Evaluating the efficiency of Insurance companies based on the common weight models

Data envelopment analysis (DEA) is a wide range of mathematical models which is used to assess therelative efficiency of a set of similar units with the same inputs and outputs. This model obtains a set ofweights for input and output variables of per units and then, calculates the relative efficiency for each oneof the units, using the obtained weights. This differences between units weights, has been followed somecriticisms for this approach. Since 1991, various linear and nonlinear models have been presented in DEAto calculate a set of common weights for decision making units. One of the most common methods wasthe proposed model by Hossein zade et,al. so as to calculate the common weights and rank units. Thelarge number of inputs and outputs to the number of units under evaluation, is another restriction of dataenvelopment analysis models that according to an empirical relation, the number of decision making unitsshould be greater than three times the sum of inputs and outputs. Therefore, when the number of inputsand outputs is high, decreasing dimensions of the problem without losing more information, is one of theexisting issues in solving this problem. In this research, we study and rank 11 of insurance companies inIran and due to the large number of inputs and outputs, we are supposed to reduce scale of the datathrough the principal component analysis and finally, we will calculate the efficiency and consequently,rank insurance companies by the common weight model.

Keywords:

common weight¹ , principal component analysis² , data envelopment analysis