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Solving Bi-Level Multi-Objective Transportation Problem under Fuzziness
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems ( IF 1.5 ) Pub Date : 2021-05-27 , DOI: 10.1142/s0218488521500185
Dharmadas Mardanya 1 , Gurupada Maity 2 , Sankar Kumar Roy 2
Affiliation  

This paper describes a study on bi-level multi-objective transportation problem in fuzzy environment. To alleviate a difficulty of transporting goods within nodes for long distances, we venture to formulate a transportation problem using bi-level criteria. Again, in this paper, we incorporate the real-life uncertain situation in bi-level transportation system through fuzziness. It produces a new class of transportation problem, namely fuzzy bi-level multi-objective transportation problem (FBMOTP). We solve FBMOTP with and without priority of the 1st level of transportation problem (TP) using the Vogal Approximation Method (VAM) which are called respectively Approach 1 and Approach 2. A special emphasis of this paper is to introduce a new approach namely Approach 3 for solving the FBMOTP in addition to the considered two approaches. In this regard, we incorporate an algorithm for Approach 3 to find compromise solution of the FBMOTP using VAM. Thereafter, the proposed algorithm is illustrated to show the usefulness by taking a numerical example. A comparative analysis with the existing studies is provided to understand the effectiveness of the proposed methodology. At last, conclusions are described with the lines of future study of the paper.

中文翻译:

模糊下求解双层多目标运输问题

本文描述了模糊环境下的双层多目标运输问题的研究。为了缓解节点内长距离运输货物的困难,我们冒险使用双层标准制定运输问题。同样,在本文中,我们通过模糊性将现实生活中的不确定情况纳入双层交通系统。它产生了一类新的交通问题,即模糊双层多目标交通问题(FBMOTP)。我们使用 Vogal 逼近法 (VAM) 分别称为方法 1 和方法 2,解决有和没有第一级交通问题 (TP) 优先级的 FBMOTP。本文特别强调的是引入一种新方法,即方法 3除了考虑的两种方法之外,用于解决 FBMOTP。在这方面,我们结合了方法 3 的算法,以使用 VAM 找到 FBMOTP 的折衷解决方案。此后,通过数值示例说明了所提出的算法以显示其有用性。提供了与现有研究的比较分析,以了解所提出方法的有效性。最后,结合本文未来研究的思路,对结论进行了阐述。
更新日期:2021-05-27
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