Neutrosophic multi-choice 4D-transportation problem for different quality items

Abstract

This study presents a transportation problem, where the transportation costs may vary with multiple options. It also explores four-dimensional transportation problem (4D-TP), which is beneficial because it includes the ideas of choosing the best route and the most appropriate conveyance option. Another new feature of this model is that it includes two different selling prices based on product quality, with premium prices for superior items and lower prices for poor quality items. Moreover, due to lack of necessary information, the problem may include some parameters which are not accurately described. Therefore, many parameters in this model are assumed as single-valued neutrosophic numbers to make it more realistic. The multi-choice 4D-TP is transformed into a single-choice 4D-TP using a ranking function that considers weighted value and weighted ambiguity. A new idea of possibility measures is introduced to solve the 4D-TP model for different quality items under neutrosophic environment. The model is illustrated with numerical data and solved using the generalized reduced gradient method with the help of LINGO-17.0 solver. Sensitivity assessments are performed to evaluate the model’s robustness against varying parameters. The research’s credibility is established by comparing the outcomes with existing methods, demonstrating the effectiveness of the proposed methodology. Additionally, the usefulness of the model is illustrated by analyzing the results of various 4-dimensional, 3-dimensional, and 2-dimensional transportation problems as special cases of the proposed model.