Detecting All Non-Dominated Points for Multi-Objective Multi-Index Transportation Problems

Abd Elazeem M. Abd Elazeem, Abd Allah A. Mousa, Mohammed A. El-Shorbagy, Sayed K. Elagan and Yousria Abo-Elnaga
Additional contact information
Abd Elazeem M. Abd Elazeem: High Institute of Marketing, Commerce, and Information System, Cairo 11865, Egypt
Abd Allah A. Mousa: Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
Mohammed A. El-Shorbagy: Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
Sayed K. Elagan: Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
Yousria Abo-Elnaga: Department of Basic Science, Higher Technological Institute, Tenth of Ramadan City 44629, Egypt

Sustainability, 2021, vol. 13, issue 3, 1-18

Abstract: Multi-dimensional transportation problems denoted as multi-index are considered as the extension of classical transportation problems and are appropriate practical modeling for solving real–world problems with multiple supply, multiple demand, as well as different modes of transportation demands or delivering different kinds of commodities. This paper presents a method for detecting the complete nondominated set (efficient solutions) of multi-objective four-index transportation problems. The proposed approach implements weighted sum method to convert multi-objective four-index transportation problem into a single objective four-index transportation problem, that can then be decomposed into a set of two-index transportation sub-problems. For each two-index sub-problem, parametric analysis was investigated to determine the range of the weights values that keep the efficient solution unchanged, which enable the decision maker to detect the set of all nondominated solutions for the original multi-objective multi-index transportation problem, and also to find the stability set of the first kind for each efficient solution. Finally, an illustrative example is presented to illustrate the efficiency and robustness of the proposed approach. The results demonstrate the effectiveness and robustness for the proposed approach to detect the set of all nondominated solutions.

Keywords: multi-objective; multi-index transportation; parametric analysis (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2021
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