Identification of inefficiencies in an additive model based IDEA (imprecise data envelopment analysis)

Abstract

We employ an additive data envelopment analysis (DEA) model and assume, without loss of generality, all the input–output data are known in the form of arbitrary linear inequalities. This is referred to as an additive imprecise DEA (IDEA) model that involves treating a non-linear programming problem. The non-linear model is then transformed into a linear programming equivalent by methods we present in this paper. To achieve the purpose of this paper which is the identification of specific inefficiencies for the decision making units (DMUs) under consideration, we develop a two-stage method. In the first stage, we obtain an aggregated measure of inefficiencies from solving the linear version of the additive IDEA model. We then retrieve exact data based upon the optimal solutions obtained in the first stage. These exact data retrieved are then used in the next stage which implies that an ordinary additive DEA model is constructed. We can thus obtain the specific inefficiencies in terms of slacks as well as peer groups and scale sizes for every DMU to be considered. Scope and purpose Data envelopment analysis (DEA) is a mathematical programming approach to evaluate the relative efficiency of decision making units (DMUs) that use multiple inputs to produce multiple outputs. An assumption underlying DEA is that all the data are known exactly. In some applications, however, the data may be imprecise. For instance, some of the data are known only within specified bounds, while other data are known only in terms of ordinal relations. To deal with imprecise data in DEA, imprecise data envelopment analysis (IDEA) models and methods have been developed previously. However, IDEA only gives us an aggregated measure of inefficiencies for each DMU. It is thus needed to develop methods from which we can obtain specific inefficiencies such as slacks, as well as peer groups and scale sizes, as have been done in ordinary DEA evaluations. The purpose of this paper is, hence, the identification of specific inefficiencies including peer groups and returns to scale for the DMUs. These information can hence be helpful to the managers in decision making toward improving the efficiency of managerial and operational tasks in their business units.