Fuzzy arithmetic DEA approach for fuzzy multi-objective transportation problem

• Published in: Operational research Vol. 22; no. 2; pp. 1479 - 1509
• Main Authors: Bagheri, M., Ebrahimnejad, A., Razavyan, S., Hosseinzadeh Lotfi, F., Malekmohammadi, N.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2022; Springer Nature B.V
• Subjects: Algorithms; Business and Management; Computational Intelligence; Data envelopment analysis; Decision making; Management Science; Operations Research; Operations Research/Decision Theory; Original Paper; Transportation problem; Fuzzy multi-objective transportation problem; Fuzzy arithmetic; Data envelopment analysis
• ISSN: 1109-2858; 1866-1505
• DOI: 10.1007/s12351-020-00592-4

In this paper, a transportation problem (TP) with fuzzy costs in the presence of multiple and conflicting objectives is investigated. In fact, a fuzzy data envelopment analysis (DEA) approach is proposed to solve the fuzzy multi-objective TP (FMOTP). To this end, each arc in FMOTP will be considered as a decision-making unit (DMU). Next, those objective functions that needs to be maximized will be used to define the outputs of DMU and those that needs to be minimized will be used to define the inputs of DMU. Consequently, two different fuzzy efficiency scores will be derived for each arc by solving fuzzy DEA models. So, a unique fuzzy attribute will be defined for each arc by combining the resulting fuzzy efficiency scores. Therefore, the FMOTP will be converted into a single objective fuzzy TP that can be solved using the standard algorithms. Finally, using a numerical example the proposed approach has been illustrated.