Abstract
This research proposes a hierarchical aggregation approach using Data Envelopment Analysis (DEA) and Analytic Hierarchy Process (AHP) for indicators. The core logic of the proposed approach is to reflect the hierarchical structures of indicators and their relative priorities in constructing composite indicators (CIs), simultaneously. Under hierarchical structures, the indicators of similar characteristics can be grouped into sub-categories and further into categories. According to this approach, we define a domain of composite losses, i.e., a reduction in CI values, based on two sets of weights. The first set represents the weights of indicators for each Decision Making Unit (DMU) with the minimal composite loss, and the second set represents the weights of indicators bounded by AHP with the maximal composite loss. Using a parametric distance model, we explore various ranking positions for DMUs while the indicator weights obtained from a three-level DEA-based CI model shift towards the corresponding weights bounded by AHP. An illustrative example of road safety performance indicators (SPIs) for a set of European countries highlights the usefulness of the proposed approach.
Highlights
Individual indicators are multidimensional measures that can assess the relative positions of entities in a given area [1]
The recent methodological advances in operations research and management science (OR/MS) have provided us with two powerful tools, namely data envelopment analysis (DEA) and analytic hierarchy process (AHP), which can be used as weighting and aggregation tools in composite indicators (CIs) construction
We develop our formulation based on the generalized distance model [56,57] in such a way the hierarchical structures of indicators, using a weighted-average approach, are taken into that the hierarchical structures of indicators, using a weighted-average approach, are taken into be the the best best attainable attainable composite composite value value for for the the Decision Making Unit (DMU)
Summary
Individual indicators are multidimensional measures that can assess the relative positions of entities (e.g., countries) in a given area [1]. There are a number of other methods that do not necessarily apply additional restrictions to a DEA model Such as converting the qualitative data in DEA to the quantitative data using AHP [27,28,29,30,31,32,33,34], ranking the efficient/inefficient units in DEA models using AHP in a two stage process [35,36,37], weighting the efficiency scores obtained from DEA using AHP [38], weighting the inputs and outputs in the DEA structure [39,40,41,42], constructing a convex combination of weights using AHP and DEA [43]. AHP in an additive three-level DEA-based model, it contributes to the set of methods currently available for CI construction
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