A new exact algorithm for the multi-depot vehicle routing problem under capacity and route length constraints

This article presents an exact algorithm for the multi-depot vehicle routing problem (MDVRP) under capacity and route length constraints. The MDVRP is formulated using a vehicle-flow and a set-partitioning formulation, both of which are exploited at different stages of the algorithm. The lower bound computed with the vehicle-flow formulation is used to eliminate non-promising edges, thus reducing the complexity of the pricing subproblem used to solve the set-partitioning formulation. Several classes of valid inequalities are added to strengthen both formulations, including a new family of valid inequalities used to forbid cycles of an arbitrary length. To validate our approach, we also consider the capacitated vehicle routing problem (CVRP) as a particular case of the MDVRP, and conduct extensive computational experiments on several instances from the literature to show its effectiveness. The computational results show that the proposed algorithm is competitive against stateof-the-art methods for these two classes of vehicle routing problems, and is able to solve to optimality some previously open instances. Moreover, for the instances that cannot be solved by the proposed algorithm, the final lower bounds prove stronger than those obtained by earlier methods

A real delivery problem dealt with Monte Carlo techniques

[EN] In this paper we use Monte Carlo Techniques to deal with a real world delivery problem of a food company in Valencia (Spain). The problem is modeled as a set of 11 instances of the well known Vehicle Routing Problem, VRP, with additional time constraints. Given that VRP is a NP-hard problem, a heuristic algorithm, based on Monte Carlo techniques, is implemented. The solution proposed by this heuristic algorithm reaches distance and money savings of about 20% and 5% respectively.This research was partially supported by MICINN, Project MTM2013-43540-P and by UPV, Project Programa de Apoyo a la Investigación y Desarrollo de la UPV PAID-06-12.S577181Fernández de Córdoba, P., L.M. García-Raffi and J.M. Sanchis Llopis (1998), A heuristic algorithm based on Monte Carlo methods for the Rural Postman Problem.Computers and Op. Research,25, No. 12, pp. 1097–1106, 1998.Fernández de Córdoba, P. and L.M. García-Raffi, E. Nieto and J.M. Sanchis Llopis (1999a), Aplicación de técnicas Monte Carlo a un problema real de Rutas de Vehículos.Anales de Ingeniería, Colombia. In press.Fernández de Córdoba, P., L.M. García-Raffi and J.M. Sanchis Llopis (1999b), A Constructive Parallel Algorithm based on Monte Carlo techniques for Routing Problems, Submitted toParallel Computers.Laporte, G. (1992), The Vehicle Routing Problem: an overview of exact and approximate algorithms,European Journal of Operations Research,59, 345.Laporte, G., M. Desrochers and Y. Nobert (1985), “Optimal Routing under Capacity and Distance Restrictions.Operations Research,33, pp. 1050–1073.Laporte G. and Y. Nobert (1987), Exact algorithms for The Vehicle Routing Problem,Surveys in Combinatorial Optimization (S. Martello, G. Laporte, M. Minoux and C. Ribeiro Eds.). North-HollandAmsterdamMayado, A. (1998), Organización de los itinerarios de la flota de camiones de reparto de una sociedad cooperativa. Optimización mediante técnicas de simulación Monte Carlo. Proyecto Fin de Carrera. E.T.S.I.I. Universidad Politécnica de Valencia

On the use of biased-randomized algorithms for solving non-smooth optimization problems

Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines

The Vehicle Routing Problem with Service Level Constraints

We consider a vehicle routing problem which seeks to minimize cost subject to service level constraints on several groups of deliveries. This problem captures some essential challenges faced by a logistics provider which operates transportation services for a limited number of partners and should respect contractual obligations on service levels. The problem also generalizes several important classes of vehicle routing problems with profits. To solve it, we propose a compact mathematical formulation, a branch-and-price algorithm, and a hybrid genetic algorithm with population management, which relies on problem-tailored solution representation, crossover and local search operators, as well as an adaptive penalization mechanism establishing a good balance between service levels and costs. Our computational experiments show that the proposed heuristic returns very high-quality solutions for this difficult problem, matches all optimal solutions found for small and medium-scale benchmark instances, and improves upon existing algorithms for two important special cases: the vehicle routing problem with private fleet and common carrier, and the capacitated profitable tour problem. The branch-and-price algorithm also produces new optimal solutions for all three problems