# capacitated arc routing problem

## Top PDF capacitated arc routing problem:

### The mixed capacitated arc routing problem with non-overlapping routes

Real world applications for vehicle collection or delivery along streets usually lead to arc routing problems, with additional and complicating constraints. In this paper we focus on arc routing with an additional constraint to identify vehicle service routes with a limited number of shared nodes, i.e. vehicle service routes with a limited number of intersections. This constraint leads to solutions that are better shaped for real application purposes. We propose a new problem, the bounded overlapping MCARP (BCARP), which is deﬁned as the mixed capacitated arc routing problem (MCARP) with an additional constraint imposing an upper bound on the number of nodes that are common to diﬀerent routes. The best feasible upper bound is obtained from a modiﬁed MCARP in which the minimization criteria is given by the overlapping of the routes. We show how to compute this bound by solving a simpler problem. To obtain feasible solutions for the bigger instances of the BCARP heuristics are also proposed. Computational results taken from two well known instance sets show that, with only a small increase in total time traveled, the model BCARP produces solutions that are more attractive to implement in practice than those produced by the MCARP model.
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### A mathematical modeling proposal for a Multiple Tasks Periodic Capacitated Arc Routing Problem

The countless accidents and incidents occurred at dams at the last years, propelled the development of politics related with dams safety. One of the strategies is related to the plan for instrumentation and monitoring of dams. The monitoring demands from the technical team the reading of the auscultation data, in order to periodically monitor the dam. The monitoring plan of the dam can be modeled as a problem of mathematical program of the periodical capacitated arcs routing program (PCARP). The PCARP is considered as a generalization of the classic problem of routing in capacitated arcs (CARP) due to two characteristics: 1) Planning period larger than a time unity, as that vehicle make several travels and; 2) frequency of associated visits to the arcs to be serviced over the planning horizon. For the dam's monitoring problem studied in this work, the frequent visits, along the time horizon, it is not associated to the arc, but to the instrument with which is intended to collect the data. Shows a new problem of Multiple tasks Periodic Capacitated Arc Routing Problem and its elaboration as an exact mathematical model. The new main characteristics presented are: multiple tasks to be performed on each edge or edges; different frequencies to accomplish each of the tasks; heterogeneous fleet; and flexibility for more than one vehicle passing through the same edge at the same day. The mathematical model was implemented and examples were generated randomly for the proposed model's validation.
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### REPOSITORIO INSTITUCIONAL DA UFOP: A cooperative coevolutionary algorithm for the multi-depot vehicle routing problem.

As far as we know, the coevolutionary paradigm has never been applied to the MDVRP. With regard to vehicle routing in general, a large scale capacitated arc routing problem is addressed in Mei, Li, and Yao (2014) using a coevolutionary algorithm. In this work, the routes are grouped into different subsets to be optimized and prob- lem instances with more than 300 edges are solved. A multi-objective capacitated arc routing problem is also studied in Shang et al. (2014). A coevolutionary algorithm is presented in Wang and Chen (2013b) for a pickup and delivery problem with time windows. To minimize the number of vehicles and the total traveling distance, the authors use two populations: one for diversiﬁcation purposes and the other for intensiﬁcation purposes. In the scheduling domain, a competi- tive coevolutionary quantum genetic algorithm for minimizing the makespan of a job shop scheduling problem is reported in Gu, Gu, Cao, and Gu (2010).
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### OPTIMIZATION MODEL FOR VEHICLE ROUTING AND EQUIPMENT REPLACEMENT IN FARM MACHINERY

ABSTRACT: An equipment replacement decision takes into account economic engineering models based on discounted cash flow (DCF) such as the Annual Equivalent Cost (AEC). Despite a large number of researches on industrial assets replacement, there is a lack of studies applied to farm goods. This study aimed at assessing an alternative model for economic decision analysis on farm machinery replacement, with no restrictions on the number of replacements and assessed goods during a defined timeline. The results of the hybrid model based on the combination of the vehicle routing problem and the equipment replacement problem (RVPSE) applied to three different farm tractors showed the model reliability, providing a wider range of decisions for management support. KEYWORDS: economic engineering, annual equivalent cost, integer linear programming.
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### Pesqui. Oper. vol.33 número1

The Figure 1 presents the citations received by the first published article of Horacio, Bitran and Yanasse (1982), Computational Complexity of the Capacitated Lot Size Problem has been cited by a large quantity of articles all over the world. The data used by the next two figures were obtained by SUCUPIRA, Alves, Yanasse and Soma (2011), from Lattes Platform and from the ISI Web of Science for the citations. The diameter of each disk is proportional to the citations volume received by that paper.

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### J. Braz. Comp. Soc. vol.14 número4

This paper presents a mathematical model and a GRASP heuristic embedded with a path relinking strat- egy to approximately solve the MPCLSP with multiple items and multiple periods. The solution method is an extension of previous research of Nascimento et al. [14] on the same problem without the setup carry-over. To treat the setup carry-over we modified the local search of the GRASP heuristic adding some moves in its neighbor- hood. The moves used were based on a modified version of the approach of Gopalakrishnan et al. [9] to consider the various plants. In order to test and evaluate the ef- ficiency of the proposed heuristic with setup carry-over considering a single plant, we compared it with the single- plant tabu search heuristic proposed by Gopalakrishnan et al. [9]. For such, we applied our heuristic to the single- plant instances from [24], i.e., the same set of instances used by Gopalakrishnan et al. [9] in their tests. We also compared the solutions of the heuristic without setup carry-over with the solutions of the Lagrangian heuristic proposed by Trigeiro et al. [24]. Regarding the multi-plant experiment, tests were performed using the data set pro- posed in [14], that is based on the instances from [23] for the CLSP with parallel machines. Computational tests indicate that the setup carry-over showed good perform- ance for both the single-plant and the multi-plant prob- lems with a slight increase of computational time in the latter case. Moreover, in both cases the strategy achieved better solutions for all instances.
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### Vehicle routing and tour planning problem: a cement industry case study

the clients [5]. Industry 4.0 has also a great impact in the transportation sector as well. Using ICT, it is possible to develop a more efficient and profitable transportation system. The work presented in this dissertation is developed under a scientific project, that aims to develop systems for smart plants, specifically cement plants. The UH4SP – Unified Hub for Smart Plants – aims to develop simulation models and heuristic optimization models to take cement plants to another level [6]. More specifically, one of the main goals of the project is the development of architectures of software and methodologies orientated to services, promoting the corporative and aggregate vision of the operations in each one of the cement plants dispersed by several geographic regions [7]. The UH4SP addresses several segments of the supply chain of a cement plant. The problem addressed in this dissertation is the one dealing with the management of the trucks entering the plant.
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### Pesqui. Oper. vol.37 número2

cannot be applied to this problem due to two main reasons: multiple recipes and storage control. Figure 5 illustrates ten different recipes used to produce product I18. These recipes are directly associated with the reactors (which from now on will be referred to as machines), that is, given a recipe number it is simple to determine in which machine this recipe has to be processed. It can be observed that feedstocks F77, F90, F117, and F129 are consumed by all recipes while feedstocks F7, F32, F137, and F139 can be used in only some recipes. Therefore, if the recipes of this product were aggregated in one product, the planning would determine how much of these last four feedstocks is necessary to meet the demand of product I18. On the other hand, the number of intermediate products kept in storage tanks is indispensable as it should be limited to the amount of storage tanks available. In addition, it is necessary to control the quantity of each designated product for the storage tank, ensuring that its limits are not violated, and thus ensuring that the solutions found are similar to those used in practice.
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### The Multi-commodity One-to-one Pickup-and-delivery Traveling Salesman Problem with Path Duration Limits

The m-t-PDTSP is inspired by the wealth of research done within pickup and delivery problems, Parragh et al. [16] and Berbeglia et al. [4] both give good introductions to these problems, reviews existing literature and proposes classification schemes. In the classification of Parragh et al. [16] the m-t-PDTSP is a Single Dial A Ride Problem (SDARP) excluding Time Windows and with the important difference that no depot is required, i.e. cargo can be carried through the depot. In the classification of Berbeglia et al. [4] the m-t-PDTSP is a [1-1|PD|1], 1-1 as each commodity has one origin and one destination, PD as each vertex must be visited exactly once for combined pickup and delivery and 1 as a single service is generated, but again an important difference from related problems is the lack of depot. The multi-commodity one-to-one pickup-and-delivery traveling salesman problem (m-PDTSP) in considered in Hernández- Pérez and Salazar-González [11], the problem is formulated and solution methods based on bender’s decomposition are implemented. The m-t-PDTSP is an extension of the m- PDTSP, with the addition of path duration, no depot or allowing cargo to be carried through it and allowing partial carriage of flow, which has an associated revenue. An often encountered type of subproblem in pickup and delivery prob- lems are Shortest Path Problems with Resource Constraints (SPPRC) which is also found in a decomposition of the m- t-PDTSP. For a review on SPPRC problems and algorithms please refer to Irnich and Desaulniers [12].
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### Optimized Crossover Genetic Algorithm for Vehicle Routing Problem with Time Windows

Abstract: Problem statement: In this study, we considered the application of a genetic algorithm to vehicle routing problem with time windows where a set of vehicles with limits on capacity and travel time are available to service a set of customers with demands and earliest and latest time for serving. The objective is to find routes for the vehicles to service all the customers at a minimal cost without violating the capacity and travel time constraints of the vehicles and the time window constraints set by the customers. Approach: We proposed a genetic algorithm using an optimized crossover operator designed by a complete undirected bipartite graph that finds an optimal set of delivery routes satisfying the requirements and giving minimal total cost. Various techniques have also been introduced into the proposed algorithm to further enhance the solutions quality. Results: We tested our algorithm with benchmark instances and compared it with some other heuristics in the literature. The results showed that the proposed algorithm is competitive in terms of the quality of the solutions found. Conclusion/Recommendations: This study presented a genetic algorithm for solving vehicle routing problem with time windows using an optimized crossover operator. From the results, it can be concluded that the proposed algorithm is competitive when compared with other heuristics in the literature.
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### Modelos matemáticos baseados no Time Dependent Vehicle Routing Problem para planejamento da logística urbana sob a ótica ambiental

Resumo: Empresas que operam com logística urbana direcionam seus esforços para soluções que buscam reduções de custo, desconsiderando questões ambientais. Isso ocorre em função da crença que soluções ambientalmente corretas são mais caras. No entanto, com as crescentes preocupações ambientais, as empresas têm levado em conta os fatores ambientais buscando a responsabilidade social. Assim, este artigo apresenta dois modelos matemáticos, ambos baseados no Time Dependent Vehicle Routing Problem (TDVRP), sendo um com objetivo de avaliar a redução do tempo das rotas e o outro com objetivo avaliar a redução da emissão de poluentes. Para testar o modelo, foi realizada uma aplicação real de uma empresa de distribuição de alimentos na região metropolitana de Vitória, ES. Usou-se o CPLEX 12.6 para rodar os modelos propostos com cenários baseados em dados reais da empresa. Os resultados mostraram que a solução com viés ambiental pode ser financeiramente vantajosa para a empresa.
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### A multi agent based system to enable dynamic vehicle routing

In a routing process, the time and vehicle speed re- lated data – which can be collected by telematics systems in the vehicle – are critical to determining routing anomalies. Analysis is conducted based on this data, problems are iden- tified, and solutions suggested. Novaes et al. (2012) apply a fault detection and diagnosis model to analyse data and estimate the number of pick-ups that will not be performed based on probabilities. In the event of an excessive service demand, the authors suggest that the transportation system (meaning the agents) should send out information to other vehicles operating in the area and to the warehouse asking help to perform the exceeding tasks. If there is no vehicle in the area to meet this demand, the central warehouse may appoint one or more externally owned vehicles (or third party) to perform the backlogged tasks.
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### Resistência de genótipos de feijoeiro a Zabrotes subfasciatus (Bohemann, 1833) (Coleoptera: Bruchidae).

Desta forma, observa-se que a resistência dos genótipos que contêm arcelina não está associada à não- preferência para oviposição ou viabilidade dos ovos. No caso de ‘Arc.1’, a atividade tóxica da proteína arcelina sobre Z. subfasciatus está relacionada à sua ligação aos gliconjugados da superfície do trato digestivo do inseto, ocasionando danos às células epiteliais, alterando a sua estrutura e penetrando na hemocele (Paes et al., 2000).

### Repositório Institucional UFC: Um Algoritmo para o problema de roteirização de veículos com frota heterogênea

In logistic distribution process is necessary deliver goods and services to geographically dispersed customers, in this process is found the Vehicle Routing Problem (VRP). The Vehicle Routing Problem (VRP), is the name of a problems class to define a sequence of visits to customers geographically dispersed with a finite set of vehicles from a common depot. To solve this problem, a algorithm was developed using the Variable Neighborhood Descent (VND) metaheuristic, comparing the results with some literature instances. The problem applies in practice on auto parts collection, industrial trash collection, residential trash collection, street cleaning, and other situations. The VRPs received many attention in the lasts years due to applicability and the economic importance in efficient strategies determination, with the objective of reduce the operational costs. The results of proposed algorithm were competitive to the algorithms studied. However, overcoming some of these algorithms in only one instance of the eight instances used.
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### A matheuristic for the consistent vehicle routing problem with service level agreements: a case study in the pharmaceutical distribution sector

Despite the advantages of adopting consistent routes, few papers have addressed the conVRP and most approaches resort to approximation methods. Groer et al. (2009) formulate the conVRP as a Mixed-Integer Program (MIP) and improve the algorithm used by Li et al. (2005) to solve very large VRPs. A real-world data set is used to generate instances with up to 700 customers which are solved by the algorithm. The obtained consistent routes are less than 10% longer on average, compared to inconsistent routes. Recently, Ridder (2014) shows that some optimal solu- tions provided by Groer et al. (2009) are not feasible because service times were not considered. The author develops an algorithm that improves solutions provided by the latter paper. Tarantilis et al. (2012) propose a Tabu Search (TS) algorithm to iteratively generate template routes and to improve the daily routes that are derived from the template routes. These routes are used as the basis to construct the vehicle routes and service schedules for both frequent and non-frequent customers over multiple days. The best reported cumulative and mean results over all conVRP- benchmark instances is improved. Kovacs et al. (2014b) construct template routes by means of an Adaptive Large Neighbourhood Search (ALNS), which uses several operators in order to destroy and repair a given solution. It is shown that solving daily VRPs may lead to inconsistent routes whereas consistent long-term solutions can be generated by using historic template routes. Kovacs et al. (2014a) state that assigning one driver to each customer and bound the variation in the arrival times over a given planning horizon may be too restrictive in some applications. They propose the generalized conVRP in which a customer is visited by a limited number of drivers and the vari- ation in the arrival times is penalized in the objective function. A Large Neighbourhood Search (LNS) metaheuristic generates solutions without using template routes. The computational results on different variants of the conVRP prove the efficiency of the algorithm, as it outperforms all published algorithms. Sungur et al. (2010) consider a real-world courier delivery problem where customers appear probabilistically. Although the authors do not call it a conVRP, their assump- tions are completely in line with this type of problem. The proposed approach generates master plans and daily schedules with the objective of maximizing both the coverage of customers and the similarity between the routes performed in each day. In order to deal with uncertain service times, it is assumed that the master plans serves frequent customers with the worst-case service times found in historical data. Once again, a mathematical formulation is proposed but the real-world problem is tackled by means of a two-phase heuristic based on insertion and TS.
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### A multi-objective Pareto ant colony algorithm for the Multi-Depot Vehicle Routing problem with Backhauls

The MDVRPB can be defined as the following graph theory problem. Let � = (�, �) be a complete undirected graph, where � = {1. . . . . �} is the set of vertices, and � is the set of edges. The set � is partitioned into two subsets: the set of customers � = {1. . . . . �} and the set of potential depots � = {1. . . . . �}. Additionally, the set � is divided into a subset of Linehaul nodes (Linehaul customers - �), and the Backhaul nodes (Backhaul customers – �). Therefore, � = � ∪ �. The Linehaul customers ask for delivering products while Backhaul customers require the collection of products. Each customer has a nonnegative amount � � ( � ∈ �) of product to be delivered (� ∈ �) or to be picked up (� ∈ �). Each depot has a fictitious demand. i.e. � � = 0, with � ∈ �. A set of � identical vehicles with a given capacity � � is initially placed at each depot. It must be clarified that all vehicles are not necessarily used. For each
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### en 0104 530X gp 0104 530X1767 16

There are about 10 company’s proper terminals along the Brazilian coast, with around 20 berths in total, distributed heterogeneously by these terminals. The berths are speciic locations inside maritime terminals, where ships dock in order to perform the loading and unloading of cargo. Each one of the berths presents physical restrictions for draft and LOA that must be met so that the ships are allowed to berth (each ship occupies a single berth). However, in practice, the draft restriction may be relaxed in some speciic cases, and this is done by limiting the load on board to a value lower than the maximum capacity of the ship. Both platforms and terminals are technically called and referred to as “operating sites”. The pairs of pickup and delivery are pre-established by tactical planning, but routing and scheduling of ships is conigured as a decision to be supported by the model. This modeling approach is called “origin-destination”, since each one of the origins (platforms) is pre-matched with its respective destination (terminal). Importantly, this pickup and delivery problem differs from most cases in relation to the maritime transport of oil, which typically involve large distances. In most cases of oil exploration around the world, the transport occurs in several producing companies for several reineries with different rules and responsibility governing the freight. In Brazil, the same company produces, reines and plans the transportation, which considerably increases the possibilities of logistical gains. It is possible to ind similar characteristics in the operations performed in the North Sea and the Gulf of Mexico.
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### Multiple Charging Station Location-Routing Problem with Time Window of Electric Vehicle

A network is normally represented by a graph that is composed of a set of nodes and edges. The task of network clustering is to divide a network into different clusters based on certain principles. Each cluster is called a community. The LRP combines two classical planning tasks in logistics, that is, optimally locating depots and planning vehicle routes from these depots to geographically scattered customers [8]. These two interdependent problems have been addressed separately for a long time, which often leads to suboptimal planning results. The idea of LRP started in the 1960s, when the interdependence of the two problems was pointed out [9,10]. The variants of the LRP have been frequently studied in recent years. Such variants include the capacitated LRP (CLRP) with constraints on depots and vehicles [20,21], the LRP with multi-echelon of networks [11,12], the LRP with inventory management [13,14], and the LRP with service time windows [15–17]. For the variant problem with time windows, Semet and Taillard incorporated the time window constraint to the LRP for a special case of the road–train- routing problem [15]. Zarandi et al. studied the CLRP with fuzzy travel time and customer time windows, in which a fuzzy chance-constrained mathematical program was used to model the problem [16]. Later, they extended the problem by adding the fuzzy demands of customers and developed a cluster-first route-second heuristic to solve the problem [17]. A detailed review of the LRP variants can be found in two recent surveys [18,19].
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### Branch-and-Cut and GRASP with Hybrid Local Search for the Multi-Level Capacitated Minimum Spanning Tree Problem

The purpose of this work is to present efficient algorithms to compute tight lower bounds and high quality upper bounds for the MLCMST problem. We propose a branch-and-cut algorithm capable to solve instances with 50 nodes, considering different locations for the central node, in a reasonable amount of time. The algorithm provides tight lower bounds for larger instances by solving relaxations on the root node. We also use the branch-and-cut within GRASP to evaluate subproblems during the construction and local search phases. This leads to a competitive algorithm to find high quality feasible solutions for the MLCMST problem.
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