Ranking method based on the difference between weighted output and input

In this paper we developed a new method to establish common weights for measuring the efficiency score of Decision-Making Units (DMUs), based on multiple inputs and multiple outputs. In the new method, these common weights are estimated according to the difference between a weighted sum of outputs and a weighted sum of inputs of the DMUs. We suggest two approaches to rank the DMUs: the first method ranks the DMUs according to the absolute "net profit" (the difference between a weighted sum of outputs and a weighted sum of inputs), while the second method ranks the DMUs according to the relative efficiency score of the ratio between a weighted sum of outputs and a weighted sum of inputs. In addition we present a method to fix objective bounds for the weights of the variables in the Data Envelopment Analysis (DEA), which is based on the above ranking method. We proved thatthese bounds are feasible solutions for the DEA methodology. The ranking methods are illustrated on a case study of 24 hospitals in Israel.