A Novel Approach to Sustainable Grain Transportation: A Neutrosophic Bi-Objective Model for Cost and Time Optimization

As the global economy continues to grow, the need for transportation also grows. Transportation researchers are developing new methods for integrating new technologies into existing transportation systems and for addressing the associated challenges. This paper addressed bi-objective fixed charge solid transportation problem that consider two objectives minimizing the total transportation cost, including fixed and variable costs, and minimizing the total transportation time. It is a challenging optimization problem, as it is difficult to find a solution that simultaneously minimizes both objectives. Additionally, the problem with bi-objective fixed-charge solid transportation problem (BOFCSTP) under uncertainty with neutrosophic concept is presented here. This problem constructed with all the parameters such as cost, fixed-charge, source availability and requirements as neutrosophic values. Neutrosophic sets are efficiently handling the indeterminacy and imprecise data in many fields and single-valued neutrosophic sets are extension and simpler form of NS. Further, to convert the neutrosophic values to crisp values a ranking function is used. To solve the considered BOFCSTP different approaches are employed namely, neutrosophic linear programming, neutrosophic goal programming, fuzzy goal programming to get the compromised solution to the problem. Additionally, a real-life problem is given with numerical example and the results compared with the different approaches.