Scatter search for a real-life heterogeneous fleet vehicle routing problem with time windows and split deliveries in Brazil

In this paper, we consider a real-life heterogeneous fleet vehicle routing problem with time windows and split deliveries that occurs in a major Brazilian retail group. A single depot attends 519 stores of the group distributed in 11 Brazilian states. To find good solutions to this problem, we propose heuristics as initial solutions and a scatter search (SS) approach. Next, the produced solutions are compared with the routes actually covered by the company. Our results show that the total distribution cost can be reduced significantly when such methods are used. Experimental testing with benchmark instances is used to assess the merit of our proposed procedure. (C) 2008 Published by Elsevier B.V.

A decision support system for a waste collection vehicle routing problem

The selective collection of municipal solid waste for recycling is a very complex and expensive process, where a major issue is to perform cost-efficient waste collection routes. Despite the abundance of commercially available software for fleet management, they often lack the capability to deal properly with sequencing problems and dynamic revision of plans and schedules during process execution. Our approach to achieve better solutions for the waste collection process is to model it as a vehicle routing problem, more specifically as a team orienteering problem where capacity constraints on the vehicles are considered, as well as time windows for the waste collection points and for the vehicles. The final model is called capacitated team orienteering problem with double time windows (CTOPdTW).We developed a genetic algorithm to solve routing problems in waste collection modelled as a CTOPdTW. The results achieved suggest possible reductions of logistic costs in selective waste collection.

A heuristic algorithm for the Capacitated Vehicle Routing Problem with Synchronized Pick-ups and Drop-offs : a case study for medications delivery and supervision in DR Congo

Dans des contextes de post-urgence tels que le vit la partie occidentale de la République Démocratique du Congo (RDC), l’un des défis cruciaux auxquels font face les hôpitaux ruraux est de maintenir un niveau de médicaments essentiels dans la pharmacie. Sans ces médicaments pour traiter les maladies graves, l’impact sur la santé de la population est significatif. Les hôpitaux encourent également des pertes financières dues à la péremption lorsque trop de médicaments sont commandés. De plus, les coûts du transport des médicaments ainsi que du superviseur sont très élevés pour les hôpitaux isolés ; les coûts du transport peuvent à eux seuls dépasser ceux des médicaments. En utilisant la province du Bandundu, RDC pour une étude de cas, notre recherche tente de déterminer la faisabilité (en termes et de la complexité du problème et des économies potentielles) d’un problème de routage synchronisé pour la livraison de médicaments et pour les visites de supervision. Nous proposons une formulation du problème de tournées de véhicules avec capacité limitée qui gère plusieurs exigences nouvelles, soit la synchronisation des activités, la préséance et deux fréquences d’activités. Nous mettons en œuvre une heuristique « cluster first, route second » avec une base de données géospatiales qui permet de résoudre le problème. Nous présentons également un outil Internet qui permet de visualiser les solutions sur des cartes. Les résultats préliminaires de notre étude suggèrent qu’une solution synchronisée pourrait offrir la possibilité aux hôpitaux ruraux d’augmenter l’accessibilité des services médicaux aux populations rurales avec une augmentation modique du coût de transport actuel.

Solving the Vehicle Routing Problem with Genetic ALgorithm and Simulated Annealing

This Thesis Work will concentrate on a very interesting problem, the Vehicle Routing Problem (VRP). In this problem, customers or cities have to be visited and packages have to be transported to each of them, starting from a basis point on the map. The goal is to solve the transportation problem, to be able to deliver the packages-on time for the customers,-enough package for each Customer,-using the available resources- and – of course - to be so effective as it is possible.Although this problem seems to be very easy to solve with a small number of cities or customers, it is not. In this problem the algorithm have to face with several constraints, for example opening hours, package delivery times, truck capacities, etc. This makes this problem a so called Multi Constraint Optimization Problem (MCOP). What’s more, this problem is intractable with current amount of computational power which is available for most of us. As the number of customers grow, the calculations to be done grows exponential fast, because all constraints have to be solved for each customers and it should not be forgotten that the goal is to find a solution, what is best enough, before the time for the calculation is up. This problem is introduced in the first chapter: form its basics, the Traveling Salesman Problem, using some theoretical and mathematical background it is shown, why is it so hard to optimize this problem, and although it is so hard, and there is no best algorithm known for huge number of customers, why is it a worth to deal with it. Just think about a huge transportation company with ten thousands of trucks, millions of customers: how much money could be saved if we would know the optimal path for all our packages.Although there is no best algorithm is known for this kind of optimization problems, we are trying to give an acceptable solution for it in the second and third chapter, where two algorithms are described: the Genetic Algorithm and the Simulated Annealing. Both of them are based on obtaining the processes of nature and material science. These algorithms will hardly ever be able to find the best solution for the problem, but they are able to give a very good solution in special cases within acceptable calculation time.In these chapters (2nd and 3rd) the Genetic Algorithm and Simulated Annealing is described in details, from their basis in the “real world” through their terminology and finally the basic implementation of them. The work will put a stress on the limits of these algorithms, their advantages and disadvantages, and also the comparison of them to each other.Finally, after all of these theories are shown, a simulation will be executed on an artificial environment of the VRP, with both Simulated Annealing and Genetic Algorithm. They will both solve the same problem in the same environment and are going to be compared to each other. The environment and the implementation are also described here, so as the test results obtained.Finally the possible improvements of these algorithms are discussed, and the work will try to answer the “big” question, “Which algorithm is better?”, if this question even exists.

Column generation for a multitrip vehicle routing problem with time windows, driver work hours, and heterogeneous fleet

This study addresses a vehicle routing problem with time windows, accessibility restrictions on customers, and a fleet that is heterogeneous with regard to capacity and average speed. A vehicle can performmultiple routes per day, all starting and ending at a single depot, and it is assigned to a single driverwhose totalwork hours are limited.Acolumn generation algorithmis proposed.The column generation pricing subproblem requires a specific elementary shortest path problem with resource constraints algorithm to address the possibility for each vehicle performingmultiple routes per day and to address the need to set the workday’s start time within the planning horizon. A constructive heuristic and a metaheuristic based on tabu search are also developed to find good solutions.

Heuristic algorithms for the Capacitated Location-Routing Problem and the Multi-Depot Vehicle Routing Problem

The Capacitated Location-Routing Problem (CLRP) is a NP-hard problem since it generalizes two well known NP-hard problems: the Capacitated Facility Location Problem (CFLP) and the Capacitated Vehicle Routing Problem (CVRP). The Multi-Depot Vehicle Routing Problem (MDVRP) is known to be a NP-hard since it is a generalization of the well known Vehicle Routing Problem (VRP), arising with one depot. This thesis addresses heuristics algorithms based on the well-know granular search idea introduced by Toth and Vigo (2003) to solve the CLRP and the MDVRP. Extensive computational experiments on benchmark instances for both problems have been performed to determine the effectiveness of the proposed algorithms. This work is organized as follows: Chapter 1 describes a detailed overview and a methodological review of the literature for the the Capacitated Location-Routing Problem (CLRP) and the Multi-Depot Vehicle Routing Problem (MDVRP). Chapter 2 describes a two-phase hybrid heuristic algorithm to solve the CLRP. Chapter 3 shows a computational comparison of heuristic algorithms for the CLRP. Chapter 4 presents a hybrid granular tabu search approach for solving the MDVRP.

Metodi euristici per il Vehicle Routing Problem

Il problema della consegna di prodotti da un deposito/impianto ai clienti mediante una flotta di automezzi è un problema centrale nella gestione di una catena di produzione e distribuzione (supply chain). Questo problema, noto in letteratura come Vehicle Routing Problem (VRP), nella sua versione più semplice consiste nel disegnare per ogni veicolo disponibile presso un dato deposito aziendale un viaggio (route) di consegna dei prodotti ai clienti, che tali prodotti richiedono, in modo tale che (i) la somma delle quantità richieste dai clienti assegnati ad ogni veicolo non superi la capacità del veicolo, (ii) ogni cliente sia servito una ed una sola volta, (iii) sia minima la somma dei costi dei viaggi effettuati dai veicoli. Il VRP è un problema trasversale ad una molteplicità di settori merceologici dove la distribuzione dei prodotti e/o servizi avviene mediante veicoli su gomma, quali ad esempio: distribuzione di generi alimentari, distribuzione di prodotti petroliferi, raccolta e distribuzione della posta, organizzazione del servizio scuolabus, pianificazione della manutenzione di impianti, raccolta rifiuti, etc. In questa tesi viene considerato il Multi-Trip VRP, in cui ogni veicolo può eseguire un sottoinsieme di percorsi, chiamato vehicle schedule (schedula del veicolo), soggetto a vincoli di durata massima. Nonostante la sua importanza pratica, il MTVRP ha ricevuto poca attenzione in letteratura: sono stati proposti diversi metodi euristici e un solo algoritmo esatto di risoluzione, presentato da Mingozzi, Roberti e Toth. In questa tesi viene presentato un metodo euristico in grado di risolvere istanze di MTVRP in presenza di vincoli reali, quali flotta di veicoli non omogenea e time windows. L’euristico si basa sul modello di Prins. Sono presentati inoltre due approcci di local search per migliorare la soluzione finale. I risultati computazionali evidenziano l’efficienza di tali approcci.

A Cooperative and Adaptive Variable Neighborhood Search for the Multi Depot Vehicle Routing Problem with Time Windows

In this paper we propose two cooperation schemes to compose new parallel variants of the Variable Neighborhood Search (VNS). On the one hand, a coarse-grained cooperation scheme is introduced which is well suited for being enhanced with a solution warehouse to store and manage the so far best found solutions and a self-adapting mechanism for the most important search parameters. This makes an a priori parameter tuning obsolete. On the other hand, a fine-grained scheme was designed to reproduce the successful properties of the sequential VNS. In combination with the use of parallel exploration threads all of the best solutions and 11 out of 20 new best solutions for the Multi Depot Vehicle Routing Problem with Time Windows were found.

Exact Solutions to the Symmetric and Asymmetric Vehicle Routing Problem with Simultaneous Delivery and Pick-Up

In reverse logistics networks, products (e.g., bottles or containers) have to be transported from a depot to customer locations and, after use, from customer locations back to the depot. In order to operate economically beneficial, companies prefer a simultaneous delivery and pick-up service. The resulting Vehicle Routing Problem with Simultaneous Delivery and Pick-up (VRPSDP) is an operational problem, which has to be solved daily by many companies. We present two mixed-integer linear model formulations for the VRPSDP, namely a vehicle-flow and a commodity-flow model. In order to strengthen the models, domain-reducing preprocessing techniques, and effective cutting planes are outlined. Symmetric benchmark instances known from the literature as well as new asymmetric instances derived from real-world problems are solved to optimality using CPLEX 12.1.

A hybrid genetic algorithm for the multi-depot vehicle routing problem

The distribution of finished products from depots to customers is a practical and challenging problem in logistics management. Better routing and scheduling decisions can result in higher level of customer satisfaction because more customers can be served in a shorter time. The distribution problem is generally formulated as the vehicle routing problem (VRP). Nevertheless, there is a rigid assumption that there is only one depot. In cases, for instance, where a logistics company has more than one depot, the VRP is not suitable. To resolve this limitation, this paper focuses on the VRP with multiple depots, or multi-depot VRP (MDVRP). The MDVRP is NP-hard, which means that an efficient algorithm for solving the problem to optimality is unavailable. To deal with the problem efficiently, two hybrid genetic algorithms (HGAs) are developed in this paper. The major difference between the HGAs is that the initial solutions are generated randomly in HGA1. The Clarke and Wright saving method and the nearest neighbor heuristic are incorporated into HGA2 for the initialization procedure. A computational study is carried out to compare the algorithms with different problem sizes. It is proved that the performance of HGA2 is superior to that of HGA1 in terms of the total delivery time.

A new three phase method (SDP method) for the multi-objective vehicle routing problem with simultaneous delvery and pickup (VRPSDP)

Transportation service operators are witnessing a growing demand for bi-directional movement of goods. Given this, the following thesis considers an extension to the vehicle routing problem (VRP) known as the delivery and pickup transportation problem (DPP), where delivery and pickup demands may occupy the same route. The problem is formulated here as the vehicle routing problem with simultaneous delivery and pickup (VRPSDP), which requires the concurrent service of the demands at the customer location. This formulation provides the greatest opportunity for cost savings for both the service provider and recipient. The aims of this research are to propose a new theoretical design to solve the multi-objective VRPSDP, provide software support for the suggested design and validate the method through a set of experiments. A new real-life based multi-objective VRPSDP is studied here, which requires the minimisation of the often conflicting objectives: operated vehicle fleet size, total routing distance and the maximum variation between route distances (workload variation). The former two objectives are commonly encountered in the domain and the latter is introduced here because it is essential for real-life routing problems. The VRPSDP is defined as a hard combinatorial optimisation problem, therefore an approximation method, Simultaneous Delivery and Pickup method (SDPmethod) is proposed to solve it. The SDPmethod consists of three phases. The first phase constructs a set of diverse partial solutions, where one is expected to form part of the near-optimal solution. The second phase determines assignment possibilities for each sub-problem. The third phase solves the sub-problems using a parallel genetic algorithm. The suggested genetic algorithm is improved by the introduction of a set of tools: genetic operator switching mechanism via diversity thresholds, accuracy analysis tool and a new fitness evaluation mechanism. This three phase method is proposed to address the shortcoming that exists in the domain, where an initial solution is built only then to be completely dismantled and redesigned in the optimisation phase. In addition, a new routing heuristic, RouteAlg, is proposed to solve the VRPSDP sub-problem, the travelling salesman problem with simultaneous delivery and pickup (TSPSDP). The experimental studies are conducted using the well known benchmark Salhi and Nagy (1999) test problems, where the SDPmethod and RouteAlg solutions are compared with the prominent works in the VRPSDP domain. The SDPmethod has demonstrated to be an effective method for solving the multi-objective VRPSDP and the RouteAlg for the TSPSDP.

A clustering approach for vehicle routing problems with hard time windows

Dissertação para obtenção do Grau de Mestre em Logica Computicional

Models and algorithms for the capacitated location-routing problem

Le problème de localisation-routage avec capacités (PLRC) apparaît comme un problème clé dans la conception de réseaux de distribution de marchandises. Il généralisele problème de localisation avec capacités (PLC) ainsi que le problème de tournées de véhicules à multiples dépôts (PTVMD), le premier en ajoutant des décisions liées au routage et le deuxième en ajoutant des décisions liées à la localisation des dépôts. Dans cette thèse on dévelope des outils pour résoudre le PLRC à l’aide de la programmation mathématique. Dans le chapitre 3, on introduit trois nouveaux modèles pour le PLRC basés sur des flots de véhicules et des flots de commodités, et on montre comment ceux-ci dominent, en termes de la qualité de la borne inférieure, la formulation originale à deux indices [19]. Des nouvelles inégalités valides ont été dévelopées et ajoutées aux modèles, de même que des inégalités connues. De nouveaux algorithmes de séparation ont aussi été dévelopés qui dans la plupart de cas généralisent ceux trouvés dans la litterature. Les résultats numériques montrent que ces modèles de flot sont en fait utiles pour résoudre des instances de petite à moyenne taille. Dans le chapitre 4, on présente une nouvelle méthode de génération de colonnes basée sur une formulation de partition d’ensemble. Le sous-problème consiste en un problème de plus court chemin avec capacités (PCCC). En particulier, on utilise une relaxation de ce problème dans laquelle il est possible de produire des routes avec des cycles de longueur trois ou plus. Ceci est complété par des nouvelles coupes qui permettent de réduire encore davantage le saut d’intégralité en même temps que de défavoriser l’apparition de cycles dans les routes. Ces résultats suggèrent que cette méthode fournit la meilleure méthode exacte pour le PLRC. Dans le chapitre 5, on introduit une nouvelle méthode heuristique pour le PLRC. Premièrement, on démarre une méthode randomisée de type GRASP pour trouver un premier ensemble de solutions de bonne qualité. Les solutions de cet ensemble sont alors combinées de façon à les améliorer. Finalement, on démarre une méthode de type détruir et réparer basée sur la résolution d’un nouveau modèle de localisation et réaffectation qui généralise le problème de réaffectaction [48].