A Shapley value index on the importance of variables in DEA models

Abstract

In many DEA applications, decision makers always confront with a problem, which is how to determine the importance of each input or output variable in performance measurement? This paper approaches this problem from a cooperative game point of view. First, we have defined an efficiency change ratio (ECR) to calculate the marginal impact of each variable on the efficiency evaluation, which compares the efficiency scores of the two radial DEA models differing in whether the given variable is included. Based upon a simple data example, this paper finds that it is not suitable to use ECR to determine the importance of each variable, for the value of the variable’s ECR is very sensitive to the selected input set and output set. Then, this paper has defined a characteristic function of each coalition (input or output variable set) based upon ECR. The characteristic function is super-additive. Thus, we use Shapley value index as the solution of the cooperative game to determine the importance of the variable under evaluation. Finally, the proposed approach has been applied to a data set from prior DEA literature.