An adaptive guidance meta-heuristic for the vehicle routing problem with splits and clustered backhauls

This paper presents the case study of an Italian carrier, Grendi Trasporti Marittimi, which provides freight transportation services by trucks and containers. Its trucks deliver container loads from a port to import customers and collect container loads from export customers to the same port. In this case study, all import customers in a route must be serviced before all export customers, each customer can be visited more than once and containers are never unloaded or reloaded from the truck chassis along any route. We model the problem using an Integer Linear Programming formulation and propose an Adaptive Guidance metaheuristic. Our extensive computational experiments show that the adaptive guidance algorithm is capable of determining good-quality solutions in many instances of practical or potential interest for the carrier within 10 min of computing time, whereas the mathematical formulation often fails to provide the first feasible solution within 3 h of computing time

A Tabu Search algorithm for the vehicle routing problem with discrete split deliveries and pickups

The Vehicle Routing Problem with Discrete Split Deliveries and Pickups is a variant of the Vehicle Routing Problem with Split Deliveries and Pickups, in which customers’ demands are discrete in terms of batches (or orders). It exists in the practice of logistics distribution and consists of designing a least cost set of routes to serve a given set of customers while respecting constraints on the vehicles’ capacities. In this paper, its features are analyzed. A mathematical model and Tabu Search algorithm with specially designed batch combination and item creation operation are proposed. The batch combination operation is designed to avoid unnecessary travel costs, while the item creation operation effectively speeds up the search and enhances the algorithmic search ability. Computational results are provided and compared with other methods in the literature, which indicate that in most cases the proposed algorithm can find better solutions than those in the literature

Algebraic structural analysis of a vehicle routing problem of heterogeneous trucks. Identification of the properties allowing an exact approach.

Although integer linear programming problems are typically difficult to solve, there exist some easier problems, where the linear programming relaxation is integer. This thesis sheds light on a drayage problem which is supposed to have this nice feature, after extensive computational experiments. This thesis aims to provide a theoretical understanding of these results by the analysis of the algebraic structures of the mathematical formulation. Three reformulations are presented to prove if the constraint matrix is totally unimodular. We will show which experimental conditions are necessary and sufficient (or only sufficient or only necessary) for total unimodularity

Models and algorithms for the empty container repositioning and its integration with routing problems

The introduction of containers has fostered intermodal freight transportation. A definition of intermodality was provided by the European Commission as “a characteristic of a transport system whereby at least two different modes are used in an integrated manner in order to complete a door-to-door transport sequence”. The intermodal container transportation leads to several benefits, such as higher productivity during handling phases and advantages in terms of security, losses and damages. However, the distribution of containers comes with a drawback: due to directional imbalances in freight flows, some areas tend to accumulate unnecessary empty containers, while others face container shortages. Several planning models were developed for carriers in order to manage both loaded and empty containers profitably. However, they were built to operate under normal circumstances, neglecting the fact that networks are increasingly affected by both uncertainty and vulnerability, which may result in disruptions. The thesis aims to survey whether the impact of uncertainty can be mitigated by a stochastic programming approach, in which disruptions and normal operations are both foreseen as possible futures or scenarios. This approach is carried out by a multi-scenario optimization model in which scenarios are linked by non-anticipativity conditions. The empty container repositioning becomes even more challenging and difficult when integrated with routing problems. In fact, carriers often face problems in which they must determine simultaneously how many empty containers are carried by a fleet of vehicles and which routes must be followed by these vehicles. These problems typically arise in inland networks, in which one must plan the distribution by trucks of loaded and empty containers to customers. The thesis addresses this type of vehicle routing problems, which are motivated by a real case study occurred during the collaboration with a carrier that operates in the Mediterranean Sea in door-to-door modality. The carrier manages a fleet of trucks based at the port. Trucks and containers are used to service two types of transportation requests, the delivery of container loads from the port to import customers, and the shipment of container loads from export customers to the port. The thesis addresses two problems which differ in the composition of the fleet of trucks. The first problem involves a heterogeneous fleet of trucks that can carry one or two containers. We present a Vehicle Routing Problem with backhauls, load splits into multiple visits, and the impossibility to separate trucks and containers during customer service. Then, we formalize the problem by an Integer Linear Programming formulation and propose an efficient meta-heuristic algorithm able to solve it. The meta-heuristic determines the initial solution by a variant of the Clarkeand-Wright algorithm, and improves it by several local search phases, in which both node movements and truck swaps are implemented. The second problem involves a homogeneous fleet of trucks that can carry more than a container. As a consequence, the identification of routes can be more difficult. We present and formalize the associated Vehicle Routing Problem by an Integer Linear Programming formulation. Then we propose an efficient adaptive guidance meta-heuristic algorithm able to solve it. The meta-heuristic determines an initial feasible solution by a Tabu Search step, and next improves this solution by appropriate adaptive guidance mechanisms

Models and algorithms for the empty container repositioning and its integration with routing problems

The introduction of containers has fostered intermodal freight transportation. A definition of intermodality was provided by the European Commission as “a characteristic of a transport system whereby at least two different modes are used in an integrated manner in order to complete a door-to-door transport sequence”. The intermodal container transportation leads to several benefits, such as higher productivity during handling phases and advantages in terms of security, losses and damages. However, the distribution of containers comes with a drawback: due to directional imbalances in freight flows, some areas tend to accumulate unnecessary empty containers, while others face container shortages. Several planning models were developed for carriers in order to manage both loaded and empty containers profitably. However, they were built to operate under normal circumstances, neglecting the fact that networks are increasingly affected by both uncertainty and vulnerability, which may result in disruptions. The thesis aims to survey whether the impact of uncertainty can be mitigated by a stochastic programming approach, in which disruptions and normal operations are both foreseen as possible futures or scenarios. This approach is carried out by a multi-scenario optimization model in which scenarios are linked by non-anticipativity conditions. The empty container repositioning becomes even more challenging and difficult when integrated with routing problems. In fact, carriers often face problems in which they must determine simultaneously how many empty containers are carried by a fleet of vehicles and which routes must be followed by these vehicles. These problems typically arise in inland networks, in which one must plan the distribution by trucks of loaded and empty containers to customers. The thesis addresses this type of vehicle routing problems, which are motivated by a real case study occurred during the collaboration with a carrier that operates in the Mediterranean Sea in door-to-door modality. The carrier manages a fleet of trucks based at the port. Trucks and containers are used to service two types of transportation requests, the delivery of container loads from the port to import customers, and the shipment of container loads from export customers to the port. The thesis addresses two problems which differ in the composition of the fleet of trucks. The first problem involves a heterogeneous fleet of trucks that can carry one or two containers. We present a Vehicle Routing Problem with backhauls, load splits into multiple visits, and the impossibility to separate trucks and containers during customer service. Then, we formalize the problem by an Integer Linear Programming formulation and propose an efficient meta-heuristic algorithm able to solve it. The meta-heuristic determines the initial solution by a variant of the Clarkeand-Wright algorithm, and improves it by several local search phases, in which both node movements and truck swaps are implemented. The second problem involves a homogeneous fleet of trucks that can carry more than a container. As a consequence, the identification of routes can be more difficult. We present and formalize the associated Vehicle Routing Problem by an Integer Linear Programming formulation. Then we propose an efficient adaptive guidance meta-heuristic algorithm able to solve it. The meta-heuristic determines an initial feasible solution by a Tabu Search step, and next improves this solution by appropriate adaptive guidance mechanisms

Meta-heuristic Solution Methods for Rich Vehicle Routing Problems

Le problème de tournées de véhicules (VRP), introduit par Dantzig and Ramser en 1959, est devenu l'un des problèmes les plus étudiés en recherche opérationnelle, et ce, en raison de son intérêt méthodologique et de ses retombées pratiques dans de nombreux domaines tels que le transport, la logistique, les télécommunications et la production. L'objectif général du VRP est d'optimiser l'utilisation des ressources de transport afin de répondre aux besoins des clients tout en respectant les contraintes découlant des exigences du contexte d’application. Les applications réelles du VRP doivent tenir compte d’une grande variété de contraintes et plus ces contraintes sont nombreuse, plus le problème est difficile à résoudre. Les VRPs qui tiennent compte de l’ensemble de ces contraintes rencontrées en pratique et qui se rapprochent des applications réelles forment la classe des problèmes ‘riches’ de tournées de véhicules. Résoudre ces problèmes de manière efficiente pose des défis considérables pour la communauté de chercheurs qui se penchent sur les VRPs. Cette thèse, composée de deux parties, explore certaines extensions du VRP vers ces problèmes. La première partie de cette thèse porte sur le VRP périodique avec des contraintes de fenêtres de temps (PVRPTW). Celui-ci est une extension du VRP classique avec fenêtres de temps (VRPTW) puisqu’il considère un horizon de planification de plusieurs jours pendant lesquels les clients n'ont généralement pas besoin d’être desservi à tous les jours, mais plutôt peuvent être visités selon un certain nombre de combinaisons possibles de jours de livraison. Cette généralisation étend l'éventail d'applications de ce problème à diverses activités de distributions commerciales, telle la collecte des déchets, le balayage des rues, la distribution de produits alimentaires, la livraison du courrier, etc. La principale contribution scientifique de la première partie de cette thèse est le développement d'une méta-heuristique hybride dans la quelle un ensemble de procédures de recherche locales et de méta-heuristiques basées sur les principes de voisinages coopèrent avec un algorithme génétique afin d’améliorer la qualité des solutions et de promouvoir la diversité de la population. Les résultats obtenus montrent que la méthode proposée est très performante et donne de nouvelles meilleures solutions pour certains grands exemplaires du problème. La deuxième partie de cette étude a pour but de présenter, modéliser et résoudre deux problèmes riches de tournées de véhicules, qui sont des extensions du VRPTW en ce sens qu'ils incluent des demandes dépendantes du temps de ramassage et de livraison avec des restrictions au niveau de la synchronization temporelle. Ces problèmes sont connus respectivement sous le nom de Time-dependent Multi-zone Multi-Trip Vehicle Routing Problem with Time Windows (TMZT-VRPTW) et de Multi-zone Mult-Trip Pickup and Delivery Problem with Time Windows and Synchronization (MZT-PDTWS). Ces deux problèmes proviennent de la planification des opérations de systèmes logistiques urbains à deux niveaux. La difficulté de ces problèmes réside dans la manipulation de deux ensembles entrelacés de décisions: la composante des tournées de véhicules qui vise à déterminer les séquences de clients visités par chaque véhicule, et la composante de planification qui vise à faciliter l'arrivée des véhicules selon des restrictions au niveau de la synchronisation temporelle. Auparavant, ces questions ont été abordées séparément. La combinaison de ces types de décisions dans une seule formulation mathématique et dans une même méthode de résolution devrait donc donner de meilleurs résultats que de considérer ces décisions séparément. Dans cette étude, nous proposons des solutions heuristiques qui tiennent compte de ces deux types de décisions simultanément, et ce, d'une manière complète et efficace. Les résultats de tests expérimentaux confirment la performance de la méthode proposée lorsqu’on la compare aux autres méthodes présentées dans la littérature. En effet, la méthode développée propose des solutions nécessitant moins de véhicules et engendrant de moindres frais de déplacement pour effectuer efficacement la même quantité de travail. Dans le contexte des systèmes logistiques urbains, nos résultats impliquent une réduction de la présence de véhicules dans les rues de la ville et, par conséquent, de leur impact négatif sur la congestion et sur l’environnement.For more than half of century, since the paper of Dantzig and Ramser (1959) was introduced, the Vehicle Routing Problem (VRP) has been one of the most extensively studied problems in operations research due to its methodological interest and practical relevance in many fields such as transportation, logistics, telecommunications, and production. The general goal of the VRP is to optimize the use of transportation resources to service customers with respect to side-constraints deriving from real-world applications. The practical applications of the VRP may have a variety of constraints, and obviously, the larger the set of constraints that need to be considered, i.e., corresponding to `richer' VRPs, the more difficult the task of problem solving. The needs to study closer representations of actual applications and methodologies producing high-quality solutions quickly to larger-sized application problems have increased steadily, providing significant challenges for the VRP research community. This dissertation explores these extensional issues of the VRP. The first part of the dissertation addresses the Periodic Vehicle Routing Problem with Time Windows (PVRPTW) which generalizes the classical Vehicle Routing Problem with Time Windows (VRPTW) by extending the planning horizon to several days where customers generally do not require delivery on every day, but rather according to one of a limited number of possible combinations of visit days. This generalization extends the scope of applications to many commercial distribution activities such as waste collection, street sweeping, grocery distribution, mail delivery, etc. The major contribution of this part is the development of a population-based hybrid meta-heuristic in which a set of local search procedures and neighborhood-based meta-heuristics cooperate with the genetic algorithm population evolution mechanism to enhance the solution quality as well as to promote diversity of the genetic algorithm population. The results show that the proposed methodology is highly competitive, providing new best solutions in some large instances. The second part of the dissertation aims to present, model and solve two rich vehicle routing problems which further extend the VRPTW with time-dependent demands of pickup and delivery, and hard time synchronization restrictions. They are called Time-dependent Multi-zone Multi-Trip Vehicle Routing Problem with Time Windows (TMZT-VRPTW), and Multi-zone Mult-Trip Pickup and Delivery Problem with Time Windows and Synchronization (MZT-PDTWS), respectively. These two problems originate from planning the operations of two-tiered City Logistics systems. The difficulty of these problems lies in handling two intertwined sets of decisions: the routing component which aims to determine the sequences of customers visited by each vehicle, and the scheduling component which consists in planning arrivals of vehicles at facilities within hard time synchronization restrictions. Previously, these issues have been addressed separately. Combining these decisions into one formulation and solution method should yield better results. In this dissertation we propose meta-heuristics that address the two decisions simultaneously, in a comprehensive and efficient way. Experiments confirm the good performance of the proposed methodology compared to the literature, providing system managers with solution requiring less vehicles and travel costs to perform efficiently the same amount of work. In the context of City Logistics systems, our results indicate a reduction in the presence of vehicles on the streets of the city and, thus, in their negative impact on congestion and environment