Abstract
This research proposes an integrated approach to the Data Envelopment Analysis (DEA) and Analytic Hierarchy Process (AHP) methodologies for ratio analysis. According to this, we compute two sets of weights of ratios in the DEA framework. All ratios are treated as outputs without explicit inputs. The first set of weights represents the most attainable efficiency level for each Decision Making Unit (DMU) in comparison to the other DMUs. The second set of weights represents the relative priority of output-ratios using AHP. We assess the performance of each DMU in terms of the relative closeness to the priority weights of output-ratios. For this purpose, we develop a parametric goal programming model to measure the deviations between the two sets of weights. Increasing the value of a parameter in a defined range of efficiency loss, we explore how much the deviations can be improved to achieve the desired goals of the decision maker.This may result in various ranking positions for each DMU in comparison to the other DMUs. An illustrated example of eight listed companies in the steel industry of China is used to highlight the usefulness of the proposed approach.
Highlights
Ratio analysis is a commonly used analytical tool for measuring the relative performance of a Decision Making Units (DMUs) by focusing on one input/output at a time [1]
Because the range of deviations computed by the objective function is different for each DMU, it is necessary to normalize it by using relative deviations rather than absolute ones [43]
On the other hand, solving Model (9) for the DMU under assessment, we adjust the priority weights of output-ratios obtained from Analytic Hierarchy Process (AHP) in such a way that they become compatible with the weights’ structure in the ratiobased Data Envelopment Analysis (DEA) models
Summary
Ratio analysis is a commonly used analytical tool for measuring the relative performance of a Decision Making Units (DMUs) by focusing on one input/output at a time [1]. The development of modern Operations Research/Management Science (OR/MS) has provided us with two powerful methods called Data Envelopment Analysis (DEA) and Analytic Hierarchy Process (AHP) which can be used to derive ratio weights. DEA is a data-oriented approach for assessing the relative efficiency of Decision Making Units (DMUs) that use multiple inputs to produce multiple outputs. In order to use ratio data in the DEA framework, ratio-based DEA models were developed as a combination of DEA methodology and ratio analysis [3]-[5]. This research applies AHP in the ratio-based DEA framework to develop a new integration between DEA, AHP and ratio analysis theory
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