13.1 TheVehicleRoutingProblem 177 The contribution of this work is then to define a powerful yet simple cMA capable of competing with the best known approaches for solving CVRP in terms of accuracy (final cost) and computational effort (the number of evalua- tions made). For that purpose, we test our algorithm over the mentioned large selection of instances (160), which will allow us to guarantee deep and mean- ingful conclusions. Besides, we compare our results against the best existing ones in the literature, some of which we even improve. In  the reader can find a seminal work with a comparison between our algorithm and some other known heuristics for a reduced set of 8 instances. In that work, we showed the advantages of embedding local search techniques into a cGA for solving CVRP, since our hybrid cGA was the best algorithm out of all those compared in terms of accuracy and time. Cellular GAs represent a paradigm much simpler to comprehend and customize than others such as tabu search (TS) [97, 249] and similar (very specialized or very abstract) algorithms [37, 207]. This is an important point too, since the greatest emphasis on simplicity and flexibility is nowadays a must in research to achieve widely useful contributions .
In a sequence line the process can be described as follows (see Fig. 2 for a sequence diagram of the procedure described next). First a client or a seller sends an order to the ERP. Typically the order is for the next day although it can be for any future request. Then, at a convenient moment, the ERP manager sends a signal to the i3FR system in order to start the optimization process. This signal goes to the i3FR-Hub which begins by requesting the necessary data from the ERP. In general, the requested data is information relevant to the optimization process which is not yet present in the i3FR-DB. On other words, static data (e.g., client delivery locations, vehicle data) was already fetched by i3FR-Hub and stored in the i3FR-DB, which means that the i3FR-Hub requests the order information (e.g., volumes and transportation categories). Nevertheless, after receiving the data, the i3FR-Hub checks that all necessary data for the optimization process is present. For instance, if a new customer or delivery location is present in the orders then the new information is retrieved from the ERP (delivery location) and the i3FR-Maps is updated. The i3FR-Maps stores the routes between all possible delivery locations, that is, it has a n × n matrix (n being the number of delivery locations) of routes including distances, travel time and corresponding routing directions details. The data in each entry is obtained in a three step procedure. First, MongoDB [Mon15] calculates distances between locations using spherical geometry. This estimation is stored as a ﬁrst approximation to the real distance between locations. Then, prioritized by the previously estimated distances, the i3FR-Maps uses the Open Street Maps Routing Machine (OSRM) [OSR15] to obtain accurate routing data between the delivery locations. Later, the routes present in the solutions returned by the optimizer are retrieved again but this time using Google Maps [Goo15] which takes into consideration other information (e.g., traﬃc reports). The use of the OSRM overcomes the limit of accesses to Google’s API.
From a practical point of view, theproblem being tackled applies to specific sectors that bene- fit from planning their routes according to the previously defined motivations. Companies that put their focus on customer service level, maintain a close relationship with the customer and operate on a tight delivery lead time have the most benefits to withdraw from using a delivery system with consistent routes. Cases of such companies are fairly common in small package distribution industries facing large competition and highly demanding customers, with pharmaceutical and au- tomobile spare parts distribution being the most well-known examples. Other activities in which consistent routing with a service level focus is relevant include home care services, better estab- lished home deliveries, which may be a potential development area for e-commerce operations, and also the transportation of children, elderly or handicapped people. These companies seek for a customer focused environment that leads to more complex and strict service level agreements as a way to increase customer loyalty. However, with stricter service level targets, the number of fail- ures and complaints tends to increase, which often leads to frequent changes to the tactical plan in order to quickly solve these problems. Making solid consistent route plans that will perform well in practice while still being efficient is therefore a very hard task that many companies struggle with. Tools that assist decision-making in these conditions and take the business characteristics in consideration are therefore very useful and desired by practitioners.
tasks and follows the route assigned to it by a vehicle rout- ing problem (VRP) algorithm. Under a static approach, when the activities cycle exceeds regular working hours, thevehicle will return to the warehouse without performing the agreed tasks, which will be fulfilled next day. In some situ- ations, service overload can result in more than one-day backlogs. Delays will certainly result in penalties since there is a service level agreement between the contractor and the third party. Under a dynamic approach, services previously planned to a particular vehicle could be trans- ferred to another one in a specified time window in order to avoid unperformed tasks at the end of a workday. Average travel speed is a parameter used to represent traffic varia- tions, since it is assumed that the time spent on the stops the OEM clients is not affected by traffic conditions.
Abstract: Urban logistics companies are seeking solutions to reduce their cost, but must of them are not paying attention to environmental issues. This is due to the belief that environmentally friendly solutions are more expensive. However, with the growing of environmental concerns, companies have been taking into account the environmental factors, seeking for their social responsibility. Thus, this paper presents two mathematical models, both based on the Time Dependent VehicleRoutingProblem (TDVRP), one to evaluate the reduction in the time of the routes and the other to evaluate the reduction of greenhouse gas emissions. In order to evaluate the model, a real case of a food distribution company in the metropolitan area of Vitória, ES was done. CPLEX 12.6 was used to run both models considering scenarios based on data from a real company. The results showed that environmentally friendly solution may be also financially advantageous for the company.
The goal of the MDVRPB is to determine the routes to be performed from the selected depots to the customers by a fleet of homogeneous vehicles in order to satisfy the demand of the customers (products to be collected or products to be delivered). The objective functions considered for the multiobjective version of the MDVRPB is to minimize the total traveled distance, the total time and the consumed energy. The first objective is the common function considered in the literature related to thevehiclerouting problems. The second objective is obtained by the allowed speed on each edge. In particular, we have considered a random speed between 30 km /hr to 90 km/hr for the complete graph on the benchmarking set of instances. Finally, the third objective is adopted from the idea of gas emission and consumption of energy introduced by Bektaş and Laporte (2011) and Demir et al. (2014).
Abstract: Many cities are facing difficulties in urban mobility and therefore are imposing restrictions on the movement of larger trucks. Thus, logistics companies developed a two level logistics strategy based on Urban Distribution Centers (CDU) that receives larger trucks and split the cargo to put in small trucks to distribute to customers. To support this type of logistics planning, this paper presents an adaptation of a mathematical model based on the Two-echelon capacitated VehicleRoutingProblem (2E-CVRP) to plan the routes from the central depot to the satelites and from these to the clients. The model was applied to thelogistics of Correios in the metropolitan area of the Espírito Santo, Brazil, and instances with up to 4 CDU and 25 clients were tested using CPLEX solver 12.6 obtaining routes for deliveries at both levels.
are abundant in the literature, the application of DM to improve the results of evolutionary algorithms is still scarce. The DM module proposed corresponds to an intensiﬁcation strategy, since it tries to discover good features in the best solutions found so far and to apply them in the generation of new solutions. The addition of the DM module into the GA signiﬁcantly improved this method and the hybrid version with local search (GADMLS), on average, produced the better results. Results could be improved if other interactions between modules and/or a more exhaustive set of experiments were conducted (perhaps, larger running times would beneﬁt the more computationally expensive version—GADMLS). Nonetheless, our proposal looks very promising, specially considering problems in which it is difﬁcult to devise efﬁcient local search algorithms.
In this paper, a bi-objective possibilistic programming model was developed to formulate the VRPTW by considering the customers’ satisfaction. In the proposed mathematical problem, the first objective function was to minimize the sum of a fixed cost related to the number of vehicles and travel distance, and the second objective function considered the customers’ satisfaction by minimizing the gap time between the arrival time and ready time by considering the customers’ priority. In this paper, for solving the proposed problem, two steps were considered; in the first step, the possibilistic proposed model was converted into an equivalent auxiliary crisp model and in the second step, an RMCGP method was employed to attain an approved adjustment solution. The proposed model provides useful awareness to help the DMs in identifying effective parameters and creates an optimal decision closer to reality. The proposed model provides a suitable way to solve bi-objectives decision-making problems, which includes multi-choice of aspiration levels. The customers’ demand was considered as fuzzy numbers. The proposed model was validated by LINGO software. In order to solve the model in large-sized problems, two meta-heuristic algorithms (i.e., simulated annealing (SA) and genetic algorithm (GA)) is used. The results demonstrated that SA outperforms GA in both objective function values and computational times. Finally, to demonstrate the validation of the proposed model, an industrial case study related to the TTC was investigated.
Abstract: Several transportation problems like traffic jam, crowded public transportation, parking shortage and pollution is caused by the actual scenario of urban mobility. The transport of passengers by charter is an alternative to improve the quality of urban mobility avoiding traffic jam and reducing pollution. Several companies offer as a benefit to their employees this type of transport to carry them to the company from their home and vice versa. Thus, it is proposed in this paper an adaptation of a mathematical model based on Open VehicleRoutingProblem (OVRP) for planning the transport of employees by a chartered bus fleet in order to reduce the total cost spent by the company. The model was applied to a company located in Vitória-ES and the results obtained by the model indicated a reduction in the cost of transportation when compared to the currently paid by the company.
Basically we use a Data Mining strategy, in which every new individual has its route analyzed to extract patterns (sequence of customers) within a given range [minP atternSize, maxP atternSize]. Each pattern found is stored in a structure called patternsList along with the frequency it has appeared in the solutions already ana- lyzed. In addition to these information, we also keep record of the average cost of the route in which the pattern was found so as to improve the robustness of the eval- uation criteria that decides how good a pattern is. Therefore we have two types of data to evaluate a pattern: frequence and average cost. Good patterns have high frequency and low average cost. Since cost value is usually much higher than the frequency value, this data must be normalized. Lets call nF requency the normal- ized frequency value, nAvgCost the normalized average cost. Therefore we define qualityIndex = (1 − nAvgCost) + nF requency, as the value used to evaluate the pat- terns, since it considers both measures. The closer to 2 the better. This is not the first time an approach combining a heuristic and a data mining algorithm is proposed for a vehicleroutingproblem. In , Santos et al proposed 4 approaches for a single vehicleroutingproblem, including one that combines a Genetic Algorithm with the data mining algorithm Apriori. Our approach is not based on their approach and is fairly different from the algorithm they developed.
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 . 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- routingproblem . 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 theproblem . Later, they extended theproblem by adding the fuzzy demands of customers and developed a cluster-first route-second heuristic to solve theproblem . A detailed review of the LRP variants can be found in two recent surveys [18,19].
Palavras-chave: Roteamento de veículos; Múltiplos entregadores; Busca Local Iterada; Busca em Vizinhança Grande. Abstract: This paper addresses thevehicleroutingproblem with time windows and multiple deliverymen, a variant of thevehicleroutingproblem which includes the decision of the crew size of each delivery vehicle, besides the usual scheduling and routing decisions. This problem arises in the distribution of goods in congested urban areas where, due to the relatively long service times, it may be dificult to serve all customers within regular working hours. Given this dificulty, an alternative consists in resorting to additional deliverymen to reduce the service times, which typically leads to extra costs in addition to travel and vehicle usage costs. The objective is to deine routes for serving clusters of customers, while minimizing the number of routes, the total number of assigned deliverymen, and the distance traveled. Two metaheuristic approaches based on Iterated Local Search and Large Neighborhood Search are proposed to solve this problem. The performance of the approaches is evaluated using sets of instances from the literature.
In this article, a vehiclerouting with backup provisioning approach is proposed for sustainable urban mobility with efficient use of resources. Besides formalizing mathematically theproblem, a heuristic is proposed that allows solutions to be obtained more quickly. Thevehiclerouting with backup provisioning approach is able to provide higher quality of service, regarding time for the backup vehicle to arrive, and it avoids new schedules/vehicles/drivers for backup provisioning. Although routes become longer, to ensure backup, thresholds on time for backup to arrive can be adequately set to keep such distances acceptable. However, since more stops are being served, the increase of routes should not be seen just as a penalty. Regarding the neighborhood formation approach and local search procedures, incorporated in the heuristic, these have proven to be effective. Route distances reduced by approximately 30%. In summary, the overall perception is that the proposed heuristic is able to effectively solve thevehiclerouting with backup provisioning problem under consideration. As future work, we expect to study fleet planning considering vehicles of different sizes. Acknowledgments: This work was supported by FCT (Foundation for Science and Technology) from Portugal within CEOT (Center for Electronic, Optoelectronic and Telecommunications) and the UID/MULTI/00631/2013 project.
In logistic distribution process is necessary deliver goods and services to geographically dispersed customers, in this process is found theVehicleRoutingProblem (VRP). TheVehicleRoutingProblem (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. Theproblem 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.
In the analysis the limited ability of particular vehicle types to serve particular demand types has been taken into account. In details the maximum annual mileage of vehicles of particular types has been divided between the 5 demand types taking into account the matching of vehicles (their load capacities) to particular demand types (an average weight of loads and number of cargo units per one route) - see Table 1. For example, tractors with semi-trailers - full tilt (thevehicle types j = 1, 2, 3 and 4), irrespectively of their load capacity (20, 24 or 26 tones / 33 pallets), are suitable to serve the long-haul - regular load shipments (the demand type i=1), characterized by an average weight of a load of 18t /30 pallets per one route being 715-kilometer long on average and, however, with the less efficiency, the short-haul - regular load shipments (the demand type i=2), characterized by an average weight of a load of 13.5t / 27 pallets per one route being 235-kilometer long on average. And, they are not suitable to serve the short-haul - temperature controlled load shipments and the urban distribution as well (the demand types i = 3, 4 and 5).
The Mixed Fleet VRP (MFVRP), implies vehicles with different capabilities (or heterogeneous capabilities), with known fixed and variable costs related to each vehicle in a fleet that must serve a series of consumers with known demands. In , Golden, Assad, Levy and Gheysens describe a series of effective heuristic procedures for theproblem of routing with a heterogeneous fleet, with the objective of determining the optimal truck fleet size and its capabilities, minimizing a cost function. The authors, Subramanian, Penna, Uchoa, and Ochi  studied the optimal composition of a fleet of vehicles through a hybrid algorithm, as well as determining the routes that would minimize travel expenses. Similarly, Salhi and Rand, in , and Taillard in , also attempt to find the ideal composition for a fleet of vehicles by solving the MFVRP. The authors of , Wassan and Osman, developed new Tabu Search (TS) variants in order to solve the heterogeneous fleet problem. At the same time, the article by Chen and Ching  suggests the alternative of employing an Ant Colony Optimization algorithm in order to solve the heterogeneous fleet routingproblem, proving that ACO is a competitive algorithm for this VRP variant; another factor influencing its adoption for this work.
extension is done by adding a parameter for setting a minimum value of the tabu list size tls called Threshold. The variation of this parameter improves the exploration of the search space by varying the compromise between intensification and diversification. It allows us to get a dynamic compromise between intensification and diversification. In summary, the more the same solutions found are repeated, the more the tabu list size increases, and vice versa; conversely, the more the solutions are different, the more the tabu list size decreases. This mechanism whereby the number of tabu solutions is increased when reaching local optima allows us to avoid the local optima trap by exploring other solutions in this case because all neighbors have become tabu. The optimization technique for the Reactive tabu with a variable threshold aimed at improving the initial solution (improvement) is developed (Fig. 3) in order to find the best compromise (optimal) solution of theproblem. It can quickly check the feasibility of the movement suggested, and then react to the repetition to guide the search. This algorithm is performed via a tabu list size (tls) update mechanism elaborated in five steps, as shown in Fig. 3. The counters and parameters used in Reactive tabu with a variable threshold are defined as follows, and initialized to the following values.
This work studies the implementation of heuristics and scatter search (SS) metaheuristic in a real heterogeneous fleet vehicleroutingproblem with time windows and split deliveries (HFVRPTWSD) in Brazil. In thevehicleroutingproblem with time windows and split deliveries (VRPSD) each client can be supplied by more than one vehicle. Theproblem is based in a single depot, the demand of each client can be greater than the vehicle’s capacity and beyond the time windows constraints, and there are also vehicle capacity and accessibility constraints (some customers cannot be served by some vehicles). The models were applied in one of the biggest retail market in Brazil that has 519 stores distributed in 12 Brazilian states. Results showed improvements over current solutions in a real case, reducing up to 8% the total cost of the operation.
This work addresses the Capacitated VehicleRoutingProblem with two-dimensional loading constraints. Given a central depot and a set of clients, where each demands a speciﬁc amount of items, theproblem aims to deﬁne minimum cost routes for a ﬂeet of homogeneous vehicles that performs customer service. The items have rectangular shapes, they must be transported in a way that there is no overlap between them, and in some cases, sequential loading restrictions, related to the order of visiting the customers, are required. To solve theproblem, two hybrid approaches combining heuristics and Column Generation are proposed. Furthermore, the literature’s Branch-and-Cut was used to solve a reformulation of the original model of theproblem. The methods developed were evaluated by means of the instances used in the literature and the results were compared with those previously published. The hybrid methods achieve satisfactory results, sometimes equal to the optima known, and the Branch-and-Cut could attest to optimality for several instances.