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In this paper, two non-linear technologies are proposed based on weak disposability definitions: weak disposability with non-uniform abatement factors and new weak disposability. Both technologies are applied to Spanish airport systems and the existing technologies are modified. To remove the computational complexity of non-linear approaches, the linearization methods are proposed. Then, in order to evaluate the efficiency measure of decision making units (DMUs), a directional distance function (DDF) is applied to the linear technologies and the analysis of the results is presented.

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Due to the changes of performance measures, a vital aspect for decision makers is finding optimal scale sizes of entities. Moreover, there are undesirable measures in many investigations. In the existing data envelopment analysis (DEA) approaches, optimal scale sizes (OSSs), average-cost efficiency (ACE) and average-revenue efficiency (ARE) of decision making units (DMUs) with desirable measures under strong disposability have been estimated while undesirable factors are presented in many real world examinations. Accordingly, in this research, OSSs and ARE of DMUs with undesirable outputs are addressed under managerial disposability. ARE is defined as the composite of scale and output allocative efficiencies under managerial disposability. To illustrate in detail, a two-stage DEA-based approach is rendered to estimate ARE and OSSs in the presence of undesirable outputs. A numerical example and an illustrative case are given to explain the proposed approach in this study.

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Supply chains often have different technologies. Additionally, organizations with multiple stages can evaluate their operational efficiency by analyzing scale elasticity, which helps determine if they are functioning optimally or if there is room for improvement. This evaluation allows for the identification of potential inefficiencies and opportunities for enhancement. Consequently, this research introduces a two-stage DEA-based approach with undesirable outputs to examine the scale elasticity of supply chains within meta and group frontiers. The measurement of group and meta performance of general systems and stages is conducted for this purpose. Moreover, the study addresses the scale elasticity of supply chains with undesirable outputs by considering the heterogeneity of technologies. To achieve this, the study focuses on the right and left scale elasticity of efficient general systems and each stage. A real-world application from the soft drink industry is provided to illustrate the proposed model. The results show the applicability of the introduced methodology.
 

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The traditional inverse data envelopment analysis (IDEA) models assess specific performance metrics in relation to changes in others, without taking into consideration the existence of random and undesirable outputs. This study presents a novel inverse DEA model with random and undesirable outputs, enabling the estimation of some random performance measures for changes of other random measures. The proposed chance-constrained inverse DEA model integrates both managerial and natural disposability constraints. By using the introduced approach, the estimation of natural disposable random inputs is presented for changes in random desirable outputs. Also, undesirable outputs are assessed for the perturbation of managerial disposable random inputs while the stochastic efficiency is maintained. The models are solved as  linear problems, with a numerical example provided to illustrate their application. The findings indicate that this approach is effective for evaluating efficiency and performance metrics in scenarios involving random and undesirable outputs.