Development of optimistic and pessimistic models using FDEA to measure performance efficiencies of DMUs

Abstract

In this paper, we develop optimistic and pessimistic models using fuzzy data envelopment analysis (FDEA). We find the fuzzy optimistic and fuzzy pessimistic efficiencies by using the α-cut method. By using super-efficiency technique, we develop models to obtain the complete ranking of the DMUs when fuzzy optimistic and pessimistic models are considered separately. Further, to rank the DMUs when both fuzzy optimistic and pessimistic models are taken simultaneously as hybrid approach. To address the overall performance using fuzzy optimistic and pessimistic situations together in FDEA, we propose a hybrid FDEA using α-cut efficiencies decision model. Finally, these developed optimistic and pessimistic FDEA models and ranking models are illustrated with two examples. The proposed model is applied to a real world problem of health sector. We determine the performance efficiencies of hospitals in Meerut District, Uttar Pradesh state, India for the calendar year 2013-2014 using the proposed model. Number of health superintendents and number of health workers are taken as input variables, and number of inpatients and number of outpatients as output variables.