Fuzzy Traveling Salesman Problem of Fuzzy Hexagonal Numbers using Ranking Method and Dijkstra's Algorithms

Abstract

The aim of this article is to find the fuzzy shortest possible distance for a fuzzy   traveling salesman problem of hexagonal fuzzy numbers. We used to formulate the numerical example using dijkstra's algorithm.

Introduction The traveling salesman problem (TSM) involves finding the shortest possible route to multiple destination and returning to the starting point. —_ there we several applications of TSP, such as vehicle routing, scheduling. The TSP in a serious challenge for the logistics and supply chain industry because of involves optimizing the delivery router for multiple destinations while considering various constraints such as, traffic, delivery windows and customer request with multiple vehicle, more cities and multiple sales professionals, TSP become a more challenging to solve. In this article we proposed shorter possible distance route from multiple destination and returning to the starting point using ranking method of hexagonal fuzzy numbers.

Conclusions: The ranking approach is used in this paper to transform hexagonal fuzzy numbers into expected time, or standard time, for each activity. Thus, using the DIJKSTRA algorithm, the fuzzy shortest path is found. It assists decision makers in selecting the optimal, shortest path in a fuzzy environment by applying the ranking algorithm.