Solving capacitated vehicle routing problem using of Clarke and Wright algorithm and LINGO in LPG distribution

The problem which is often experienced in the delivery of goods from distributor to the destination is the delivery route which is not sufficient with the capacity of the vehicle. This matter is very important because it can affect the trust of the clients on the shippers in the distributor. This problem can be analyzed using Capacitated Vehicle Routing Problem (CVRP) with Clarke and Wright Algorithm. This research begins with determining the distance between all coordinates with Euclidean Distance, making the distance matrix between places to go. After that, the calculation CVRP using Clarke and Wright Algorithm is exected in this study, a calculate CVRP using Clarke and Wright algorithm can help of the computer. The study was conducted at 15 shop coordinates, the results obtained by 4 routes with total load 3750 kg and distance 29.8510 km. Route of delivery the first route 1100 kg load and distance 11.5963 km, second route 1000 kg load and distance 6.6493 km, third route 1000 kg load and distance 2.7549 km, and the fourth route 650 kg load and distance 8.8505 km.Keywords: Distributor, Vehicle Routing Problem, Capacitated Vehicle Routing Problem, Clarke and Wright Algorithm

Capacitated vehicle routing problem is extension of vehicle routing Problem where the purpose is to determine a set of routes to fulfil all the transportation requests with a given fleet of vehicles in such a way that the travelling cost comes out to be a minimum. In this paper, the demands of the customers will be very well known in advance, but they are known imprecisely. To deal with such kind of impreciseness, interval type-2 fuzzy number (IT2FN) can be used. Therefore, a capacitated vehicle routing problem with interval type-2 fuzzy number has been modelled. A procedure to solve the model has been introduced using Clark and Wright algorithm.

Particle swarm optimization (PSO) is adopted to solve capacitated vehicle routing problems (CVRPs). A nonlinear S decrease curve is employed to adjust the inertia weight of PSO to balance global and local searches. Meanwhile, local search and path relink are also involved to improve the quality of solutions. Experiments were conducted on Auger at problems in the OR Library. Experimental results will were compared with those from other studies. Experimental results prove the algorithm designed in this article can effectively solve capacitated type vehicle routing problems.

Combining genetic local search into a multi-population Imperialist Competitive Algorithm for the Capacitated Vehicle Routing Problem

Design and development of a hybrid artificial bee colony algorithm for the environmental vehicle routing problem

Combined route capacity and route length models for unit demand vehicle routing problems

Vehicle Routing Problem (VRP) is a classical NP-hard problem in combinational optimization with great practicality. A branch of VRP is the Capacitated Vehicle Routing Problem (CVRP), where vehicles have capacity constraints. In this paper, a Hybrid Chaotic Particle Swarm Optimization (HCPSO) is proposed to solve CVRP. To make this algorithm successful, three main components play an important role. Firstly, we introduce a new mutual mapping method to encode and decode between decimal numbers and integer solutions. Secondly, the ergodicity and sensitivity on initial conditions of chaos theory are utilized to achieve chaotic initialization and renewing. Thirdly, various local search strategies like neighbor change strategy, move strategy are employed to improve the local search ability. In the end, benchmarks have been tested. It is clearly shown that for small and medium sized CVRP, the algorithm is efficient and effective and the results are better than those of some recent papers.

Crow Search Algorithm is a novel Metaheuristic method based on the intelligent behavior of crows. It has been used to solve some optimization problems like engineering design problems, feature extraction and classification problems but has not been applied to vehicle routing problem. In this paper, crow search algorithm has been utilized to solve capacitated vehicle routing problem and the performance of it on various size-capacitated vehicle routing problem instances is analyzed. The factorial design ANOVA is used to determine the performance of crow search algorithm under different parameter settings on capacitated vehicle routing problem instances.

A hybrid genetic search and dynamic programming-based split algorithm for the multi-trip time-dependent vehicle routing problem

We consider the asymmetric capacitated vehicle routing problem (CVRP), a particular case of the standard asymmetric vehicle routing problem in which only the vehicle capacity constraints are imposed. CVRP is known to be NP-hard and finds practical applications in distribution and scheduling. We describe two new bounding procedures for CVRP, based on the so-called additive approach. Each procedure computes a sequence of nondecreasing lower bounds, obtained by solving different relaxations of CVRP. Effective implementations of the procedures are also outlined which considerably reduce the computational effort. The two procedures are combined into an overall bounding algorithm. A branch-and-bound exact algorithm is then proposed, whose performance is enhanced by means of reduction procedures, dominance criteria, and feasibility checks. Extensive computational results on both real-world and random test problems are presented, showing that the proposed approach favorably compares with previous algorithms from the literature.

eCommerce, postal and logistics’ planners require to solve large-scale capacitated vehicle routing problems (CVRPs) on a daily basis. CVRP problems are NP-Hard and cannot be easily solved for large problem instances. Given their complexity, we propose a methodology to reduce the size of CVRP problems that can be later solved with state-of-the-art optimization solvers. Our method is an efficient version of clustering that considers the constraints of the original problem to transform it into a more tractable version. We call this approach Constrained Clustering Capacitated Vehicle Routing Solver (CC-CVRS) because it produces a soft-clustered vehicle routing problem with reduced decision variables. We demonstrate how this method reduces the computational complexity associated with the solution of the original CVRP and how the computed solution can be transformed back into the original space. Extensive numerical experiments show that our method allows to solve very large CVRP instances within seconds with optimality gaps of less than 16%. Therefore, our method has the following benefits: it can compute improved solutions with small optimality gaps in near real-time, and it can be used as a warm-up solver to compute an improved solution that can be used as an initial solution guess by an exact solver.

A vehicle routing problem involves finding a set of optimal route for a fleet of capacitated vehicles which are available at a location to service the demands of a set of customers. In its simplest form, a customer is required to be visited once and the capacity of a vehicle must not be exceeded. In this paper, a review of four common and applicable variants of the vehicle routing problem, namely, capacitated vehicle routing problem, vehicle routing problem with time windows, periodic vehicle routing problem and the dynamic vehicle routing problem, are considered based on formulation techniques, methods of solution and areas of application. A summary table is presented for each variant to emphasis some key features that represent direction of current research.

Vehicle Routing Problem (VRP) is concerned with the optimal design of routes to be used by a fleet of vehicles to serve a set of customers. In this study we analyze constructive heuristics for a subcase of VRP, where the vehicles have a limited capacity – Capacitated Vehicle Routing Problem (CVRP). The problem is NP-hard, therefore heuristic algorithms which provide near-optimal polynomial-time solutions are still actual. The aim of this work is to make a comparison of constructive heuristics as there were not found any such classification. Finally, the leader by a criterion of quality is admitted being a Clarke and Wright Savings heuristic; however, this algorithm cannot find the solution for all used instances. This fact and other ones are discussed in the paper. Our future goal is to make an experimental comparison of the most common and state-of-the-art metaheuristics using well suited constructive heuristic to build a suboptimal solution.

The vehicle routing problem is one of the most studied combinatorial optimization problems in operations research. The problem deals with a homogenous fleet of capacitated vehicles that operates from a central depot serving a set of customers with known demands. The objective of the problem is to design a set of routes serving customers with minimum cost. The vehicle routing problem is classified as NP-hard problem. Exact and approximate algorithms have been developed in the literature to solve the Capacitated Vehicle Routing Problem (CVRP). However, exact methods can only solve relatively small-size problems while approximate algorithms have been able to reach near-optimum solutions of large problems. The purpose of this paper is to develop a new hybrid search algorithm that combines the evolutionary genetic search with a new local search heuristic to solve the CVRP. The proposed heuristic calculates a resultant objective function based on both the distance travelled and the demand associated with the given customer. A new set of genetic operators suited for the problem was employed. Several computational experiments were conducted. The algorithm was validated and was capable of converging to the optimum solution of the tested benchmark instance.KeywordsVehicle routing problemTransportationOptimizationEvolutionary search

The last-mile delivery problem is one of the most complex and resource-intensive aspects of modern logistics, especially within the growing e-commerce sector. As online shopping continues to expand, companies are under immense pressure to deliver goods more quickly, efficiently, and at lower costs, all while meeting the demands of increasingly time-sensitive customers. This has created a need for innovative solutions that can tackle challenges related to dynamic traffic patterns, fluctuating customer preferences, and operational constraints such as vehicle capacities and delivery windows. In response to these challenges, this paper explores the application of predictive analytics as a tool for optimizing last-mile delivery routes in real-time.The study begins by identifying the core challenges inherent in last-mile logistics, particularly in the U.S. e-commerce landscape, where the cost of last-mile delivery can represent up to 53% of total shipping costs. With traffic congestion, unpredictable customer availability, and delivery time constraints posing significant hurdles, conventional static route planning models often fall short. In this paper, predictive analytics is proposed as a solution to these challenges, utilizing real-time data to inform more efficient routing decisions. By processing vast amounts of real-time traffic data, customer preferences, and delivery constraints, predictive models can offer a more flexible and responsive approach to last-mile delivery.The research then presents a comprehensive literature review of existing route optimization methods, such as the traditional Vehicle Routing Problem (VRP) and its extensions, including VRP with Time Windows (VRPTW), Dynamic VRP (DVRP), and Capacitated VRP (CVRP). While these models have proven useful, their limitations are exposed when faced with real-time operational complexities in the e-commerce sector. Therefore, this study introduces an advanced dynamic routing model that integrates machine learning algorithms—such as decision trees and neural networks—with traditional VRP frameworks. These machine learning models, trained on historical data, are capable of predicting future traffic patterns, customer behavior, and delivery time windows.A case study is conducted using data from U.S.-based e-commerce companies to demonstrate the practical application of predictive analytics in optimizing last-mile delivery. The case study outlines how predictive models are used to dynamically adjust delivery routes based on real-time conditions, leading to significant improvements in efficiency, cost savings, and customer satisfaction. Key performance indicators such as delivery times, fuel consumption, and vehicle utilization are examined before and after the implementation of the predictive models, with the results showing a reduction in delivery time by 20% and fuel costs by 15%, alongside improved on-time delivery rates.The paper concludes by presenting the proposed dynamic route optimization model as a solution that combines the flexibility and responsiveness of predictive analytics with the robust framework of traditional VRP models. Through the integration of machine learning, real-time data processing, and dynamic routing, the model is shown to significantly improve last-mile delivery efficiency. This study's findings highlight the potential for predictive analytics to revolutionize the logistics industry, particularly in the high-demand e-commerce sector, where quick and reliable delivery is paramount. The research suggests that as e-commerce continues to grow, predictive analytics will play an increasingly critical role in ensuring that last-mile delivery is both cost-effective and responsive to the evolving needs of consumers.