Maximum Profit Chinese Postman Problems Using Fuzzy Weighted Edge Length

Abstract

The problem of the Chinese postman is one of the types of the problem of the Chinese postman, which includes 4 models in this paper. In the first case, the postman moves from the origin, he must go through each edge at least once and then move to the destination, which in the first case, the destination is the same as the original origin. That is, the postman returns to the original origin. In the second case, the postman moves from the origin. We determine the destination so that the postman does not have to go back to the original source to incur a fee. In the third case, the postman moves from the origin to the destination that the computer program determines for him, in this way, he incurs a lower cost than in the second case because the GAMS programming determines a destination for us that costs less than all destinations. In the fourth case, both the origin and the destination are determined by programming so that all the edges are covered, which is less expensive than all the origins and destinations. The weight of edges is not constant due to different factors. Triangular fuzzy numbers are used in this study, which is included in the coefficients of the objective function of these fuzzy numbers. Two different ranking methods are used for fuzzification and the obtained results are compared with each other. The solution is done using GAMS software. Mathematical models cannot find solutions in large sizes and for this reason, the Lagrangian algorithm is used to solve these problems. After the problems are solved using the Lagrangian algorithm, the results of different fuzzy ranking methods are compared