Abstract
In this paper, a novel combination method is offered to integrate the results of two new relative closeness models, called relative closeness benevolent (RCB) and relative closeness aggressive (RCA) models, for ranking all DMUs. To prove the applicability of the proposed method, it is examined in three numerical examples, performance assessment problem, six nursing homes and fourteen international passenger airlines. Firstly, RCB and RCA models were formulated in order to generate the cross-efficiency intervals matrix (CEIM). After obtaining CEIM, the RC index was utilized to generate a combined cross-efficiency matrix (combined CEM). In combined CEM, target DMUs were viewed as criteria and DMUs were viewed as alternatives. After that, the weights of each criterion were generated using a new weighting method based on standard deviation technique (MSDT). Finally, all DMUs were evaluated and ranked. Comparison with existing cross-efficiency models indicates the more reliable results through the use of the proposed method.
Highlights
The data envelopment analysis (DEA) is a linear programming model that was first described by Farrel (1957), but a mathematical model was first introduced in the Charnes et al paper (Charnes, Cooper, & Rhodes, 1979)
It is well known that the efficiency score of each decision making units (DMUs) cannot be greater than 1, and DMUs can be defined as being efficient DMUs if their efficiency scores are 1; otherwise the DMUs are inefficient (Wang, Chin, & Luo, 2011; Wichapa, Khokhajaikiat, & Chaiphet, 2021)
This paper proposes a new objective weighting method based on the standard deviation technique (MSDT) for determining criteria weights
Summary
The data envelopment analysis (DEA) is a linear programming model that was first described by Farrel (1957), but a mathematical model was first introduced in the Charnes et al paper (Charnes, Cooper, & Rhodes, 1979) This non-parametric model evaluates the relative efficiency of decision making units (DMUs) with multiple inputs and outputs (Zerafat Angiz, Mustafa, & Kamali, 2013). The crossefficiency method, first introduced by Sexton et al (1986), has long been suggested as a power tool for the ranking of DMUs based on the cross-efficiency concept. Based on this idea, a combination of self-evaluation and peer-evaluation was suggested for overcoming the weakness of DEA’s discrimination power.
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