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Purpose This paper aims to present two-stage network models in the presence of stochastic ratio data. Design/methodology/approach Black-box, free-link and fix-link techniques are used to apply the internal relations of the two-stage network. A deterministic linear programming model is derived from a stochastic two-stage network data envelopment analysis (DEA) model by assuming that some basic stochastic elements are related to the inputs, outputs and intermediate products. The linkages between the overall process and the two subprocesses are proposed. The authors obtain the relation between the efficiency scores obtained from the stochastic two stage network DEA-ratio considering three different strategies involving black box, free-link and fix-link. The authors applied their proposed approach to 11 airlines in Iran. Findings In most of the scenarios, when alpha in particular takes any value between 0.1 and 0.4, three models from Charnes, Cooper, and Rhodes (1978), free-link and fix-link generate similar efficiency scores for the decision-making units (DMUs), While a relatively higher degree of variations in efficiency scores among the DMUs is generated when the alpha takes the value of 0.5. Comparing the results when the alpha takes the value of 0.1–0.4, the DMUs have the same ranking in terms of their efficiency scores. Originality/value The authors innovatively propose a deterministic linear programming model, and to the best of the authors’ knowledge, for the first time, the internal relationships of a two-stage network are analyzed by different techniques. The comparison of the results would be able to provide insights from both the policy perspective as well as the methodological perspective.

Measuring sustainable efficiency is a wide research topic that has gained increased relevance over the course of the years, particularly in the field of supply chain management. In this paper, novel Data Envelopment Analysis—ratio data (DEA-R) models are used to assess sustainable efficiency in two-echelon supply chains based on endogenous factors. Genetic algorithms are employed to determine optimal productive weights for each echelon and the overall supply chain by taking into account the hidden correlation structures among them as expressed in non-linear multi-objective functions. A case study on 20 firefighting stations is presented to illustrate the approach proposed and its accuracy for decision-making, as long as the issues of pseudo inefficiency and over estimation of efficiency scores are mitigated. Results indicate that the method proposed is capable of reducing efficiency estimation biases due to endogenous sustainable factors by yielding overall scores lower than or equal to the product of the efficiencies of the individual stages.