# On the Use of Data Envelopment Analysis for Multi-Criteria Decision Analysis
## 1 Introduction  
The impetus to achieve triple bottom line outcomes by businesses, ecologically sustainable development goals by governments, and social, economic, and ecological sustainability in natural resource use has resulted in a wide range of management options being developed that produce different combinations of outcomes across the broad set of criteria being used for their assessment. In many cases, these management alternatives result in trade-offs in outcomes against different objectives. For example, achieving environmental goals may result in a loss of employment opportunities at a national level, while at the business level, social considerations may result in loss of profits. Assessing trade-offs in these outcomes, however, is complex, particularly when different management options produce substantially different outcomes against each criterion. This trade-off is made more difficult when the outcomes of the different management options are measured in different and non-commensurable units (e.g., pollution in tons, profits in monetary values, employment impacts in terms of number of jobs lost, etc.). Several approaches have been developed to rank different management options given their impact on the different criteria of interest, usually through the estimate of a composite indicator that allows the overall impacts to be compared. These approaches fall under the general area of multi-criteria decision analysis (MCDA), which aggregates outcomes over multiple objectives or criteria to provide a ranking of management alternatives given these potential trade-offs. Key to the application of MCDA is the use of preference weights associated with each objective, allowing a weighted composite value to be estimated by aggregation across all objectives. The use of MCDA to support management decisions has been applied in a wide range of areas, such as healthcare [1; 2], agriculture, [3; 4], transportation, [5; 6] and resource and environmental management, [7; 8; 9; 10], to name a few. Data envelopment analysis (DEA) has also been broadly employed in an MCDA context. DEA is commonly used to estimate productivity measures such as technical efficiency, technical change, and capacity utilisation of individual firms or businesses. These firms are generally considered individual decision making units (DMUs). These measures reflect the extent to which a set of outputs produced by a DMU are maximized given the set of inputs employed (an output-oriented approach), or the degree to which their input use is minimized to achieve a given level of output (an input-oriented approach). From a decision support perspective, outcomes under different management options (even for a given firm) can also be considered effectively as the unit of production, where the outputs are the expected set of outcomes associated with each criterion or objective under each management option. Consistent with DEA terminology, we will consider these equivalent to DMUs, even though they represent the set of alternatives rather than decision makers per se. The similarities between DEA and MCDA have long been established [11; 12; 13; 14], and the use of DEA as an MCDA approach is gaining increasing interest in the decision making literature, often combined with criterion preference weights derived using other approaches, such as the analytic hierarchy process (AHP) [15], or used to estimate the criteria weights based on AHP-type pairwise comparisons [16]. [PERSON] et al. [15] identified over 220 papers published between 1994 and 2022 that combined DEA and MCDA approaches or where DEA was used in an MCDA context. Applications of DEA as an MCDA tool have been undertaken in a wide variety of industries, such as agriculture [12], energy [17], fisheries [18], and railways [19]. DEA has also been applied to compare the efforts of different countries in protecting biodiversity [20] and improving water quality [21], where outputs are expressed in terms of biodiversity or water quality indices, respectively.