Second-order conic programming for data envelopment analysis models

Abstract

Data envelopment analysis (DEA) is a widely used benchmarking technique. Its strength stems from the fact that it can include several inputs and outputs of not necessarily the same type to evaluate efficiency scores. Indeed, the aforesaid method is based on mathematical optimization. This paper constructs a second-order conic optimization problem unifying several DEA models. Moreover, it presents an algorithm that solves the former problem, and provides a MATLAB function associated with it. As far as known, no MATLAB function solves DEA models. Among different types of DEA, this function can handle deterministic, Malmquist index, and stochastic models. In fact, DEA is involved in various practical applications, thus, this work will provide some possible future extensions, not only for MATLAB but also for any programming software in applications of decision science and efficiency analysis.

Evaluating the Super-Efficiency of Working Capital Management Using Data Envelopment Analysis: Does COVID-19 Matter?

“…Second, Dalwai et al [47], Shahwan and Habib [48], Habib and Mourad [11], and Shahwan and Habib [49] confirm that the DEA technique delivers critical information for continual improvement. Finally, Habib and Mourad [11], Shahwan and Habib [49], Cooper et al [50], Mourad [51], and Mourad et al [52] confirm that the DEA technique focuses on the best practice concept as a base of benchmarking, that is, the relatively efficient firm (located on the efficient frontier curve), on the efficiency frontier curve, as opposed to conventional techniques that focus on central tendencies.…”

“…Typically, the DEA efficiency scores of firms range from zero to one, where a score of "one" indicates a relatively efficient firm (located on the efficient frontier curve), and a score less than "one" indicates a relatively inefficient firm [11,16,45,51,52]. Moreover, the DEA super-efficiency scores of firms may exceed "one" as the super-efficiency technique involves further ranking for the efficient firms located on…”

Does the Efficiency of a Firm’s Intellectual Capital and Working Capital Management Affect Its Performance?

“…Various methodological techniques, such as stochastic frontier, deterministic frontier, and mathematical programming techniques, have been employed to evaluate the efficiency of DMUs; however, mathematical programming is distinguished by being non-parametric, thus providing better flexibility and ease of use (Cooper et al, 2007 ; Habib & Shahwan, 2020 ; Mourad, 2022 ; Mourad et al, 2022 ; Olesen & Petersen, 2016 ; Wu et al, 2013 ).…”

“…Various methodological techniques, such as stochastic frontier, deterministic frontier, and mathematical programming techniques, have been employed to evaluate the efficiency of DMUs; however, mathematical programming is distinguished by being non-parametric, thus providing better flexibility and ease of use (Cooper et al, 2007;Mourad, 2022;Mourad et al, 2022;Olesen & Petersen, 2016;Wu et al, 2013). One well-known mathematical programming application is the DEA approach, which depends on mathematical programming to estimate the relative efficiency scores of DMUs.…”