Solving Fully Neutrosophic Incompatible Multi-Item Fixed Charge Four-Dimensional Transportation Problem with Volume Constraints

Abstract

Transportation problem (TP) describes the goods distribution process from production centers to retailers. The transportation-related parameters like demands, availabilities, and unit transportation costs become uncertain due to insufficient data, etc. With the carried items total weight restriction, each vehicle has a volume capacity that restricts the total articles volume. So far, volume restriction has been ignored in TP. Nowadays, with worldwide infrastructural developments, different connecting routes and conveyances are available for transportation. Therefore, conveyances capacities and fixed charges are also uncertain, and hence the decision variables are expected to be uncertain. When both parameters and decision variables are neutrosophic, TP is named fully neutrosophic. Considering these facts, fully neutrosophic multi-item four-dimensional TPs with fixed charges are formulated for cost minimization. Here, items are pairwise incompatible and vehicles volume capacities are imposed. In particular, proposed TP for compatible items is solved. (i) Score and accuracy function and (ii) weighted value function methods are used for deneutrosophication. Converted crisp problems are solved using the generalized reduced gradient method via LINGO 11.0. The methods and solutions are illustrated by a real-life experiment. Significances of several routes and vehicle types are presented. One proposed method gives better results for some existing problems.