Two-echelon Vehicle Routing Problem Research Articles

A gradient-descent-based framework for solving a stochastic two-echelon delivery problem with cargo-bikes

In this paper, we examine a stochastic two-echelon vehicle routing problem (2e-VRP) using cargo bikes within hyperconnected networks. The focus is on the integration of both delivery and pickup of reusable containers, incorporating transshipment operations, time windows, and stochastic demand constraints. The model also considers the flow consolidation for empty and full containers at the satellites and allows for load splitting. Moreover, this study introduces an innovative gradient-descent-based optimization framework to handle the combinatorial complexity of the proposed model, opening new avenues in stochastic programming. Furthermore, the performance of this novel method is compared against the sample average approximation method, evaluating both solution quality and computational efficiency. Experimental results demonstrate the model’s advanced integration and flexibility, significantly enhancing urban delivery systems and advancing logistics and transportation optimization research.

Collaborative last mile delivery: A two-echelon vehicle routing model with collaboration points

Collaboration is key to addressing operational efficiencies, and in the context of last mile delivery, operational inefficiencies arising from empty trips, low load factor, and long dwell times require collaboration amongst multiple logistics service providers (LSPs). However, existing studies in the last mile delivery adopting collaboration as a means of sharing strategic infrastructure assets, such as distribution centers (DCs), satellites, and driving vehicles, might not be seen as favorable for logistics service providers due to ownership disputes and loss of control over assets. To address this limitation, a new routing method for addressing operational efficiencies in last mile delivery has been proposed in this study, allowing for collaboration across multiple logistics service providers without sharing strategic assets. We have formulated a two-echelon vehicle routing problem with collaboration Points (2E-VRP-CP) where the exchange of goods happens between second-echelon vehicles belonging to different logistics service providers. The method uses a mixed-integer linear programming model (MILP) that minimizes the total distribution cost and has been tested on randomly generated instances. Results suggest that the proposed collaborative approach of exchanging goods between second-echelon vehicles belonging to different logistics service providers can reduce costs by up to 10% relative to the non-collaborative approach and up to 9% compared to the existing collaborative approach that shares strategic assets. A four-phase heuristic algorithm has also been developed to tackle computationally expensive larger instances, which can obtain cost savings of up to 15% compared to a non-collaborative approach. Future work will involve developing a profit-allocation mechanism and will consider additional constraints to make the model more realistic in addressing a real-world problem. Overall, this model can help fleet managers achieve efficient fulfillment in last mile delivery, while the proposed heuristics can enable stakeholders to scale their solutions to real-world scenarios.

Two-echelon multi-commodity multimodal vehicle routing problem considering user heterogeneity in city logistics

The considerable increase in parcel deliveries has negatively impacted the accessibility and livability of cities. One solution strategy is to decouple short-distance from long-distance shipping so that last-mile transport can be performed with low-footprint vehicles. Such solutions are referred to in the literature as multi-echelon distribution systems. This study introduced a new variant of the two-echelon vehicle routing problem that considers multiple alternative transport modes as well as multiple commodities over a multi-period time horizon, where customers can obtain their commodities from any store. We referred to this problem as the two-echelon multi-commodity multimodal vehicle routing problem (MCM-2E-VRP). The objective of service providers is to minimize total generalized costs while satisfying customer requirements. We formulated this as a mathematical model based on a space–time network and introduced a random utility discrete choice model to capture variations in performance and preferences. We developed an adaptive large-neighborhood search (ALNS) algorithm to provide solutions for newly generated MCM-2E-VRP instances based on the Beijing Yizhuang transportation network. Extensive numerical experiments were conducted to verify the effectiveness of the proposed model and algorithm. A sensitivity analysis revealed some policy-relevant findings regarding the effects of store distribution and vehicle capacity.

An integrated temporal and spatial synchronization for two-echelon vehicle routing problem in waste collection system

This paper presents a two-echelon vehicle routing problem (2E-VRP) with vehicle synchronization at meeting points for the reverse logistic network to collect waste in the urban area. Low-capacity vehicles are utilized to perform collection only in the inner part of the city because of restricted access and limited infrastructure to be expanded. While, high-capacity vehicles are used to transform waste from the border of the inner city to the recycling centers located outside of city. Vehicles of the first and second echelons visit each other at meeting points, which do not have storage capacity mainly because of environmental and social consequences of the transshipment of waste. The timing aspect plays a critical role at meeting points to ensure the reasonable sequence of operations. So, temporal synchronization, a critical aspect of 2E-VRP, is considered in this paper, as well as minimization of waiting time of vehicles in meeting points to avoid long dwelling time. Moreover, because the previous study of 2E-VRP has not dealt with space limitation of meeting points, this paper presents a 2E-VRP that incorporates temporal synchronization, waiting time, and temporal capacity simultaneously for the first time to address a more practical model. To solve the mentioned problem a set of capable and latest metaheuristics are proposed as well as the hybrid ones to probe their efficiency and reasonably construct high quality routes. Moreover, the impact of the temporal capacity is investigated compared to temporal synchronization without considering temporal capacity.

A Two-echelon Vehicle Routing Problem with time-dependent travel times in the city logistics context

The fast rates at which urban population is growing coupled with increasing demands expressed within cities have given rise to challenging freight transportation problems. The Two-echelon Vehicle Routing Problem (2E-VRP) has been proposed as a scheme to tackle city-related problems. To better evaluate its pertinence in large congested city areas, this work addresses a version of the 2E-VRP in which synchronization is required among the two echelons. Besides, it considers time-dependent travel times at both echelons as well as time windows at customers. Other characteristics such as open routes at second echelon offer a degree of flexibility on the efficiency of the distribution specially when dealing with outsourcing schemes. The primary goal is to minimize the number of vehicles. Meanwhile, travel and waiting times, as well as penalties for late deliveries are minimized as a secondary objective. A two-phase metaheuristic approach is proposed to solve the problem on existing benchmarks; as well on a new set of instances based on real information from the city of Bogota, provided by an industrial partner. The experiments prove that including time-dependent travel times is of utmost importance for practical applications.

A multi-objective two-echelon vehicle routing problem with multiple delivery options

The classical two-echelon vehicle routing problem (2E-VRP) has commodities transported from depots to intermediate facilities and then delivered to customers from these facilities. In this study, we consider another type of 2E-VRP, in which vehicles from both echelons can be used for home delivery. We also present a sustainable model, which considers customers' preferred delivery locations, economic and environmental costs. Also, we present a meta-heuristic algorithm to solve real-world size instances in a timely manner. The computational results demonstrate that the proposed solution method can effectively solve small instances with a minimal gap when compared to an exact solver, and it can also handle large instances in a timely manner.

Stochastic two-echelon vehicle routing problem with time windows: city logistics case study

Stochastic two-echelon vehicle routing problem with time windows: city logistics case study

The two-echelon vehicle routing problem with time windows, intermediate facilities, and occasional drivers

The two-echelon vehicle routing problem with time windows, intermediate facilities, and occasional drivers

Enhancing E-Grocery-Delivery-Network Resilience with Autonomous Delivery Robots

This paper examines the challenges associated with the efficient planning and operation of an E-grocery delivery system using Autonomous Delivery Robots (ADR) during unforeseen events. The primary objective is to minimize unfulfilled customer demands rather than focusing solely on cost reduction, considering the humanitarian aspect. To address this, a two-echelon vehicle routing problem is formulated, taking into account stochastic service times and demands. Two models, namely a deterministic model and a chance-constraint model, are employed to solve this problem. The results demonstrate that the chance-constraint model significantly reduces unmet demands compared to the deterministic model, particularly when the delivery deadline has a broad time window and the ADR/van speed ratio is moderate.

A fast simulated annealing heuristic for the multi-depot two-echelon vehicle routing problem with delivery options

ABSTRACT We studied a variant of the vehicle routing problem (VRP) arising in last-mile distribution, called the multi-depot two-echelon vehicle routing problem with delivery options (MDTEVRP-DO). The MDTEVRP-DO involves two decision levels: (i) designing routes for a fleet of vehicles located in multiple depots to transport customer demands to a set of satellites and (ii) routing a fleet of vehicles from the satellites to serve the final customers. Nowadays, a relevant feature of the problem characterizing delivery services is that customers can collect their packages at pickup stations near their homes or workplaces. We designed an effectively simulated annealing (SA) heuristic for the problem. The new algorithm was extensively tested on benchmark instances from the literature, and its results were compared with those of start-of-the-art algorithms. The results show that the proposed SA obtains 30 out of the 36 best solutions for the MDTEVRP-DO benchmark instances. Moreover, its computation performance is superior to state-of-the-art algorithms for the MDTEVRP-DO.

Reconfiguration of last-mile supply chain for parcel delivery using machine learning and routing optimization

Last-mile delivery has several negative environmental impacts in urban areas because of its high levels of greenhouse gas emissions and air pollution, as well as traffic congestion. These issues motivate decision-makers to redesign the delivery networks and make them more sustainable and efficient. A well-planned territory design can reduce total travel times and distances in urban distribution systems, in addition to balancing the workload between drivers. In this study, a two-echelon parcel distribution network modeled as the two-echelon vehicle routing problem with territory design and satellite location decisions is considered. A three-stage decomposition algorithm is proposed to solve this problem. In the first stage, a non-supervised machine learning clustering method is applied, followed by an algorithm based on the nearest-neighbor routing procedure, to find a set of routes for the second and first echelons. An improvement heuristic was also applied to improve the results in terms of the second echelon routing, considering the computational complexity of a large-scale instance. A case study based on real data from a delivery company in the city of Paris, France is adopted to perform the experiments. The outcomes of this paper show an improvement of 22.6% in travel time and distance. This reduction is also assessed with performance indicators like land use, fixed costs, energy consumption, carbon dioxide equivalent, and fine particles emissions.

Computational approaches for solving two-echelon vehicle and UAV routing problems for post-disaster humanitarian operations

During and after Hurricane Maria in 2017, the island of Puerto Rico faced an impossible situation: the transportation, power, and communication networks were all damaged, leading to numerous people being trapped. Humanitarian logistics service providers have the responsibility to reach as many affected populations as possible within short periods of time. Their extremely difficult operations are further hindered by these failures in our built environment. Failures in transportation mean that some routes cannot be used by conventional ground vehicles; failures in communication mean that demands are uncertain, and the locations of said demands may be difficult to pinpoint. In this work, we propose a novel two-echelon vehicle routing framework for performing many of the humanitarian logistics operations using aerial uncrewed autonomous vehicles (drones) to address the issues associated with these infrastructure failures. In our proposed framework, we assume that ground vehicles cannot always reach the trapped population directly, but they can transport drones from a depot to some intermediate satellite locations. The drones launched from these locations can serve to both identify demands for medical and other aids (e.g., epi-pens, medical supplies, dry food, water) and make deliveries to satisfy them. Specifically, we present an expert decision support system, in which the resulting optimization problem is formulated as a two-echelon vehicle routing problem with trucks as the first echelon vehicles and drones as the second echelon vehicles. Our framework utilizes two types of drones. Hotspot or communication providing drones have the capability of providing cell phone and internet reception, and hence, are used to capture demands and their locations. Delivery drones are subsequently employed to satisfy these obtained demands. To handle demand uncertainty, we decompose the decision problem into two stages: providing telecommunications capabilities in the first stage, thereby capturing demands precisely, and satisfying the resulting demands in the second stage. To solve the resulting models, we propose a matheuristic computational approach in the form of a decomposition algorithm inspired by column generation to identify optimal drone routes. To showcase the application of our proposed framework, we present results from numerical experiments on datasets created to simulate the demand for medical aid in Puerto Rico after Hurricane Maria.

Machine learning-based optimisation in a two-echelon logistics network for the dry port operation in China

ABSTRACT Efforts of creating economic recovery after the COVID-19 pandemic stipulate international logistics demands in the countries and regions affected by China's Belt and Road initiative. Considering the increasing number of small and middle-sized enterprises, there is a great challenge to make transportation plans for the hub port, dry ports, and related enterprises. We investigate a two-echelon vehicle routing problem with simultaneous pickups and deliveries. On one hand, freights are transported from a central depot to multiple satellites, then distributed from the satellites to customers. On the other hand, freights collected from the customers will be loaded at the satellites, then transported back to the depot. We model the problem as mixed integer programming and propose a machine learning-based hybrid algorithm to solve the problem. Our hybrid algorithm comprises a K-Nearest Neighbour algorithm and an Adaptive Large Neighbourhood Search heuristic. We apply our modelling and solution approach to a real case based on the online digital platform ‘Inland Port Cloud Wharf’ in China, which matches international demands of commodities with domestic supplies. Our computational experiments based on a practical case study show the efficiency of our KNN_ALNS algorithm in optimising networks with multimodal coordination and addressing real-world logistics complexities.

Multi-objective optimization of two-echelon vehicle routing problem: Vaccines distribution as a case study

During pandemics, the efficiency of the vaccine supply chain may be compromised, especially the last-mile distribution, due to poor infrastructure that is unable to support the urgent need for vaccination. In developing countries, this becomes even more challenging due to limited vehicles, road conditions, and inadequate cold storage. Since it is impractical to construct permanent warehouses when pandemics occur, vaccine distribution would be extravagant both environmentally and financially. In this study, a new multi-objective MILP model combining two-echelon vehicle routing problem (2E-VRP) and vaccine supply chain (VSC) is presented to minimize the number of unsatisfied doses undelivered to customers. A heuristic solution based on the greedy random search is proposed to solve the model, as it is classified as NP-hard model. The model is solved using the commercial solver CPLEX for different datasets. Then the heuristic is used to solve the same datasets, and the results are compared based on the solution’s quality and computation efforts. Moreover, Pareto fronts were constructed to demonstrate the trade-offs between the conflicting objective functions. Finally, a real case study is solved using the proposed model to demonstrate its effectiveness compared to the original VRP, and the results showed an improvement of average 11.97% in the number of doses delivered.

A stochastic formulation of the two-echelon vehicle routing and loading bay reservation problem

This paper studies a goods delivery problem for multiple courier companies in central city areas integrated with a loading bay scheduling problem. The goods delivery problem is formulated as a stochastic two-echelon vehicle routing problem, while the loading bays are managed through a central reservation system, which assigns loading bays to courier vehicles taking into account their delivery demands. A stochastic programming model with chance constraints is formulated to find the optimal vehicle routing and loading bay reservation strategy, and a hybrid genetic algorithm is developed to solve the model. Numerical results suggest that the reservation system can help coordinate deliveries from different courier companies and substantially improve the overall delivery efficiency and loading space utilisation.

Two-echelon vehicle routing problem with direct deliveries and access time windows

Nowadays, heavy-duty trucks are usually restricted from entering urban areas due to emission and congestion problems in most cities. So, a two-echelon distribution system becomes vastly applicable, in which satellites transfer cargo and avoid heavy-duty trucks entering urban areas. However, with the development of new energy vehicles and access policies and regulations, some environmentally friendly trucks are accessible to urban areas within specific time windows of daytime directly. In light of this, we introduce a two-echelon vehicle routing problem with direct deliveries and access time windows (2E-VRPDDATW) arising in city logistics. In this problem, customers are served by the two-echelon distribution systems within their required time windows and are allowed to be directly delivered by the first echelon vehicles within access time windows, which provides more flexible routing schemes. A novel mixed integer linear programming (MILP) model for the above problem is presented, and the corresponding adaptive large neighborhood algorithm is developed. The computational experiments are provided to verify the validity of the proposed model and the effectiveness of the algorithm. Finally, the sensitivity analysis shows some interesting findings about the number of two-echelon vehicles and the assignment of customers. Moreover, we conclude that direct deliveries are advantageous in transportation costs when the proportion of the end time of access time window to the last end time of customers is greater than 0.25.

Evolutionary Optimization of COVID-19 Vaccine Distribution With Evolutionary Demands

Vaccination uptake has become the key factor that will determine our success in containing the coronavirus pneumonia (COVID-19) pandemic. Efficient distribution of vaccines to inoculation spots is crucial to curtailing the spread of the novel COVID-19 pandemic. Normally, in a big city, a huge number of vaccines need to be transported from central depot(s) through a set of satellites to widely scattered inoculation spots by special-purpose vehicles every day. Such a large two-echelon vehicle routing problem is computationally difficult. Moreover, the demands for vaccines evolve with the epidemic spread over time, and the actual demands are hard to determine early and exactly, which not only increases the problem difficulty but also prolongs the distribution time. Based on our practical experience of COVID-19 vaccine distribution in China, we present a hybrid machine learning and evolutionary computation method, which first uses a fuzzy deep learning model to forecast the demands for vaccines for each next day, such that we can predistribute the forecasted number of vaccines to the satellites in advance; after obtaining the actual demands, it uses an evolutionary algorithm (EA) to route vehicles to distribute vaccines from the satellites/depots to the inoculation spots on each day. The EA saves historical problem instances and their high-quality solutions in a knowledge base, so as to capture inherent relationship between evolving problem inputs to solutions; when solving a new problem instance on each day, the EA utilizes historical solutions that perform well on the similar instances to improve initial solution quality and, hence, accelerate convergence. Computational results on real-world instances of vaccine distribution demonstrate that the proposed method can produce solutions with significantly shorter distribution time compared to state-of-the-arts and, hence, contribute to accelerating the achievement of herd immunity.

An exact algorithm for the two-echelon vehicle routing problem with drones

This paper studies a new variant of the vehicle routing problem with drones, i.e., the two-echelon vehicle routing problem with drones, where multiple vehicles and drones work collaboratively to serve customers. Drones can perform multiple back-and-forth trips when their paired vehicle stops at a customer node, forming a two-echelon network. Several practical constraints such as customers’ delivery deadlines and drones’ energy capacity are considered. Different from existing studies, we treat the number of drones taken by each vehicle as a decision variable instead of a given parameter, which provides more flexibility for planning vehicle and drone routes. We first formulate this problem as a mixed-integer linear programming model, which is solvable by off-the-shelf commercial solvers. To tackle instances more efficiently, we next construct a set-partitioning model. To solve it, an exact branch-and-price algorithm is proposed, where a bidirectional labeling algorithm is used to solve the pricing problem. To speed up the algorithm, a tabu search algorithm is first applied before the exact labeling algorithm for finding desired columns in each iteration of the column generation process. Extensive numerical tests show that our algorithm can solve most instances within 25 customers to optimality in a short time frame and some instances of 35 customers to optimality within a three-hour time limit. Results also demonstrate that the allocation decisions of drones can help save the duration of all routes by 3.44% on average for 25-customer instances, compared to the case of fixing the number of paired drones on each vehicle. In addition, sensitivity analyses show that multiple strategies, e.g., adopting batteries of a higher energy density and developing faster drones, can be applied to further improve the delivery efficiency of a truck–drone system.

The Two-Echelon Vehicle Routing Problem with Pickups, Deliveries, and Deadlines

The Two-Echelon Vehicle Routing Problem with Pickups, Deliveries, and Deadlines

Stochastic two-echelon vehicle routing problem with time windows: city logistics case study

Stochastic two-echelon vehicle routing problem with time windows: city logistics case study