A New Two-phase Approach for Holding the Strict Positivity Restriction of Weights in DEA Models

Data Envelopment Analysis (DEA) is a well-known non-parametric management science approach for measuring relative efficiency of decision making units (DMUs) performing similar tasks in a production system that consumes multiple inputs to produce multiple outputs. This approach evaluates efficiency score of a DMU as the maximum ratio of the weighted sum of outputs to the weighted sum of inputs subject to the condition that corresponding ratios for each DMU be less than or equal to one. From the theoretical and the computational points of view, strict positivity of the weights is an important and controversial condition to identify an efficient DMU. One significant method to achieve this condition is considering a positive lower bound on weights, known as non-Archimedean infinitesimal epsilon, nevertheless under some conditions the selected value for epsilon is quite small (sometimes even smaller than the zero tolerance of the computer). There is a two-phase approach which evaluates the efficiency of DMUs in envelopment model without determining a suitable value for epsilon, however it fails to give us a set of positive weights. In fact, finding a set of positive weights among all alternative solutions of multiplier model is a technical challenge in DEA. To meet the challenge, we propose a new two-phase approach which deals with multiplier model and determines positive weights, if there are. A case study of Iranian banking industry is taken as an example to illustrate the potential application of the suggested approach.