اندازه گیری تراکم در تحلیل غیر پارامتری تحت فناوری به طور ضعیف قابل حذف ( با حذف پذیری ضعیف) Congestion measurement in nonparametric analysis under the weakly disposable technology

۱٫ Introduction The concept of congestion, first introduced by Färe and Svensson (1980), is a widely phenomenon where excessive amounts of the input cause a reduction of the output. Subsequently, it was extended and developed by Färe et al. (1985) and Cooper et al. (1996, 2000) in the context of DEA (data envelopment analysis). Since then, the treatment of congestion within the DEA framework has received considerable attention and several approaches have been proposed to identify congestion (Brockett et al., 1998; äre and Grosskopf, 2000; Cooper et al. ,2001a; Cherchye et al., 2001;Tone and Sahoo, 2004; Sueyoshi and Sekitani 2009; Kao 2010; Khoveyni et al., 2013). Färe et al. (1985) proposed a radial‐model approach in which congestion is measured as the difference between technologies under weak and strong disposability inputs. Cooper et al. (1996) proposed a slack‐based approach, where the congestion effect is measured as the difference between the observed amounts and the expected amounts. Cooper et al. (2001a) compared the above approaches and claimed that the approach by Färe et al. (1985) can fail to identify congestion in some situations. See some debates on the subject of congestion (Färe and Grosskopf, 2000; Cooper et al. ,2001b; Cherchye et al. ,2001). Further, Tone and Sahoo (2004) provided a theoretical linkage between congestion and returns to scale (RTS). Moreover, their approach can detect the strong and weak congestion status. However, Tone and Sahoo (2004) implicitly assume a unique optimal solution in the investigation on DEA‐based congestion. In the presence of multiple solutions in the congestion measurement, the economic implications of congestion obtained by Tone and Sahoo (2004) are all problematic from both theoretical and practical perspectives. To deal with the issue, Sueyoshi and Sekitani (2009) proposed an analytical approach to handle an occurrence of multiple solutions and measure the degree of wide congestion. However, all the previous approaches on congestion only consider desirable outputs. In the production process, undesirable outputs are usually jointly produced with desirable outputs. Therefore, a new framework for measuring congestion should be developed in the presence of desirable and undesirable outputs simultaneously. A pioneering paper by Färe et al. (1989) considers undesirable outputs to be weakly disposable, which means that a reduction in the good outputs should result in an equiproportionate reduction of the undesirable outputs (Chung et al. 1997; Weber and Domazlicky 2001; Färe and Grosskopf 2003, 2004, 2009; Kuosmanen 2005; Kuosmanen and Kortelainen,2005; Zhou et al. 2008; Kuosmanen and Podinovski 2009; Kuosmanen and Matin 2011; Picazo‐Tadeo et al. 2012). Treating undesirable outputs in their original forms with the assumption of weak‐disposability is consistent with the physical laws and the standard axioms of production theory (Färe and Grosskopf, 2003, 2004, 2009; Sahoo et al. 2011). Based on the weak disposable technology, many empirical studies utilized the directional distance function model (Chung et al. 1997), which expands the desirable outputs and contracts inputs and undesirable outputs along the direction vector path to assess the efficiency. In this paper, based on the directional distance function, we develop an approach to identify the occurrence of congestion (strong and weak) in the presence of desirable and undesirable outputs simultaneously. Different from the traditional circumstance with desirable outputs only, we find that even if a DMU is efficient by the directional distance function, it maybe evidences congestion when considering both desirable outputs and undesirable outputs. Through our proposed approach, we can discriminate between the congested DMUs and the truly efficient DMUs, which are all efficient according to the scores calculated by the directional distance function. The remaining structure of this research is organized as follows: In Section2, the concepts of strong and weak congestions in the presence of desirable and undesirable outputs are defined. Section 3 proposes an approach to identify the occurrence of strong and weak congestions. Section 4 compares the proposed approach with the existing three representative approaches and applies the proposed approach to analyze an empirical dataset consisting of 20 power plants. Section 5 concludes the paper.