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Advances in Capacitated Vehicle Routing Problem—Models, Methods, Applications and New Challenges

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A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Transportation and Future Mobility".

Deadline for manuscript submissions: closed (10 November 2022) | Viewed by 27996

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Dr. Jarosław Wikarek

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Department of Electrical Engineering and Computer Science, Kielce University of Technology, Kielce, Poland
Interests: modeling and solving problems with constraints in manufacturing, distribution, logistics, etc.; decision support; optimization; artificial intelligence
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Prof. Dr. Paweł Sitek

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Department of Control and Management Systems, Kielce University of Technology, 25-314 Kielce, Poland
Interests: constraint programming; operation research; optimization; decision support; logistics; manufacturing; supply chain management
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Dear Colleagues,

The capacitated vehicle routing problem (CVRP) is a key to efficient distribution, transportation and supply-chain coordination. In broad terms, it deals with the optimal assignment of a set of transportation tasks to a fleet of vehicles and the sequencing of stops for each vehicle. Currently, due to the development of means of transport, the concept of a vehicle is much broader (AVG, UAV, EV, etc.). The CVRP has a large number of real-life applications and comes in many variants, depending on the type of task, the objective, the time frames and the types of constraints that must be met. The CVRP is a computationally hard discrete optimization problem. Outside of transportation, logistics and supply chains, the CVRP has less intuitive but still important applications, e.g., in robotics and manufacturing.

For this Special Issue titled “Advances in Capacitated Vehicle Routing Problem—Models, Methods, Applications and New Challenges”, we invite authors to submit articles that take up the discussion and present solutions in the field of models, methods, applications and new challenges for the CVRP.

Dr. Jarosław Wikarek
Prof. Dr. Paweł Sitek
Guest Editors

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Keywords

Supply chains
Urban transportation
Last-mile logistics
Allocation of resources
Multi-modal processes
AI-driven approach to modeling and solving CVRP
UAV fleet routing and scheduling
Milk-run systems
Dynamic routing and scheduling
Fuzzy CVRP

Published Papers (13 papers)

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Research

31 pages, 8720 KiB

Open AccessArticle

Signal Control Study of Oversaturated Heterogeneous Traffic Flow Based on a Variable Virtual Waiting Zone in Dedicated CAV Lanes

by Haiyang Yu, Jixiang Wang, Yilong Ren, Siqi Chen and Chenglin Dong

Appl. Sci. 2023, 13(5), 3054; https://doi.org/10.3390/app13053054 - 27 Feb 2023

Cited by 3 | Viewed by 1411

Abstract

To meet the demand for cooperative signal control at oversaturated heterogeneous traffic flow intersections containing CAVs and HVs, cooperative control including dedicated CAV lanes has been explored to improve intersection safety capacity and reduce vehicle delays while avoiding uncertain HV driving behaviour. However, this approach does not fully exploit CAV network connectivity advantages and intersection spatial and temporal resources. Here, an oversaturated heterogeneous traffic flow signal control model based on a variable virtual waiting zone with a dedicated CAV lane is proposed. Within the model, CAVs going straight or left share a dedicated CAV lane, a CAV variable virtual waiting zone is within the intersection ahead of the dedicated CAV lane, and CAVs and HVs share the straight-through lane. The model framework has three layers. The upper layer optimizes the barrier time using a rolling time domain scheme. The middle layer optimizes the phase duration and variable virtual waiting zone switching time based on the fixed phase sequence, returning the vehicle delay to the upper optimization model. The lower layer performs CAV grouping and trajectory planning in the dedicated CAV lane based on signal timing and variable virtual waiting zone duration, returning the CAV delays to the middle level. Full article

(This article belongs to the Special Issue Advances in Capacitated Vehicle Routing Problem—Models, Methods, Applications and New Challenges)

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15 pages, 760 KiB

Open AccessArticle

Solving Vehicle Routing Problems under Uncertainty and in Dynamic Scenarios: From Simheuristics to Agile Optimization

by Majsa Ammouriova, Erika M. Herrera, Mattia Neroni, Angel A. Juan and Javier Faulin

Appl. Sci. 2023, 13(1), 101; https://doi.org/10.3390/app13010101 - 21 Dec 2022

Cited by 3 | Viewed by 2652

Abstract

Many real-life applications of the vehicle routing problem (VRP) occur in scenarios subject to uncertainty or dynamic conditions. Thus, for instance, traveling times or customers’ demands might be better modeled as random variables than as deterministic values. Likewise, traffic conditions could evolve over time, synchronization issues should need to be considered, or a real-time re-optimization of the routing plan can be required as new data become available in a highly dynamic environment. Clearly, different solving approaches are needed to efficiently cope with such a diversity of scenarios. After providing an overview of current trends in VRPs, this paper reviews a set of heuristic-based algorithms that have been designed and employed to solve VRPs with the aforementioned properties. These include simheuristics for stochastic VRPs, learnheuristics and discrete-event heuristics for dynamic VRPs, and agile optimization heuristics for VRPs with real-time requirements. Full article

(This article belongs to the Special Issue Advances in Capacitated Vehicle Routing Problem—Models, Methods, Applications and New Challenges)

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25 pages, 5049 KiB

Open AccessArticle

Ontology Support for Vehicle Routing Problem

by Anita Agárdi, László Kovács and Tamás Bányai

Appl. Sci. 2022, 12(23), 12299; https://doi.org/10.3390/app122312299 - 01 Dec 2022

Cited by 3 | Viewed by 1451

Abstract

This paper aims to present a generalized ontology model for the Vehicle Routing Problem (VRP) and it gives some out-plant material handling case studies. The Vehicle Routing Problem is a logistics task where customers with a specific need for products are served within the least possible distance traveled by vehicles. The Vehicle Routing Problem has been highly investigated in operations research, computer science, transportation science, and mathematics. As our new approach shows, the VRP can be used to model in-plant and out-plant material handling and out-plant passenger transport. The Vehicle Routing Problem is a complex, multi-component heterogeneous environment, where consistent handling and integrity of components is a more difficult problem. In this alignment (integrity management, automation), our goal was to develop a unified semantic background framework. Our ontology describes the concepts and the relationships between concepts for the investigated domain. The paper presents the construction and application of ontology for a sample framework and presents test runs based on case studies. The paper shows that ontology can be built into the logic of software applications related to logistic problems. The last part of the article focuses on case studies for our ontology model from the field of tank, money, parcel, and perishable food transportation. Full article

(This article belongs to the Special Issue Advances in Capacitated Vehicle Routing Problem—Models, Methods, Applications and New Challenges)

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21 pages, 3668 KiB

Open AccessArticle

A Proactive Approach to Extended Vehicle Routing Problem with Drones (EVRPD)

by Paweł Sitek, Jarosław Wikarek and Mieczysław Jagodziński

Appl. Sci. 2022, 12(16), 8255; https://doi.org/10.3390/app12168255 - 18 Aug 2022

Cited by 5 | Viewed by 1726

Abstract

Unmanned aerial vehicles (UAVs), also known as drones, are increasingly common and popular due to their relatively low prices and high mobility. The number of areas for their practical applications is rapidly growing. The most promising are: last-mile delivery, emergency response, the inspection of technical devices and installations, etc. In these applications, it is often necessary to solve vehicle routing problems, formulated as a variant of the vehicle routing problems with drones (VRPD). This study presents a proactive approach to a modified and extended VRPD, including: the dynamic selection of drone take-off points, bidirectional delivery (delivery and pick up), various types of shipments, allocation of shipments to drones and drones to vehicles, the selection of the optimal number of drones, etc. Moreover, a formal model of constraints and questions for the extended vehicle routing problem with drones (EVRPD) and exact and approximate methods for solving it have been proposed. The proposed model can be the basis for supporting proactive and reactive decisions regarding last-mile delivery, particularly the selection of the necessary fleet, starting points, the identification of specific shipments that prevent delivery with available resources, etc. The study also includes the results of numerous computational experiments verifying the effectiveness of the implementation methods. The time to obtain a solution is at least 20 times shorter for the proposed DGA (dedicated genetic algorithm) than for the mathematical programming solvers such as Gurobi or LINGO. Moreover, for larger-sized data instances, these solvers do not allow obtaining any solution in an acceptable time, or they obtain worse solutions. Full article

(This article belongs to the Special Issue Advances in Capacitated Vehicle Routing Problem—Models, Methods, Applications and New Challenges)

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18 pages, 724 KiB

Open AccessArticle

Hybrid Heuristic for Vehicle Routing Problem with Time Windows and Compatibility Constraints in Home Healthcare System

by Payakorn Saksuriya and Chulin Likasiri

Appl. Sci. 2022, 12(13), 6486; https://doi.org/10.3390/app12136486 - 26 Jun 2022

Cited by 7 | Viewed by 2021

Abstract

This work involves a heuristic for solving vehicle routing problems with time windows (VRPTW) with general compatibility-matching between customer/patient and server/caretaker constraints to capture the nature of systems such as caretakers’ home visiting systems or home healthcare (HHC) systems. Since any variation of VRPTW is more complicated than regular VRP, a specific, custom-made heuristic is needed to solve the problem. The heuristic proposed in this work is an efficient hybrid of a novice Local Search (LS), Ruin and Recreate procedure (R&R) and Particle Swarm Optimization (PSO). The proposed LS acts as the initial solution finder as well as the engine for finding a feasible/local optimum. While PSO helps in moving from current best solution to the next best solution, the R&R part allows the solution to be over-optimized and LS moves the solution back on the feasible side. To test our heuristic, we solved 56 benchmark instances of 25, 50, and 100 customers and found that our heuristics can find 52, 21, and 18 optimal cases, respectively. To further investigate the proficiency of our heuristic, we modified the benchmark instances to include compatibility constraints. The results show that our heuristic can reach the optimal solutions in 5 out of 56 instances. Full article

(This article belongs to the Special Issue Advances in Capacitated Vehicle Routing Problem—Models, Methods, Applications and New Challenges)

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12 pages, 6195 KiB

Open AccessArticle

Solving a Multi-Class Traffic Assignment Model with Mixed Modes

by Seungkyu Ryu and Minki Kim

Appl. Sci. 2022, 12(7), 3678; https://doi.org/10.3390/app12073678 - 06 Apr 2022

Viewed by 1749

Abstract

In comparison to conventional human-driven vehicles (HVs), connected and automated vehicles (CAVs) provide benefits (e.g., reducing travel time and improving safety). However, before the period of fully CAVs appears, there will be a situation in which both HVs and CAVs are present, and the traffic flow pattern may differ from that of a single class (e.g., HV or CAV). In this study, we developed a multi-class traffic assignment problem (TAP) for a transportation network that explicitly considered mixed modes (e.g., HV and CAV). As a link’s travel time is dependent on the degree of mixed flows, each mode required an asymmetric interaction cost function. For TAP, the multi-class user equilibrium (UE) model was used for the route choice model. A route-based variational inequality (VI) formulation was used to represent the multi-class TAP and solve it using the gradient projection (GP) algorithm. It has been demonstrated that the GP algorithm is an effective route-based solution for solving the single-class user equilibrium (UE) problem. However, it has rarely been applied to solving asymmetric UE problems. In this study, the single-class GP algorithm was extended to solve the multi-class TAP. The numerical results indicated the model’s efficacy in capturing the features of the proposed TAP utilizing a set of simple networks and real transportation networks. Additionally, it demonstrated the computational effectiveness of the GP algorithm in solving the multi-class TAP. Full article

(This article belongs to the Special Issue Advances in Capacitated Vehicle Routing Problem—Models, Methods, Applications and New Challenges)

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14 pages, 1670 KiB

Open AccessArticle

Optimal Route Planning for Truck–Drone Delivery Using Variable Neighborhood Tabu Search Algorithm

by Bao Tong, Jianwei Wang, Xue Wang, Feihao Zhou, Xinhua Mao and Wenlong Zheng

Appl. Sci. 2022, 12(1), 529; https://doi.org/10.3390/app12010529 - 05 Jan 2022

Cited by 14 | Viewed by 3569

Abstract

The optimal delivery route problem for truck–drone delivery is defined as a traveling salesman problem with drone (TSP-D), which has been studied in a wide range of previous literature. However, most of the existing studies ignore truck waiting time at rendezvous points. To fill this gap, this paper builds a mixed integer nonlinear programming model subject to time constraints and route constraints, aiming to minimize the total delivery time. Since the TSP-D is non-deterministic polynomial-time hard (NP-hard), the proposed model is solved by the variable neighborhood tabu search algorithm, where the neighborhood structure is changed by point exchange and link exchange to expand the tabu search range. A delivery network with 1 warehouse and 23 customer points are employed as a case study to verify the effectiveness of the model and algorithm. The 23 customer points are visited by three truck–drones. The results indicate that truck–drone delivery can effectively reduce the total delivery time by 20.1% compared with traditional pure-truck delivery. Sensitivity analysis of different parameters shows that increasing the number of truck–drones can effectively save the total delivery time, but gradually reduce the marginal benefits. Only increasing either the truck speed or drone speed can reduce the total delivery time, but not to the greatest extent. Bilateral increase of truck speed and drone speed can minimize the delivery time. It can clearly be seen that the proposed method can effectively optimize the truck–drone delivery route and improve the delivery efficiency. Full article

(This article belongs to the Special Issue Advances in Capacitated Vehicle Routing Problem—Models, Methods, Applications and New Challenges)

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17 pages, 1062 KiB

Open AccessArticle

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

by Dan Wang and Hong Zhou

Appl. Sci. 2021, 11(22), 10779; https://doi.org/10.3390/app112210779 - 15 Nov 2021

Cited by 6 | Viewed by 2331

Abstract

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. Full article

(This article belongs to the Special Issue Advances in Capacitated Vehicle Routing Problem—Models, Methods, Applications and New Challenges)

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23 pages, 652 KiB

Open AccessArticle

Hybrid Chaotic Discrete Bat Algorithm with Variable Neighborhood Search for Vehicle Routing Problem in Complex Supply Chain

by Yuanhang Qi and Yanguang Cai

Appl. Sci. 2021, 11(21), 10101; https://doi.org/10.3390/app112110101 - 28 Oct 2021

Cited by 4 | Viewed by 1494

Abstract

Driven by the supply chain, suppliers, manufacturers and warehouses are working more closely together for improving service quality. However, tremendous cost may incur in the supply chain if transportation is not planned properly and efficiently, which frustrates enterprises in the intense market. In this paper, we present a model of vehicle routing problem in complex supply chain (VRPCSC) and propose an intelligent algorithm called hybrid chaotic discrete bat algorithm with variable neighborhood search for minimizing the purchase cost of materials, processing cost, and delivery cost along the path from suppliers, to manufacturers and warehouses in the vehicle routing problem. Based on the principles of bat algorithm, a discrete chaotic initialization strategy (DCIS) and a variable neighborhood search (VNS) are adopted to enhance the convergence capacity. Finally, two sets of experiments are conducted, which show that the proposed algorithm can solve the VRPCSC effectively. Full article

(This article belongs to the Special Issue Advances in Capacitated Vehicle Routing Problem—Models, Methods, Applications and New Challenges)

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22 pages, 5891 KiB

Open AccessArticle

Reactive Planning-Driven Approach to Online UAVs Mission Rerouting and Rescheduling

by Radzki Grzegorz, Bocewicz Grzegorz, Dybala Bogdan and Banaszak Zbigniew

Appl. Sci. 2021, 11(19), 8898; https://doi.org/10.3390/app11198898 - 24 Sep 2021

Cited by 2 | Viewed by 1617

Abstract

The presented problem concerns the route planning of a UAV fleet carrying out deliveries to spatially dispersed customers in a highly dynamic and unpredictable environment within a specified timeframe. The developed model allows for predictive (i.e., taking into account forecasted changing weather conditions) and reactive (i.e., enabling contingency UAVs rerouting) delivery mission planning (i.e., NP-hard problem) in terms of the constraint satisfaction problem. Due to the need to implement an emergency return of the UAV to the base or handling ad hoc ordered deliveries, sufficient conditions have been developed. Checking that these conditions are met allows cases to be eliminated if they do not guarantee acceptable solutions, thereby allowing the calculations to be sped up. The experiments carried out showed the usefulness of the proposed approach in DSS-based contingency planning of the UAVs’ mission performed in a dynamic environment. Full article

(This article belongs to the Special Issue Advances in Capacitated Vehicle Routing Problem—Models, Methods, Applications and New Challenges)

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15 pages, 2652 KiB

Open AccessArticle

A Two-Stage Hybrid Metaheuristic for a Low-Carbon Vehicle Routing Problem in Hazardous Chemicals Road Transportation

by Jieyin Lyu and Yandong He

Appl. Sci. 2021, 11(11), 4864; https://doi.org/10.3390/app11114864 - 25 May 2021

Cited by 4 | Viewed by 1788

Abstract

Low-carbon economy advances the sustainable development of the transportation of hazardous chemicals. This paper focuses on the multi-trip heterogeneous vehicle routing problem that includes the prioritization of customers and transportation of incompatible cargoes (MTHVRP-PCIC) in which some customers are prioritized for delivery by heterogeneous vehicles and more than one type of cargo is transported. This is an issue because some cargoes are incompatible with each other and therefore cannot be loaded into the same vehicle. MFHVRP-PCIC aims to find a set of routes resulting in minimal costs including fixed cost, travel cost and carbon emission cost. This problem occurs in real-life applications in the hazardous chemicals road transportation industry. This paper contributes to addressing the MTHVRP-PCIC from a problem definition, model, and methodological point of view. We establish a mathematical formulation for this problem. A two-stage hybrid metaheuristic approach (TSHM) is also devised to solve this problem. First, an improved greedy randomized adaptive search procedure is designed to generate initial feasible solutions. Then, a hybrid genetic algorithm including local search strategies, split-feasibility procedure, and simulated annealing is designed to solve this problem. Finally, the proposed approach is applied to solve a real case of hazardous chemical delivery and a benchmark dataset, and the resulting solutions indicate the advantage of our algorithm compared with those solutions obtained from managerial experience and classical algorithms. Full article

(This article belongs to the Special Issue Advances in Capacitated Vehicle Routing Problem—Models, Methods, Applications and New Challenges)

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18 pages, 6353 KiB

Open AccessArticle

A Proposal and Analysis of New Realistic Sets of Benchmark Instances for Vehicle Routing Problems with Asymmetric Costs

by Keyju Lee and Junjae Chae

Appl. Sci. 2021, 11(11), 4790; https://doi.org/10.3390/app11114790 - 23 May 2021

Cited by 5 | Viewed by 2083

Abstract

Despite their importance, relatively little attention has been paid to vehicle routing problems with asymmetric costs (ACVRPs), or their benchmark instances. Taking advantage of recent advances in map application programming interfaces (APIs) and shared spatial data, this paper proposes new realistic sets of ACVRP benchmark instances. The spatial data of urban distribution centers, postal hubs, large shopping malls, residential complexes, restaurant businesses and convenience stores are used. To create distance and time matrices, the T map API, one of the most frequently used real time path analysis and distance measurement tools in Korea, is used. This paper also analyzes some important issues prevailing in urban transportation environments. These include the challenges of accounting for the frequency and distance in which air travel differs from reality when measuring closeness, the differences in distance and time for outgoing and return trips, and the rough conversion ratios from air distance to road distance and to road time. This paper contributes to the research community by providing more realistic ACVRP benchmark instances that reflect urban transportation environments. In addition, the cost matrix analyses provide insights into the behaviors of urban road networks. Full article

(This article belongs to the Special Issue Advances in Capacitated Vehicle Routing Problem—Models, Methods, Applications and New Challenges)

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16 pages, 9721 KiB

Open AccessArticle

A Mobile Robot Position Adjustment as a Fusion of Vision System and Wheels Odometry in Autonomous Track Driving

by Jarosław Zwierzchowski, Dawid Pietrala, Jan Napieralski and Andrzej Napieralski

Appl. Sci. 2021, 11(10), 4496; https://doi.org/10.3390/app11104496 - 14 May 2021

Cited by 4 | Viewed by 1996

Abstract

Autonomous mobile vehicles need advanced systems to determine their exact position in a certain coordinate system. For this purpose, the GPS and the vision system are the most often used. These systems have some disadvantages, for example, the GPS signal is unavailable in rooms and may be inaccurate, while the vision system is strongly dependent on the intensity of the recorded light. This paper assumes that the primary system for determining the position of the vehicle is wheel odometry joined with an IMU (Internal Measurement Unit) sensor, which task is to calculate all changes in the robot orientations, such as yaw rate. However, using only the results coming from the wheels system provides additive measurement error, which is most often the result of the wheels slippage and the IMU sensor drift. In the presented work, this error is reduced by using a vision system that constantly measures vehicle distances to markers located in its space. Additionally, the paper describes the fusion of signals from the vision system and the wheels odometry. Studies related to the positioning accuracy of the vehicle with both the vision system turned on and off are presented. The laboratory averaged positioning accuracy result was reduced from 0.32 m to 0.13 m, with ensuring that the vehicle wheels did not experience slippage. The paper also describes the performance of the system during a real track driven, where the assumption was not to use the GPS geolocation system. In this case, the vision system assisted in the vehicle positioning and an accuracy of 0.2 m was achieved at the control points. Full article

(This article belongs to the Special Issue Advances in Capacitated Vehicle Routing Problem—Models, Methods, Applications and New Challenges)

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