A nonparametric least-squares model in network data envelopment analysis

Data envelopment analysis (DEA) is generally used to measure the relative efficiency of decision making units (DMUs) with multiple inputs and multiple outputs when DMUs are considered as a single-stage process. Network DEA (NDEA) is developed to accommodate DMUs having a two-stage process where the outputs from the first stage become the inputs to the second stage. The current study first proposes a regression-based network sign-constrained convex nonparametric least-squares (NSCNLS) model and establishes its equivalence to the mathematical programming-based NDEA model. Subsequently, NSCNLS is integrated with stochastic frontier analysis (SFA) to develop a two-step method, referred to as network stochastic non-smooth envelopment of data (NStoNED), to account for stochastic noise in the observed data. The first step of NStoNED applies the NSCNLS with relaxed sign constraints to enable the unique estimation of each DMU’s deviation from the whole production frontier as well as its deviation from each stage’s production frontier. Given that the deviation is jointly attributable to inefficiency and stochastic noise, the second step employs SFA to estimate the expected values of the overall inefficiency and the divisional inefficiencies for each DMU. As illustrated in Monte Carlo simulations, under noisy environments, the NStoNED method achieves up to a fivefold reduction in average mean squared error (AMSE) compared to classical NDEA models. Finally, we apply the proposed NSCNLS and NStoNED methods to an empirical dataset related to information technology.