Computational tractability of chance constrained data envelopment analysis

Chance constrained data envelopment analysis (DEA) is developed for modeling data uncertainty in inputs and outputs of a set of decision making units (DMUs). In the existing literature, chance constrained DEA includes E-model and P-model. The E-model maximizes functions related to the expectation of random inputs and outputs. The P-model maximizes the probability of stochastic events related to the random inputs and outputs. However, optimization methods for solving these models lack a formulation to convert the resulting DEA models into tractable optimization methodologies. The current study examines the nonlinearity of the chance constrained DEA models by identifying and reformulating tractable optimization models into conic optimization problems. We relax the uncorrelation assumption which is usually adopted in the existing chance constrained DEA models. We extend chance constrained DEA from the Gaussian model to a distributionally robust model in order to deal with datasets where distributions of random inputs and outputs are only partially known in advance. An example is provided to demonstrate the reformulated forms of chance constrained DEA.