Addressing infeasibility in super-efficiency models with non-discretionary inputs and undesirable outputs: A directional distance function approach

Existing studies have rarely examined the infeasibility of super-efficiency data envelopment analysis (DEA) models that incorporate non-discretionary inputs and undesirable outputs under weak disposability and null-jointness (WDNJ). This study identifies the conditions under which conventional directional distance function (DDF)-based super-efficiency models become infeasible once non-discretionary inputs are introduced, under both constant and variable returns to scale, even in the absence of undesirable outputs. To address this issue, a constraint-adjustment model with deviation variables is proposed, serving as the foundation for an improved radial super-efficiency DDF model that guarantees feasibility. The conditions for direction vectors to maintain unit invariance are derived, and direction vectors that preserve unit invariance, ensure bounded DDF super-efficiency measures, and accommodate negative data are presented. Validation through numerical examples and an empirical case study confirms the effectiveness and practical relevance of the proposed model.