Uncertain Maximum Benefit about Chinese Postman Problem

Abstract

This research deals with the generalization of profit maximization of the Chinese postman with several vehicles under uncertainty, and then it is solved using the Lagrangian algorithm. Four different cases of the model are discussed. The first mode performs Chinese postman routing and assumes that the origin and destination are the same for each vehicle for each cycle and is provided by the user, which is the case of a typical postman. The second takes into account the assumption that the origin and destination of each vehicle should not be the same and allows users to choose the possible origin or destination of the vehicles. The third case takes the origin of each vehicle as input and generates a solution based on finding the best destination for each vehicle. The last parameter, which is very general, allows the optimization model to choose possibly different locations for the origin and destination of the vehicle during each cycle. Modeling these issues in the real world requires the use of uncertainty theory. Liu expressed the theory of uncertainty. Here, is a model of the Chinese postman’s multiple profit maximization problem. So far, there is no such uncertainty analysis of these models. After stating the uncertainty problem of the maximum profit problem of the Chinese postman, we will state the problem using the Lagrangian algorithm. We then compare the results.