Solving Capacitated Vehicle Routing Problem Using Football Game Algorithm

The Capacitated Vehicle Routing Problem (CVRP) presents significant challenges in shipping route optimization and logistics management. These challenges include balancing vehicle capacity, minimizing travel distance, and efficiently grouping delivery points, all of which are crucial for enhancing operational efficiency and reducing costs. This research aims to apply a combination of the Sweep and Nearest Neighbor algorithms to address the CVRP, seeking to improve route efficiency and manage vehicle capacity effectively. The Sweep algorithm is employed to cluster pickup points based on their polar angle from the depot, facilitating efficient grouping and optimal vehicle capacity management. Within each cluster, the Nearest Neighbor algorithm is implemented to optimize the sequence of visits, minimizing total travel distance by sequentially selecting the next closest point. The Haversine Distance is used to calculate the distances between points, ensuring geographical accuracy compared to the Euclidean method. Experimental results demonstrate that this hybrid approach yields shorter routes. Quantitative analysis shows a significant reduction 13% in total travel distance when using this combination of algorithms, highlighting its effectiveness in solving the CVRP. This research demonstrates that combining the Sweep and Nearest Neighbor algorithms provides an efficient solution to the CVRP, improving route optimization and vehicle capacity management. The findings contribute valuable insights to logistics management, with practical implications for enhancing shipping route efficiency.

Capacitated vehicle routing problem is a vehicle routing problem that has constraints in the form of vehicle capacity. It is a matter of optimization to find the optimal route for some vehicles with a specific capacity and homogeneous vehicles that serve some agents with several known requests before the distribution process takes place. LPG distribution is the application of capacitated vehicle routing problems. This research aims to determine the LPG distribution route based on the Clarke and Wright Algorithm and LINGO. The capacitated vehicle routing problem model will be solved in two phases. The first stage completes the capacitated vehicle routing problem model using the Clarke and Wright algorithm. The second stage is completing the results of the first stage in the form of LINGO-based sub tours to obtain the optimal solution. The solution of the capacitated vehicle routing problem in distribution LPG using the Clarke and Wright algorithm has a total distance of 151.94 km. The solution of the capacitated vehicle routing problem in distribution LPG using LINGO has a total distance of 161.59 km.

This research investigates supply chain resilience through simulation-based optimization, focusing on the Capacitated Vehicle Routing Problem (CVRP) using Kuwait Danish Dairy Company (KDD) as a case study. It aims to enhance logistic robustness against disruptions such as demand spikes, traffic congestion, and regulatory restrictions. Using Google OR-Tools implemented in Python, scenarios representing baseline operations, urban congestion, demand surges, Ramadan operational constraints, and lockdown scenarios were simulated. The CVRP model minimizes total travel cost, considering vehicle capacity and route constraints to maintain cold chain integrity. Results highlighted significant impacts from compounded disruptions; traffic congestion increased total travel distance by 13%, while demand surges stretched operational limits. Ramadan scenarios required precise routing to meet delivery constraints within shorter timeframes. Lockdown scenarios showed reduced operational costs but potential revenue losses from inaccessible nodes. The comparative analysis demonstrated that optimized routing significantly mitigates disruption effects, improving efficiency by up to 20%. Recommendations include adaptive logistics strategies, real-time data integration, diversified supplier networks, and preemptive inventory management. The findings offer practical insights applicable broadly to food supply chains facing similar vulnerabilities in the Gulf region. This research advances the application of CVRP for enhancing supply chain resilience, offering a robust methodology and actionable solutions for managing logistic vulnerabilities. Future research directions include real-time route adjustments, multi-depot scenarios, and environmental sustainability considerations.

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 Capacitated Vehicle Routing Problem (CVRP) is a well-known NP-hard problem of importance to real life applications such as transportation and logistics. The CVRP finds the best set of paths between a specific number of customers to deliver goods by a number of vehicles with a fixed capacity. In this paper, we apply a new nature inspired optimization algorithm called Intelligent Water Drops (IWD) inspired by water flow. The results of this IWD approach are compared against a classical approach and show that IWD algorithm gives optimal and near optimal solutions for some CVRP instances.

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.

In this work, we propose a Genetic Algorithm (GA) for effectively scheduling ambulances aftermath of a disaster. Given the limited number and capacity of ambulances, we aim to minimize the number of ambulance tours and the average time to take all injured people to a hospital. Both of these goals require that the total tour length of all routes should be minimized as well. This problem can be considered as an extension of the well-known Capacitated Vehicle Routing Problem (CVRP). We developed a Genetic Algorithm (GA) and tested using some of the CVRP benchmark files. For the possible number of injures at each location, we define three different scenarios. The proposed GA aims to minimize the tour lengths of the ambulances while respecting all real life constraints given in these scenarios. In order to evaluate the proposed GA, we also developed a rival method based on the Nearest Neighbor (NN) heuristic. The results of extensive simulation test NN heuristic.

Fuel distribution optimization is crucial to meet growing demand and reduce operational costs, especially in cities like Malang, where vehicle numbers are increasing. This research addresses the distribution challenges of PT Pertamina, focusing on designing efficient routes to minimize distance, cost, and delivery time while meeting fuel demands effectively. The problem, classified as a Capacitated Vehicle Routing Problem (CVRP), is solved using the Clarke-Wright Savings (CWS), Nearest Neighbour (NN), and Goal Programming (GP). The CWS is applied to group routes efficiently by reducing travel distances, while NN determined the delivery sequence within each route. GP addressed multi-objective optimization, minimizing costs and delivery time, maximizing Pertashop demands, and optimizing vehicle use. The results show that the combination of CWS and NN algorithms reduced the total travel distance by 140 km, or 12.5% reduction. Additionally, the GP method optimized vehicle use to 13, achieving a 59.68% cost reduction and a 48.68% time savings. These findings highlight the effectiveness of combining these algorithms in fuel distribution optimization, providing a more efficient solution compared to existing routes. Moreover, this approach is adaptable to similar logistics problems, offering a foundation for further research in multi-objective optimization for distribution systems.

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.

A New Capacitated Vehicle Routing Problem with Split Service for Minimizing Fleet Cost by Simulated Annealing

We consider the route optimization problem of transporting valuables in cash‐in‐transit (CIT) operations. The problem arises as a rich variant of the capacitated vehicle routing problem (CVRP) with time windows and pickup and deliveries. Due to the high‐risk nature of this operation (e.g., robberies) we consider a bi‐objective function where we attempt to minimize the total transportation cost and the security risk of transporting valuables along the designed routes. For risk minimization, we propose a composite risk measure that is a weighted sum of two risk components: (i) following the same or very similar routes, and (ii) visiting neighborhoods with low socio‐economic status along the routes. We also consider vehicle capacities in terms of monetary value carried as per insurance regulations. We develop an adaptive randomized bi‐objective path selection algorithm that uses the composite risk measure in choosing alternative paths between origin‐destination pairs over a sequence of days. We solve the rich CVRP approximately for each day with updated costs. We test our solution approach on a data set from a CIT delivery service provider and provide insights on how the routes diversify daily. Our approach generates a spectrum of solutions with cost‐risk trade‐off to support decision making. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 69(3), 256–269 2017

Solving vehicle routing problem by using improved K-nearest neighbor algorithm for best solution

The rapid outbreak of COVID-19 pandemic invoked scientists and researchers to prepare the world for future disasters. During the pandemic, global authorities on healthcare urged the importance of disinfection of objects and surfaces. To implement efficient and safe disinfection services during the pandemic, robots have been utilized for indoor assets. In this paper, we envision the use of drones for disinfection of outdoor assets in hospitals and other facilities. Such heterogeneous assets may have different service demands (e.g., service time, quantity of the disinfectant material etc.), whereas drones have typically limited capacity (i.e., travel time, disinfectant carrying capacity). To serve all the facility assets in an efficient manner, the drone to assets allocation and drone travel routes must be optimized. In this paper, we formulate the capacitated vehicle routing problem (CVRP) to find optimal route for each drone such that the total service time is minimized, while simultaneously the drones meet the demands of each asset allocated to it. The problem is solved using mixed integer programming (MIP). As CVRP is an NP-hard problem, we propose a lightweight heuristic to achieve sub-optimal performance while reducing the time complexity in solving the problem involving a large number of assets.

Utilization of gas as an energy source has become a principal issue in recent years. The Minister of Energy and Mineral Resources of the Republic of Indonesia have a plan to guarantee national energy security and improve the national trade balance, as well as accelerate the use of gas in the electricity sector. The Ministry of Energy and Mineral Resources issued a regulation to conduct the gasification process at 52 power plants in Indonesia through Ministerial Decree No. 13K of 2020. In this study, LNG distribution was designed using the Capacitated Vehicle Routing Problem (CVRP) method to minimize the transportation costs and optimal use of the fleet. The vehicles used have a limited capacity and can supply all demands at nine power plants in the Bali and Nusa Tenggara regions. In the distribution there is also have a Hub which purpose to reduce the distance travelled by a ship. The ships that will be used are Mini LNG-Carrier for the route from the LNG refinery to HUB, LCT ship for the route from HUB to each port near the power plant, and ISO Tank transport truck for the route from the port to the plant. The distribution uses four Vessel 1, and one LCT 300 vessel, with Hubs located in Benoa and Flores, and two Mini LNG-Carriers with a capacity of 15,600 m3 to Benoa and 10,000 m3 to Flores. The total cost for this scenario is US$ 51,398,568, with a minimum sales margin of US$ 2.5 per MMBTU.

The dramatic growth of online shopping worldwide in the last few years generated negative consequences for local small retailers who do not adopt information technologies. Furthermore, the e-commerce sector is considered a good opportunity to develop sustainable logistic processes. To reach this goal, the proposed paper presents a mathematical model and a metaheuristic algorithm to solve a multi-objective capacitated vehicle routing problem (CVRP) distinguished by economic, green, and ethical objective functions. The proposed algorithm is a multi-objective simulated annealing (MOSA) that is implemented in a software architecture and validated with real-world instances that differ for the product type delivered and the geographic distribution of customers. The main result of each test is a tri-dimensional Pareto front, i.e., a decision-support system for practitioners in selecting the best solution according to their needs. From these fronts, it can be observed that if the economic and environmental performances slightly deteriorate by 1.6% and 4.5%, respectively, the social one improves by 19.4%. Furthermore, the developed MOSA shows that the environmental and social objective functions depend on the product dimensions and the geographic distribution of customers. Regarding the former aspect, this paper reports that, counter-intuitively, the metabolic energy consumption per driver decreases with bigger products because the number of necessary vehicles (and drivers) increases, and, thus, the workload is divided among more employees. Regarding the geographic distribution, this manuscript illustrates that, despite similar traveled distances, highly variable altitudes cause more carbon emissions compared to flat distributions. Finally, this contribution shows that delivering small goods decreases the distance that vehicles travel empty by 59%, with a consequent cost reduction of 16%.