This paper proposes an integer linear mathematical formulation for Vehicle Routing Problem (VRP), where the capital cost for deploying each Vehicle is minimized together with other on-link transportation costs. The model has been formulated as a multi-commodity network flow model with capacity constraints. It is well known that the computational complexity to this type of Problems is NP-hard. Thus, the ACO algorithm, which has been known to be a powerful meta-heuristic algorithm for solving VRPs in large networks, has been adapted to solve the Problem. Although the ACO algorithm has repeatedly been used to solve the Capacitated VRP, it has a drawback that cannot consider the capital cost of each Vehicle along with other operational costs of the Vehicles (associated with the total distance traveled within a day) in its initial form. More specifically, naturally it assumes that each Vehicle returns to the depot if it becomes full or the demand finishes, each met first; this paper seeks to propose an adapted ACO algorithm in which this assumption is released. To assess the capability of the proposed model in large-scale networks, the case study of Mashhad city, consisting of 253 traffic analysis zones and over than 3800 links, has been considered. Results show that the proposed algorithm converges to near-to-optimal solutions within two seconds of cpu time, which is encouraging.

The Vehicle Routing Problem with the capacity constraints was considered in this paper. It is quite difficult to achieve an optimal solution with traditional optimization methods by reason of the high computational complexity for large-scale Problems. Consequently, new heuristic or metaheuristic approaches have been developed to solve this Problem. In this paper, we constructed a new heuristic algorithm based on the tabu search and adaptive large neighborhood search (ALNS) with several specifically designed operators and features to solve the Capacitated Vehicle Routing Problem (CVRP). The effectiveness of the proposed algorithm was illustrated on the benchmark Problems.The algorithm provides a better performance on largescaled instances and gained advantage in terms of CPU time.In addition, we solved a real-life CVRP using the proposed algorithm and found the encouraging results by comparison with the current situation that the company is in.

The Capacitated Vehicle Routing Problem (CVRP) is a significant variant of the Vehicle Routing Problem that incorporates constraints related to customer demand and Vehicle capacity. Owing to its extensive applications in logistics and transportation, CVRP has attracted substantial research attention, with numerous algorithms proposed from the perspective of intelligent search. A common solution strategy involves two phases: first, assigning customers to different Vehicles to form feasible routes, and second, optimizing these routes. This paper presents a two-phase CVRP solution framework through the clustering concept with intelligent search to improve route planning. In the first phase, a set of clustering methods - fuzzy c-means, k-means, and k-medoids - combined with a nearest neighbor heuristic search, are applied to generate feasible routes for each Vehicle. In the second phase, these routes are iteratively optimized using the Simulated Annealing (SA) algorithm. The process yields three distinct solution pathways: fuzzy c-means with SA, k-means with SA, and k-medoids with SA. For performance evaluation, 46 benchmark CVRP datasets from a publicly available library are used. Simulation results demonstrate that k-means with SA performs the best, surpassing the other two approaches and outperforming other clustering-based two-phase state-of-the-art algorithms in terms of solution quality.

Capacitated Vehicle Routing Problem (CVRP) is one of the most well-known and applicable issues in the field of transportation. It has been proved to be an NP-Complete Problem. To this end, it is needed to develop a high-performance algorithm to solve the Problem, particularly in large scales. This paper develops a novel mathematical model for the CVRP considering the satisfaction level of demand nodes. Then, the proposed model is validated using a numerical example and sensitivity analyses that are implemented by CPLEX solver/GAMS software. To solve the Problem efficiently, a Genetic Algorithm (GA) is designed and implemented. The obtained results demonstrate that the proposed GA can yield high-quality solutions compared to exact solutions.

The overall cost of companies dealing with the distribution tasks is considerably affected by the way that distributing Vehicles are procured. In this paper, a more practical version of Capacitated Vehicle Routing Problem (CVRP) in which the decision of purchase or hire of Vehicles is simultaneously considered is investigated. In CVRP model Capacitated Vehicles start from a single depot simultaneously and deliver the demanded items of several costumers with known demands where each costumer must be met once. Since the optimal Vehicle procurement cost is a function of total distance it traverses during the planning horizon, the model is modified in a way that the decision of purchasing or hiring of each Vehicle is made simultaneously. The Problem is formulated as a mixed integer programming (MIP) model in which the sum of net present value (NPV) of procurement and traveling costs is minimized. To solve the Problem, a hybrid electromagnetism and parallel simulated annealing (PSA-EM) algorithm and a Shuffled Frog Leaping Algorithm (SFLA) are presented. Finally, the presented methods are compared experimentally. Although in some cases the SFLA algorithm yields better solutions, experimental results show the competitiveness of PSA-EM algorithm from the computational time and performance points of view.