the weights of criteria as a central issue (Riabacke, Danielson, & Ekenberg, 2012). Eisenführ, Weber, and Langer (2010) give a broad overview on weights elicitation procedures for additive models.
Previous studies on experimental analysis (Borcherding et al., 1991, Weber and Borcherding, 1993) on the main elicitation procedures for additive models have identified some major difficulties and challenges. The results of these studies prompted our research and led to the original achievement proposals to overcome those issues that this article sets out. First of all, it has long been held that the tradeoff elicitation procedure (Keeney, 1992, Keeney and Raiffa, 1976) has a strong axiomatic foundation (Weber & Borcherding, 1993). Nevertheless, experimental studies have shown that inconsistencies have been found when applying this procedure (Weber & Borcherding, 1993).
The method proposed in this paper contributes to overcoming some of these inconsistencies. This paper proposes a flexible elicitation procedure, which collects information from the DM, and evaluates this information. The main difference from previous studies is related to the elicitation process. In flexible elicitation, incomplete or imprecise information, a priori, is not assumed. Whether the DM is or is not able to give complete information, this is evaluated in the elicitation process itself, in a flexible way. For this reason, right from the start, the flexible process seeks complete information, based on the tradeoff elicitation procedure. However, at any point further on, it may consider incomplete information in either of the following two situations: when a unique solution is found or when the DM is not able to give additional information.
The method is built into a DSS (decision support system), which uses a flexible elicitation concept that requires less effort from the DM (Decision Maker). Before presenting the method proposed and its DSS, a brief review of the related literature is presented. In order to illustrate how the method named FITradeoff (Flexible and Interactive Tradeoff) works, the DSS is used on two applications dealing with supplier selection problems (Barla, 2003, Xia and Wu, 2007).
Section snippets
Literature related to the additive model and the elicitation of weights
As previously stated, eliciting a criterion weight (ki) is probably the main concern of an additive model with regard to aggregating the value functions vi(xi) over the consequences xi for all criteria i (i = 1,…, n), which is represented (Fishburn, 1967, Keeney, 1972, Keeney, 1992, Keeney and Raiffa, 1976) in (1), usually assuming the normalization in (2).
In many studies the use of the term scaling constant for ki is preferred to weight, considering that
FITradeoff: flexible and interactive tradeoff elicitation method
Before introducing FITradeoff, a brief, mostly qualitative, description of its logic and the rationale for using this process is presented, including a few related issues from previous studies. Then, basic aspects are presented of the procedure for eliciting weights employing tradeoffs (Keeney, 1992, Keeney and Raiffa, 1976), since this is the basis for FITradeoff.
FITradeoff method applied to supplier selection problems
Supplier selection is amongst the main problems studied in the management literature, in which many supplier selection multicriteria models may be found. As stated by Xia and Wu (2007), supplier selection is a multi-criteria decision making problem, which includes qualitative and quantitative criteria. Supplier selection is one of the most important issues in competitive strategies and in many situations a supplier selection problem is found to be associated with other related problems, such
Conclusions
This paper presents an elicitation method for implementing a multicriteria additive model, using the concept of flexible elicitation in order to improve the applicability of the classical tradeoff elicitation procedure. The method is built into a decision support system (DSS), which can be obtained upon request from the authors. It has been discussed and illustrated how the proposed method improved the elicitation process, compared with the classical tradeoff procedure, requiring less
Role of the funding source
This work had partial support from CNPq (the Brazilian Research Council). The CNPq was not involved in the study or in writing this paper.
Acknowledgments
The authors would like to acknowledge the Editor and the anonymous reviewers for their insightful and positive critique of a previous version of this paper in which they identified its potential and for making valuable suggestions by means of which they encouraged the authors to improve its presentation.
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