Data Envelopment Analysis (DEA) is a popular non-parametric technique for the assessment of efficiency of a set of homogeneous decision making units (DMUs) with the same set of inputs and outputs. In the conventional DEA models, it is assumed that all variables are fully controllable. However, in the real-world applications of DEA, some of the variables are completely uncontrollable or partially controllable. In this paper, we are concerned about partially controllable variables which are called semi-discretionary variables. In DEA models, in the presence of semi-discretionary variables, decision makers have partial control on these variables and the proportional changes are possible to some extent. Previous DEA models with semi-discretionary variables consider a certain level of control on the variables which is fixed and it is given by decision makers or a higher authority.  Since this level is usually given by experts, it is possible that in some cases all experts may not come up with an agreement, so in this paper we consider variable instead of fixed level of control on each semi-discretionary variable. In the presence of semi-discretionary variables, the proportional changes in inputs and outputs may not be feasible and as a result the obtained target value by conventional DEA models is not achievable for an inefficient DMU. Thus, we propose a bi–objective model to evaluate DMUs when modifying a variable to its target value should be managed by decision makers in a voting system. One of the advantages of the proposed model is including decision making conditions directly into a DEA model.

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Purpose Uncertainty in data, whether in real-valued or integer-valued data, may result in infeasible optimal solutions or unreliable efficiency scores and ranking of decision-making units. To handle the uncertainty in integer-valued factors in data envelopment analysis (DEA) models, this study aims to propose a robust DEA model which is applicable in the presence of such factors. Design/methodology/approach This research focuses on the application of fuzzy interpretation of efficiency to a mixed-integer DEA (MIDEA) model. The robust optimization approach is used to address the uncertain integer-valued parameters in the proposed MIDEA model. Findings In this study, the authors proposed an MIDEA model without any equality constraint to avoid the arise problem by such constraints in the construction of the robust counterpart of the conventional MIDEA models. We have studied the characteristics and conditions for constructing the uncertainty set with uncertain integer-valued parameters and a robust MIDEA model is proposed under a combined box-polyhedral uncertainty set. The applicability of the developed models is shown in a case study of Malaysian public universities. Originality/value This study develops an MIDEA model equivalent to the conventional MIDEA model excluding any equality constraint which is crucial in robust approach to avoid restricted feasible region or infeasible solutions. This study proposes a robust DEA approach which is applicable in cases with uncertain integer-valued parameters, unlike previous studies in robust DEA field where uncertain parameters are generally assumed to be only real-valued.

DEA models and their applicability is heavily depended on the type of data that has been used for efficiency assessment. Conventional DEA models assume the all the involved data in the efficiency evaluation are non-negative, which in many cases seems unrealistic specially when the profit or the rate of growth are involved in the evaluation of organizations. Moreover, the perturbation in data is unavoidable in real-world applications and negative data also might be affected by error. In this paper we propose a robust DEA model to handle uncertain negative data that guarantees the robustness of solution against the uncertainty in data. The proposed robust DEA model is constructed under a box-ellipsoidal uncertainty set and an application of banking in Malaysia is presented to validate the applicability of proposed model and evaluate the effect of uncertainty in efficiency assessment and ranking of 30 banks in Malaysia. The result shows that our proposed model provides a better and more discriminative ranking of banks.