Enrique Mota

The Capacitated Arc Routing Problem: Lower bounds

In this paper, we consider the Capacitated Arc Routing Problem (CARP), in which a fleet of vehicles, based on a specified vertex (the depot) and with a known capacity Q, must service a subset of the edges of a graph, with minimum total cost and such that the load assigned to each vehicle does not exceed its capacity. New lower bounds are developed for this problem, producing at least as good results as the already existing ones. Three of the proposed lower bounds are obtained from the resolution of a minimum cost perfect matching problem. The fourth one takes into account the vehicle capacity and is computed using a dynamic programming algorithm. Computational results, in which these bounds are compared on a set of test problems, are included.

Polyhedral results for a vehicle routing problem

Abstract The Vehicle Routing Problem is a well known, and hard, combinatorial problem, whose polyhedral structure has deserved little attention. In this paper we consider the particular case in which all the demands are equal (since in the general case the associated polytope may be empty). From a known formulation of the problem we obtain the dimension of the corresponding polytope and we study the facetial properties of every inequality in it.

Heuristic Procedures for the Capacitated Vehicle Routing Problem

In this paper we present two new heuristic procedures for the Capacitated Vehicle Routing Problem (CVRP). The first one solves the problem from scratch, while the second one uses the information provided by a strong linear relaxation of the original problem. This second algorithm is designed to be used in a branch and cut approach to solve to optimality CVRP instances. In both heuristics, the initial solution is improved using tabu search techniques. Computational results over a set of known instances, most of them with a proved optimal solution, are given.

A comparison of two different formulations for arc routing problems on mixed graphs

Arc routing problems on mixed graphs have been modelled in the literature either using just one variable per edge or associating to each edge two variables, each one representing its traversal in the corresponding direction. In this paper, and using the mixed general routing problem as an example, we compare theoretical and computationally both formulations as well as the lower bounds obtained from them using Linear Programming based methods. Extensive computational experiments, including some big and newly generated random instances, are presented.

A new metaheuristic for the vehicle routing problem with split demands

In this paper we present a metaheuristic procedure constructed for the special case of the Vehicle Routing Problem in which the demands of the clients can be split, i.e., any client can be serviced by more than one vehicle. The proposed algorithm, based on the scatter search methodology, produces a feasible solution using the minimum number of vehicles. The results obtained compare with the best results known up to date on a set of instances previously published in the literature.

A Scatter Search Algorithm for the Split Delivery Vehicle Routing Problem

In this chapter we present a metaheuristic procedure constructed for the special case of the Vehicle Routing Problem in which the demands of clients can be split, i.e., any client can be serviced by more than one vehicle. The proposed algorithm, based on the scatter search methodology, produces a feasible solution using the minimum number of vehicles. The quality of the obtained results is comparable to the best results known up to date on a set of instances previously published in the literature.

The multiple vehicle pickup and delivery problem with LIFO constraints

This paper approaches a pickup and delivery problem with multiple vehicles in which LIFO conditions are imposed when performing loading and unloading operations and the route durations cannot exceed a given limit. We propose two mixed integer formulations of this problem and a heuristic procedure that uses tabu search in a multi-start framework. The first formulation is a compact one, that is, the number of variables and constraints is polynomial in the number of requests, while the second one contains an exponential number of constraints and is used as the basis of a branch-and-cut algorithm. The performances of the proposed solution methods are evaluated through an extensive computational study using instances of different types that were created by adapting existing benchmark instances. The proposed exact methods are able to optimally solve instances with up to 60 nodes.

Analisis de heuristicos para el problema del cartero rural

ResumenEn este artículo se estudia el comportamiento en el peor de los casos de dos algoritmos heurísticos propuestos para el Problema del Cartero Rural definido sobre un grafo no dirigido (RPP) y sobre un grafo dirigido (DRPP). En ambos problemas se determina el radio del peor caso de los heurísticos estudiados, que para el RPP es 3/2, mientras que para el DRPP no está acotado. Para conseguir cotas que sean más significativas, se ha determinado también este radio en función de ciertos parámetros que se pueden calcular a partir de los datos particulares de cada ejemplo, lo que ha permitido obtener una cota finita para el comportamiento en el peor caso del algoritmo heurístico para el DRPP.SummaryIn this paper we study the worst case performance of two heuristic algorithms proposed for the Rural Postman Problem on a non directed graph (RPP) and on a directed graph (DRPP). In both case, the worst case ratio is obtained; for the RPP this ratio is 3/2, whereas for the DRPP the ratio is unbounded. In order to obtain more significant bounds, this ratio has also been obtained as a function of certain parameters that can be computed from the particular data of each instance, thus producing a finite bound for the worst case ratio of the heuristic algorithm for the DRPP.

ARC: a Computerized System for Urban Garbage Collection

SummaryIn this paper we present ARC a computerized system developed for urban garbage collection. The package is intended to help the planners in the design of efficient collection routes and to facilitate the study and evaluation of alternatives concerning issues such as the type and number of vehicles, frequency of collection and type and location of refuse containers. The final product is a “user friendly” system designed to be used by the planners without outside assistance.

Some recent contributions to routing and location problems

CORAL 2003, a Conference on Routing and Location, washeld in Puerto de la Cruz (Tenerife, Spain) from February24–26, 2003. A wonderful place, close to the black sand ofthe beach, and a nice temperature welcomed a group ofsenior and young researchers from Canada, England,France, Germany, and Spain. Social activities were alsoprovided and sponsored by the Cabildo Insular de Tenerife(the local government) and TITSA (the public bus transpor-tation company on the island). The conference corre-sponded to the third annual meeting of a research project,funded by the Spanish Ministry of Science and Technology,developing a Decision Support System for Vehicle Routingand Facility Location Problems (SADERYL, TIC-2000-1750-C06), in which research groups from six Spanishuniversities are collaborating. The conference was open toother participants and it was a pleasure to attend presenta-tions by G. Laporte (CRT, Montreal), A. Letchford (Uni-versity of Lancaster), J. Pacheco (University of Burgos), C.Prins (University of Troyes), G. Reinelt and D. Theis (Uni-versity of Heidelberg), and F. Semet (University of Valen-ciennes). Although the conference focused on routing andlocation problems, other optimization problems were alsoconsidered. Updated information, as well as the extendedabstracts of the presentations, can be found at the followingsite: http://webpages.ull.es/users/saderyl/Coral.htm.The SADERYL project is based on a global understand-ing of the logistics chain and its requirements for an effi-cient management. The decision problems arising in theintegrated management of the logistics chain can be classi-fied as strategic, tactical, and operational problems. Withinthe SADERYL project, we have focused mainly on thestrategic and tactical aspects, concerning routing, location,and combined location-routing problems. All these prob-lems are of great economic interest and the use of combi-natorial optimization-based packages for their managementhas proved to produce substantial savings. However, a muchdeeper understanding of these problems is needed to im-prove the quantitative tools that should be provided to themanagers as a basis for making their decisions. ThroughCORAL 2003, we have tried to contribute to this objectivewith some papers giving more theoretical insights, model-ing approaches, and heuristic and exact algorithms for theseproblems.This report highlights the main results presented at theconference. To give a quick overview, the presentationshave been grouped into four areas: routing problems (gen-eral, arc routing, and node routing), combined location-routing problems, pure location problems, and other topics.On general routing, Dirk Theis [20] showed new resultson “The Undirected General Routing Problem.” This prob-lem, GRP, is a generalization of the well-known RuralPostman Problem (RPP) in which, besides a set of requirededges, a set of nodes is also required to be visited by the“postman.” Most of the previous results for the RPP/GRP