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Keywords:
bi-objective transportation problem; single-valued trapezoidal neutrosophic numbers; weighted possibility mean; neutrosophic TOPSIS approach; sensitivity analysis
bi-objective transportation problem; single-valued trapezoidal neutrosophic numbers; weighted possibility mean; neutrosophic TOPSIS approach; sensitivity analysis
Summary:
The Transportation Problem is an optimization problem which aims to optimize the objective function of the products from various sources to destinations. In real-world situations, decision makers face a variety of conflicting objectives such as transportation costs, time, deterioration rates and so on which yields them with comprehensive profits. In these situations, the transportation problem becomes Multi-objective Transportation Problem. In real life, the parameters are unpredictable due to factors such as incomplete input data, market fluctuations, environmental influences and so on. To address these uncertainties, the parameters are expressed as single-valued trapezoidal neutrosophic number. This article explores a bi-objective transportation problem in a neutrosophic environment, aiming to determine the Pareto optimal solution. First, the neutrosophic problem is transformed into its deterministic problem using the Weighted Possibility Mean. In road safety, delineator design and placement often involve conflicting objectives like visibility, cost, installation time and safety. Balancing these is challenging due to complex road conditions, traffic, geometry and weather. In this point of view, we have proposed the approach namely, Neutrosophic TOPSIS approach for single valued trapezoidal neutrosophic numbers to transform the bi-objective problem into its single objective problem. Then the problem is solved by LINGO software to determine the Pareto optimal solution. Our approach provides a systematized method to assess alternatives and identify the optimal delineator design by balancing conflicting objectives, aiding decision makers in selecting the most suitable road configuration. A Sensitivity Analysis is performed to determine the sensitivity ranges for all the parameters of the problem. To illustrate the applicability, effectiveness and usefulness of the approach, a numerical example is provided and the comparison was made with the existing approaches. It is observed that the obtained Pareto optimal solution extracted from the proposed approach provides better result than the existing approaches. Finally, the conclusions are drawn along with the future work.
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