The Hierarchical Chinese Postman Problem (HCPP) is a Chinese Postman Problem with the arcs partitioned into priority classes ordered by a precedence relation. The problem under the sum criterion is polynomially solvable if the ordering is linear and each class is connected. For a known HCPP algorithm we give an O(n) improvement (n the number of nodes) leading to O(kn) with k the number of class...

In this paper we address a real life optimization problem, the Rail Track Inspection Scheduling Problem (RTISP). This problem consists of scheduling railway network inspection tasks. The objective is to minimize the total deadhead distance while performing all inspection tasks. Different 0-1 integer formulations for the problem are presented. A heuristic based on both Benders and Dantzig-Wolfe ...

This paper describes the methodology that we have applied for the solution of an urban waste collection problem in the municipality of Sant Boi de Llobregat, within the metropolitan area of Barcelona (Spain). The basic nature of the considered problem is that of a capacitated arc routing problem, although it has several specific characteristics, mainly derived from traffic regulations. We prese...

In this paper we study the Windy Postman Problem. This is a well known Arc Routing Problem which contains the Mixed Chinese Postman Problem as a special case. We present here a full description of the polyhedron associated to the Windy Postman Problem over graphs with up to 4 vertices and 10 edges. We introduce two new families of facet-inducing inequalities and we prove that these inequalities...

Split procedures have been proved to be efficient within global framework optimization for routing problems by splitting giant tour into trips. This is done by generating optimal shortest path within an auxiliary graph built from the giant tour. An efficient application has been introduced for the first time by Lacomme et al. (2001) within a metaheuristic approach to solve the Capacitated Arc R...

We study the general routing problem de ned on a mixed graph and subject to capacity constraints. Such a problem aims to nd the set of routes of minimum overall cost servicing a subset of required elements like vertices, arcs and edges, without exceeding the capacity of a eet of homogeneous vehicles based at the same depot. The problem is a generalization of a large variety of node and arc rout...

In this paper, we introduce a multi vehicle version of the Time-Dependent PrizeCollecting Arc Routing Problem (TD-MPARP). It is inspired by a situation where a transport manager has to choose between a number of full truck load pick-ups and deliveries to be performed by a fleet of vehicles. Real-life traffic situations where the travel times change with the time of day are taken into account. T...

Arc routing problems (ARPs) are a special kind of vehicle problem, in which the demands located on edges or arcs, instead nodes. There is huge literature ARPs, and variety exact heuristic algorithms available. Recently, however, we encountered some real-life ARPs with over 10 000 roads, much larger than those usually considered literature. For these problems, develop fast upper- lower-bounding ...

The capacitated arc routing problem (CARP) is a difficult combinatorial optimization problem that has been intensively studied in the last decades. We present a hybrid metaheuristic approach (HMA) to solve this problem which incorporates an effective local refinement procedure, coupling a randomized tabu thresholding procedure with an infeasible descent procedure, into the memetic framework. Ot...

The Open Capacitated Arc Routing Problem (OCARP) is an 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, an...