On path ranking in time-dependent graphs

In this paper we study a property of time-dependent graphs, dubbed path ranking invariance. Broadly speaking, a time-dependent graph is path ranking invariant if the ordering of its paths (w.r.t. travel time) is independent of the start time. In this paper we show that, if a graph is path ranking invariant, the solution of a large class of time-dependent vehicle routing problems can be obtained by solving suitably defined (and simpler) time-independent routing problems. We also show how this property can be checked by solving a linear program. If the check fails, the solution of the linear program can be used to determine a tight lower bound. In order to assess the value of these insights, the lower bounds have been embedded into an enumerative scheme. Computational results on the time-dependent versions of the \textit{Travelling Salesman Problem} and the \textit{Rural Postman Problem} show that the new findings allow to outperform state-of-the-art algorithms.Comment: 28 pages, 2 figure

Arc routing problems: A review of the past, present, and future

[EN] Arc routing problems (ARPs) are defined and introduced. Following a brief history of developments in this area of research, different types of ARPs are described that are currently relevant for study. In addition, particular features of ARPs that are important from a theoretical or practical point of view are discussed. A section on applications describes some of the changes that have occurred from early applications of ARP models to the present day and points the way to emerging topics for study. A final section provides information on libraries and instance repositories for ARPs. The review concludes with some perspectives on future research developments and opportunities for emerging applicationsThis research was supported by the Ministerio de Economia y Competitividad and Fondo Europeo de Desarrollo Regional, Grant/Award Number: PGC2018-099428-B-I00. The Research Council of Norway, Grant/Award Numbers: 246825/O70 (DynamITe), 263031/O70 (AXIOM).Corberán, Á.; Eglese, R.; Hasle, G.; Plana, I.; Sanchís Llopis, JM. (2021). Arc routing problems: A review of the past, present, and future. Networks. 77(1):88-115. https://doi.org/10.1002/net.21965S8811577

An updated annotated bibliography on arc routing problems

The number of arc routing publications has increased significantly in the last decade. Such an increase justifies a second annotated bibliography, a sequel to Corberán and Prins (Networks 56 (2010), 50–69), discussing arc routing studies from 2010 onwards. These studies are grouped into three main sections: single vehicle problems, multiple vehicle problems and applications. Each main section catalogs problems according to their specifics. Section 2 is therefore composed of four subsections, namely: the Chinese Postman Problem, the Rural Postman Problem, the General Routing Problem (GRP) and Arc Routing Problems (ARPs) with profits. Section 3, devoted to the multiple vehicle case, begins with three subsections on the Capacitated Arc Routing Problem (CARP) and then delves into several variants of multiple ARPs, ending with GRPs and problems with profits. Section 4 is devoted to applications, including distribution and collection routes, outdoor activities, post-disaster operations, road cleaning and marking. As new applications emerge and existing applications continue to be used and adapted, the future of arc routing research looks promising.info:eu-repo/semantics/publishedVersio

Arc Routing Problems for Road Network Maintenance

RÉSUMÉ : Cette thèse présente deux problèmes rencontrés dans l’entretien des réseaux routiers, soit la surveillance des réseaux routiers pour la détection de verglas sur la chaussée et la reprogrammation des itinéraires pour les activités de déneigement et d’épandage de sel. Nous représentons ces problèmes par des modèles de tournées sur les arcs. La dépendance aux moments et la nature dynamique sont des caractéristiques propres de ces problèmes, par conséquence le cas de surveillance des réseaux routiers est modélisé comme un problème de postier rural avec fenêtres-horaires (RPPTW), tandis que le cas de la reprogrammation utilise des modèles obtenus à partir des formulations de problèmes de tournées sur les arcs avec capacité. Dans le cas du problème de surveillance, une patrouille vérifie l’état des chemins et des autoroutes, elle doit principalement détecter le verglas sur la chaussée dans le but d’assurer de bonnes conditions aux chauffeurs et aux piétons. Étant donné un réseau routier et des prévisions météo, le problème consiste à créer une tournée qui permette de détecter opportunément le verglas sur les rues et les routes. L’objectif poursuivi consiste à minimiser le coût de cette opération. En premier, on présente trois formulations basées sur la programmation linéaire en nombres entiers pour le problème de surveillance des réseaux qui dépend du moment et deux méthodes de résolution: un algorithme de coupes et un algorithme heuristique appelé adaptive large neighborhood search (ALNS). La méthode exacte inclut des inéquations valides tirées du problème du voyageur de commerce avec fenêtres-horaires et aussi du problème de voyageur du commerce avec contraintes de précédence. La méthode heuristique considère deux phases: en premier, on trouve une solution initiale et après dans la deuxième phase, l’algorithme essaie d’améliorer la solution initiale en utilisant sept heuristiques de destruction et deux heuristiques de réparation choisies au hasard. La performance des heuristiques est évaluée pendant les itérations. Une meilleure performance correspond à une plus grande probabilité de choisir une heuristique. Plusieurs tests ont été faits sur deux ensembles d’exemplaires de problèmes. Les résultats obtenus montrent que l’algorithme de coupes est capable de résoudre des réseaux avec 104 arêtes requises et des fenêtres-horaires structurées par tranches horaires ; l’algorithme peut aussi résoudre des réseaux avec 45 arêtes requises et des fenêtres-horaires structurées pour chaque arête requise. Pour l’algorithme ALNS, différentes versions de l’algorithme sont comparées. Les résultats montrent que cette méthode est efficace parce qu’elle est capable de résoudre à l’optimalité 224 des 232 exemplaires et de réduire le temps de calcul significativement pour les exemplaires les plus difficiles. La dernière partie de la thèse introduit le problème de la reprogrammation de tournées sur les arcs avec capacité (RCARP), lequel permet de modéliser la reprogrammation des itinéraires après une panne d’un véhicule lors de la phase d’exécution d’un plan initial des activités de déneigement ou d’épandage de sel. Le planificateur doit alors modifier le plan initial rapidement et reprogrammer les véhicules qui restent pour finir les activités. Dans ce cas, l’objectif poursuivi consiste à minimiser le coût d’opération et le coût de perturbation. La distance couverte par les véhicules correspond au coût d’opération, cependant une nouvelle métrique est développée pour mesurer le coût de perturbation. Les coûts considérés sont des objectifs en conflit. On analyse quatre politiques à la phase de re-routage en utilisant des formulations de programmation linéaire en nombres entiers. On propose une solution heuristique comme méthode pour résoudre le RCARP quand les coûts d’opération et de perturbation sont minimisés en même temps et quand une réponse rapide est nécessaire. La méthode consiste à fixer une partie de l’itinéraire initial et après à modifier seulement les itinéraires des véhicules les plus proches de la zone de l’interruption de la tournée du véhicule défaillant. La méthode a été testée sur des exemplaires obtenus d’un réseau réel. Nos tests indiquent que la méthode peut résoudre rapidement des exemplaires avec 88 arêtes requises et 10 véhicules actifs après la panne d’un véhicule. En conclusion, la principale contribution de cette thèse est de présenter des modèles de tournées sur les arcs et de proposer des méthodes de résolution d’optimisation qui incluent la dépendance aux temps et l’aspect dynamique. On propose des modèles et des méthodes pour résoudre le RPPTW, et on présente des résultats pour ce problème. On introduit pour la première fois le RCARP. Trois articles correspondant aux trois principaux chapitres ont été acceptés ou soumis à des revues avec comité de Lecture: “The rural postman problem with time windows” accepté dans Networks, “ALNS for the rural postman problem with time windows” soumis à Networks, and “The rescheduling capacitated arc routing problem” soumis à International Transactions in Operational Research.----------ABSTRACT : This dissertation addresses two problems related to road network maintenance: the road network monitoring of black-ice and the rescheduling of itineraries for snow plowing and salt spreading operations. These problems can naturally be represented using arc routing models. Timing-sensitive and dynamic nature are inherent characteristics of these problems, therefore the road network monitoring is modeled as a rural postman problem with time windows (RPPTW) and in the rescheduling case, models based on capacitated arc routing formulations are suggested for the rerouting phase. The detection of black-ice on the roads is carried out by a patrol to ensure safety conditions for drivers and pedestrians. Specific meteorological conditions cause black-ice on the roads; therefore the patrol must design a route covering part of the network in order to timely detect the black-ice according to weather forecasts. We look for minimum-cost solutions that satisfy the timing constraints. At first, three formulations based on mixed integer linear programming are presented for the timing-sensitive road network monitoring and two solution approaches are proposed: a cutting plane algorithm and an adaptive large neighborhood search (ALNS) algorithm. The exact method includes valid inequalities from the traveling salesman problem (TSP) with time windows and from the precedence constrained TSP. The heuristic method consists of two phases: an initial solution is obtained, and then in the second phase the ALNS method tries to improve the initial solution using seven removal and two insertion heuristics. The performance of the heuristics is evaluated during the iterations, and therefore the heuristics are selected depending on their performance (with higher probability for the better ones). Several tests are done on two sets of instances. The computational experiments performed show that the cutting plane algorithm is able to solve instances with up to 104 required edges and with time windows structured by time slots, and problems with up to 45 required edges and time windows structured by each required edge. For the ALNS algorithm, several versions of the algorithm are compared. The results show that this approach is efficient, solving to optimality 224 of 232 instances and significantly reducing the computational time on the hardest instances. The last part of the dissertation introduces the rescheduling capacitated arc routing problem (RCARP), which models the rescheduling of itineraries after a vehicle failure happens in the execution of an initial plan of snow plowing or salt spreading operations. A dispatcher must quickly adjust the remaining vehicles and modify the initial plan in order to complete the operations. In this case we look for solutions that minimize operational and disruption costs. The traveled distance represents the operational cost, and a new metric is discussed as disruption cost. The concerned objectives are in conflict. Four policies are analyzed in the rerouting phase using mixed integer linear programming formulations. A heuristic solution is developed to solve the RCARP when operational and disruption costs are minimized simultaneously and a quick response is needed. The idea is to fix part of the initial itinerary and only modify the itinerary of vehicles closer to the failure zone. The method is tested on a set of instances generated from a real network. Our tests indicate that the method can solve instances with up to 88 required edges and 10 active vehicles after the vehicle breakdown. In short the main contribution of this dissertation is to present arc routing models and optimization solution techniques that consider timing-sensitive and dynamic aspects. Formulations and solution methods with computational results are given for the RPPTW, and the RCARP is studied for the first time here. Three articles corresponding to the main three chapters have been accepted or submitted to peer review journals: “The rural postman problem with time windows” accepted in Networks, “ALNS for the rural postman problem with time windows” submitted to Networks, and “The rescheduling capacitated arc routing problem” submitted to International Transactions in Operational Research

Optimization of vehicle routing and scheduling with travel time variability - application in winter road maintenance

This study developed a mathematical model for optimizing vehicle routing and scheduling, which can be used to collect travel time information, and also to perform winter road maintenance operations (e.g., salting, plowing). The objective of this research was to minimize the total vehicle travel time to complete a given set of service tasks, subject to resource constraints (e.g., truck capacity, fleet size) and operational constraints (e.g., service time windows, service time limit). The nature of the problem is to design vehicle routes and schedules to perform the required service on predetermined road segments, which can be interpreted as an arc routing problem (ARP). By using a network transformation technique, an ARP can be transformed into a well-studied node routing problem (NRP). A set-partitioning (SP) approach was introduced to formulate the problem into an integer programming problem (I PP). To solve this problem, firstly, a number of feasible routes were generated, subject to resources and operational constraints. A genetic algorithm based heuristic was developed to improve the efficiency of generating feasible routes. Secondly, the corresponding travel time of each route was computed. Finally, the feasible routes were entered into the linear programming solver (CPL EX) to obtain final optimized results. The impact of travel time variability on vehicle routing and scheduling for transportation planning was also considered in this study. Usually in the concern of vehicle and pedestrian\u27s safety, federal, state governments and local agencies are more leaning towards using a conservative approach with constant travel time for the planning of winter roadway maintenance than an aggressive approach, which means that they would rather have a redundancy of plow trucks than a shortage. The proposed model and solution algorithm were validated with an empirical case study of 41 snow sections in the northwest area of New Jersey. Comprehensive analysis based on a deterministic travel time setting and a time-dependent travel time setting were both performed. The results show that a model that includes time dependent travel time produces better results than travel time being underestimated and being overestimated in transportation planning. In addition, a scenario-based analysis suggests that the current NJDOT operation based on given snow sector design, service routes and fleet size can be improved by the proposed model that considers time dependent travel time and the geometry of the road network to optimize vehicle routing and scheduling. In general, the benefit of better routing and scheduling design for snow plowing could be reflected in smaller minimum required fleet size and shorter total vehicle travel time. The depot location and number of service routes also have an impact on the final optimized results. This suggests that managers should consider the depot location, vehicle fleet sizing and the routing design problem simultaneously at the planning stage to minimize the total cost for snow plowing operations

Efficient routing of snow removal vehicles

This research addresses the problem of finding a minimum cost set of routes for vehicles in a road network subject to some constraints. Extensions, such as multiple service requirements, and mixed networks have been considered. Variations of this problem exist in many practical applications such as snow removal, refuse collection, mail delivery, etc. An exact algorithm was developed using integer programming to solve small size problems. Since the problem is NP-hard, a heuristic algorithm needs to be developed. An algorithm was developed based on the Greedy Randomized Adaptive Search Procedure (GRASP) heuristic, in which each replication consists of applying a construction heuristic to find feasible and good quality solutions, followed by a local search heuristic. A simulated annealing heuristic was developed to improve the solutions obtained from the construction heuristic. The best overall solution was selected from the results of several replications. The heuristic was tested on four sets of problem instances (total of 115 instances) obtained from the literature. The simulated annealing heuristic was able to achieve average improvements of up to 26.36% over the construction results on these problem instances. The results obtained with the developed heuristic were compared to the results obtained with recent heuristics developed by other authors. The developed heuristic improved the best-known solution found by other authors on 18 of the 115 instances and matched the results on 89 of those instances. It worked specially better with larger problems. The average deviations to known lower bounds for all four datasets were found to range between 0.21 and 2.61%

Optimization problems in the postal sector

Supply chain optimization is a widely studied field of operations research. Nevertheless, adapting the existing solutions to the specifications of each company is an interesting and stimulating challenge. With this in mind, the project described herein, developed in partnership with CTT, looks to provide the company with precious tools to more efficiently manage the labour allocated to mail delivery and increase the productivity of the workforce as a whole. To achieve these objectives, it follows up on a previous work by Pereira[26], where an extension of the Vehicle Routing Problem (VRP) was proposed to optimize the last-mile delivery step of the mail distribution procedure, but this time giving particular relevance to the adequacy of the model developed to the intricacies imposed by the company and exploring suitable adaptations. One of the requirements, for standardization purposes, is the creation of segments, composed of sets of postal codes that serve as input to the optimization model. Finally, it was necessary to merge this work with the company’s workflow by integrating the model with SISMA, a productivity assessment tool already used by CTT.A otimização de uma cadeia de abastecimento é um campo vastamente estudado no âm- bito da investigação operacional. Contudo, adaptar as soluções existentes aos critérios de cada empresa é um desafio bastante interessante e estimulante. Tendo isto em consi- deração, este projeto, desenvolvido em parceria com os CTT – Correios de Portugal, S.A. (CTT), procura fornecer à empresa ferramentas que permitam uma gestão eficiente da força de trabalho afeta à distribuição de correio. Para atingir este propósito, este trabalho teve como ponto de partida uma proposta de- senvolvida por Pereira[26], onde uma adaptação do Vehicle Routing Problem (VRP) foi desenvolvida para otimizar a etapa last-mile do processo de distribuição. No presente trabalho, dá-se uma atenção redobrada à compatibilidade do modelo desenvolvido com as complexidades impostas pela empresa e explora-se algumas melhorias consideradas apropriadas. Um dos requisitos, para manter alguma estibilidade nos resultados, é a introdução de segmentos, compostos por conjuntos contíguos de códigos postais, que ali- mentam o modelo. Finalmente, para combinar este trabalho com o fluxo de trabalho da empresa, fez-se a integração do modelo de otimização com o SISMA, uma ferramenta de avalição de produtividade já utilizada pelos CTT