Vehicle Routing Research Articles

Fixed-Ratio Approximation Algorithm for the Minimum Cost Cover of a Digraph by Bounded Number of Cycles

We consider polynomial time approximation for the minimum cost cycle cover problem of an edge-weighted digraph, where feasible covers are restricted to have at most k disjoint cycles. In the literature this problem is referred to as Min-k-SCCP. The problem is closely related to classic Traveling Salesman Problem (TSP) and Vehicle Routing Problem (VRP) and has many important applications in algorithms design and operations research. Unlike its unconstrained variant, the Min-k-SCCP is strongly NP-hard even on undirected graphs and remains intractable in very specific settings. For any metric, the problem can be approximated in polynomial time within ratio 2, while in fixed-dimensional Euclidean spaces it admits Polynomial Time Approximation Schemes (PTAS). In the same time, approximation of the more general asymmetric Min-k-SCCP still remains weakly studied. In this paper, we propose the first fixed-ratio approximation algorithm for this problem, which extends the recent breakthrough Svensson-Tarnawski-Vegh and Traub-Vygen results for the Asymmetric Traveling Salesman Problem.

Multi-depot vehicle routing problem with drones in emergency logistics

Multi-depot vehicle routing problem with drones in emergency logistics

Improved Whale Optimization Algorithm with Variable Neighbourhood Search Strategy (WOA-VNS) in Solving Vehicle Routing Problem (VRP) for Recommending Multi-days Tourist Routes in Yogyakarta

Improved Whale Optimization Algorithm with Variable Neighbourhood Search Strategy (WOA-VNS) in Solving Vehicle Routing Problem (VRP) for Recommending Multi-days Tourist Routes in Yogyakarta

A Multi‐Trip Vehicle Routing Problem With Release Dates and Interrelated Periods

ABSTRACTThis article proposes a new multi‐trip vehicle routing problem variant, originally motivated by a practical application, namely a car components distribution to repair centers (warehouses). The problem is named the multi‐trip vehicle routing with release dates and interrelated periods (MTVRP‐RDIP). The routes may start at different pre‐defined periods, called departure periods, and may have different durations. Thus, two routes that start at different periods may be active at the same period, leading to the so‐called interrelated periods. Moreover, a route may only start at a period if a vehicle is available, and the availability of the vehicle depends not only on the existing vehicles but also on the active routes at that time period. The clients are classified according to their importance and represent warehouses that require car components that are made available throughout the time horizon, thus leading to the consideration of release dates. Delays in satisfying client orders and not serving orders in the time horizon result in penalty costs that must be minimized. The objective to minimize also includes routing costs and vehicle utilization costs. Two metrics are defined to compute an order's delay, each leading to a different mixed integer linear model. Computational results showed that one model clearly outperforms the other and even this one is only suited to address the smallest instances. A matheuristic based on a rolling‐horizon process that iteratively solves the better‐performing model with fewer periods was designed to tackle the largest instances. The matheuristic can provide feasible solutions for all test instances in an efficient manner that are, on average, better than the ones provided by the model in most of the compared key performance indicators.

Optimization of carbon emission in an integrated machine-piece scheduling and vehicle routing problem and its solution using MOPSO and NSGAII metaheuristic algorithms

The growth of the global economy is accompanied by significant energy consumption, and greenhouse gas emissions create various problems such as global warming and environmental degradation. To protect the environment, governments are seeking to reduce carbon emissions. Production systems that operate solely based on economic factors in the workshop only consider problems such as production speed, cost, and processing time. Two aspects can be effective in saving energy and reducing emissions at the production planning level: using routing to find the shortest path for collecting workpieces to the workshop, and turning off machines with long idle times and restarting them at the appropriate time. If the workshop production problem is combined with vehicle routing, a new problem arises. According to the research conducted so far, an integrated mathematical model for production routing has not been designed in a situation where the routing is before the production workshop. In this research, this bi-objective model is introduced, and it is solved using the augmented epsilon-constraint (AEC) method. The proposed mixed-integer linear programming model of this research includes three dimensions: environmental, social (customer satisfaction), and economic simultaneously. Given the high complexity of the mathematical model, MATLAB software and MOPSO and NSGA-II algorithms were used to solve it at higher dimensions. Seven evaluation criteria were used to compare the two proposed algorithms, and the results show that the MOPSO algorithm performs better. The findings suggest that minimizing pollution may involve sacrificing on-time delivery to customers. Consequently, decision-makers must carefully weigh the trade-off between reducing environmental impact and maintaining satisfactory delivery performance, ultimately deciding on an acceptable pollution level.

Application of the Clark–Wright Method to Improve the Sustainability of the Logistic Chain

The incessant consumption of goods and materials underscores the need to address the growing problem of waste generation and its profound impact on environmental sustainability. The problem of waste removal can be approached in different ways, whether it is the routing of vehicles, the work of drivers, the optimal distribution of waste bins, or other matters in the entire waste process. The aim of this study is to investigate the possibilities of optimizing waste collection processes in the region using a slightly modified Clark–Wright method. Optimal waste collection routes are defined with a focus on cost reduction and overall optimization of logistic chain processes. The established mathematical model for the capacitated vehicle routing problem includes the principles of sustainability and environmental friendliness. The results indicate that the largest messenger of all the newly proposed routes are the routes containing the surrounding settlements. Newly designed routes lead to significant reductions in fuel consumption and vehicle maintenance, which has a positive impact on financial and environmental resources. The conclusion indicates that by applying the Clark–Wright method, we have achieved a reduction in the number of routes of twenty fewer routes. This study provides regions with a detailed plan to improve waste management practices, contributing to a future of increased sustainability and environmental awareness.

Dynamic Programming Implementation for Delivery Route Optimization in E-Commerce Logistics

The rapid growth of e-commerce has created new challenges in logistics optimization, particularly in terms of delivery route efficiency. This research develops a dynamic programming model to optimize delivery routes in the context of e-commerce in Indonesia. Using a modified Vehicle Routing Problem with Time Windows (VRPTW) approach, we implemented an algorithm that considers various factors such as distance, time, and cost. Simulations using synthetic datasets showed efficiency improvements of 18.7% in travel distance and 22.3% in delivery time compared to conventional methods. Field trials with an e-commerce partner resulted in a 21.5% reduction in travel distance and an increase in on-time delivery rate from 87% to 94%. Sensitivity analysis revealed that the algorithm's performance is most affected by demand fluctuations and changes in traffic conditions. Implementation challenges include integration with existing systems and consideration of workforce impact. This research opens avenues for further development in algorithm scalability, integration of sustainability factors, and adaptation to various geographical contexts, demonstrating significant potential for improving e-commerce logistics efficiency in the future.

Modelling and Simulation of the Single-Period Vehicle Routing Problem in the Agriculture Industry

Modelling and Simulation of the Single-Period Vehicle Routing Problem in the Agriculture Industry

Applying quantum approximate optimization to the heterogeneous vehicle routing problem

Quantum computing offers new heuristics for combinatorial problems. With small- and intermediate-scale quantum devices becoming available, it is possible to implement and test these heuristics on small-size problems. A candidate for such combinatorial problems is the heterogeneous vehicle routing problem (HVRP): the problem of finding the optimal set of routes, given a heterogeneous fleet of vehicles with varying loading capacities, to deliver goods to a given set of customers. In this work, we investigate the potential use of a quantum computer to find approximate solutions to the HVRP using the quantum approximate optimization algorithm (QAOA). For this purpose we formulate a mapping of the HVRP to an Ising Hamiltonian and simulate the algorithm on problem instances of up to 21 qubits. We show that the number of qubits needed for this mapping scales quadratically with the number of customers. We compare the performance of different classical optimizers in the QAOA for varying problem size of the HVRP, finding a trade-off between optimizer performance and runtime.

Delivery routing for electric vehicles with en-route mobile battery swapping

Amid increasing environmental concerns, electric vehicles (EVs) are gaining traction as a sustainable transportation alternative. However, the widespread adoption of EVs is hindered by range limitations, inadequate charging infrastructure, and unpredictable access to charging facilities. The battery swapping van (BV) has been proposed as an innovative approach to actively offer on-demand charging at designated locations. This study leverages the novel BV concept and proposes a novel electric vehicle routing model with time windows and en-route mobile battery swapping (EVRPTW-EMBS). This achieves flexible mobile battery swapping services provided by BVs to EVs that are either en route or at customer sites. A tailored heuristic algorithm called CIP-TDP-ILNS is adopted, combining improved large neighborhood search (ILNS) with tree-template dynamic programming (TDP) and cluster-aided integer programming (CIP) to reduce the search space and enhance solving efficiency. Through extensive testing, the CIP-TDP-ILNS algorithm exhibits robust performance, yielding up to 16% cost reductions for the EVRPTW-EMBS compared to the benchmark model. The findings of this study suggest that (1) the EVRPTW-EMBS system is particularly beneficial for servicing clients with wider time windows, and (2) the optimal balance between the quantity of batteries carried and their capacity should be tailored to the logistics network’s size.

Solving a real-world package delivery routing problem using quantum annealers.

Research focused on the conjunction between quantum computing and routing problems has been very prolific in recent years. Most of the works revolve around classical problems such as the Traveling Salesman Problem or the Vehicle Routing Problem. The real-world applicability of these problems is dependent on the objectives and constraints considered. Anyway, it is undeniable that it is often difficult to translate complex requirements into these classical formulations. The main objective of this research is to present a solving scheme for dealing with realistic instances while maintaining all the characteristics and restrictions of the original real-world problem. Thus, a quantum-classical strategy has been developed, coined Q4RPD, that considers a set of real constraints such as a heterogeneous fleet of vehicles, priority deliveries, and capacities characterized by two values: weight and dimensions of the packages. Q4RPD resorts to the Leap Constrained Quadratic Model Hybrid Solver of D-Wave. To demonstrate the application of Q4RPD, an experimentation composed of six different instances has been conducted, aiming to serve as illustrative examples.

Comparison of Urban Environment Factors for Solar-Powered Vehicles

Abstract. Urban areas face significant environmental challenges, including high CO2 emissions largely attributed to the transportation sector. Introducing solar-powered vehicles (SPVs) presents a promising solution to reduce urban carbon footprints. However, in dense urban settings, the effectiveness of SPVs is often compromised by shading from buildings, which significantly diminishes solar power generation. This study explores the impact of shading on urban roads, aiming to identify roads with substantial shadow variations that affect solar energy harvesting. Using Geographic Information Systems (GIS) and hillshade analysis, the study examines how nearby buildings and road orientation influence shadow variability. The findings reveal considerable variability in shadow throughout the year, with significant fluctuations during transitional months like February, August, October, and November. These results highlight the importance of considering shadow patterns in urban planning and vehicle routing to optimise the use of solar energy in urban settings.

Uncrewed Aerial Vehicle Routing Problem for Integrated Crewed and Uncrewed Aircraft Operations

Last-mile delivery systems are one of the numerous industrial applications of uncrewed aircraft systems (UAS). This study analyzes UAS-based package delivery systems in the context of the integrated operations of crewed and uncrewed aircraft. It introduces a multi-trip, time-dependent vehicle routing problem aimed at optimizing UAS delivery routes within integrated operations. By conducting numerical simulations of helicopters (crewed aircraft) and UAS missions sharing the same airspace, the optimal UAS routes for resolving potential conflicts in the shared airspace can be effectively determined without any adverse impact on helicopter operations. Knowing the helicopter mission times in advance enables the efficient planning of UAS missions. The results of this study provide valuable insights regarding the implementation of integrated crewed and uncrewed aircraft operations.

Layered Graph Models for the Electric Vehicle Routing Problem With Nonlinear Charging Functions

AbstractElectric vehicle routing problems (EVRPs) involve the routing of a fleet of electric vehicles (EVs) to visit a set of customers while typically minimizing the total travel and charging time. Due to their limited autonomy, EVs may need to recharge their batteries en‐route at charging stations (CSs). Thus, routing decisions also include which CSs to visit, and how much energy to charge during those visits. These decisions are compounded by the fact that charging times follow a nonlinear charging function with respect to the EV's state of charge (SoC). We propose a layered graph representation for the EVRP with nonlinear charging functions (EVRP‐NL). Specifically, the layers correspond to discretized SoC values. Therefore, the arcs' energy consumption is approximated to match those values. We develop two compact formulations based on the layered graph. Furthermore, we introduced two charging policies that facilitate aligning charging duration with practical considerations. Computational results demonstrate the effectiveness of our formulations. Our best formulation effectively handles instances with up to 40 customers. On those instances, compared to the state‐of‐the‐art compact formulation, our formulation solves 13 more instances to optimality with less than half of the computational time. Considering instances solved by both formulations to optimally, the approximation entailed by our formulation yields a 0.94% deviation on average. Since our best performing formulation is compact, it may be readily used by a broad audience. Furthermore, as the majority of algorithms for the EVPR and its variants are heuristics, our formulation could be beneficial in evaluating the performance of these methods.

Sustainable last mile logistics employing drones and e-bikes

Last mile delivery is an important and growing part of the supply chain that has a sizeable negative environmental impact. This paper considers more sustainable approaches to home-delivery that are pragmatic for many non-rural environments. We address the two-echelon, multi-trip, capacitated vehicle routing problem with home-delivery and optional self-pickup services using different combinations of drones, trucks, and electric-assisted bikes (i.e. e-bikes). In the proposed approach, parcels are transported from a depot to parcel lockers by either drones or trucks and are then delivered to customer locations by either e-bikes or trucks. The four approaches range from the most sustainable (drones then e-bikes) to partly green (drone then truck or truck then e-bike) to finally the traditional (truck then truck). We formulate a mathematical model that determines the vehicle routes to minimize the total cost, which consists of vehicle operational cost and operator wages. The four types of delivery networks are assessed and compared for both costs and emissions. Experimental results suggest that with a modest increase in total cost (as little as 13%), emission reductions of up to 92%, on average, can be achieved when using the greenest delivery strategy of drones and e-bikes. The other delivery options have varying tradeoffs between costs and environmental impact. The percentage of self-pickup customers is an influencing factor to consider when choosing the delivery strategy that best meets the organization’s budget and environmental goals, especially when using e-bikes in the second echelon.

Urban freight distribution with electric vehicles: comparing some solution procedures

The Vehicle Routing Problem (VRP) is a well-known discrete optimization problem that has an impact on theoretical and practical applications. In this paper, a freight distribution model that includes a charging system located at the depot, making it feasible for real world-implementation, is proposed. Two different solution methods are proposed and compared: a genetic algorithm (GA) and a population-based simulated annealing (PBSA) with the number of moves increasing during the iterations. Among the variety of algorithm used to solve the VRP, population-based search methods are the most useful, due to the ability to update the memory at each iteration. To demonstrate the practical aspects of the proposed solution a case study is solved using travel time on a real network to evaluate the potentiality for a real-world application.

Resilient shuttle vehicle plan under route disruption scenarios and ticketing policies: a case study of the Qiandaohu archipelago scenic area, China

ABSTRACT Scenic areas in an archipelago context are often accessed with shuttle vehicles to transport tourists between different scenic spots. Vehicle routing and schedule planning could be challenging when route disruptions are considered frequent and fragile areas are protected and conserved. Transport provisions also affect the number, sequence and patterns of visited spots for each tourist, which in turn may not only impact the revenue of the scenic area but also on visitor satisfaction. This paper develops a mixed-integer programming model for this optimisation problem at scenic areas by considering two common ticketing policies: ‘all-inclusive policy’ and the ‘two-part tariff policy’. Experimental results based on the case study of Qiandaohu scenic area in China demonstrate that our method can obtain high-quality solutions for real-sized problems where some routes are disrupted. It is found that ticketing policies may have different impacts on shuttle vehicle planning. Under the all-inclusive policy, the shuttle vehicle planning maximises the total profit. Under the two-part tariff policy, however, the plan needs to maximise the profit to strike a balance between the operational cost and the number of spots visited by tourists. Our study may shed light on the effectiveness of shuttle vehicle planning and ticketing policy selection.

Energy-Saving Multi-Agent Deep Reinforcement Learning Algorithm for Drone Routing Problem.

With the rapid advancement of drone technology, the efficient distribution of drones has garnered significant attention. Central to this discourse is the energy consumption of drones, a critical metric for assessing energy-efficient distribution strategies. Accordingly, this study delves into the energy consumption factors affecting drone distribution. A primary challenge in drone distribution lies in devising optimal, energy-efficient routes for drones. However, traditional routing algorithms, predominantly heuristic-based, exhibit certain limitations. These algorithms often rely on heuristic rules and expert knowledge, which can constrain their ability to escape local optima. Motivated by these shortcomings, we propose a novel multi-agent deep reinforcement learning algorithm that integrates a drone energy consumption model, namely EMADRL. The EMADRL algorithm first formulates the drone routing problem within a multi-agent reinforcement learning framework. It subsequently designs a strategy network model comprising multiple agent networks, tailored to address the node adjacency and masking complexities typical of multi-depot vehicle routing problem. Training utilizes strategy gradient algorithms and attention mechanisms. Furthermore, local and sampling search strategies are introduced to enhance solution quality. Extensive experimentation demonstrates that EMADRL consistently achieves high-quality solutions swiftly. A comparative analysis against contemporary algorithms reveals EMADRL's superior energy efficiency, with average energy savings of 5.96% and maximum savings reaching 12.45%. Thus, this approach offers a promising new avenue for optimizing energy consumption in last-mile distribution scenarios.

Comparative Analysis of Electric and Conventional Vehicles Performance in the Evacuation Process of Mount Semeru Eruption Victims Based on Geographic Information Systems

The Lumajang Regency is highly vulnerable to various natural disasters, particularly the potential eruption of Mount Semeru. In disaster response efforts, the local government needs to prepare effective and efficient evacuation routes, taking into account the magnitude of the eruption impact in the Semeru disaster-prone area. This research focuses on evacuating vulnerable residents using electric and conventional vehicles. This study is categorized as a vehicle routing problem with energy constraint (VRPEC) because the electric vehicles utilized in this research do not require recharging during their operational process, ensuring rapid evacuation as it is essential. By utilizing Geographic Information Systems (GIS)-based optimization, the best route to evacuate all victims within 12 h is determined. This study involves developing scenarios considering the number of vehicles and their travel distances. There are also evacuation guidelines, including the implementation of priority points and evacuation zone usage. The research results indicate that scenarios EV 5, 8, and 10 are the most optimal for using electric vehicles. Meanwhile, the optimal scenario for conventional vehicles is scenario 5. This analysis shows that implementing electric vehicle scenarios is superior to conventional vehicle scenarios in terms of the total time required to evacuate all victims.

Order dispatch problem of the inter-city or inter-district ridesplitting service

This study formulates the order dispatch problem of the inter-city/inter-district ridesplitting service as an integer linear programming, and a solution framework that combines Lagrangian relaxation (LR) and alternating direction methods of multipliers is constructed. Specifically, LR problem is constructed by relaxing coupling constraints; based on this, the augmented Lagrangian relaxation (ALR) problem is constructed by adding a quadratic penalty term. Then, the ALR problem can be decomposed into a series of interdependent vehicle route subproblems by using linearisation technique and block coordinate descent method. The upper bound of the model is generated by ALR and a heuristic, and the solution quality can be evaluated by the lower bound provided by LR. Finally, numerous experiments are conducted to verify the effectiveness of proposed algorithms. The results show that the proposed algorithm could achieve an average cost saving of 10% and an average detour reduction of over 20% than the existing algorithm.