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Item type:Publication, An introduction to data envelopment analysis(Springer Science+Business Media, 2021-12-11)Following the seminal work of Farrell (1957), Charnes et al. (1978) introduced DEA as a deterministic and nonparametric efficiency evaluation tool. DEA is a linear programming-based technique that has been widely accepted as a competing methodology to evaluate the relative efficiency of entities or decision-making units, DMUs (Charles et al., 2016, 2018; Tsolas et al., 2020). DEA is a data-oriented technique (Zhu, 2020) that is used to construct an empirical production frontier to measure efficiency. Note that the original DEA program of Charnes et al. (1978) is based on the CRS specification of technology and is used to measure the technical and scale efficiency of DMUs. However, Banker et al. (1984) extended this program to the case of VRS to estimate purely technical efficiency. Over the past three decades, DEA has been widely used to evaluate the relative efficiency of production firms, the nature of the returns-to-scale, and the productivity changes. The DEA literature has seen a wide variety of applications across a plethora of domains, having become a powerful management science tool (Charles et al., 2018). In this chapter, we briefly review the fundamental concepts in DEA, along with the basic technologies and programs. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Analytics under uncertainty: a novel method for solving linear programming problems with trapezoidal fuzzy variables(Springer Science+Business Media, 2021-11-23)Linear programming (LP) has long proved its merit as the most flexible and most widely used technique for resource allocation problems in various fields. To solve an LP problem, we have traditionally considered crisp values for the parameters, which are unrealistic in real-world decision-making under uncertainty. The fuzzy set theory has been used to model the imprecise parameter values in LP problems to overcome this shortcoming, resulting in a fuzzy LP (FLP) problem. This paper proposes a new method for solving fuzzy variable linear programming (FVLP) problems in which the decision variables and resource vectors are fuzzy numbers. We show how to use the standard simplex algorithm to solve this problem by converting the fuzzy problem into a crisp one once a linear ranking function is chosen. The novelty of the proposed model resides in that it requires less effort on fuzzy computations as opposed to the existing fuzzy methods. Furthermore, to solve the FVLP problem using the existing methods, fuzzy arithmetic operations and the solution to fuzzy systems of equations are required. By contrast, only arithmetic operations of real numbers and the solution to crisp systems of equations are required to solve the same problem with the method proposed in this study. Finally, a transportation case study in the coal industry is presented to demonstrate the applicability of the proposed algorithm.