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<p>In this study, we developed a mathematical model of a multi-objective capacitated fractional transportation problem (MOCFTP) with mixed constraints formulated as a multi-objective linear fractional programming problem (MOLFPP). Two advanced methodologies were applied to solve this mathematical model: the proposed weighted goal programming method (PWGPM) and the proposed neutrosophic goal programming approach (PNGPA). The PWGPM model minimizes deviations from predefined goals for each objective while adhering to linear constraints. In contrast, the PNGPA leverages neutrosophic optimization, integrating truth, falsity, and indeterminacy to address uncertainty in decision-making. The mathematical model of MOCFTP aims to optimize transportation schedules by minimizing total cost, total time, and damage cost while satisfying supply and demand constraints. A numerical example is provided to demonstrate the practicality and effectiveness of the mathematical model of MOCFTP. The compromise optimal solution for the proposed problem is obtained using the Pulp optimization library in Python. The findings indicate that the PNGPA outperforms others regarding solutions, and it offers a robust framework for complex, real-world transportation scenarios potentially beneficial for various logistics applications.</p>

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A solution programming approaches on the multi-objective capacitated fractional transportation problem

  • 期刊论文

  • 发表日期：

    2025年2月7日

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  • Wajahat Ali,
  • Sheema Sadia,
  • Firoz Ahmad,
  • Shakeel Javaid,
  • Naseem Abidi

摘要

In this study, we developed a mathematical model of a multi-objective capacitated fractional transportation problem (MOCFTP) with mixed constraints formulated as a multi-objective linear fractional programming problem (MOLFPP). Two advanced methodologies were applied to solve this mathematical model: the proposed weighted goal programming method (PWGPM) and the proposed neutrosophic goal programming approach (PNGPA). The PWGPM model minimizes deviations from predefined goals for each objective while adhering to linear constraints. In contrast, the PNGPA leverages neutrosophic optimization, integrating truth, falsity, and indeterminacy to address uncertainty in decision-making. The mathematical model of MOCFTP aims to optimize transportation schedules by minimizing total cost, total time, and damage cost while satisfying supply and demand constraints. A numerical example is provided to demonstrate the practicality and effectiveness of the mathematical model of MOCFTP. The compromise optimal solution for the proposed problem is obtained using the Pulp optimization library in Python. The findings indicate that the PNGPA outperforms others regarding solutions, and it offers a robust framework for complex, real-world transportation scenarios potentially beneficial for various logistics applications.