On the collaboration uncapacitated arc routing problem

This paper introduces a new arc routing problem for the optimization of a collaboration scheme among carriers. This yields to the study of a profitable uncapacitated arc routing problem with multiple depots, where carriers collaborate to improve the profit gained. In the first model the goal is the maximization of the total profit of the coalition of carriers, independently of the individual profit of each carrier. Then, a lower bound on the individual profit of each carrier is included. This lower bound may represent the profit of the carrier in the case no collaboration is implemented. The models are formulated as integer linear programs and solved through a branch-and-cut algorithm. Theoretical results, concerning the computational complexity, the impact of collaboration on profit and a game theoretical perspective, are provided. The models are tested on a set of 971 instances generated from 118 benchmark instances for the Privatized Rural Postman Problem, with up to 102 vertices. All the 971 instances are solved to optimality within few seconds.Peer ReviewedPostprint (author's final draft

A spatial decomposition based math-heuristic approach to the asset protection problem

This paper addresses the highly critical task of planning asset protection activities during uncontrollable wildfires known in the literature as the Asset Protection Problem (APP). In the APP each asset requires a protective service to be performed by a set of emergency response vehicles within a specific time period defined by the spread of fire. We propose a new spatial decomposition based math-heuristic approach for the solution of large-scale APPs. The heuristic exploits the property that time windows are geographically correlated as fire spreads across a landscape. Thus an appropriate division of the landscape allows the problem to be decomposed into smaller more tractable sub-problems. The main challenge then is to minimise the difference between the final locations of vehicles from one division to the optimal starting locations of the next division. The performance of the proposed approach is tested on a set of benchmark instances from the literature and compared to the most recent Adaptive Large Neighborhood Search (ALNS) algorithm developed for the APP. The results show that our proposed solution approach outperforms the ALNS algorithm on all instances with comparable computation time. We also see a trend with the margin of out-performance becoming more significant as the problems become larger

Multi-depot rural postman problems

The final publication is available at Springer via http://dx.doi.org/10.1007/s11750-016-0434-zThis paper studies multi-depot rural postman problems on an undirected graph. These problems extend the well-known undirected rural postman problem to the case where there are several depots instead of just one. Linear integer programming formulations that only use binary variables are proposed for the problem that minimizes the overall routing costs and for the model that minimizes the length of the longest route. An exact branch-and-cut algorithm is presented for each considered model, where violated constraints of both types are separated in polynomial time. Despite the difficulty of the problems, the numerical results from a series of computational experiments with various types of instances illustrate a quite good behavior of the algorithms. When the overall routing costs are minimized, over 43 % of the instances were optimally solved at the root node, and 95 % were solved at termination, most of them with a small additional computational effort. When the length of the longest route is minimized, over 25 % of the instances were optimally solved at the root node, and 99 % were solved at termination.Peer ReviewedPostprint (author's final draft

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

New models and algorithms for several families of Arc Routing Problems

Some of the most common decisions to be taken within a logistic systems at an operational level are related to the design of the vehicle routes. Vehicle Routing Problems and Arc Routing Problems are well-known families of problems addressing such decisions. Their main difference is whether service demand is located at the vertices or the edges of the operating network. In this thesis we focus on the study of several arc routing problems. We concentrate on three families of problems. The first family consists of Multi Depot Rural Postman Problems, which are an extension of Rural Postman Problems where there are several depots instead of only one. The second family of problems that we study are Location-Arc Routing Problems, in which the depots are not fixed in advance, so their location becomes part of the decisions of the problem. We finally study Target-Visitation Arc Routing Problems, where the service is subject to an ordering preference among the connected components induced by demand arcs. Different models are studied for each considered family. In particular, two different Multi Depot Rural Postman Problem models are considered, which differ in the objective function: the minimization of the overall transportation cost or the minimization of the makespan. Concerning Location-Arc Routing Problems, we study six alternative models that differ from each other in their objective function, whether there is an upper bound on the number of facilities to be located, or whether there are capacity constraints on the demand that can be served from selected facilities. Finally, two Target-Visitation Arc Routing Problem models are studied, which differ from each other in whether or not it is required that all the required edges in the same component are visited consecutively. The aim in this thesis is to provide quantitative tools to the decision makers to identify the best choices for the design of the routes. To this end and for each considered problem, we first study and analyze its characteristics and properties. Based on them we develop different Integer Linear Programming formulations suitable for being solved trough branch-and-cut. Finally, all formulations are tested trough extensive computational experience. In this sense, for Multi Depot Rural Postman Problems and Location-Arc Routing Problems we propose natural modeling formulations with three-index variables, where variables are associated with edges and facilities. For some of the models we also present alternative formulations with only two-index variables, which are solely associated with edges. Finally, for the Target-Visitation Arc Routing Problems we propose three different formulations, two alternative formulations for the general case, and one for the clustered version, where all the edges in the same components are served sequentially, which exploits some optimality conditions of the problem.Algunes de les decisions més habituals que es prenen en un sistema logístic a nivell operatiu estan relacionades amb el disseny de rutes de vehicles. Els coneguts Vehicle Routing Problems i Arc Routing Problems són famílies de problemes que s'ocupen d'aquest tipus de decisions. La principal diferència entre ambdós recau en si la demanda de servei es troba localitzada als vèrtexs o a les arestes de la xarxa. Aquesta tesi es centra en l'estudi de diversos problemes de rutes per arcs. Ens centrem en tres famílies de problemes. La primera família consisteix en els Multi Depot Rural Postman Problems, que són una extensió del Rural Postman Problem on hi ha diversos dipòsits en lloc d'un de sol. La segona família de problemes que estudiem són els Location-Arc Routing Problems, en els quals els dipòsits no estan fixats amb antelació i, per tant, la seva ubicació esdevé part de les decisions a prendre en el problema. Finalment, estudiem els Target-Visitation Arc Routing Problems, on el servei està subjecte a una preferència d'ordenació entre les components connexes induïdes pels arcs amb demanda. S'estudien diferents models per a cadascuna de les famílies considerades. En particular, es consideren dos models diferents per al Multi Depot Rural Postman Problem, que es diferencien en la funció objectiu: la minimització del cost general de transport o la minimització de la ruta més llarga. Pel que fa als Location-Arc Routing Problems, estudiem sis models alternatius que difereixen en la seva funció objectiu, considerant si hi ha un límit màxim sobre la quantitat de dipòsits a ubicar o si hi ha restriccions de capacitat sobre la demanda que es pot servir des dels dipòsits seleccionats. Finalment, s'estudien dos models de Target-Visitation Arc Routing Problem, que es diferencien en si es necessari que totes les arestes requerides en la mateixa component es visitin de forma consecutiva. L'objectiu d'aquesta tesi és proporcionar eines quantitatives als responsables, que permetin identificar les millors opcions de disseny de les rutes. Per això, i per a cadascundels problemes considerats, primer estudiem i analitzem les seves característiques i propietats. A partir d'aquestes, desenvolupem diferents formulacions de Programació Lineal Entera, adequades per a la seva solució mitjançant un branch-and-cut. Finalment, totes les formulacions són provades mitjançant un ampli testeig computacional. En aquest sentit, per als Multi Depot Rural Postman Problems i els Location-Arc Routing Problems, proposem formulacions naturals amb variables de tres índexs, on les variables estan associades a les arestes i als dipòsits. Per a alguns dels models també presentem formulacions alternatives, amb variables de només dos índexs, que només estan associades a les arestes. Finalment, per als Target-Visitation Arc Routing Problems proposem tres formulacions diferents, dues formulacions alternatives per al cas general i una per a la versió en clúster, on totes les arestes de la mateixa component es serveixen seqüencialment, cosa que explora algunes condicions d'optimització pròpies.Algunas de las decisiones más habituales que se toman en un sistema logístico a nivel operativo están relacionadas con el diseño de rutas de vehículos. Los conocidos Vehicle Routing Problems y Arc Routing Problems son familias de problemas que se ocupan de este tipo de decisiones. La principal diferencia entre ambas reside en si la demanda de servicios está localizada en los vértices o en las aristas de la red. Esta tesis se centra en el estudio de diversos problemas de rutas por arcos. Nos centramos en tres familias de problemas. La primera familia consiste en los Multi Depot Rural Postman Problems, que son una extensión del Rural Postman Problem donde hay varios depósitos en lugar de solamente uno. La segunda familia de problemas que estudiamos son los Location-Arc Routing Problems, en los que los depósitos no están fijados con antelación y, por lo tanto, su ubicación se convierte en parte de las decisiones a tomar en el problema. Finalmente, estudiamos los Target-Visitation Arc Routing Problems, donde el servicio está sujeto a una preferencia de ordenación entre las componentes conexas inducidas por los arcos con demanda. Se estudian diferentes modelos para cada una de las familias consideradas. En particular, se consideren dos modelos diferentes para el Multi Depot Rural Postman Problem que se diferencian en la función objetivo: la minimización del coste general de transporte o la minimización de la ruta más larga. En cuanto a los Location-Arc Routing Problems, estudiamos seis modelos alternativos que difieren en su función objetivo, en si hay un limite máximo sobre la cantidad de depósitos a ubicar, o en si hay restricciones de capacidad sobre la demanda que se puede servir desde los depósitos seleccionados. Finalmente, se estudian dos modelos de Target-Visitation Arc Routing Problem, que se diferencian en si es necesario que todas las aristas requeridas en la misma componente se visiten de forma consecutiva. El objetivo de esta tesis es proporcionar herramientas cuantitativas a los responsables, que permitan identificar las mejores opciones de diseño de las rutas. Por ello, y para cada uno de los problemas considerados, primero estudiamos y analizamos sus características y propiedades. A partir de estas, desarrollamos diferentes formulaciones de Programación Lineal Entera, adecuadas para su solución mediante un branch-and-cut. Finalmente, todas las formulaciones son probadas mediante un amplio testeo computacional. En este sentido, para los Multi Depot Rural Postman Problems y los Location-Arc Routing Problems, proponemos formulaciones naturales con variables de tres índices, donde las variables están asociadas a las aristas y a los depósitos. Para algunos de los modelos también presentamos formulaciones alternativas con variables de sólo dos índices, que sólo están asociadas a las aristas. Finalmente, para los Target-Visitation Arc Routing Problems proponemos tres formulaciones diferentes, dos formulaciones alternativas para el caso general y una para la versión en clúster, donde todas las aristas de la misma componente se sirven secuencialmente, lo que explora algunas condiciones de optimización propia

On the collaboration uncapacitated arc routing problem

This paper introduces a new arc routing problem for the optimization of a collaboration scheme among carriers. This yields to the study of a profitable uncapacitated arc routing problem with multiple depots, where carriers collaborate to improve the profit gained. In the first model the goal is the maximization of the total profit of the coalition of carriers, independently of the individual profit of each carrier. Then, a lower bound on the individual profit of each carrier is included. This lower bound may represent the profit of the carrier in the case no collaboration is implemented. The models are formulated as integer linear programs and solved through a branch-and-cut algorithm. Theoretical results, concerning the computational complexity, the impact of collaboration on profit and a game theoretical perspective, are provided. The models are tested on a set of 971 instances generated from 118 benchmark instances for the Privatized Rural Postman Problem, with up to 102 vertices. All the 971 instances are solved to optimality within few seconds.Peer Reviewe