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Cross efficiency evaluation was developed as an extension of DEA. But the traditional DEA models usually have alternative optimal solutions and, as a result, cross efficiency scores may not be unique. It is recommended that without changing the DEA efficiency scores, the secondary goal should be introduced for optimization of the inputs/outputs weights.  Several reports evaluated the performance ranking of DMUs by optimizing the rank position. These reports used ILP models for computation appropriate weights in cross efficiency evaluation. However, the LP models are easier and more applicable than ILP models. The present work proposes a goal programming model (LP model) that could be used as a secondary goal to choose suitable weights in cross efficiency evaluation. Also, the Numerical examples are provided to illustrate the approach.  

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Cross-efficiency is an effective approach for evaluation of DMUs which can be performed with different secondary goals. DEA and cross-efficiency view all variables as behaving in a linear fashion and regardless of the amounts of a variable held by DMUs, DEA apply a same multiplier to those various amounts. But in certain situations, this linearity assumption is not appropriate, and the conventional models need to be altered to accommodate nonlinear representations. This paper proposed a modified cross efficiency structure of Liang et al. that captures certain form of nonlinear behavior. A numerical example is provided to illustrate the approach.

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Information and Communication Technology (ICT) is an important structural part of modern society. This is why countries strive for constant progress in ICT. Information Technology Development Index (IDI) ranks countries’ performance in terms of ICT infrastructure and uptake. It aims to provide an objective international performance evaluation based on quantitative indicators and benchmarks. The results for this metric help policymakers monitor trends, identify areas for policy action, and compare their ICT developments. Bearing this in mind, the main purpose of this paper is to introduce a generalized DEA method that incorporates decision makers' preferences and offers a new perspective on measuring the ICT development index. In addition, preferred solutions are introduced depending on preferential information and improvement axis. Since the opinions of the decision-makers have been applied to reach the preferred solution, more realistic results are obtained. The results show that these solutions are a subset of efficient solutions. A total of 11 IDI indicators are identified based on International Telecommunication Union data. Assessments and rankings were performed using the DEA output-oriented model without input and the cross-efficiency model. In addition, for low-level countries, using preferred solutions, realistic targets are set following the preferential information of decision-makers to reach higher levels.