Two-echelon Vehicle Routing Problem Research Articles

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

An adaptive large neighborhood search heuristic for multi-commodity two-echelon vehicle routing problem with satellite synchronization

<p style='text-indent:20px;'>In considering route optimization from multiple distribution centers called depots via some intermediate facilities called satellites to final customers with multiple commodities request, we introduce the Multi-Commodity Two-Echelon Vehicle Routing Problem with Satellite Synchronization (MC-2E-VRPSS). The MC-2E-VRPSS involves the transportation from multiple depots to satellites on the first echelon and the deliveries from satellites to final customers on the second echelon. The MC-2E-VRPSS integrates satellite synchronization constraints and time window constraints for satellites on the two-echelon network and aims to determine cost-minimizing routes for the two echelons. The satellite synchronization constraints which trucks from the multiple depots to some satellites need to be coordinated guarantee the efficiency of the second echelon network. In this study, we develop a mixed-integer programming model for the MC-2E-VRPSS. For validating the model formulation, we conduct the computational experiments on a set of small-scale instances using GUROBI and an adaptive large neighborhood search (ALNS) heuristic which we develop for the problem. Furthermore, the computation experiments for evaluating the applicability of the ALNS heuristic compared with large neighborhood search (LNS) on a set of large-scale instances are also conducted, which proved the effectiveness of the ALNS.</p><p style='text-indent:20px;'> </p><p style='text-indent:20px;'>Addendum: The Acknowledgement “This study was supported by the Humanities and Social Sciences Foundation Program of the Ministry of Education (Project No.19YJA630122), and the "National Key R&D Program of China"(Grant No.2020YFB1712900)” is added. We apologize for any inconvenience this may cause.</p>

The Two-Echelon Vehicle Routing Problem with Transshipment Nodes and Occasional Drivers: Formulation and Adaptive Large Neighborhood Search Heuristic

This research introduces a new variant of the two-echelon vehicle routing problem (2EVRP) called the two-echelon vehicle routing problem with transshipment nodes and occasional drivers (2EVRP-TN-OD). In addition to city freighters in the second-echelon network, a set of occasional drivers (ODs) is available to serve customers. ODs are the basis of a crowd-shipping system in which crowds with planned trips are willing to take detours to deliver packages in exchange for some compensation. To serve customers, ODs collect the assigned packages at either satellite served by first-echelon trucks or transshipment nodes served by city freighters. We formulate this problem as a mixed-integer nonlinear programming model and develop an adaptive large neighborhood search (ALNS) to solve it. New problem-specific destroy and repair operators and a tailored local search procedure are embedded into ALNS to deal with the problem’s unique characteristics. The experiments show that the proposed ALNS effectively solves 2EVRP-TN-OD by outperforming Gurobi in terms of both solution quality and computational time. Moreover, the experiments confirm that employing occasional drivers leads to lower operational costs. Sensitivity analyses on the characteristics of occasional drivers and the impact of transshipment nodes are presented as interesting managerial insights from 2EVRP-TN-OD.

Physical Internet-enabled E-grocery delivery Network:A load-dependent two-echelon vehicle routing problem with mixed vehicles

Autonomous delivery robots (ADRs) as green last-mile delivery alternatives to traditional vans have received much attention due to the rapid development of Physical Internet (PI). However, their low efficiency limits the application in the last-mile delivery because few orders per trip are delivered. Also, the cost and emission impact of new motilities on the PI-enabled last-mile delivery network is still not clear. To address these issues, this study developed an innovative two-echelon delivery system that combines traditional vans and ADRs to take their advantages for the last-mile delivery. The objective of this study was to minimize transportation costs and emissions through solving an extension of a two-echelon vehicle routing problem considering load-dependent unit transport costs and unit emissions with mixed vehicles and multiple depots. The problem was formulated as a mixed-integer programming model and then efficiently solved by a cluster-based artificial immune algorithm, in which an improved clustering method was employed to assign the customers. The experimental results showed that the proposed solution approach efficiently solved the problem with better solutions than existing approaches in the relevant literature. Several managerial implications on configuring the two-echelon delivery system were also provided for potential applications.

A Fuzzy Two-Echelon Model to Optimize Energy Consumption in an Urban Logistics Network with Electric Vehicles

With the increase in pollutants, the need to use electric vehicles (EVs) in various urban logistics activities is an increasingly important issue. Currently, there are issues with the efficiency of transport companies in recognizing the effects of uncertain factors in daily logistics operations. Thus, this research proposes a novel fuzzy two-echelon vehicle routing problem involving heterogeneous fleet EVs and internal combustion vehicles (ICVs). The first echelon is recyclable wastes collected from waste pickup points and transported to the primary centers by EVs. The second echelon is transporting recyclable wastes to recycling centers by ICVs. In the proposed models, fuzzy numbers are used to express the rate and energy consumption depending on the amount of load, vehicle speed, and recyclable waste. In addition, a penalty cost of the time windows is considered in both echelons. The models are solved by CPLEX and two meta-heuristic algorithms, gray wolf optimizer (GWO) and tabu search (TS), based on different instance sizes. The results show the efficiency of the proposed algorithms.

A Chance-Constrained Two-Echelon Vehicle Routing Problem with Stochastic Demands

Two-echelon distribution systems are often considered in city logistics to maintain economies of scale and satisfy the emission zone requirements in the cities. In this work, we formulate the two-echelon vehicle routing problem with stochastic demands as a chance-constrained stochastic optimization problem, where the total demand of the customers in each second-echelon route should fit within the second-echelon vehicle capacity with a high probability. We propose two efficient solution procedures based on column generation. Key to the efficiency of these procedures is the underlying labeling algorithm to generate new columns. We propose a novel labeling algorithm based on simultaneous construction of second-echelon routes and a labeling algorithm that builds second-echelon routes sequentially. To further enhance the performance of the solution procedure, we use statistical inference tests to ensure that the chance constraints are met. We reduce the number of customer combinations for which the chance constraint needs to be verified by imposing feasibility bounds on the stochastic customer demands. With these bounds, the runtimes of the labeling algorithms are reduced significantly. The novel labeling algorithm, statistical inference, and feasibility bounds can also be applied to dependent, correlated, and data-driven (scenario-based) demand distributions. Finally, we show the value of the stochastic formulation in terms of improved solution cost and guaranteed feasibility of second-echelon routes. Funding: This work was funded by the Dutch Research Council (NWO) DAREFUL project [Grant 629.002.211] and was carried out on the Dutch national e-infrastructure with the support of SURF Cooperative. Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2022.1162 .

An Embedded Hamiltonian Graph-Guided Heuristic Algorithm for Two-Echelon Vehicle Routing Problem.

Two-echelon vehicle routing problem (2E-VRP) is an NP-hard combinatorial optimization problem and a basic mathematical model of modern city logistics. While it is difficult to obtain the optimal solution of 2E-VRP, this study finds a breakthrough that the structure of the optimal route planning for 2E-VRP is usually an embedded Hamiltonian graph. In the graph, routes can be drawn in a planar graph as Hamiltonian circuits without intersections. Based on this finding, an embedded Hamiltonian graph-guided heuristic algorithm is proposed to solve 2E-VRP. As a crucial part of the algorithm, an initialization scheme is designed to search for the farthest vertices from each route and insert the rest of the vertices. In the satellite-adjustment process, a dynamic adjustment for satellites scheme is proposed to adjust the state of satellites. The two schemes aim to construct Hamiltonian circuits with few intersections. Experiments have been conducted on 207 instances to demonstrate the effect of the proposed algorithm on solving 2E-VRP. Experimental results show that the proposed algorithm can obtain more solutions of 2E-VRP with significantly smaller objective-function values. Furthermore, the number of intersections in routes generated by the proposed algorithm is much less than those obtained by the compared algorithms. With the use of the two schemes, the embedded Hamiltonian graph-guided heuristic algorithm significantly outperforms the compared algorithms for 2E-VRP.

New Mobility-Assist E-Grocery Delivery Network: a Load-Dependent Two-Echelon Vehicle Routing Problem With Mixed Vehicles

New forms of transport, such as autonomous delivery robots (ADRs), have attracted considerable attention in recent years for their potential use as green last-mile delivery alternatives because of their flexibility in some areas unreachable by van. However, their low efficiency, delivering a limited number of orders each trip, limits their application in the last mile. Also, the cost and emission impact of new forms of transport on the last-mile delivery network is still not clear. To address these issues, we developed a new two-echelon delivery system that combines traditional vans and ADRs, making use of their individual advantages to overcome their drawbacks and enhance efficiency in the deliveries. The objective of this study was to develop a new approach based on a metaheuristics methodology to minimize transport and emission costs through modeling and to solve the extension of two-echelon load-dependent vehicle routing problems with mixed vehicles (2E-LDVRP-MV). The complicated 2E-LDVRP-MV problem was formulated as a mixed-integer programming (MIP) model and solved efficiently with a cluster-based artificial immune algorithm (C-AIA) in which clustering was employed to allocate customers. We performed a set of numerical experiments with a solver and the proposed C-AIA heuristics. C-AIS highlights the operational implications of four parameters: ratios between load and the empty vehicle weight; vehicle types; emission levels; and customer densities. Our results provide a unique perspective on tactical planning for a sustainable urban logistics system, and this new two-echelon system could be applied in e-grocery last-mile delivery networks where vans and ADRs are combined.

Hybrid adaptive large neighborhood search for vehicle routing problems with depot location decisions

This article considers three variants of the vehicle routing problem (VRP). These variants determine the respective depot locations from which customers are supplied, i.e., the two-echelon VRP (2E-VRP), the location routing problem (LRP), and the multi-depot VRP (MDVRP). Both the LRP and the MDVRP can be formulated as special cases of the 2E-VRP, so that all three problem classes can be readily solved via a single solution approach. We develop such a unified solution approach for all three problem classes based on the recently proposed hybrid adaptive large neighborhood search (HALNS). The HALNS uses a population of solutions generated by an efficient ALNS. Individuals of this population are subject to a crossover and selection phase, using elements of genetic algorithms resulting in a hybrid heuristic. Computational experiments on several sets of instances from literature demonstrate the competitive performance of the HALNS. The HALNS outperforms all approaches for solving the 2E-VRP and is on par with heuristics that are dedicated either to the LRP or the MDVRP. Furthermore, the HALNS shows superior robustness, i.e., the variance of results from several runs is comparatively low. The HALNS especially outperforms all existing pure ALNS implementations on these problem classes, demonstrating the value of hybridization. Additionally, the HALNS finds three new best-known solutions for LRP instances.

A Branch-Cut-and-Price Approach for the Single-Trip and Multi-Trip Two-Echelon Vehicle Routing Problem with Time Windows

The paper studies the two-echelon capacitated vehicle routing problem with time windows, in which delivery of freight from depots to customers is performed using intermediate facilities called satellites. We consider the variant of the problem with precedence constraints for unloading and loading freight at satellites. In this variant allows for storage and consolidation of freight at satellites. Thus, the total transportation cost may decrease in comparison with the alternative variant with exact freight synchronization at satellites. We suggest a mixed integer programming formulation for the problem with an exponential number of route variables and an exponential number of precedence constraints that link first-echelon and second-echelon routes. Routes at the second echelon connecting satellites and clients may consist of multiple trips and visit several satellites. A branch-cut-and-price algorithm is proposed to solve efficiently the problem. This is the first exact algorithm in the literature for the multi-trip variant of the problem. We also present a postprocessing procedure to check whether the solution can be transformed to avoid freight consolidation and storage without increasing its transportation cost. It is shown that all single-trip literature instances solved to optimality admit optimal solutions of the same cost for both variants of the problem either with precedence constraints or with exact synchronization constraints. Experimental results reveal that our algorithm can be used to solve these instances significantly faster than another recent approach proposed in the literature.

Multidepot Two-Echelon Vehicle Routing Problem for Earthwork Allocation Optimization

Prior to the construction of most engineering projects, earthwork is a complex and time-consuming task, requiring iterative operations in civil engineering. The effectiveness of earthworks determines the cost of many AEC (architecture, engineering, and construction) projects (e.g., road, embankment, railway, and slope engineering). As a result, creating effective earthwork planning is critical. The earthwork allocation problem is simplified in this study to the vehicle route problem (VRP), which is often studied in the field of transportation and logistics. An optimization model for the earthwork allocation path based on the modified genetic algorithm with a self-adaptive mechanism is developed to work out the global optimal hauling path for earthwork. The findings of the study are also used to shape the basic topographic shape of the Winter Olympic Skiing Course Project. Furthermore, a comparative study with the former methods is conducted to validate the performance of our proposed method on tackling such a multidepot two-echelon vehicle routing problem. Because of its flexibility, this optimization model is extremely compatible with various evolutionary methods in many fields, making future development viable and practicable.

A variable neighborhood search algorithm with constraint relaxation for the two-echelon vehicle routing problem with simultaneous delivery and pickup demands

This paper considers a special vehicle routing problem, the two-echelon vehicle routing problem with simultaneous delivery and pickup demands (2E-VRPSDP). The 2EVRPSDP differs from classic transportation and vehicle routing problems in two ways. First, freight delivery from the depot to the customers is managed by shipping the freight through intermediate satellites. Second, each customer in the 2E-VRPSDP may have simultaneous delivery and pickup demands. The 2E-VRPSDP is an extension of the two-echelon vehicle routing problem (2E-VRP) and the vehicle routing problem with simultaneous delivery and pickup (VRPSDP). A variable neighborhood search algorithm is designed to solve the 2E-VRPSDP in which both feasible and infeasible solutions can be explored. Numerical results show that the proposed algorithm is effective and that the algorithm can provide reasonable solutions within an acceptable computational time.

Two-echelon vehicle routing problem with time windows and simultaneous pickup and delivery

This paper proposes a tabu search algorithm for the two-echelon vehicle routing problem with time windows and simultaneous pickup and delivery (2E-VRPTWSPD), which is a new variant of the two-echelon vehicle routing problem. 2E-VRPTWSPD involves three stages of routing: (1) the first-echelon vehicles start from the depot to deliver cargoes to satellites; (2) the second-echelon vehicles start from satellites to serve customers within time windows in a simultaneously pickup and delivery manner and finally return to their satellites with pickup cargoes; (3) the first-echelon vehicles start from the depot to collect cargoes on satellites. To solve this problem, we formulate it with a mathematical model. Then, we implement a variable neighborhood tabu search algorithm with a tailored solution representation to solve large-scale instances. Dummy satellites time windows are applied in our algorithm to speed up the search. Finally, we generate two benchmark instance sets to analyze the performance of our algorithm. Computational results show that our algorithm can obtain the optimal results for 10 out of 11 small-scale instances and produce promising solutions for 200-customer instances within a few minutes. Additional experiments indicate that the usage of dummy satellite time windows can save 19% computation time on average.

A heuristic for two-echelon urban distribution systems

The negative impacts of urban freight transport have fostered the design of new distribution systems for inner city deliveries. One of the proposed city logistics solutions is the establishment of two-echelon distribution systems, where freight originating from the periphery of the city is transferred at intermediate locations (satellites) from larger vehicles (urban freighters) to smaller more environmentally friendly vehicles (city freighters), deemed more suited to operate in the city centre. In this paper, we address a variant of the two-echelon (capacitated) vehicle routing problem (2E-CVRP) arising in the context of city logistics encompassing characteristics such as a heterogeneous fleet of city freighters, time windows, vehicles synchronisation at satellites, direct deliveries, the possibility of freight transfers at customers, and multiple trips by city freighters. We propose a heuristic solution method for this problem based on a Variable Neighbourhood Search (VNS) heuristic, as well as a set of auxiliary evaluation metrics designed to support the decision making process. Preliminary results show the flexibility of the proposed heuristic to account for different problem characteristics, as well as the impacts of considering different best insertion criteria for the initial solution construction. Additionally, the proposed evaluation metrics have allowed for an improved assessment of the trade-offs between different city logistic solutions, and may be considered when developing decision support systems.

A Branch-Price-and-Cut Algorithm for the Two-Echelon Vehicle Routing Problem with Time Windows

In this paper, we propose an exact branch-price-and-cut (BPC) algorithm for the two-echelon vehicle routing problem with time windows. This problem arises in city logistics when high-capacity and low-capacity vehicles are used to transport items from depots to satellites (first echelon) and from satellites to customers (second echelon), respectively. The aim is to determine a set of least-cost first- and second-echelon routes such that the load on the routes respect the capacity of the vehicles, each second-echelon route is supplied by exactly one first-echelon route, and each customer is visited by exactly one second-echelon route within its time window. We model the problem with a route-based formulation where first-echelon routes are enumerated a priori, and second-echelon routes are generated using column generation. The problem is solved using BPC. To generate second-echelon routes, one pricing problem per satellite is solved using a labeling algorithm which keeps track of the first-echelon route associated with each (partial) second-echelon route considered. Furthermore, to speed up the solution process, we introduce effective deep dual-optimal inequalities and apply known valid inequalities. We perform extensive computational experiments on benchmark instances and show that our method outperforms a state-of-the-art algorithm. We also conduct sensitivity analyses on the different components of our algorithm and derive managerial insights related to the structure of the first-echelon routes.

Collaborative Hybrid Aerial and Ground Vehicle Routing for Post-Disaster Assessment

Hybrid aerial and ground vehicles are seen as a promising option for deployment in a post-disaster assessment due to the risk of infrastructure damage that may hinder the assessment operation. The efficient operation of the hybrid aerial and ground vehicle, particularly routings, remains a challenge. The present study proposed a collaborative hybrid aerial and ground vehicle to support the operation of post-disaster assessment. The study developed two models, i.e., the Two-Echelon Vehicle Routing Problem combined with Assignment (2EVRPA) and the Two-Echelon Collaborative Vehicle Routing Problem (2ECoVRP) to evaluate optimal routings for both aerial and ground vehicles. The difference lies in the second echelon in which the 2EVRPA uses a single point-to-point assignment, whereas the 2ECoVRP considers the collaborative routings between the ground vehicle and the aerial vehicle. To demonstrate its applicability, the developed models were applied to solve the post-disaster assessment for the Mount Merapi eruption in Yogyakarta, Indonesia. Sets of numerical experiments based on the empirical case were conducted. The findings indicate that the 2ECoVRP performs better than 2EVRPA in terms of the total operation time. The tabu search algorithm was found to be a promising method to solve the models due to its good quality solution and computational efficiency. The deployment of eight drones appears to be optimum for the given network configuration of the studied case. Flight altitude and battery capacity were found to be influential to the operation time, hence requiring further exploration. Other potential avenues for future research are also discussed.

A Two-Echelon Electric Vehicle Routing Problem with Time Windows and Battery Swapping Stations

Driven by the new laws and regulations concerning the emission of greenhouse gases, it is becoming more and more popular for enterprises to adopt cleaner energy. This research proposes a novel two-echelon vehicle routing problem consisting of mixed vehicles considering battery swapping stations, which includes one depot, multiple satellites with unilateral time windows, and customers with given demands. The fossil fuel-based internal combustion vehicles are employed in the first echelon, while the electric vehicles are used in the second echelon. A mixed integer programming model for this proposed problem is established in which the total cost, including transportation cost, handling cost, fixed cost of two kinds of vehicles, and recharging cost, is minimized. Moreover, based on the variable neighborhood search, a metaheuristic procedure is developed to solve the problem. To validate its effectiveness, extensive numerical experiments are conducted over the randomly generated instances of different sizes. The computational results show that the proposed metaheuristic can produce a good logistics scheme with high efficiency.

Design of a two-echelon freight distribution system in last-mile logistics considering covering locations and occasional drivers

This research addresses a new variant of the vehicle routing problem, called the two-echelon vehicle routing problem with time windows, covering options, and occasional drivers (2E-VRPTW-CO-OD). In this problem, two types of fleets are available to serve customers, city freighters and occasional drivers (ODs), while two delivery options are available to customers, home delivery and alternative delivery. For customers choosing the alternative delivery, their demands are delivered to one of the available covering locations for them to pick up. The objective of 2E-VRPTW-CO-OD is to minimize the total cost consisting of routing costs, connection costs, and compensations paid to ODs while satisfying all demands. We formulate a mixed integer linear programming model and propose an effective adaptive large neighborhood search (ALNS) for solving 2E-VRPTW-CO-OD. In addition, the proposed ALNS provides comparable results with those obtained by state-of-the-art algorithms for the two echelon vehicle routing problem, which is a special case of 2E-VRPTW-CO-OD. Lastly, the effects of occasional drivers and covering locations are presented.