Abstract
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 out-puts 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.
Highlights
Data envelopment analysis (DEA) pioneered by Farrel [9], who proposed a non-parametric frontier analysis for solving a linear programing to measure productive efficiency
In the conventional DEA models, whether it is radial or non-radial, it is supposed that all inputs and outputs are managed and under the control of a decision maker, in other words it is assumed that all variables are fully controllable which are called discretionary variables
In the conventional DEA models, it is assumed that all variables are fully controllable, in many real-life applications there are some partially controllable variables that cannot be fully controlled and decision makers are willing to have control on such variables in order to achieve more reliable target values
Summary
Data envelopment analysis (DEA) pioneered by Farrel [9], who proposed a non-parametric frontier analysis for solving a linear programing to measure productive efficiency. External non-discretionary factors are those factors that affect the production process but cannot be considered as a part of it, and they should not be allowed to define the PPS They proposed a new model to assess the efficiency of DMUs with both internal and external non-discretionary variables while treating them differently in the model. Golany and Roll [10] were the first to take into account semi-discretionary variables in the efficiency assessment They proposed an approach for handling semi-discretionary inputs and outputs which decision maker is able to change them by a certain percentage. Bi et al [5] proposed a DEA model for two-stage production system with semi-discretionary variables in order to achieve more reliable improvement directions for inefficient DMUs. Later, Bi et al [4] proposed a mixed integer linear model to handle semi-discretionary variables.
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