Analyzing properties of K-cones in the generalized data envelopment analysis model

We study the properties of the K-cone in a generalized Data Envelopment Analysis (DEA) model. This model includes the following four important classes of models: Charnes et al. (1978) model, Banker et al. (1984) and Charnes et al. (1985) model, Fنre and Grosskopf (1985) model, and Seiford and Thrall (1990) model as its special cases. The main contribution of this paper is to introduce to the above four models (a) the input-output preference cone W to represent the relative importance of different input/output categories viewed by the evaluator (one who evaluates the decision-making units (DMUs)); and (b) the so-called predilection cone to describe preference of the evaluator to selected DMUs. We discuss the new characterizations of DEA efficient DMUs in the case of K-cone. We also describe the use of elementary predilection operators to achieve special preference for one or more DMUs. This method can be easily applied to find all the DEA efficient DMUs that are on a common efficient face as one or more prespecified DMUs. The method provided in this paper is complete in the sense that only those DMUs that are on a common efficient face with the predileccted ones will be DEA efficient after predilection. We believe that the results of this paper will play in important role in determining the structure of efficient frontiers.