# On the Use of Data Envelopment Analysis for Multi-Criteria Decision Analysis
## 1 Introduction
The DEA efficiency measure is sometimes referred to as the 'benefit of the doubt' indicator (BODI) [22; 23] in an MCDA context, as it implicitly recognizes that DMUs may have different objective preferences and that their choices of output mix may reflect these preferences. In the case of DMUs actually representing different management options (rather than decision makers per se), these options may have been designed with achieving particular outcomes in mind, and hence their performance across multiple criteria may reflect this. A key advantage of the benefit of the doubt indicator is that objective preference weights do not need to be explicitly provided, as they are assumed implicit in the production mix of the DMU. However, as noted above, decision maker preferences can be directly included in the DEA model. A feature of these studies is that all criterion indicators and their associated outcomes are compared at the same time. Where these indicators could be considered sub-indicators of a broader objective set (e.g., ecological, economic, or social objectives), different numbers of indicators in each implicitly apply different importance weightings to their corresponding broader objective, as they have a greater overall influence on the BODI/efficiency score. For example, an objective represented by five indicators would have (implicitly) greater influence on the overall efficiency score than an objective with two or three indicators. While this may be intentional in some cases, in others it may reflect availability of indicators rather than an implicit preference for some outcomes. For example, environmental indicators may be more readily accessible than social indicators (or vice versa). Without some compensating analysis, the environmental outcomes would dominate the determination of the 'best' management option in this case. Two key approaches to DEA are the radial [24] and additive (slacks-based) [25] approaches. Both approaches have been widely applied in efficiency analysis, and each has particular theoretical and practical advantages and disadvantages. Radial models are conceptually simple, assuming that outputs (or inputs) change proportionally given an output (input) orientation, subject to any underlying returns to scale conditions. Slacks-based measures remove the proportionality assumption and assume that outputs (or inputs) can change individually based on what combinations are observed in the data [26]. The previously cited applications of DEA used either the radial approach [12; 17; 18] or the slacks-based approach [19], without consideration of the impact of the approach used on the outcomes of the analysis. In this study, we consider the implications of both approaches when using DEA for MCDA. We also consider the impact of imposing a hierarchical structure on the resultant ranking of options. Hierarchical structures are commonly imposed in MCDA [27], with one method--the analytic hierarchy process (AHP) [28]--designed specifically to provide decision support through a hierarchical structure. AHP is generally used to estimate weights associated with each objective, with the weights estimated for each level of the hierarchy (i.e., higher-level objectives such as maximizing overall'social' or 'economic' outcomes; lower level (but more specific) objectives such as community benefits, equity, etc.). We consider the impact on option ranking of ignoring the implicit hierarchical structure when there are different number of indicators associated with each higher order objective. The overall purpose of the study is to provide guidance to future applications of DEA for multi-criteria decision making as to the implications of the approach adopted. Specifically, we consider how the type of DEA model used and how it is applied affects the estimated relative efficiency score related to each management alternative being considered by decision makers.