Two-phase branch-and-cut for the mixed capacitated general routing problem

The Mixed Capacitated General Routing Problem (MCGRP) is defined over a mixed graph, for which some vertices must be visited and some links must be traversed at least once. The problem consists of determining a set of least-cost vehicle routes that satisfy this requirement and respect the vehicle capacity. Few papers have been devoted to the MCGRP, in spite of interesting real-world applications, prevalent in school bus routing, mail delivery, and waste collection. This paper presents a new mathematical model for the MCGRP based on two-index variables. The approach proposed for the solution is a two-phase branch-and-cut algorithm, which uses an aggregate formulation to develop an effective …

Preface: Special issue on arc routing problems and other related topics

The periodic rural postman problem with irregular services on mixed graphs

Abstract In this paper, we deal with an extension of the rural postman problem in which some links of a mixed graph must be traversed a given number of times over a time horizon. These links represent entities that must be serviced a specified number of times in some subsets of days (or periods) of the time horizon. The aim is to design a set of minimum-cost tours, one for each day/period of the time horizon, that satisfy the service requirements. We refer to this problem as the periodic rural postman problem with irregular services (PRPP–IS). Some practical applications of the problem can be found in road maintenance operations and road network surveillance, for example. In order to solve …