Mixed Stochastic Input Oriented Data Envelopment Analysis Model
Nahia Mourad, Assem Tharwat · HAL (Le Centre pour la Communication Scientifique Directe) · 2019
Data envelopment analysis (DEA) is a mathematical tool used to evaluate relative efficiency of decision making units (DMUs). It is a bench-marking method for these units. To measure this relative efficiency, data related to a set of inputs and outputs are provided from all the DMUs under analysis, and then implemented in a suitable DEA model. Stochastic DEA allows the inputs or outputs to be stochastic random variables. In this article, we consider combination of deterministic and stochastic inputs following Normal and/or Poisson distribution. To the best of our knowledge, variables following Poisson distribution are not yet considered in these methods. We introduce the stochastic input oriented data envelopment analysis (SIODEA) model. The random inputs, following either normal or Poisson distributions, are controlled by chance constrained. Using functional analysis techniques, the chance constrained with Poisson variables is replaced by difference of Marcum functions evaluated at points related to the parameters of these variables. Consequently, we formulate a deter-ministic equivalent model with mixed random inputs. Finally, a numerical example is presented and the efficiencies of different DMUs are calculated using the obtained equivalent model to test its validity.