In this dissertation, mainly two problems are considered, both of which are routing problems. The first part of the dissertation explores the Capacitated Arc Routing Problem (CARP), which was first suggested by Golden and Wond 1981 [1]. This is the problem of servicing a set og edges in a graph, using a fleet of capacity-constrained vehicles. The problem occurs in practice in situations where s...

In this work we present the Prize-collecting Arc Routing Problem and some extensions. We derive properties that allow determining linear defining systems for the problems and solution approaches based on upper bounds obtained from relaxations reinforced with cuts, and lower bounds derived from heuristics. We also present numerical results from computational experiments that show that in many ca...

The Capacitated Arc Routing Problem (CARP) is useful for modeling urban waste collection or winter gritting, at the operational decision level. Many applications require a tactical version, the periodic CARP (PCARP), in which the trips are planned over a multiperiod horizon, subject to frequency constraints. The paper presents this new and hard theoretical problem, its variants, and a powerful ...

The Open Capacitated Arc Routing Problem (OCARP) is a NP-hard combinatorial optimization problem where, given an undirected graph, the objective is to find a minimum cost set of tours that services a subset of edges with positive demand under capacity constraints. This problem is related to the Capacitated Arc Routing Problem (CARP) but differs from it since OCARP does not consider a depot, and...

The Team Orienteering Arc Routing Problem (TOARP) is the extension to the arc routing setting of the Team Orienteering Problem (TOP). In the TOARP a set of potential customers, each associated with an arc of a directed graph, is available and a profit is collected when a potential customer is served that is when the associated arc is traversed. A fleet of vehicles is available to visit the cust...

The talk presents two non-standard extensions for singlevehicle arc-routing problems a.k.a. postman problems: First, street segments that require a service on both sides of the street can be covered either by two separate services or by a single zigzag service. Instead of deciding the type of service beforehand, we propose to take into account the zigzagging option when designing a tour. We pre...

The Capacitated Arc Routing Problem (CARP) is a difficult optimisation problem in vehicle routing with applications where a service must be provided by a set of vehicles on specified roads. A heuristic algorithm based on Tabu Search is proposed and tested on various sets of benchmark instances. The computational results show that the proposed algorithm produces high quality results within a rea...

The close-enough arc routing problem (CEARP) has an interesting real-life application to routing for meter reading. In this article, we propose a new mathematical formulation for this problem. We analyze our formulation and compare it with two formulations in the literature. We also develop branch-and-cut algorithms to solve the problem to optimality. We present computational results for instan...