On the periodic hierarchical Chinese postman problem

Abstract

This paper presents a mathematical formulation and a heuristic approach for a new variant of the Hierarchical Chinese Postman Problem (HCPP). Indeed, we introduce the concept of periodicity, and we define and solve, for the first time, the Periodic-HCPP, denoted as P-HCPP. Given that the resulting integer programming model makes use of a big number of binary variables and given the extended time horizon considered, 30 days in our case, the problem is characterized by a high level of complexity. However, our developed heuristic is able to solve instances having up to 40 nodes, 520 arcs and 5 hierarchies, whereas a general-purpose solver like Gurobi was not able to provide solutions for instances having more than 10 nodes. While the collected results are very encouraging, we provide at the end of this paper a set of possible future extensions of this work.

Solving the hierarchical windy postman problem with variable service costs using a math-heuristic algorithm

“…Some of the abovementioned applications may be characterized by the fact that the edges do not have the same importance of being serviced but are rather categorized according to their class of priority (called hierarchies). We deal here with the Hierarchical Windy Postman Problem (HWPP) that has the same features of the HCPP (Hierarchical Chinese Postman Problem) with the only exception that the service costs do not have to be symmetric (see Keskin and Triki 2022).…”