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

Pemodelan Penentuan Rute Truk Tangki Untuk Optimalisasi Permasalahan Penyiraman Taman Kota Di Surabaya

Berdasarkan UU No 26 Tahun 2007, proporsi minimal Ruang Terbuka Hijau (RTH) adalah 30% dari luas wilayah kota yang terdiri dari 20% RTH publik dan 10% RTH privat. Untuk menjalankan peraturan tersebut, Pemerintah Kota Surabaya sedang giat menambah jumlah RTH publik dengan membuat taman kota dan dikelola oleh Dinas Kebersihan dan Ruang Terbuka Hijau (DKRTH) Kota Surabaya. Dengan jumlah RTH yang semakin besar, maka dibutuhkan perawatan dan pemeliharaan, salah satunya adalah dengan melakukan penyiraman yang rutin dilakukan setiap hari. Permasalahan yang sering dihadapi oleh DKRTH Surabaya adalah menentukan rute truk yang dapat mengoptimalkan waktu tempuh. Banyak variabel yang dapat mempengaruhi, antara lain demand, jumlah kendaraan, kapasitas kendaraan, time windows, jam kerja operasi dan rute angkut kendaraan. Namun pada praktiknya, banyaknya jumlah lokasi penyiraman, rute dan penugasan area service yang tidak merata seringkali mengakibatkan overtime. Overtime ini berimbas pada jam kerja shift berikutnya. Penugasan dan penentuan rute pada truk tangki penyiraman termasuk dalam sebuah permasalahan NP-hard, yaitu sulit diselesaikan dengan menggunakan metode konvensional dan membutuhkan waktu komputasi yang lama. Permasalahan optimasi rute truk penyiraman secara matematis termasuk dalam Vehicle Routing Problem (VRP). Prinsip dasar VRP berkaitan dengan kunjungan setiap titik hanya dilakukan satu kali dirasa kurang cocok untuk menyelesaikan permasalahan ini, sehingga perlu dimodifikasi dengan tambahan split service agar pembagian tugas antar kendaraan merata. Sehingga memenuhi batasan constraint, terutama permasalahan batasan waktu (time windows). Untuk dapat menyelesaikan suatu permasalahan pada proses penjadwalan dan penentuan rute dapat menggunakan metode optimasi dengan pendekatan metaheuristik menggunakan algoritma Ant Colony Optimization. Tujuan dari penelitian ini adalah meminimasi waktu total penyiraman dan menghasilkan model yang terkait dengan jumlah minimum kendaraan dan rute dalam melakukan proses pengisian dan penyiraman dari depot menuju ke taman. Penelitian ini membangun model dengan empat skenario dalam proses penyiraman taman. Skenario pertama dengan menggunakan split service untuk melakukan penyiraman taman, skenario kedua menggunakan split service dan saving value, skenario ketiga menggunakan saving value tanpa split service (Hard No Split), dan skenario keempat menggunakan saving value tanpa split service (Soft No Split). Keempat skenario memberikan rekomendasi penggunaan 8 truk dari 9 truk yang tersedia. Jika dilihat dari fungsi tujuan, skenario 4 lebih unggul dari sisi total waktu tempuh dan menghasilkan penghematan sebesar 31,18% dari total waktu tempuh rute existing. ===================================================================================================================================== Based on Law No. 26/2007, the minimum proportion of Green Open Space is 30% of the city area consisting of 20% of public green open space and 10% private green open space. To carry out these regulations, the Surabaya City Government is actively increasing the number of public green space by creating city parks and is managed by Dinas Kbersihan dan Ruang Terbuka Hijau (DKRTH) Surabaya. With the ever-increasing amount of green open space, care and maintenance are needed, one of which is to do routine watering every day. The problem often faced by DKRTH Surabaya is determining truck routes that can optimize travel time. Many variables can affect, among others, demand, number of vehicles, vehicle capacity, time windows, operating hours and vehicle transport routes. But in practice, a large number of watering locations, irregular routes, and uneven service area assignments often result in overtime. This overtime impacts the next shift work hours. Assigning and determining the route on the watering tank truck is included in an NP-hard problem, which is difficult to solve using conventional methods and requires a long computational time. Problems with optimizing the route of the watering truck mathematically included in the Vehicle Routing Problem (VRP). The basic principle of VRP about visiting each point only once is not suitable to solve this problem, so it needs to be modified with the addition of split service so that the division of tasks between vehicles is evenly distributed. So that it meets the constraints, especially the problem of time constraints (time windows). To be able to solve a problem in the process of scheduling and determining routes can use the optimization method with a metaheuristic approach using the Ant Colony Optimization algorithm. The purpose of this study is to minimize the total watering time and produce a model related to the minimum number of vehicles and routes in the process of filling and watering from the depot to the park. This research builds a model with four scenarios in the process of watering the park. The first scenario uses split service to do garden watering, the second scenario uses split service and saving value, the third scenario uses saving value without split service (Hard No Split), and the fourth scenario uses saving value without split service (Soft No Split). The four scenarios provide recommendations for using 8 of the 9 available trucks. If viewed from the objective function, scenario 4 is the best in terms of total travel time and results in savings of 31.18% of the total travel time of existing routes

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

The Hierarchical Mixed Rural Postman Problem

[DE] In this paper, we study a generalization of the Hierarchical Chinese Postman Problem on a mixed graph where only a subset of arcs and edges require a service to be accomplished following a hierarchical order. The problem, called the Hierarchical Mixed Rural Postman Problem, also generalizes the Rural Postman Problem and thus is NP-hard. We propose a new mathematical formulation, and introduce two effective solution algorithms. The first procedure is a matheuristic that is based on the exact solution of a variant of the Mixed Rural Postman Problem for each hierarchy. The second approach is a tabu search algorithm based on different improvement and diversification strategies. Computational results on an extended set of instances show how the proposed solution methods are quite effective and efficient when compared to the solutions of a branch-and-cut algorithm stopped after one hour of computation.The work by Angel Corberan, Isaac Plana, and Jose M. Sanchis was supported by the Spanish Ministerio de Economia y Competitividad and Fondo Europeo de Desarrollo Regional (FEDER) through [project MTM2015-68097-P] (MINECO/FEDER) and by the Generalitat Valenciana [project GVPROMETEO2013-049].Colombi, M.; Corberán, Á.; Mansini, R.; Plana, I.; Sanchís Llopis, JM. (2017). The Hierarchical Mixed Rural Postman Problem. Transportation Science. 51(2):755-770. https://doi.org/10.1287/trsc.2016.0686S75577051

The Hierarchical Mixed Rural Postman Problem: Polyhedral analysis and a branch-and-cut algorithm

[EN] The Hierarchical Mixed Rural Postman Problem is defined on a mixed graph where arcs and edges that require a service are divided into clusters' that have to be serviced in a hierarchical order. The problem generalizes the Mixed Rural Postman Problem and thus is NP-hard. In this paper, we provide a polyhedral analysis of the problem and propose a branch-and-cut algorithm for its solution based on the introduced classes of valid inequalities. Extensive computational experiments are reported on benchmark instances. The exact approach allows to find the optimal solutions in less than 1 hour for instances with up to 999 vertices, 2678 links, and five clusters.The work by Angel Corberan, Isaac Plana, and Jose M. Sanchis was supported by the Spanish Ministerio de Economia y Competitividad and Fondo Europeo de Desarrollo Regional (FEDER) through project MTM2015-68097-P (MINECO/FEDER) and by the Generalitat Valenciana (project GVPROMETEO2013-049).Colombi, M.; Corberán, A.; Mansini, R.; Plana, I.; Sanchís Llopis, JM. (2017). The Hierarchical Mixed Rural Postman Problem: Polyhedral analysis and a branch-and-cut algorithm. European Journal of Operational Research. 257(1):1-12. https://doi.org/10.1016/j.ejor.2016.07.026S112257

The Hierarchical Mixed Rural Postman Problem: Polyhedral analysis and a branch-and-cut algorithm

The Hierarchical Mixed Rural Postman Problem is defined on a mixed graph where arcs and edges that require a service are divided into clusters' that have to be serviced in a hierarchical order. The problem generalizes the Mixed Rural Postman Problem and thus is NP-hard. In this paper, we provide a polyhedral analysis of the problem and propose a branch-and-cut algorithm for its solution based on the introduced classes of valid inequalities. Extensive computational experiments are reported on benchmark instances. The exact approach allows to find the optimal solutions in less than 1 hour for instances with up to 999 vertices, 2678 links, and five clusters