Integrated framework for robustness analysis using ratio-based efficiency model with application to evaluation of Polish airports $ Milosz Kadziński n , Anna Labijak, Malgorzata Napieraj Institute of Computing Science, Poznań University of Technology, Piotrowo 2, 60-965 Poznań, Poland article info Article history: Received 29 April 2015 Accepted 5 March 2016 Keywords: Data envelopment analysis Ratio-based efficiency Robustness analysis Stochastic multicriteria acceptability analysis Airport efficiency Software abstract We consider a problem of evaluating efficiency of Decision Making Units (DMUs) based on their deter- ministic performance on multiple consumed inputs and multiple produced outputs. We apply a ratio- based efficiency measure, and account for the Decision Maker's preference information representable with linear constraints involving input/output weights. We analyze the set of all feasible weights to answer various robustness concerns by deriving: (1) extreme efficiency scores and (2) extreme efficiency ranks for each DMU, (3) possible and necessary efficiency preference relations for pairs of DMUs, (4) efficiency distribution, (5) efficiency rank acceptability indices, and (6) pairwise efficiency outranking indices. The proposed hybrid approach combines and extends previous results from Ratio-based Effi- ciency Analysis and the SMAA-D method. The practical managerial implications are derived from the complementary character of accounted perspectives on DMUs' efficiencies. We present an innovative open-source software implementing an integrated framework for robustness analysis using a ratio-based efficiency model on the diviz platform. The proposed approach is applied to a real-world problem of evaluating efficiency of Polish airports. We consider four inputs related to the capacities of a terminal, runways, and an apron, and to the airport's catchment area, and two outputs concerning passenger traffic and number of aircraft movements. We present how the results can be affected by integrating the weight constraints and eliminating outlier DMUs. & 2016 Elsevier Ltd. All rights reserved. 1. Introduction The framework of Data Envelopment Analysis (DEA) offers a variety of methods for evaluating the relative efficiency of Decision Making Units (DMUs) which consume multiple inputs and pro- duce multiple outputs [18,39,38]. Conceptually, efficiency is the ratio between virtual output and virtual input, i.e., respectively, outputs or inputs aggregated using some weights assigned to these factors [14]. Typically, DEA methods have been used to classify the DMUs into efficient and inefficient ones. By definition, the former ones have an efficiency score equal to one, whereas for the latter ones this measure is less than one. For the inefficient DMUs, such scores convey information on how close to being efficient they are. Analysis of these measures may lead to for- mulating the corrective actions, revealing an excess use of some inputs or shortfalls in the production of outputs, as well as to indicating a reference set of some comparable DMUs. 1.1. Critical view on the traditional methods of data envelopment analysis Although DEA has proven its usefulness when applied to a variety of real-world problems (see, e.g., [23,18,40]), some criti- cism has been leveled against its discriminative power and the way the efficiency scores are computed. Firstly, the efficiency measures for each DMU are derived from the analysis of the input/ output weights which are the most favorable to it. However, a weight vector for which a DMU attains its maximal efficiency is not unique [36]. Thus, choosing among them is arbitrary to a large extent. Secondly, the underlying Linear Programming (LP) tech- niques require some normalization of weights for each DMU individually. This implies that scaling affects the optimal weights and a meaningful comparison of these weights across different DMUs is difficult. Thirdly, the efficiency measures fail to reflect how the efficiencies of DMUs compare to each other for other feasible weight vectors [53]. In fact, only extremely small share of feasible weights is taken into account in the analysis, while others are neglected despite being equally desirable. Fourth, DEA mea- sures efficiency relative to the efficient frontier. This requires some assumptions about possible returns to scale (e.g., constant or variable). These may be, however, difficult to formulate or justify. Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/omega Omega http://dx.doi.org/10.1016/j.omega.2016.03.003 0305-0483/& 2016 Elsevier Ltd. All rights reserved. ☆ This manuscript was processed by Associate Editor Lim. n Corresponding author. Tel.: þ48 61 665 3022. E-mail addresses: milosz.kadzinski@cs.put.poznan.pl (M. Kadziński), anna.labijak@student.put.poznan.pl (A. Labijak), napieraj.malgorzata@gmail.com (M. Napieraj). Please cite this article as: Kadziński M, et al. Integrated framework for robustness analysis using ratio-based efficiency model with application to evaluation of Polish airports. Omega (2016), http://dx.doi.org/10.1016/j.omega.2016.03.003i Omega ∎ (∎∎∎∎) ∎∎∎–∎∎∎