Introducing heterogeneous users and vehicles into models and algorithms for the dial-a-ride problem

AbstractDial-a-ride problems deal with the transportation of people between pickup and delivery locations. Given the fact that people are subject to transportation, constraints related to quality of service are usually present, such as time windows and maximum user ride time limits. In many real world applications, different types of users exist. In the field of patient and disabled people transportation, up to four different transportation modes can be distinguished. In this article we consider staff seats, patient seats, stretchers and wheelchair places. Furthermore, most companies involved in the transportation of the disabled or ill dispose of different types of vehicles. We introduce both aspects into state-of-the-art formulations and branch-and-cut algorithms for the standard dial-a-ride problem. Also a recent metaheuristic method is adapted to this new problem. In addition, a further service quality related issue is analyzed: vehicle waiting time with passengers aboard. Instances with up to 40 requests are solved to optimality. High quality solutions are obtained with the heuristic method

A branch-and-cut algorithm for vehicle routing problems with three-dimensional loading constraints

This paper presents a new branch-and-cut algorithm based on infeasible path elimination for the three-dimensional loading capacitated vehicle routing problem (3L-CVRP) with different loading problem variants. We show that a previously infeasible route can become feasible by adding a new customer if support constraints are enabled in the loading subproblem and call this the incremental feasibility property. Consequently, different infeasible path definitions apply to different 3L-CVRP variants and we introduce several variant-depending lifting steps to strengthen infeasible path inequalities. The loading subproblem is solved exactly using a flexible constraint programming model to determine the feasibility or infeasibility of a route. An extreme point-based packing heuristic is implemented to reduce time-consuming calls to the exact loading algorithm. Furthermore, we integrate a start solution procedure and periodically combine memoized feasible routes in a set-partitioning-based heuristic to generate new upper bounds. A comprehensive computational study, employing well-known benchmark instances, showcases the significant performance improvements achieved through the algorithmic enhancements. Consequently, we not only prove the optimality of many best-known heuristic solutions for the first time but also introduce new optimal and best solutions for a large number of instances.Comment: 33 pages, 13 figures, 7 tables, Submitted to Transportation Scienc

A Tight Formulation for the Dial-a-Ride Problem

Ridepooling services play an increasingly important role in modern transportation systems. With soaring demand and growing fleet sizes, the underlying route planning problems become increasingly challenging. In this context, we consider the dial-a-ride problem (DARP): Given a set of transportation requests with pick-up and delivery locations, passenger numbers, time windows, and maximum ride times, an optimal routing for a fleet of vehicles, including an optimized passenger assignment, needs to be determined. We present tight mixed-integer linear programming (MILP) formulations for the DARP by combining two state-of-the-art models into novel location-augmented-event-based formulations. Strong valid inequalities and lower and upper bounding techniques are derived to further improve the formulations. We then demonstrate the theoretical and computational superiority of the new model: First, the formulation is tight in the sense that, if time windows shrink to a single point in time, the linear programming relaxation yields integer (and hence optimal) solutions. Second, extensive numerical experiments on benchmark instances show that computational times are on average reduced by 49.7% compared to state-of-the-art event-based approaches

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

Problèmes de tournées de véhicules avec contraintes de chargement

Cette thèse s’intéresse aux problèmes de tournées de véhicules où l’on retrouve des contraintes de chargement ayant un impact sur les séquences de livraisons permises. Plus particulièrement, les items placés dans l’espace de chargement d’un véhicule doivent être directement accessibles lors de leur livraison sans qu’il soit nécessaire de déplacer d’autres items. Ces problèmes sont rencontrés dans plusieurs entreprises de transport qui livrent de gros objets (meubles, électroménagers). Le premier article de cette thèse porte sur une méthode exacte pour un problème de confection d’une seule tournée où un véhicule, dont l’aire de chargement est divisée en un certain nombre de piles, doit effectuer des cueillettes et des livraisons respectant une contrainte de type dernier entré, premier sorti. Lors d’une collecte, les items recueillis doivent nécessairement être déposés sur le dessus de l’une des piles. Par ailleurs, lors d’une livraison, les items doivent nécessairement se trouver sur le dessus de l’une des piles. Une méthode de séparation et évaluation avec plans sécants est proposée pour résoudre ce problème. Le second article présente une méthode de résolution exacte, également de type séparation et évaluation avec plans sécants, pour un problème de tournées de véhicules avec chargement d’items rectangulaires en deux dimensions. L’aire de chargement des véhicules correspond aussi à un espace rectangulaire avec une orientation, puisque les items doivent être chargés et déchargés par l’un des côtés. Une contrainte impose que les items d’un client soient directement accessibles au moment de leur livraison. Le dernier article aborde une problème de tournées de véhicules avec chargement d’items rectangulaires, mais où les dimensions de certains items ne sont pas connus avec certitude lors de la planification des tournées. Il est toutefois possible d’associer une distribution de probabilités discrète sur les dimensions possibles de ces items. Le problème est résolu de manière exacte avec la méthode L-Shape en nombres entiers.In this thesis, we study mixed vehicle routing and loading problems where a constraint is imposed on delivery sequences. More precisely, the items in the loading area of a vehicle must be directly accessible, without moving any other item, at delivery time. These problems are often found in the transportation of large objects (furniture, appliances). The first paper proposes a branch-and-cut algorithm for a variant of the single vehicle pickup and delivery problem, where the loading area of the vehicle is divided into several stacks. When an item is picked up, it must be placed on the top of one of these stacks. Conversely, an item must be on the top of one of these stacks to be delivered. This requirement is called “Last In First Out” or LIFO constraint. The second paper presents another branch-and-cut algorithm for a vehicle routing and loading problem with two-dimensional rectangular items. The loading area of the vehicles is also a rectangular area where the items are taken out from one side. A constraint states that the items of a given customer must be directly accessible at delivery time. The last paper considers a stochastic vehicle routing and loading problem with two- dimensional rectangular items where the dimensions of some items are unknown when the routes are planned. However, it is possible to associate a discrete probability distribution on the dimensions of these items. The problem is solved with the Integer L-Shaped method

Tools and Algorithms for the Construction and Analysis of Systems

This open access two-volume set constitutes the proceedings of the 27th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2021, which was held during March 27 – April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The total of 41 full papers presented in the proceedings was carefully reviewed and selected from 141 submissions. The volume also contains 7 tool papers; 6 Tool Demo papers, 9 SV-Comp Competition Papers. The papers are organized in topical sections as follows: Part I: Game Theory; SMT Verification; Probabilities; Timed Systems; Neural Networks; Analysis of Network Communication. Part II: Verification Techniques (not SMT); Case Studies; Proof Generation/Validation; Tool Papers; Tool Demo Papers; SV-Comp Tool Competition Papers