Improving the discrimination power with a new multi-criteria data envelopment model

Abstract

Data envelopment analysis (DEA) allows evaluation of the relative efficiencies of similar entities, known as decision making units (DMUs), which consume the same types of resources and offer similar types of products. It is known that under certain circumstances, when the number of DMUs does not meet the DEA Golden Rule, that is, this number is not sufficiently large compared to the total number of inputs and outputs, traditional DEA models often yield solutions that identify too many DMUs as efficient. In fact, this weak discrimination power and unrealistic weight distribution presented by DEA models remain a major challenge, leading to the development of models to improve this performance, such as: multiple criteria data envelopment analysis (MCDEA), bi-objective multiple criteria data envelopment analysis, goal programming approaches to solve weighted goal programming (WGP–MCDEA) and extended–MCDEA. This paper proposes a new MCDEA model which is based on goal programming, with and without super efficiency concepts, and presents test results that show its advantages over the above cited models. A set of problems from the literature and real-world applications are used in these tests. The results show that the new MCDEA model provides better discrimination of DMUs in all tested problems, and provides a weight dispersion that is statistically equal to that obtained by other MCDEA models. An additional feature of the proposed model is that it allows the identification of the input and output variables that are most important to the problem, to make it easier for the decision maker to improve the efficiency of the DMUs involved. This is very useful in practice, because in general, the available resources are scarce, so it is a further advantage of the proposed MCDEA model over the others tested.