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The Capacitated Vehicle Routing Problem (CVRP) is a combinatorial optimization problem that seeks to determine the optimal set of routes for a fleet of vehicles, with limited capacity, to deliver goods to customers while minimizing the total cost. Due to its NP-hard nature, finding exact solutions for the large-scale CVRP instances is computationally intractable. Therefore, heuristics and metaheuristics are widely employed to find approximate optimal solutions. Among these, the Clarke-Wright (CW) algorithm is a popular greedy approach that constructs routes by iteratively merging nodes to minimize transportation costs. This study presents an implementation of the CW algorithm in graphics processing units (GPUs) using the CUDA (Compute Unified Device Architecture) framework. The GPU implementation is compared to its CPU counterpart in terms of execution time and performance. The results demonstrate significant speed-ups achieved by the GPU implementation, particularly for large-scale instances. Performance gains can be attributed to the parallel processing capabilities of GPUs, enabling efficient execution of the algorithm computational steps. [ABSTRACT FROM AUTHOR]

The paper presents an optimization model and its implementation using a hybrid approach for the Capacitated Vehicle Routing Problem with Pick-up and Alternative Delivery (CVRPPAD). The development of the CVRPPAD was motivated by postal items distribution issues. The model proposed combines various features of Vehicle Routing Problem variants. The novelty of this model lies in the introduction of alternativeness of item delivery points, differentiation of delivery point types in terms of their capacity (parcel lockers) and possibility of collecting the items during the execution of delivery routes. The model also takes into account a possibility of introducing time windows related to delivery time. The proposed data structure in the form of sets of facts facilitates the implementation of the model in all environments, Constraint Logic Programming (CLP), Mathematical Programming (MP), metaheuristics, databases, etc. The model is implemented in the MP, hybrid CLP/MP, and hybrid CLP/heuristic environments. The hybrid CLP/MP approach is the authors' original solution, which has already been used to solve Supply Chain Management problems, scheduling problems, routing problems etc. For large size problems, considering their combinatorial character, the proposed CLP/MP approach is ineffective. Its effectiveness will improve when MP is replaced by a heuristic. All implementations were performed on the same data instances (facts), which made it possible to compare them according to the solution search time, number of decision variables and number of constraints. The directions into which the model can be further developed were also presented. [ABSTRACT FROM AUTHOR]

In the city of Tunja there are no sources of information and exact indicators that establish the amount of tires used and discarded in clandestine dumps, house yards and storage centers, which generate negative impact on the environment and the health of the inhabitants, evidencing the need to generate a logistic solution. An investigation of quantitative approach of type applied as a case study is presented. The CVRP method was used, which consists of the design of a set of routes of lower cost, where each client is visited only once by a single vehicle and all routes begin and end at a center of gravity; as results, the characterization and design of a logistic model was achieved, which integrated the location of collection point, demand, collection routes, capacities, as a solid and updated tool that would generate environmental alternatives for the city. [ABSTRACT FROM AUTHOR]

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