Windy Postman Problem Under Uncertainty

Abstract

The postman problem is one of the optimization problems that has many applications in today’s world. With the progress of science, such optimization problems are used more. The postman’s problem is to find a route that has the minimum cost. The postman starts the route from one point and returns to the same point and must travel all the routes. If the round-trip costs are symmetric, in other words, the round-trip cost is the same, the problem is called the Chinese postman problem, and if the costs are asymmetric, that is, the round-trip cost is different from the return cost, the problem is called the windy postman problem (WPP). Here we describe two models of the WPP, which include the WPP and the rural WPP. The model for these problems in the real world needs to apply uncertainty theory. Liu expressed the theory of uncertainty. Here is a model of the windy postman uncertainty problem and a model of the windy rural postman uncertainty problem. So far, there has been no such uncertainty analysis on these models. To solve these problems, we use the Lagrangian heuristic method after turning it into a deterministic model. To solve these problems, after turning the problem into a deterministic problem, the heuristic Lagrangian method was used, and for the wind postman problem, we stated the corresponding Lagrangian algorithm and for the rural wind postman, the Lagrangian algorithm. Examples of these are problems and uncertainties. We expressed them and finally solved them by direct and Lagrangian methods.