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Top1. Introduction
Supplier selection plays a key role in supply chain management (SCM). One of the important aims of supply chains is to increase the level of customer satisfaction. The increased outsourcing and reduced supply bases have increased buyers' confidence (Ballew and Schnorbus, (1994); Handfield and Nichols, (1999); Ballew and Schnorbus, (1994)). Tseng and Chiu, (2013) introduced some non-environmental and environmental factors and suggested using grey relational analysis. Hutchins and Sutherland, (2008) presented a method for examining criteria. They introduced a framework for assessing the impact of social factors on sustainable supply chains. To analyze the sustainability of organizations, we should consider economic, environmental, and social factors (Clift, (2003), Izadikhah et al., (2020)). Sustainability factors play a key role in achieving a long-term relationship in SCM (Seuring and Müller, (2008), Mehlawat et al., (2019); Yu et al., (2019)).
On the other hand, mathematical programming is a good tool to compare the alternatives by considering different indicators. Among the various methods of mathematical programming, data envelopment analysis (DEA) is a successful method and has been used in many settings. Since the novel work of Charnes et al., (1978), DEA has been utilized to assess the relative efðciency of decision making units (DMUs) (Izadikhah and Farzipoor Saen, (2015); Roman et al., (2005)). The main objective of this paper is to assess the sustainability of suppliers. The assessment needs some criteria that the conventional DEA models cannot handle them. In assessing the sustainability of suppliers we face with a couple of criteria, including i) Distance that is considered as a nondiscretionary input, ii) Rate of losses that is considered as an undesirable output, iii) Rate of the increasing success of shipping that can take both negative and non-negative values, and iv) Number of obtained ISO certificates that can be regarded as either input or output (dual-role factor).
In the conventional DEA models, to achieve the maximum efficiency score, flexibility of weights is assumed. However, the flexibility of weights can be in contrast with the decision maker's opinions. Weight restriction has been introduced to overcome weight flexibility in DEA. Also, classical DEA models assume that all inputs and outputs are not only discretionary but also desirable and can be changed at the discretion of management. However, in real-world problems, there might be undesirable outputs and non-discretionary inputs and outputs. It is, therefore, necessary to consider both discretionary and non-discretionary factors in the efficiency evaluation of DMUs (Ruggiero, (1996); Syrjänen, (2004)). Although classical DEA models deal with positive data, there are circumstances in which negative inputs and outputs exist (e.g., financial losses when we consider net profit as an output) (Kazemi Matin and Azizi, (2011)). Also, some factors are both inputs and outputs, which are named as the dual-role criteria.