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Access type: UnknownAuthor: search.filters.author.Madjid Tavana

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    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.
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    A novel inverse data envelopment analysis model with negative ratio data
    (Springer Science+Business Media, 2025-06-01)
    Data envelopment analysis (DEA) is a mathematical programming method for evaluating the efficiency of a homogeneous set of decision-making units (DMUs) using multiple inputs and outputs. Inverse DEA estimates a DMU’s input (or output) when some or all DMU outputs (or inputs) are changed. Ratio DEA (DEA-R) combines DEA with ratio analysis to handle ratio data. Real-world DEA-R models often involve negative values for the inputs or outputs. This study presents a novel model for solving inverse DEA problems with negative ratio data for the first time. We present a real-life case study to demonstrate the applicability and efficacy of the DEA models proposed in this study.
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