A Balanced Route Design for Min-Max Multiple-Depot Rural Postman Problem (MMMDRPP): a police patrolling case

A branch-price-and-cut method for the min-max k-windy rural postman problem

Given the edges of a graph, the postman problem consists of determining for a vehicle (postman) a shortest route that traverses all edges at least once. Each edge can be traversed in either direction and, when an edge is traversed more than once, the vehicle is said to be deadheading after its first traversal. The rural postman problem is the same as the postman problem except that the edges ar...

New facets and an enhanced branch-and-cut for the min-max K-vehicles windy rural postman problem

In this paper the Min-Max version of the Windy Rural Postman Problem with several vehicles is introduced. For this problem, in which the objective is to minimize the length of the longest tour in order to find a set of balanced tours for the vehicles, we present here an ILP formulation and study its associated polyhedron. Based on its partial description, a branch-and-cut algorithm has been imp...

Solving the large-scale min-max K-rural postman problem for snow plowing

On games arising from multi-depot Chinese postman problems

This paper introduces cooperative games arising from multi-depot Chinese postman problems and explores the properties of these games. A multi-depot Chinese postman problem (MDCP) is represented by a connected (di)graph G, a set of k depots that is a subset of the vertices of G, and a non-negative weight function on the edges of G. A solution to the MDCP is a minimum weight tour of the (di)graph...

Capacitated Windy Rural Postman Problem with Several Vehicles: A Hybrid Multi-Objective Simulated Annealing Algorithm

This paper presents the capacitated Windy Rural Postman Problem with several vehicles. For this problem, two objectives are considered. One of them is the minimization of the total cost of all vehicle routes expressed by the sum of the total traversing cost and another one is reduction of the maximum cost of vehicle route in order to find a set of equitable tours for the vehicles. Mathematical ...