On the heterogeneous vehicle routing problem under demand uncertainty

In this paper we study the heterogeneous vehicle routing problem under demand uncertainty, on which there has been little research to our knowledge. The focus of the paper is to provide a strong formulation that also easily allows tractable robust and chance-constrained counterparts. To this end, we propose a basic Miller-Tucker-Zemlin (MTZ) formulation with the main advantage that uncertainty is restricted to the right-hand side of the constraints. This leads to compact and tractable counterparts of demand uncertainty. On the other hand, since the MTZ formulation is well known to provide a rather weak linear programming relaxation, we propose to strengthen the initial formulation with valid inequalities and lifting techniques and, furthermore, to dynamically add cutting planes that successively reduce the polyhedral region using a branch-and-cut algorithm. We complete our study with extensive computational analysis with different performance measures on different classes of instances taken from the literature. In addition, using simulation, we conduct a scenario-based risk level analysis for both cases where either unmet demand is allowed or not

Thirty years of heterogeneous vehicle routing

It has been around thirty years since the heterogeneous vehicle routing problem was introduced, and significant progress has since been made on this problem and its variants. The aim of this survey paper is to classify and review the literature on heterogeneous vehicle routing problems. The paper also presents a comparative analysis of the metaheuristic algorithms that have been proposed for these problems

Algorithms for Routing Unmanned Vehicles with Motions, Resource, and Communication Constraints

Multiple small autonomous or unmanned aerial and ground vehicles are being used together with stationary sensing devices for a wide variety of data gathering, monitoring and surveillance applications in military, civilian, and agricultural applications, to name a few. Even though there are several advantages due to the small platforms for these vehicles, they pose a variety of challenges. This dissertation aims to address the following challenges to routing multiple small autonomous aerial or ground vehicles: (i) limited communication capabilities of the stationary sensing devices, (ii) dynamics of the vehicles, (iii) varying sensing capabilities of all the vehicles, and (iv) resource constraints in the form of fuel restrictions on each vehicle. The dissertation formulates four different routing problems for multiple unmanned vehicles, one for each of the aforementioned constraints, as mixed-integer linear programs and develops numerically efficient algorithms based on the branch-and-cut paradigm to compute optimal solutions for practically reasonable size of test instances

A p-step formulation for the capacitated vehicle routing problem

We introduce a _p_-step formulation for the capacitated vehicle routing problem (CVRP). The parameter _p_ indicates the length of partial paths corresponding to the used variables. This provides a family of formulations including both the traditional arc-based and path-based formulations. Hence, it is a generalization which unifies arc-based and path-based formulations, while also providing new formulations. We show that the LP bound of the _p_-step formulation is increasing in _p_, although not monotonically. Furthermore, we prove that computing the set partitioning bound is NP-hard. This is a meaningful result in itself, but combined with the _p_-step formulation this also allows us to show that there does not exist a strongest compact formulation for the CVRP, if _P ≠ NP_. While ending the search for a strongest compact formulation, we propose th

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].The capacitated location-routing problem (CLRP) arises as a key problem in the design of distribution networks. It generalizes both the capacitated facility location problem (CFLP) and the multiple depot vehicle routing problem (MDVRP), the first by considering additional routing decisions and the second by adding the location decision variables. In this thesis we use different mathematical programming tools to develop and specialize new models and algorithms for solving the CLRP. In Chapter 3, three new models are presented for the CLRP based on vehicle-flow and commodity-flow formulations, all of which are shown to dominate, in terms of the linear relaxation lower bound, the original two-index vehicle-flow formulation [19]. Known valid inequalities are complemented with some new ones and included using separation algorithms that in many cases generalize extisting ones found in the literature. Computational experiments suggest that flow models can be efficient for dealing with small or medium size instances of the CLRP (50 customers or less). In Chapter 4, a new branch-and-cut-and-price exact algorithm is introduced for the CLRP based on a set-partitioning formulation. The pricing problem is a shortest path problem with resource constraints (SPPRC). In particular, we consider a relaxation of such problem in which routes are allowed to contain cycles of length three or more. This is complemented with the development of new valid inequalities that are shown to be effective for closing the optimality gap as well as to restrict the appearance of cycles. Computational experience supports the fact that this method is now the best exact method for the CLRP. In Chapter 5, we introduce a new metaheuristic with the aim of finding good quality solutions in short or moderate computing times. First, a bundle of good solutions is generated with the help of a greedy randomized adaptive search procedure (GRASP). Following this, a blending procedure is applied with the aim of producing a better upper bound as a combination of all the others in the bundle. An iterative destroy-and-repair method is then applied using a location-reallocation model that generalizes the reallocation model due to de Franceschi et al. [48]

Ambulance routing problems with rich constraints and multiple objectives

Humanitäre non-profit Organisationen im Bereich des Patiententransports sehen sich dazu verpflichtet alle möglichen Einsparungs- und Optimierungspotentiale auszuloten um ihre Ausgaben zu reduzieren. Im Gegensatz zu Notfalleinsatzfahrten, bei denen ein Zusammenlegen mehrerer Transportaufträge normalerweise nicht möglich ist, besteht bei regulären Patiententransporten durchaus Einsparungspotential. Diese Tatsache gibt Anlass zur wissenschaftlichen Analyse jener Problemstellung, welche die täglich notwendige Planung regulärer Patiententransportaufträge umfasst. Solche Aufgabenstellungen werden als Dial-A-Ride-Probleme modelliert. Eine angemessene Service-Qualität kann entweder durch entsprechende Nebenbedingungen gewährleistet oder durch eine zusätzliche Zielfunktion minimiert werden. Beide Herangehensweisen werden hier untersucht. Zuerst wird eine vereinfachte Problemstellung aus der Literatur behandelt und ein kompetitives heuristisches Lösungsverfahren entwickelt. Diese vereinfachte Problemstellung wird in zwei Richtungen erweitert. Einerseits wird, zusätzlich zur Minimierung der Gesamtkosten, eine zweite benutzerorientierte Zielfunktion eingeführt. Andererseits werden eine heterogene Fahrzeugflotte und unterschiedliche Patiententypen in die Standardproblemstellung integriert. Letztendlich wird das reale Patiententransportproblem, basierend auf Informationen des Roten Kreuzes, definiert und gelöst. Neben heterogenen Fahrzeugen und unterschiedlichen Patienten, werden nun auch die Zuordnung von Fahrern und sonstigem Personal zu den verschiedenen Fahrzeugen, Mittagspausen und weitere Aufenthalte am Depot berücksichtigt. Alle eingesetzten exakten Methoden, obwohl sie auf neuesten Erkenntnissen aus der Literatur aufbauen, können Instanzen von realistischer Größe nicht lösen. Dieser Umstand macht die Entwicklung von passenden heuristischen Verfahren nach wie vor unumgänglich. In der vorliegenden Arbeit wird ein relativ generisches System basierend auf der Variable Neighborhood Search Idee entwickelt, das auf alle behandelten Einzielproblemversionen angewandt werden kann; auch für die bi-kriterielle Problemstellung, in Kombination mit Path Relinking, werden gute Ergebnisse erzielt.Humanitarian non-profit ambulance dispatching organizations are committed to look at cost reduction potentials in order to decrease their expenses. While in the context of emergency transportation cost reduction cannot be achieved by means of combined passenger routes, this can be done when dealing with regular patients. This research work is motivated by the problem situation faced by ambulance dispatchers in the field of patient transportation. Problems of this kind are modeled as dial-a-ride problems. In the field of patient transportation, the provision of a certain quality of service is necessary; the term “user inconvenience” is used in this context. User inconvenience can either be considered in terms of additional constraints or in terms of additional objectives. Both approaches are investigated in this book. The aim is to model and solve the real world problem based on available information from the Austrian Red Cross. In a first step, a competitive heuristic solution method for a simplified problem version is developed. This problem version is extended in two ways. On the one hand, besides routing costs, a user-oriented objective, minimizing user inconvenience, in terms of mean user ride time, is introduced. On the other hand, heterogeneous patient types and a heterogeneous vehicle fleet are integrated into the standard dial-a-ride model. In a final step, in addition to heterogeneous patients and vehicles, the assignment of drivers and other staff members to vehicles, the scheduling of lunch breaks, and additional stops at the depot are considered. All exact methods employed, although based on state of the art concepts, are not capable of solving instances of realistic size. This fact makes the development of according heuristic solution methods necessary. In this book a rather generic variable neighborhood search framework is proposed. It is able to accommodate all single objective problem versions and also proves to work well when applied to the bi-objective problem in combination with path relinking

Optimisation of vehicle routing problem with time windows using Harris Hawks optimiser

Vehicle routing problem is one of the combinatorial optimisation problems that have gained attraction for studies because of its complexity and significant impact to service providers and passengers. Vehicle routing problem with time windows (VRPTW) is a variant where vehicles need to visit the predetermined stop points within the given time frame. This problem has been widely studied and optimised using different methods. Since the performance of algorithms in different problems is dissimilar, the study to optimise the VRPTW is ongoing. This paper presents a VRPTW study for a public transportation network in Kuantan and Pekan districts, located in East Pahang, Malaysia. There were 52 stop points to be visited within two hours. The main objective of the study is to minimise the number of vehicles to be assigned for the routing problem subjected to the given time windows. The problem was optimised using a new algorithm known as Harris Hawks Optimiser (HHO). To the best of authors’ knowledge, this is the first attempt to build HHO algorithm for VRPTW problem. Computational experiment indicated that the HHO came up with the best average fitness compared with other comparison algorithms in this study including Artificial Bee Colony (ABC), Particle Swarm Optimisation (PSO), Moth Flame Optimiser (MFO), and Whale Optimisation Algorithm (WOA). The optimisation results also indicated that all the stop points can be visited within the given time frames by using three vehicles

Path Planning Algorithms for Multiple Heterogeneous Vehicles

Unmanned aerial vehicles (UAVs) are becoming increasingly popular for surveillance in civil and military applications. Vehicles built for this purpose vary in their sensing capabilities, speed and maneuverability. It is therefore natural to assume that a team of UAVs given the mission of visiting a set of targets would include vehicles with differing capabilities. This paper addresses the problem of assigning each vehicle a sequence of targets to visit such that the mission is completed with the least "cost" possible given that the team of vehicles is heterogeneous. In order to simplify the problem the capabilities of each vehicle are modeled as cost to travel from one target to another. In other words, if a vehicle is particularly suited to visit a certain target, the cost for that vehicle to visit that target is low compared to the other vehicles in the team. After applying this simplification, the problem can be posed as an instance of the combinatorial problem called the Heterogeneous Travelling Salesman Problem (HTSP). This paper presents a transformation of a Heterogenous, Multiple Depot, Multiple Traveling Salesman Problem (HMDMTSP) into a single, Asymmetric, Traveling Salesman Problem (ATSP). As a result, algorithms available for the single salesman problem can be used to solve the HMDMTSP. To show the effectiveness of the transformation, the well known Lin-Kernighan-Helsgaun heuristic was applied to the transformed ATSP. Computational results show that good quality solutions can be obtained for the HMDMTSP relatively fast. Additional complications to the sequencing problem come in the form of precedence constraints which prescribe a partial order in which nodes must be visited. In this context the sequencing problem was studied seperately using the Linear Program (LP) relaxation of a Mixed Integer Linear Program (MILP) formulation of the combinatorial problem known as the "Precedence Constrained Asymmetric Travelling Salesman Problem" (PCATSP)