Dynamic Vehicle Routing Problem Research Articles

An Integrated Framework for Dynamic Vehicle Routing Problems with Pick-up and Delivery Time Windows and Shared Fleet Capacity Planning

This paper proposes a novel route optimization framework to solve the problem of instant pick-up and delivery for e-grocery orders. The proposed framework extends the traditional time-windowed package delivery problem. We demonstrate the effectiveness of our approach for this integrated problem using actual delivery data from HepsiJet, a leading e-commerce logistics provider in Turkey. We first employ several machine learning algorithms and simulations to investigate the capacity of the courier. Subsequently, a dynamic route planning workflow is executed with a highly specialized and novel routing algorithm. Our proposed heuristic approach considers combined fleet operations for delivering regular packages originating from a central depot and dynamic e-grocery orders picked up at local supermarkets and delivered to the customers. The heuristic algorithm constitutes k-opt and node transfer operation variations customized for this integrated problem. We report the performance of our approach in problem instances from the literature and instances from HepsiJet’s daily operations, which we also publicly share as new route optimization problem instances. Our results suggest that, despite the more complex nature of the integrated problem, our proposed algorithm and solution framework produce more efficient and cost-effective solutions that offer additional business opportunities for companies such as HepsiJet. The computational analyses reveal that implementing our proposed approach yields significant efficiency gains and cost reductions for the company, with a distance reduction of over 30%, underscoring our approach’s effectiveness in achieving substantial cost savings and enhanced efficiency through integrating two distinct delivery operations.

Dynamic vehicle routing problem with drone resupply for same-day delivery

We study a same-day delivery problem where customer orders arrive dynamically throughout the day and the service operator must determine, in real-time, whether to accept the orders and how to adjust the ongoing distribution plan. We develop a route-based Markov Decision Process and an efficient online policy to dynamically route a truck that can receive newly arrived orders along its route via drones dispatched from a depot. Numerical experiments show that our online policy has an average fill rate decrease of at most 20% over the perfect-information counterpart. Further, this online policy has a fill rate increase of up to 8% over a naïve greedy policy. We also show that drone resupply increases fill rates by up to 21% compared to a conventional truck-only resupply system. Computational times to make each decision are in the hundredths of a second, thus allowing real-time feedback to customers regarding their eligibility for same-day delivery.

Dynamic, fair, and efficient routing for cooperative autonomous vehicle fleets

This paper addresses challenges in agricultural cooperative autonomous fleet routing through the proposition, modeling, and resolution of the Dynamic Vehicle Routing Problem with Fair Profits and Time Windows (DVRP-FPTW). The aim is to dynamically optimize routes for a vehicle fleet serving tasks within assigned time windows, emphasizing fair and efficient solutions. Our DVRP-FPTW accommodates unforeseen events like task modifications or vehicle breakdowns, ensuring adherence to task demand, vehicle capacities, and autonomies. The proposed model incorporates mandatory and optional tasks, including optional ones in operational vehicle routes if not compromising the vehicles’ profits. Including asynchronous and distributed column generation heuristics, the proposed Multi-Agent-based architecture DIMASA for the DVRP-FPTW dynamically adapts to unforeseen events. Systematic Egalitarian social welfare optimization is used to iteratively maximize the profit of the least profitable vehicle, prioritizing fairness across the fleet in light of unforeseen events. This improves upon existing dynamic and multi-period VRP models that rely on prior knowledge of demand changes. Our approach allows vehicle agents to maintain privacy while sharing minimal local data with a fleet coordinator agent. We propose publicly available benchmark instances for both static and dynamic VRP-FPTW. Simulation results demonstrate the effectiveness of our DVRP-FPTW model and our multi-agent system solution approach in coordinating large, dynamically evolving cooperative autonomous fleets fairly and efficiently in close to real-time.

Research on Dynamic Takeout Delivery Vehicle Routing Problem under Time-Varying Subdivision Road Network

For the dynamic takeout delivery vehicle routing problem, which faces fluctuating order demand and time-varying speeds, this study presents a novel approach. We analyze the time distribution of takeout orders and apply a Receding Horizon Control (RHC) strategy to convert the dynamic challenge into a static one. The driving speed of delivery vehicles on different roads at different times is determined based on the subdivision criteria of the urban road network and a traffic congestion measurement method. We propose a dynamic takeout delivery vehicle routing optimization model and a time-varying subdivision road network is established to minimize the total delivery cost. We validated the model through simulation examples. The optimization results show that the total distribution cost is reduced after considering the time-varying subdivision road network, with the penalty cost decreasing by 39%. It is evident that considering the subdivision of the road network can enhance order delivery efficiency and optimize the overall dining experience. The sensitivity analysis of various parameters reveals that the delivery platform must appropriately determine the time domain and allocate the number of delivery personnel based on order scale to avoid escalating delivery costs. These findings provide theoretical guidance for vehicle routing planning in the context of delivery platforms.

Handling dynamic capacitated vehicle routing problems based on adaptive genetic algorithm with elastic strategy

With the development of e-commerce platforms, the logistics industry is also booming. The transportation process is at the core of the logistics industry, which influences the timeliness and rationality of logistics distribution. In the real world, there are many dynamic demands in logistics distribution, so logistics distribution should deal with dynamic demands quickly to realize more effective route planning. This paper proposes an adaptive genetic algorithm (AGA) with elastic strategy (AGA-ES) to solve the dynamic capacitated vehicle routing problems (DCVRPs). Firstly, AGA designs an adaptive local search operator, which can adaptively adjust the quantity of nodes that need local search, according to the fitness value of different individuals. At the same time, AGA develops adaptive crossover and mutation operators, which can automatically adjust the crossover and mutation probability based on the different fitness values. The experimental results verify the better performance of AGA on the traditional capacitated vehicle routing problems (CVRPs). After that, AGA combines elastic strategy (AGA-ES) to solve DCVRPs. This paper mainly concerns three types of actual demand information in DCVRPs: distribution nodes increase, distribution nodes decrease, and distribution road conditions change, according to the actual background. AGA-ES could interact with demand information and judge the types of different demands, and then adaptively plan new and reasonable routes after receiving one or more of the above demand information. The verification of benchmark data sets shows that AGA-ES can effectively deal with DCVRPs. Furthermore, this paper collects the longitude and latitude coordinates of 100 SF express stations in Xi’an, constructs the distribution information of these express stations, and verifies that AGA-ES can solve the DCVRPs under the actual background.

Combinatorial Optimization-Enriched Machine Learning to Solve the Dynamic Vehicle Routing Problem with Time Windows

With the rise of e-commerce and increasing customer requirements, logistics service providers face a new complexity in their daily planning, mainly due to efficiently handling same-day deliveries. Existing multistage stochastic optimization approaches that allow solving the underlying dynamic vehicle routing problem either are computationally too expensive for an application in online settings or—in the case of reinforcement learning—struggle to perform well on high-dimensional combinatorial problems. To mitigate these drawbacks, we propose a novel machine learning pipeline that incorporates a combinatorial optimization layer. We apply this general pipeline to a dynamic vehicle routing problem with dispatching waves, which was recently promoted in the EURO Meets NeurIPS Vehicle Routing Competition at NeurIPS 2022. Our methodology ranked first in this competition, outperforming all other approaches in solving the proposed dynamic vehicle routing problem. With this work, we provide a comprehensive numerical study that further highlights the efficacy and benefits of the proposed pipeline beyond the results achieved in the competition, for example, by showcasing the robustness of the encoded policy against unseen instances and scenarios. History: This paper has been accepted for the Transportation Science special issue on DIMACS Implementation Challenge: Vehicle Routing Problems. Funding: This work was supported by Deutsche Forschungsgemeinschaft [Grant 449261765].

An adaptive variable neighbourhood search approach for the dynamic vehicle routing problem

In the traditional vehicle routing problem (VRP), a route plan is pre-determined and remains unchanged afterwards. However in practice, several unforeseen events could occur at any point, which cause traffic congestion and delay to the original planned routes. It is therefore important to re-optimise the routes by taking into consideration the real-time information, leading to the Dynamic VRP (DVRP). While most of the DVRP literature mainly focused on the customer requests as the dynamic aspect, this paper, however, concentrates on the dynamic traffic information based on the level of urgency of the accidents. Critical nodes are introduced into the network to provide a diversion opportunity for the en-route vehicle. This novel concept of ‘criticality’ is also more practical than the commonly adopted strategy that allows instantaneous diversion at the current vehicle location. We proposed an adaptive variable neighbourhood search (AVNS) algorithm to generate routes in the static environment which is then adapted accordingly for the dynamic setting. This is a two stage VNS approach with the first one acts as a learning stage whose information is then used in stage 2. Here, a smaller number of neighbourhoods and local searches are chosen at each iteration while adopting a pseudo-random selection procedure derived from stage 1. To provide solution diversity, a large neighbourhood search is also embedded into the search. The flexibility and adaptability of our AVNS approach are demonstrated by the high quality solutions obtained when tested on the commonly used VRP datasets, ranging in size from 50 to 1200 customers, which are modified accordingly. In addition, managerial insights related to the tightness of the routes are also presented and analysed.

Review of Stochastic Dynamic Vehicle Routing in the Evolving Urban Logistics Environment

Urban logistics encompass transportation and delivery operations within densely populated urban areas. It faces significant challenges from the evolving dynamic and stochastic nature of on-demand and conventional logistics services. Further challenges arise with application doctrines shifting towards crowd-sourced platforms. As a result, “traditional” deterministic approaches do not adequately fulfil constantly evolving customer expectations. To maintain competitiveness, logistic service providers must adopt proactive and anticipatory systems that dynamically model and evaluate probable (future) events, i.e., stochastic information. These events manifest in problem characteristics such as customer requests, demands, travel times, parking availability, etc. The Stochastic Dynamic Vehicle Routing Problem (SDVRP) addresses the dynamic and stochastic information inherent in urban logistics. This paper aims to analyse the key concepts, challenges, and recent advancements and opportunities in the evolving urban logistics landscape and assess the evolution from classical VRPs, via DVRPs, to state-of-art SDVRPs. Further, coupled with non-reactive techniques, this paper provides an in-depth overview of cutting-edge model-based and model-free reactive solution approaches. Although potent, these approaches become restrictive due to the “curse of dimensionality”. Sacrificing granularity for scalability, researchers have opted for aggregation and decomposition techniques to overcome this problem and recent approaches explore solutions using deep learning. In the scope of this research, we observed that addressing real-world SDVRPs with a comprehensive resolution encounters a set of challenges, emphasising a substantial gap in the research field that warrants further exploration.

Solving dynamic vehicle routing problem with time windows by ant colony system with bipartite graph matching

Dynamic Vehicle Routing Problem with Time Windows (DVRPTW) is an extension of the traditional VRPTW by considering dynamic customer characteristics. In this problem, new customers with specific time windows are received dynamically as time progresses and must be incorporated into the evolving schedule. The goal of DVRPTW is to use the minimum number of vehicles to fulfill all the customer demands with the minimum total traveling time. Little work has been done for solving this dynamic variant. In this paper, an evolutionary algorithm using Ant Colony System and Kuhn-Munkres bipartite graph matching, named ACS-KM, is proposed. It can tackle the dynamic issues during the evolutionary process. Experiments show that the proposed algorithm is very effective and has fast convergence. It achieves the best results on 40 out of 48 benchmark instances. For the DVRPTW instances with different levels of dynamicity, the algorithm can always produce better solutions than the previous works.

Elastic Strategy-Based Adaptive Genetic Algorithm for Solving Dynamic Vehicle Routing Problem With Time Windows

Elastic Strategy-Based Adaptive Genetic Algorithm for Solving Dynamic Vehicle Routing Problem With Time Windows

Dinamik araç rotalama problemleriyle ilgili çalışmaların bibliyometrik analizi

Dynamic Vehicle Routing Problems (DVRP) have been highly studied by researchers and decision-makers for the last couple of decades with the effect of developments in GPS and mobile digital tools. Particularly, the digital transformation in logistic and supply chain activities under Industry 4.0 paradigm provides a more suitable environment for DVRP applications. In this study, we conduct a bibliometric analysis related to studies in the DVRP area to understand relationships among publications in terms of countries, institutions, citations, journals, authors, etc., and to show related information and possible trends to the current and prospective researchers and decision-makers. A total of 831 articled retrieved from the Scopus database are examined for the analysis. As a result, the highest number of studies are published by researchers in China while the most impactful studies in terms of citations are carried out by researchers affiliated with US institutions. DVRPs have been frequently studied in Industrial/System Engineering and Management Schools whereas journals in transportation science and operations research/industrial engineering have mostly published DVRP studies. From the application side, ride-sharing, ride-hailing, and crowdsourced delivery appear as new trends for DVRPs in terms of co-occurrence analysis. On the other hand, heuristic and metaheuristic solution approaches frequently co-occur with DVRPs.

A mathematical model and metaheuristic approach to solve the real-time feeder vehicle routing problem

Unlike classic vehicle routing problems, real-time vehicle routing problems (RTVRPs) are real-world dynamic vehicle routing problems (DVRPs) in which customer requests are identified over the time horizon of operations without previous knowledge. In this problem, received requests are answered as quickly as possible and then dispatched to a service vehicle. Considering the RTVRP’s timing constraints, a solution must provide the best trade-off between the computation time required to find the solution and the proposed solution’s costs. A feeder vehicle routing problem (FVRP) consists of a heterogeneous fleet of vehicles, including trucks and motorcycles. In this problem, motorcycles pass easily in crowded areas, and the traffic of urban logistics is distributed easily. The feeder approach also lowers the number of times the vehicle returns to the central depot for loading, resulting in cost and time savings. The present article proposes a real-time feeder vehicle routing problem (RTFVRP) in a situation where every truck and every motorcycle can join during the freight delivery process. After modeling the RTFVRP through mixed-integer linear programming, a dynamic inertia weight particle swarm optimization (DIWPSO) algorithm is offered to solve the problem. The results of the static version of the FVRP in the small and the last time slices show that the GAMS outputs outperform those of the DIWPSO and differential evolution (DE), both indicating a similar performance. The results of running these algorithms for 21 DVRP test instances revealed that the PSO outperforms the DE in quality and solution runtime in both static and dynamic versions. Overall, the PSO and DE algorithms generated 34.33% and 30.37% cost savings in implementing RTFVRP, respectively, compared to the case that all requests were available at the beginning of the working day.

Time Window Oriented IoT Vehicle Pathway Study for the Dynamically Changing Needs of E-Commerce Customers

The main dynamic truck routing problem also presents a significant difficulty in the logistics sector, which is an unavoidable development trend of the contemporary technological changing society. A dynamic vehicle routing problem with time window model is suggested by the study in order to establish an effective and low-energy dynamic response method. The fundamental concept is to disrupt the conventional strategy of static dynamic consumers responding in time slots by dividing the dynamic time window into a static time window with several time slice intervals. The study makes use of cutting-edge ideas including dynamic attitude, before-and-after time slicing, and continuous optimisation while proposing a new method for model solution to optimise dynamic vehicle route issues effectively and affordably. The study employs the Solomon optimisation dataset and runs simulation studies on the Java platform to confirm its efficacy. The experimental findings demonstrated that the optimisation technique employed in the study reduced the cost of travelling by 83.8 miles while also considerably increasing the average vehicle utilisation by 3.6%. Because driving distance cost and vehicle number cost are typically positively connected with dynamic attitude, the study employs solutions that can increase dynamic response efficiency and save money. As a result, their robustness is higher.

A branch-and-regret algorithm for the same-day delivery problem

We study a dynamic vehicle routing problem where stochastic customers request urgent deliveries characterized by restricted time windows. The aim is to use a fleet of vehicles to maximize the number of served requests and minimize the traveled distance. The problem is known in the literature as the same-day delivery problem, and it is of high importance because it models a number of real-world applications, including the delivery of online purchases. We solve the same-day delivery problem by proposing a novel branch-and-regret algorithm in which sampled scenarios are used to anticipate future events and an adaptive large neighborhood search is iteratively invoked to optimize routing plans. The branch-and-regret is equipped with four innovation elements: a new way to model the subproblem, a new policy to generate scenarios, new consensus functions, and a new branching scheme Extensive computational experiments on a large variety of instances prove the outstanding performance of the branch-and-regret, also in comparison with recent literature, in terms of served requests, traveled distance, and computational effort.

A survey of dynamic pickup and delivery problems

Due to the ubiquitous real-world applications of logistics and supply chain management over the past two decades, dynamic pickup and delivery problems (DPDPs), as a subclass of dynamic vehicle routing problems in which objects or people must be collected and delivered in real time, have become a popular research topic in the field of combinatorial optimization. This article provides a comprehensive review of the DPDP literature from 2004 to 2023, in which their corresponding characteristics, principles, and theoretical analysis are discussed in detail. Furthermore, a taxonomy of the related solution methods for DPDPs is given, which can be segmented into four categories: exact methods, heuristics, metaheuristics, and learning-based methods. Moreover, some experimental comparisons and analysis of up-to-date real-word DPDP benchmarks from Huawei Company are included. Finally, a brief conclusion is given to summarize some potential future directions for DPDPs.

Dynamic electric vehicle routing problem considering mid-route recharging and new demand arrival using an improved memetic algorithm

With the widespread popularity of electric vehicles (EVs) in recent years, electric vehicle routing problem (EVRP) has received considerable attention from logistics management field. However, the real-world logistics and transportation system is always time-varying, such as new customer demand arrives dynamically. This dynamic transportation environment poses a great deal of challenges upon the decision-making of EVRP since the mid-route recharging of EVs has to be considered to meet the dynamic arrival of new customer demand due to the limited battery capacity. Therefore, a dynamic EVRP (DEVRP) with mid-route recharging and new demand arrival is investigated in this study. A mathematical model considering both recharging and routing decision-makings is developed, and then an improved memetic algorithm (IMA) with adaptive local search and economical random immigrant strategy is proposed. Four peer algorithms are used to test the performance of the proposed IMA on numerous extended benchmarks. It is observed that IMA can be treated as a more effective solution tool to achieve a better routing plan as well as the improved energy efficiency of EVs.

A dynamic approach for the multi-compartment vehicle routing problem in waste management

Urban areas worldwide face a significant environmental challenge which is increasing municipal solid waste rate. Addressing its negative consequences necessitates advancements in waste management systems. Although the previous research focused on the static routing approach in the collection phase, this paper adds a dynamic municipal solid waste collection scheme to optimize vehicle routing, accounting for fluctuations in waste generation and changes in transportation systems. This study employs, for the first time, the application of a discrete choice model (DCM) to streamline the process of re-optimization in dynamic vehicle routing problems (DVRP). At each decision epoch, DCM is applied to determine the likelihood of choosing the next geographical zone to visit bins based on current waste generation levels and traveling costs. Moreover, the multi-compartment vehicles are considered to preserve waste segregation during transportation, thereby increasing operational efficiency and regulatory compliance. Another contribution of this paper is to determine visiting priority for each bin by adjusting the time window based on the threshold waste level. Hence, this paper proposes a framework for sustainable, efficient, and effective waste management practices by integrating the benefits of dynamic and multi-compartment routing. Furthermore, a hybrid Genetic and Particle Swarm Optimization algorithm has been designed to find the best solution for the studied problem as well as some of the latest and most proficient metaheuristic algorithms. Finally, the Best Worst Method is applied to find the best-proposed algorithm to solve the presented problem, indicating that the hybrid algorithm has the highest performance in providing high-quality route plans.

Reinforcement Learning-based approach for dynamic vehicle routing problem with stochastic demand

This paper studies a dynamic vehicle routing problem under stochastic demands, drawn from a real-world situation. Specifically, a single courier must accomplish two kinds of tasks: deliveries known at the beginning of the operation and pickups that appear throughout the daily operation with specific patterns. The objective is to maximise the rewards obtained from serving both types of customers during a limited period. Our contribution lies in using the neural network and historical couriers’ decisions to learn a base policy that captures human experience for better decision making. The reinforcement learning framework is then used to make the base policy explore new scenarios through simulations and further train the base policy with newly generated data. We show that our approach allows the serving of an average of 12% and 8% more customers under some conditions than the nearest-neighbour policy in high density area and low density area, respectively.

Reoptimisation strategies for dynamic vehicle routing problems with proximity-dependent nodes

Autonomous vehicles create new opportunities as well as new challenges to dynamic vehicle routing. The introduction of autonomous vehicles as information-collecting agents results in scenarios, where dynamic nodes are found by proximity. This paper presents a novel dynamic vehicle-routing problem variant with proximity-dependent nodes. Here, we introduced a novel variable, detectability, which determines whether a proximal dynamic node will be detected, based on the sight radius of the vehicle. The problem considered is motivated by autonomous weed-spraying vehicles in large agricultural operations. This work is generalisable to many other autonomous vehicle applications. The first step to crafting a solution approach for the problem is to decide when reoptimisation should be triggered. Two reoptimisation trigger strategies are considered—exogenous and endogenous. Computational experiments compared the strategies for both the classical dynamic vehicle routing problem as well as the introduced variant. Experiments used extensive standardised vehicle-routing problem benchmarks with varying degrees of dynamism and geographical node distributions. The results showed that for both the classical problem and the novel variant, an endogenous trigger strategy is better in most cases, while an exogenous trigger strategy is only suitable when both detectability and dynamism are low. Furthermore, the optimal level of detectability was shown to be dependent on the combination of trigger, degree of dynamism, and geographical node distribution, meaning practitioners may determine the required detectability based on the attributes of their specific problem.

A Bibliometric Visualized Analysis and Classification of Vehicle Routing Problem Research

The vehicle routing problem (VRP), as a classic combinatorial optimization problem, has always been a hot research topic in operations research. In order to gain a deeper understanding of the VRP problem, this work uses the knowledge graph to comprehensively analyze and summarize the literature related to VRP from 1959 to 2022 in the Web of Science (WoS) database. Firstly, according to the basic statistical information of the literature, the annual publications, the authors, their institutions and countries, the keyword co-occurrence, and the literature co-citation network are analyzed to comprehensively summarize and generalize the research on VRP and predict its future development trend. The results show that, in the past 60 years, there have been abundant changes in the research on VRP. The United States and China have made the most important contributions in the field of VRP. According to the WoS literature retrieval results and classification methods, the VRP models and their solutions are comprehensively classified, and the model solving algorithms are divided into exact algorithms, heuristic algorithms, metaheuristic algorithms, hyper-heuristic algorithms, machine learning, etc. The results show that the development of information computing technology plays an important role in research on the VRP problem, and dynamic VRP, hyper-heuristic algorithms, deep reinforcement learning, etc. are the future development directions of the VRP model and its optimization. The results of this research can provide help and guidance for beginners and scholars outside the industry to comprehensively understand the development and research hotspots of VRP.