How to Deal with Imprecise Weights in Multiple Criteria Decision Making

By Park, K. Sam; Shin, Dong Eun | Global Business and Management Research: An International Journal, April 2011 | Go to article overview

How to Deal with Imprecise Weights in Multiple Criteria Decision Making


Park, K. Sam, Shin, Dong Eun, Global Business and Management Research: An International Journal


Introduction

The great number and variety of applications of multi-criteria decision making (MCDM)--including project prioritization, location and policy analysis, and managerial performance evaluation--has arisen in tandem with critical developments in its theory and methodology. The fundamental intent of MCDM is to evaluate a finite set of alternatives (including organizations) whose consequences are measured in multiple conflicting criteria, in order to select an optimal alternative and/or rank-order the performance of alternatives. Multi-attribute value theory (MAVT) forms a significant body of theory, and represents the most widely used framework for MCDM (Keeney and Raiffa, 1976). Typically, this theory requires two types of input--alternative values (or marginal values) and scaling factors (criterion weights)--for the evaluation of alternatives. Although a sizeable number of formally elegant procedures have been developed to assess these values precisely, the implementations of those procedures, in practice, are often difficult and time-consuming.

Frequently, the decision-maker may only be able to rank the criteria according to their importance, rather than assigning them numerical weights. She might instead categorize the importance as "very important," "important," or "less important." How are the alternatives to be evaluated in cases like these ordinal weights?

In this paper, we take the even broader cases wherein the importance is known only to the extent that the true values lie within prescribed bounds. Such preference information is referred to as imprecise, incomplete, or partial weights. Its basic assumption is that the decision-maker may be unwilling or unable to provide exact estimations of weights. This assumption is realistic in situations involving time pressure, lack of knowledge, and/or in which the decision-maker has limited attention and information processing capability (Kahneman et al., 1982; Weber, 1987; Park and Kim, 1997). There are also more specific reasons for the infeasibility of assuming the exact weights. For instance, Barron and Barrett (1996) previously stated that various methods for eliciting exact weights from the decision-maker may suffer on several counts, because the weights depend heavily on the elicitation method and there is no agreement as to which method yields more accurate results since the "true" weights remain unknown.

In this article, we develop a new linear programming method to prioritize the performance of alternatives under incomplete weights. This is based on extensions to the micro-economic concept of Debreu-Farrell's price efficiency measurement. Following Debreu (1951), who provided first measure of efficiency, Farrell (1957) proposed a nonparametric way of estimating the price efficiency of production units on the bases of their input-output data and market prices. He suggested measuring the price efficiency by means of comparing a target unit with the unit attaining maximum benefit at the given price scenario. Replacing production unit by decision alternative and extending price to preference information, it follows that the concept of Farrell's measurement can be utilized in the context of MCDM to evaluate the performance of alternatives. Further extensions are needed to treat incomplete weights since the Farrell measure requires exact knowledge of prices, which we plan to develop in this paper. Advantages to our method are shown in relation to the earlier linear programming approach to MCDM. We also demonstrate an application of our method to the performance evaluation of telecommunication branch offices in Korea.

It should be noted that the Farrell approach has found numerous applications, following the elaboration of his work by Charnes et al. (1978), who extended it and originated data envelopment analysis (DEA). We refer the reader to Cooper et al. (2000) for details on DEA. See also Charnes et al. (1990) and Thompson et al. …

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