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

Profitable mixed capacitated arc routing and related problems

Mixed Capacitated Arc Routing Problems (MCARP) aim to identify a set of vehicle trips that, starting and ending at a depot node, serve a given number of links, regarding the vehicles capacity, and minimizing a cost function. If both profits and costs on arcs are considered, the Profitable Mixed Capacitated Arc Routing Problem (PMCARP) may be defined. We present compact flow based models for the PMCARP, where two types of services are tackled, mandatory and optional. Adaptations of the models to fit into some other related problems are also proposed. The models are evaluated, according to their bounds quality as well as the CPU times, over large sets of test instances. New instances have been created from benchmark ones in order to solve variants that have been introduced here for the first time. Results show the new models performance within CPLEX and compare, whenever available, the proposed models against other resolution methods.info:eu-repo/semantics/publishedVersio

The Vehicle Routing Problem with Service Level Constraints

We consider a vehicle routing problem which seeks to minimize cost subject to service level constraints on several groups of deliveries. This problem captures some essential challenges faced by a logistics provider which operates transportation services for a limited number of partners and should respect contractual obligations on service levels. The problem also generalizes several important classes of vehicle routing problems with profits. To solve it, we propose a compact mathematical formulation, a branch-and-price algorithm, and a hybrid genetic algorithm with population management, which relies on problem-tailored solution representation, crossover and local search operators, as well as an adaptive penalization mechanism establishing a good balance between service levels and costs. Our computational experiments show that the proposed heuristic returns very high-quality solutions for this difficult problem, matches all optimal solutions found for small and medium-scale benchmark instances, and improves upon existing algorithms for two important special cases: the vehicle routing problem with private fleet and common carrier, and the capacitated profitable tour problem. The branch-and-price algorithm also produces new optimal solutions for all three problems

A matheuristic for the Team Orienteering Arc Routing Problem

In the Team OrienteeringArc Routing Problem (TOARP) the potential customers are located on the arcs of a directed graph and are to be chosen on the basis of an associated profit. A limited fleet of vehicles is available to serve the chosen customers. Each vehicle has to satisfy a maximum route duration constraint. The goal is to maximize the profit of the served customers. We propose a matheuristic for the TOARP and test it on a set of benchmark instances for which the optimal solution or an upper bound is known. The matheuristic finds the optimal solutions on all, except one, instances of one of the four classes of tested instances (with up to 27 vertices and 296 arcs). The average error on all instances fo rwhich the optimal solution is available is 0.67 percent.Angel Corberan, Isaac Plana and Jose M. Sanchis wish to thank the Ministerio de Economia y Competitividad (project MTM2012-36163-C06-02) of Spain and the Generalitat Valenciana (project GVPROMETEO2013-049) for their support.Archetti, C.; Corberan, A.; Plana, I.; Sanchís Llopis, JM.; Speranza, MG. (2015). A matheuristic for the Team Orienteering Arc Routing Problem. European Journal of Operational Research. 245(2):392-401. https://doi.org/10.1016/j.ejor.2015.03.022S392401245

Distribution with Quality of Service Considerations:The Capacitated Routing Problem with Profits and Service Level Requirements

Inspired by a problem arising in cash logistics, we propose the Capacitated Routing Problem with Profits and Service Level Requirements (CRPPSLR). The CRPPSLR extends the class of Routing Problems with Profits by considering customers requesting deliveries to their (possibly multiple) service points. Moreover, each customer imposes a service level requirement specifying a minimum-acceptable bound on the fraction of its service points being delivered. A customer-specific financial penalty is incurred by the logistics service provider when this requirement is not met. The CRPPSLR consists in finding vehicle routes maximizing the difference between the collected revenues and the incurred transportation and penalty costs in such a way that vehicle capacity and route duration constraints are met. A fleet of homogeneous vehicles is available for serving the customers. We design a branch-and-cut algorithm and evaluate the usefulness of valid inequalities that have been effectively used for the capacitated vehicle routing problem and, more recently, for other routing problems with profits. A real-life case study taken from the cash supply chain in the Netherlands highlights the relevance of the problem under consideration. Computational results illustrate the performance of the proposed solution approach under different input parameter settings for the synthetic instances. For instances of real-life problems, we distinguish between coin and banknote distribution, as vehicle capacities only matter when considering the former. Finally, we report on the effectiveness of the valid inequalities in closing the optimality gap at the root node for both the synthetic and the real-life instances and conclude with a sensitivity analysis on the most significant input parameters of our model

Water truck routing optimization in open pit mines using the general algebraic modelling system approach

This paper presents a methodological approach for routing optimization in open pit mines which is a trending topic for dust emission reduction in mining process. In this context, the aim of the research and its contribution to the knowledge is firstly described based on a comprehensive literature survey in the field. Then, as an arc routing problem, the mathematical model for the process is generated including the objective function, minimizing the total distance traveled by the water truck fleets, practical constraints that should be met and the used assumptions. Finally, the formulated optimization problem solved employing General Algebraic Modelling System (GAMS) approach respect to the nature of the mathematical equations. The tested results by simulations discussed to confirm the effectiveness of the proposed method in dealing with the in-hand problem. This methodological approach could be used in optimization of other similar engineering problem as well

INTEGRATED HUB LOCATION AND CAPACITATED VEHICLE ROUTING PROBLEM OVER INCOMPLETE HUB NETWORKS

Hub location problem is one of the most important topics encountered in transportation and logistics management. Along with the question of where to position hub facilities, how routes are determined is a further challenging problem. Although these two problems are often considered separately in the literature, here, in this study, the two are analyzed together. Firstly, we relax the restriction that a vehicle serves between each demand center and hub pair and propose a mixed-integer mathematical model for the single allocation p-hub median and capacitated vehicle routing problem with simultaneous pick-up and delivery. Moreover, while many studies in hub location problem literature assume that there is a complete hub network structure, we also relax this assumption and present the aforementioned model over incomplete hub networks. Computational analyses of the proposed models were conducted on various instances on the Turkish network. Results indicate that the different capacity levels of vehicles have an important impact on optimal hub locations, hub arc networks, and routing design

The Time-Dependent Multiple-Vehicle Prize-Collecting Arc Routing Problem

In this paper, we introduce a multi vehicle version of the Time-Dependent Prize-Collecting Arc Routing Problem (TD-MPARP). It is inspired by a situation where a transport manager has to choose between a number of full truck load pick-ups and deliveries to be performed by a fleet of vehicles. Real-life traffic situations where the travel times change with the time of day are taken into account. Two metaheuristic algorithms, one based on Variable Neighborhood Search and one based on Tabu Search, are proposed and tested for a set of benchmark problems, generated from real road networks and travel time information. Both algorithms are capable of finding good solutions, though the Tabu Search approach generally shows better performance for large instances whereas the VNS is superior for small instances. We discuss the structural differences of the implementation of the algorithms which explain these results

Routing Applications in Newspaper Delivery

-The goal of this report is to give an up-to-date account of routing applications in the newspaper business. We describe the newspaper supply chain, and focus on the “last mile” distribution that has been advocated as an application of arc routing in the literature. A literature survey is provided, followed by a discussion of the arc routing model and its adequacy to newspaper applications. A more general and normally more adequate model: The Node, Edge, and Arc Routing Problem, is discussed. Characteristics of routing problems in carrier delivery are presented, together with a case study from the development of a web-based route design and revision system. Finally, summary, conclusions, and prospects for the future are given