Solving a multi-choice solid fractional multi objective transportation problem: involving the Newton divided difference interpolation approach

Vishwas Deep Joshi; Medha Sharma; Huda Alsaud; Vishwas Deep Joshi; Medha Sharma; Huda Alsaud

doi:10.3934/math.2024777

AIMS Mathematics

2024, Volume 9, Issue 6: 16031-16060. doi: 10.3934/math.2024777

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Research article

Solving a multi-choice solid fractional multi objective transportation problem: involving the Newton divided difference interpolation approach

1.
Department of Mathematics, Faculty of Science, JECRC University, Jaipur, Rajasthan, India
2.
Department of Mathematics, College of Science, King Saud University, P. O. Box-22452, Riyadh 11495, Saudi Arabia

Received: 13 February 2024 Revised: 12 April 2024 Accepted: 18 April 2024 Published: 07 May 2024
MSC : 62F07, 90B06, 90C29,

Multi-objective transportation problems (MOTPs) are mathematical optimization problems that involve simultaneously considering multiple, often conflicting objectives in transportation planning. Unlike traditional transportation problems, which typically focus on minimizing a single objective such as cost or distance, MOTPs aim to balance multiple objectives to find the optimal solution. These problems appear in various real-world applications such as logistics, supply chain management, and transportation, where decision-makers need to consider multiple criteria when designing transportation networks, routing vehicles, or scheduling deliveries. The primary challenge lies in the uncertainty in real-world transportation scenarios, where logistics involve factors beyond cost and distance. We investigated a multi-choice solid fractional multi-objective transportation problem (MCSF-MOTP) based on supply, demand, and conveyance capacity, where the coefficients of the objective functions were of the multi-choice type due to uncertainty. To address this uncertainty, the proposed model employed the Newton divided difference interpolation polynomial method, and the suitability of this model was validated through a numerical illustration employing a ranking approach.
- solid fractional transportation problem,
- Newton divided difference,
- multi-choice random parameter,
- goal programming,
- ranking,
- multi-objective programming
Citation: Vishwas Deep Joshi, Medha Sharma, Huda Alsaud. Solving a multi-choice solid fractional multi objective transportation problem: involving the Newton divided difference interpolation approach[J]. AIMS Mathematics, 2024, 9(6): 16031-16060. doi: 10.3934/math.2024777

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Abstract

Multi-objective transportation problems (MOTPs) are mathematical optimization problems that involve simultaneously considering multiple, often conflicting objectives in transportation planning. Unlike traditional transportation problems, which typically focus on minimizing a single objective such as cost or distance, MOTPs aim to balance multiple objectives to find the optimal solution. These problems appear in various real-world applications such as logistics, supply chain management, and transportation, where decision-makers need to consider multiple criteria when designing transportation networks, routing vehicles, or scheduling deliveries. The primary challenge lies in the uncertainty in real-world transportation scenarios, where logistics involve factors beyond cost and distance. We investigated a multi-choice solid fractional multi-objective transportation problem (MCSF-MOTP) based on supply, demand, and conveyance capacity, where the coefficients of the objective functions were of the multi-choice type due to uncertainty. To address this uncertainty, the proposed model employed the Newton divided difference interpolation polynomial method, and the suitability of this model was validated through a numerical illustration employing a ranking approach.

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