## 1 Introduction  
The accurate estimation of production possibility set (PPS) boundaries is crucial for performance analysis and efficient estimation. Different papers propose alternative approaches to handle the issue of estimating PPSs and their respective boundaries. Non-parametric data envelopment analysis (DEA) is possibly one of the most used linear programming (LP) approaches to build up piecewise PPS boundaries. DEA is a useful tool to evaluate decision making units (DMUs). Efficiency criterion can be considered as a number between 0 and 1 for evaluating a DMU in DEA. If the efficiency criterion for a DMU is 1, the mentioned DMU is efficient, else, it is inefficient. Evaluating DMUs in input-oriented, output-oriented, and combined-oriented radial and non-radial models were developed from a proposal by [PERSON] (1957) [1], and were then followed by the development of the CCR model by [PERSON] et al. (1978) [2]. The CCR model was then developed into the BCC model by [PERSON] et al. (1984) [3]. Additive models were then suggested to separate efficient and non-efficient DMUs [4]. [PERSON] (2001) proposed a slack based model which evaluates DMUs considering the relationship between CCR models [5]. The Russel Graph Model (RGM) and the relationship between SBM and additive DEA models are very important subjects that have been studied [6]. These models determine the benchmark for efficient DMUs, in addition to calculating efficiency and non-efficiency criterion of DMUs. Over three decades, extensive and useful studies on DEA have been undertaken to calculate DMU efficiencies [7, 8] and to find DMU benchmarks [9, 10]. [PERSON] and [PERSON] (2020) completed efficient and non-efficient definitions on the basis of slack variables using the -slack based method, and showed that additive slacks-based models (ASBM) and enhanced RGM are equal. Moreover, the authors showed that the simultaneous use of ASBM and network DEA models can create a comparable DEA score. Finding DMU targets in ASBM by eliminating convexity conditions can be investigated in practical studies [11]. The use of non-radial FDH models based on ASBM can also be beneficial in practical studies. Specifically, Free Disposal Hull (FDH) is a subclass of DEA models where DMUs are not projected on the piecewise convex envelope, but are projected on the actual maximal attainable boundary, which results in a staircase shape for the single input-output case. In other words, FDH, which was first introduced by [PERSON] et al. (1984), evaluates DMU efficiency by considering the closest inner approximation of the true non-convex (disposable) boundary [12]. Many studies have been investigated FDH models. [PERSON] et al. estimated returns-to-scale in FDH models [13]. [PERSON] and [PERSON] proposed a polynomial-time algorithm to estimate returns to scale in FDH models [14]. [PERSON] and [PERSON] proposed the definition, characterization and calculation of global sub-increasing and global sub-decreasing returns to scale in FDH technologies [15]. [PERSON] et al. measured efficiency with non-convex FDH technology [16]. [PERSON] and [PERSON] studied FDH efficiency scores of units with network structures [17]. [PERSON] et al. measured the efficiency of hospital cardiology wards using the FDH approach [18]. [PERSON] and [PERSON] reviewed solution methods for nonconvex FDH models and give some critical comments [19]. [PERSON] and [PERSON] identified the anchor points in FDH models [20]. [PERSON] et al. proposed an improved DEA model based on SBM and FDH models [21]. One issue that is frequently neglected in FDH models is the identification of DMU targets, which is a cumbersome task due to boundary non-convexity, especially when the number of inputs and outputs increase. A possible approach is to define a multiple objective function for measuring the closeness among the DMU under analysis and its eventual targets [22]. Multiple objective linear programming (MOLP) is a form of multiple objective decision making (MODM).