Single prince method for efficiency measurement: a case study of a branch banking

• Autores: Ana García Bernabéu, Enrique Ballestero
• Localización: XXV Congreso Nacional de Estadística e Investigación Operativa: Vigo, 4-7 de abril de 2000, 2000, ISBN 84-8158-152-6, págs. 31-32
• Idioma: inglés
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• Resumen

  • Nowadays, Data Envelopment Analysis (DEA) is considered a standard tool for selecting efficient alternatives. The DEA scores do not strictly measure efficiency levels.

    They rather categorise two sets of activities, the efficient and inefficient alternatives. There are various DEA models, the core of which is CCR approach to global efficiency. Indeed, CCR is a natural beginning for other DEA models. In the CCR original approach, the analyst labels the activities as global efficient (which are assigned a score equal to one) and inefficient (which are assigned positive scores less than one). Another well-known approach is BCC where efficiency is conceived from a double perspective, the technical and scale measurement. Technical inefficiencies are associated with weaknesses in the production process. In contrast, scales inefficiencies reflect failures to achieve the most productive scale size. The technical efficient alternatives lie on a polygonal frontier which is dominated by the CCR global efficient set. In both approaches, the efficient units are obtained by the constrained maximisation of benefit/cost ratios. Both benefit and cost are aggregate variables, the aggregation weights or prices being the unknown decision variables derived from fractional or linear programming. Therefore, the prices are directly provided by the model without resorting to subjective specifications from the decisionmaker.

    However, the DEA price system changes with the courses of action chosen by the analyst to construct the objective function. This non-invariance price system discards the possibility of measuring efficiency strictly, ranking the activities, and determining the most productive scale size.

    Another methodology to measure efficiency has been recently proposed elsewhere. This methodology - called single price model -is developed in two stages. In the first stage, the alternative courses of action are classified in two groups, the inefficient set of activities and the non-inefficient set. The inefficient courses of action are defined as activities dominated (in both benefits and costs) by combinations of alternatives. The results in the first stage are achieved via linear programming. In the second stage, a model to rank the activities according with their efficiency levels is designed. This model is based on the following assumption: �the aggregate cost of any non-inefficient activity must always be less than (or equal to) the respective aggregate benefit, since costs greater than benefits involve inefficiency. Under this assumption the non-inefficient activities are proven to lie on a convex frontier, namely, the efficient frontier of a convex set. They satisfy a remarkable property, both benefits and costs are aggregated by a single price system, which objectively derives from the model. In other words the price system obtained from the main assumption is the same regardless of the alternative course of action selected by the analyst to play the role of an objective function. By aggregating benefits on the one hand, as well as costs on the other with the single price system, the method leads to scores capable of measuring the efficiency of every alternative. The DEA global efficient alternatives are checked to be closely correlated with the highly scored alternatives given by the single price model. This last model has a critical advantage because of its ability to achieve a complete ranking of all the alternative courses of action. The single price scores are ranged over (0, ��). In this way single price indexation allows to determine the best alternative, the second best, and so on.