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تعداد صفحات این فایل: ۲۹ صفحه

بخشی از مقاله انگلیسیعنوان انگلیسی:A bi-objective weighted model for improving the discrimination power in MCDEA~~en~~

Abstract

Lack of discrimination power and poor weight dispersion remain major issues in Data Envelopment Analysis (DEA). Since the initial multiple criteria DEA (MCDEA) model developed in the late 1990s, only goal programming approaches; that is, the GPDEA-CCR and GPDEA-BCC were introduced for solving the said problems in a multi-objective framework. We found GPDEA models to be invalid and demonstrate that our proposed bi-objective multiple criteria DEA (BiO-MCDEA) outperforms the GPDEA models in the aspects of discrimination power and weight dispersion, as well as requiring less computational codes. An application of energy dependency among 25 European Union member countries is further used to describe the efficacy of our approach.

۱ Introduction

Data envelopment analysis (DEA) was first proposed by Charnes, Cooper, and Rhodes (1978) and remained the leading technique for measuring the relative efficiency of decision-making units (DMUs) based on their respective multiple inputs and outputs. DEA has been the fastest growing discipline in the past three decades covering easily over a thousand papers in the Operations Research and Management Science discipline (Emrouznejad, Parker, & Tavares, 2008; Hatami-Marbini, Emrouznejad, & Tavana, 2011). The efficiency of a DMU is defined as a weighted sum of its outputs divided by the weighted sum of its inputs on a bounded ratio scale.

One of the drawbacks of DEA is the lack of discrimination among efficient decision making units (DMUs), hence yielding many DMUs to be efficient. The problem is highlighted when the number of DMUs evaluated is significantly lesser than the number of inputs and outputs used in the evaluation. The weights derived from a DEA analysis may reveal that some inputs or outputs have zero values. This is counter-intuitive especially in a decision making exercise, where one expects to use all the inputs and output values that are rated for the DMUs. Hence, it further implies that some of the variables were not used in the evaluation judgment in achieving the final ranking. On the contrary, the unrealistic weight distribution for DEA also occurs when some DMUs are rated as efficient due to extremely large weights in a single output and/ or extremely small weights in a single input.

Thompson, Singleton, Thrall, and Smith (1986) are among the first authors to propose the use of weight restriction to increase the discrimination power of DMUs. The issue was immediately picked up by many authors, including Dyson and Thanassoulis (1988), Charnes, Cooper, Huang, and Sun (1990), Thanassoulis and Allen (1998). Hence, several methods such as assurance region (AR) procedure (Khalili, Camanho, Portela, & Alirezaee, 2010; Mecit & Alp, 2013; Sarrico & Dyson, 2004; Thompson, Langemeier, Lee, & Thrall, 1990) and cone ratio envelopment (Cao & Kong, 2010; Charnes et al., 1990) were addressed in the literature as strategies to solve problems arising from unrealistic weight distribution. However, there are some drawbacks to the methods – AR and cone ratio techniques are highly dependent on the measurement of the inputs-outputs units, which may lead to infeasible solutions. In other words, both the methods incorporate extra constraints to the model; thus, making it harder to solve the problem.

Subsequently, other DEA models were introduced in the literature to overcome the discriminant power problems, such as the super-efficiency model (Andersen & Petersen, 1993; Chen, 2005; Chen, Du, & Huo, 2013; Lee, Chu, & Zhu, 2011) and cross-efficiency evaluation technique (Anderson, Hollingsworth, & Inman, 2002; Doyle & Green, 1995; Green, Doyle, & Cook, 1996; Sexton, Silkman, & Hogan, 1986; Wang & Chin, 2010, 2011). The super-efficiency DEA model may obtain infeasible solutions for efficient DMUs; particularly, under variable returns to scale (VRS) model. However, attempts had been made to solve the infeasibility problem in super efficiency methods. Chen (2005) proposed an approach in which both input-oriented and output-oriented super-efficiency models are used to fully characterize the super-efficiency model, thus claiming that the approach kept infeasibility to a rare occasion. However, Soleimani-damaneh, Jahanshahloo, and Foroughi (2006) presented some counter examples to negate Chen’s (2005) claims without any proposed alternative. Drawing from two main sources (i.e. Chen, 2005; Cook, Liang, Zha, & Zhu, 2009), Lee et al. (2011) later provided a solution by a two-stage process catering to adjustments in input saving and output surpluses. Chen and Liang (2011) subsequently formulated a one-model solution to the two-stage process. Lee and Zhu (2012) found that the solution can still be infeasible should some of the input variables have zero values.

With regards to cross-efficiency evaluation technique, the nonuniqueness of the DEA weights could provide a large number of multiple optimal solutions for DEA models. Although recent improvements of cross-efficiency evaluation techniques were proposed (Angiz & Sajedi, 2012), the solution is computationally expensive with the need to solve a series of linear programming problems. The suggestion of imposing secondary goals to improve variability of cross efficiency scores still leaves the non-uniqueness problem looming (see Cook & Zhu, 2013).

Drawing from a multiple objective decision making framework, the multiple criteria (or multi-objective) DEA model (Chen, Larbani, & Chang, 2009; Foroughi, 2011; Li & Reeves, 1999) was suggested as a means to overcome discriminant power and weight dispersion problems. However, the original formulation of Li and Reeves (1999) does not promise complete ranking but merely presupposes the decision maker to use its model’s 3 objectives interactively. Thus, in the MCDEA model, the three objectives are analyzed separately; one at a time, and no preference order was set for those objectives. Bal, rkcü, and Celebioglu (2010) recently proposed the goal programming approach for solving all 3 objectives of the MCDEA model simultaneously. Their GPDEA models (i.e. constant returns to scale and variable returns to scale) were claimed to improve the dispersion of weights and discriminatory power in a MCDEA framework. This paper highlights that those claims were unfounded, and goes onto show a new bi-objective multiple criteria DEA (BiO-MCDEA) model that could solve those drawbacks.

The focus of this paper is to introduce a weighted model for improving the discrimination power and weight dispersion in the domain of Multiple Criteria Data Envelopment Analysis (MCDEA). The rest of the paper is organized as follows. Section 2 gives a brief description of the multiple criteria data envelopment analysis (MCDEA) and the more recent goal programming data envelopment analysis (GPDEA) as a procedure for MCDEA. Section 3 highlights the drawbacks of using GPDEA to represent MCDEA analysis. We therefore introduce an alternative bi-objective multiple criteria model (BiO-MCDEA) to improve the discrimination power of MCDEA in Section 4. An application of energy dependency among 25 EU member countries demonstrates the efficacy of the model in Section 5. Concluding remarks are given in Section 6.

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