A Pessimistic Two-Stage Network DEA Model with Interval Data and Endogenous Weight Restrictions

This paper develops a pessimistic two-stage network data envelopment analysis (DEA) model that integrates interval-valued data and endogenous weight restrictions within a unified linear programming framework. The proposed approach explicitly captures internal network structures while addressing bounded data uncertainty through an interval-to-deterministic transformation that preserves linearity and avoids probabilistic assumptions. Robustness is interpreted in the pessimistic interval DEA sense, where efficiency is evaluated under worst-case realizations of observed bounds rather than through explicit uncertainty-set optimization. To mitigate weight degeneracy and enhance discrimination power, data-driven proportional weight restrictions are introduced; these endogenous bounds are constructed solely from observed data and regularize the multiplier space without relying on subjective preferences or tuning parameters, while maintaining scale invariance and the nonparametric nature of DEA. The model admits equivalent multiplier and envelopment formulations and enables meaningful decomposition of overall efficiency into stage-specific components. Fundamental theoretical properties—including feasibility, boundedness, monotonicity, efficiency decomposition, and special case consistency—are rigorously established. An empirical application to OECD macroeconomic data, accompanied by sensitivity evaluation, demonstrates the stability and discriminatory capability of the proposed framework under bounded variability. Computational analysis confirms that the model retains linear programming structure and exhibits linear growth in problem size with respect to the number of decision-making units, thereby preserving the scalability characteristics of classical two-stage network DEA formulations. The proposed framework provides a theoretically grounded and computationally tractable approach for network efficiency analysis under bounded interval uncertainty.