Heterogeneous Vehicle Routing Problem Research Articles

Heuristic Algorithms for Heterogeneous and Multi-Trip Electric Vehicle Routing Problem with Pickup and Delivery

In light of the widespread use of electric vehicles for urban distribution, this paper delves into the electric vehicle routing problem (EVRP): specifically addressing multiple trips per vehicle, diverse vehicle types, and simultaneous pickup and delivery. The primary objective is to minimize the overall cost, which encompasses travel expenses, waiting times, recharging costs, and fixed vehicle costs. The focal problem is formulated as a heterogeneous and multi-trip electric vehicle routing problem with pickup and delivery (H-MT-EVRP-PD). Additionally, we introduce two heuristic algorithms to efficiently approximate solutions within a reasonable computational time. The variable neighborhood search (VNS) algorithm and the adaptive large neighborhood search (ALNS) algorithm are presented and compared based on our computational experiences with both. Through solving a series of large-scale real-world instances for the H-MT-EVRP-PD and smaller instances using an exact method, we demonstrate the efficacy of the proposed approaches.

MOEA/D with customized replacement neighborhood and dynamic resource allocation for solving 3L-SDHVRP

Split delivery heterogeneous vehicle routing problem with three-dimensional loading (3L-SDHVRP) is a critical issue in manufacturing logistics. Current mainstream research formulates this problem as a single objective optimization problem, which fails to reveal the relationship among multiple conflicting objectives and cannot provide various trade-off solutions for decision-makers in real-world logistics scenarios. This paper concentrates on a multi-objective 3L-SDHVRP and proposes a multi-objective evolutionary algorithm based on decomposition with customized replacement neighborhood and dynamic resource allocation (called MOEA/D-RD) to deal with it. The numerical experiments on the dataset from the 11th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2021) show the superior performance of the proposed method over some state-of-the-art ones. The source code of MOEA/D-RD is available at https://github.com/CIAM-Group/EvolutionaryAlgorithm_Codes/tree/main/MOEAD-RD.

Optimization of heterogeneous VRP model by considering recharging station using mixed integer programming

Optimization of heterogeneous VRP model by considering recharging station using mixed integer programming

Mathematical model of routing problem for hazardous biomedical waste: A multi-objective particle swarm optimization solution approach

Purpose: This model aims at solving a Green Heterogeneous and Stochastic Capacitated Vehicle Routing Problem that takes into account the risks and environmental hazards.
 Research Methodology: Regarding an NP-hard and complex problem, and after confirming the accuracy of the problem-solving in smaller dimensions by GAMS software, the problem is solved by the metaheuristic algorithm of multi-objective particle swarm optimization (MOPSO) and its coding in MATLAB software.
 Results: The results urge that using random sampling and probability distribution, non-deterministic parameters turned into deterministic ones, and high-quality solutions were obtained.
 Limitation: The proposed method is a routing problem and has been applied for the Green Heterogeneous and Stochastic Capacitated Vehicle Routing Problem. Future researchers may work on real data sets and hazardous biomedical waste data.
 Contribution: Based on the results presented, the model derived in this paper can support decisions such as routing, prioritization, time to reach each node, etc. so that the costs of routing, system reliability, environmental issues, and penalties for violation of the priority and maximum time elapsed for vehicles are taken into account.

Boosting sustainable development goals: a hybrid metaheuristic approach for the heterogeneous vehicle routing problem with three-dimensional packing constraints and fuel consumption

Boosting sustainable development goals: a hybrid metaheuristic approach for the heterogeneous vehicle routing problem with three-dimensional packing constraints and fuel consumption

Improving the efficiency of patient diagnostic specimen collection with the aid of a multi-modal routing algorithm

The Sustainable Specimen Collection Problem (SSCP), in which diagnostic specimens are collected from GP surgeries (doctor’s office/clinics) and subsequently transported to a hospital laboratory for analysis using more sustainable transport modes, is introduced in this paper. Using a weighted objective function, we solve a new multi-objective problem using cycle consolidation to limit driving time and the numbers of vans used whilst improving overall service quality, reducing costs and emissions. This particular heterogeneous vehicle routing problem is explored and applied to two real-world case studies in the UK, where 97 and 22 sites (respectively) are currently served, using a column generation based heuristic algorithm with some additional improvement heuristics. The results demonstrated a potential improvement in the system’s maximum delivery time between 41% and 74% compared to business-as-usual activity using solely road vehicles. Road vehicle (van) fleets could be reduced by up to 40%, and the total driving time across the fleet by between 41% and 65%. Operational costs were estimated to increase by up to 38%, though additional workloads for gig-economy cycle couriers and improvement in specimen quality and service reliability may make this trade-off worthwhile. Tailpipe CO2 emissions were also reduced by up to 43%. The proposed algorithm was effective, reducing computational time by up to 99% whilst achieving an average of 5% deviation from optimality.

Solving a heterogeneous fleet multi-compartment vehicle routing problem:a case study

Vehicle Routing Problem (VRP) is a complex optimisation problem in the field of supply chain management, especially in the Oil & Gas sector. Due to the rising cost of fuel, effective planning of transportation routes has become a crucial success factor for distribution companies, increasing operational efficiency as well as the corresponding service level. In this paper, we present an optimisation model to solve a heterogeneous fleet multi-compartment vehicle routing problem (MCVRP), a variant of the conventional vehicle routing problem (VRP). Real data are obtained from a medium size oil distribution company, operating in Greece and incorporates 19 petrol stations served from a central oil depot using a fleet of various multi-compartment tanker trucks. The main objective of this research is to design an optimum set of routes minimising distance and truck operating costs. The MCVRP with a heterogeneous fleet of vehicles is modelled as a Mixed-Integer Linear Programming (MILP) problem and the proposed solution determines the number of assigned vehicles, the planning of daily routes and the allocation of different fuels to vehicles compartments, while satisfying customer demand following specific requirements, as detailed in the Carriage of Dangerous Goods (ADR) Regulations.

Metaheuristics with variable diversity control and neighborhood search for the Heterogeneous Site-Dependent Multi-depot Multi-trip Periodic Vehicle Routing Problem

The planning of vehicle routes is a major issue involved in supply chains. In real environment, we can find situations involving a very large number of clients or constraints which indicate that exact methods should be avoided. In this context, this paper presents two metaheuristcs which are used to solve a complex problem named the Heterogeneous Site-Dependent Multi-depot Multi-trip Periodic Vehicle Routing Problem (HSDMDMTPVRP). The HSDMDMTPVRP is a real problem found in the automotive industry and considers several well-known Vehicle Routing Problems (VRP). The first metaheuristic is an adaptation of the Unified Hybrid Genetic Search (UHGS) which considers an advanced diversity control, feasibility control and a restart mechanism. The second one is a new metaheuristic named Adaptive Variable Neighborhood Race (AVNR) which combines variable neighborhood search and adaptive mechanisms integrated with a shrinking population managed with a diversity mechanism. Both approaches are also used for solving some variants of the VRP: Heterogeneous VRP, Site dependent VRP, Periodic VRP and Multi-trip VRP. Our computational experiments used 398 available instances in the literature with generic code path and also present 20 new instances for the HSDMDMTPVRP. The metaheuristics solved all instances with only one set of parameters and the results outperform or present the same solutions found by several state-of-the-art algorithms, showing the good performance of the approaches. Out of the 398 previously tested literature instances, the proposed metaheuristics found 140 new best-known solutions and 209 of the best-known ones. For the remaining instances, both approaches found results very close to best ones known.

Efficient Network Selection Using Multi-Depot Routing Problem for Smart Cities

Smart cities make use of a variety of smart technology to improve societies in better ways. Such intelligent technologies, on the other hand, pose significant concerns in terms of power usage and emission of carbons. The suggested study is focused on technological networks for big data-driven systems. With the support of software-defined technologies, a transportation-aided multicast routing system is suggested. By using public transportation as another communication platform in a smart city, network communication is enhanced. The primary objective is to use as little energy as possible while delivering as much data as possible. The Attribute Decision Making with Capacitated Vehicle (CV) Routing Problem (RP) and Half Open Multi-Depot Heterogeneous Vehicle Routing Problem is used in the proposed research. For the optimum network selection, a Multi-Attribute Decision Making (MADM) method is utilized. For the sake of reducing energy usage, the Capacitated Vehicle Routing Problem (CVRP) is employed. To reduce the transportation cost and risk, Half Open Multi-Depot Heterogeneous Vehicle Routing Problem is used. Moreover, a mixed-integer programming approach is used to deal with the problem. To produce Pareto optimal solutions, an intelligent algorithm based on the epsilon constraint approach and genetic algorithm is created. A scenario of Auckland Transport is being used to validate the concept of offloading the information onto the buses for energy-efficient and delay-tolerant data transfer. Therefore the experiments have demonstrated that the buses may be used effectively to carry out the data by customer requests while using 30% of less energy than the other systems.

Joint routing of conventional and range-extended electric vehicles in a large metropolitan network

Range-extended electric vehicles combine the higher efficiency and environmental benefits of battery-powered electric motors with the longer mileage and autonomy of conventional internal combustion engines. This combination is particularly advantageous for time-constrained delivery routing in dense urban areas, where battery recharging along routes can be too time-consuming to economically justify the use of all-electric vehicles. However, switching from electric to conventional fossil fuel modes also results in higher costs and emissions and lower efficiency. This paper analyzes this heterogeneous vehicle routing problem and describes two solution methods: an exact branch-price-and-cut algorithm and an iterated tabu search metaheuristic. From a methodological perspective, we find that the exact algorithm consistently obtains tight lower bounds that also serve to certify the metaheuristic solutions as near-optimal. From a policy standpoint, we examine a large-scale real-world case study concerning parcel deliveries in the Chicago metropolitan area and quantify various operational metrics including energy costs and vehicle miles traveled. We find that by deploying roughly 20% of range-extended vehicles with a modest all-electric range of 33 miles, parcel distributors can save energy costs by up to 17% while incurring less than 0.5% increase in vehicle miles traveled. Increasing the range to 60 miles further reduces costs by only 4%, which can alternatively be achieved by decreasing the average service time by 1 minute or increasing driver working time by 1 hour. Our study reveals several key areas of improvement on which vehicle manufacturers, distributors, and policy makers can focus their attention.

Modelling and heuristically solving many-to-many heterogeneous vehicle routing problem with cross-docking and two-dimensional loading constraints

In light of the existing practical applications of the two-dimensional loading on vehicle scheduling and many-to-many supply-demand relationships between suppliers and customers, we address a many-to-many heterogeneous vehicle routing problem with cross-docking and two-dimensional loading constraints (or the heterogeneous 2L-MVRPCD). The newly proposed problem can be regarded as a generalized problem of the many-to-many vehicle routing with cross-docking (MVRPCD) and capacitated vehicle routing problem with two-dimensional loading constraints (2L-CVRP). To solve small-scale 2L-MVRPCDs, a mixed integer linear programming (MILP) model is developed, whereas two hybrid optimization heuristic algorithms are proposed to solve large-scale 2L-MVRPCDs. The first heuristic incorporates a basic adaptive large neighborhood search (ALNS) algorithm and a new best-fit-skyline (BFS) packing heuristic, while the second heuristic, a Tabu-based ALNS (ALNS/TS), extends the first one by embedding an insert-tabu strategy to enhance the intensity and diversity of search. Wide-ranging instances with various many-to-many supply-demand scenarios and different loading configurations are employed to verify the efficacy of the proposed MILP model and two heuristics. Numerical results show that small-scale heterogeneous 2L-MVRPCD instances with and without the rotation constraints can be solved to optimality by commercial solvers, and the proposed heuristics can achieve high-quality solutions within a reasonable computational time for large-scale instances. Meanwhile, the comparison between the proposed heuristics and existing methods verifies the effectiveness and applicability of the proposed heuristics for solving MVRPCD and 2L-CVRP.

Integrated production and inventory routing planning of oxygen supply chains

In this work, we address a production and inventory routing problem for a liquid oxygen supply chain comprising production facilities, distribution network, and distribution resources. The key decisions of the problem involve production levels of production plants, delivery schedule and routing through heterogeneous vehicles, and inventory strategies for national stock-out prevention. Due to the problem complexity, we propose a two-level hybrid solution approach that solves the problem using both exact and metaheuristic methods. At the upper level, we develop a mixed-integer linear programming (MILP) model that determines production and inventory decisions and customer allocation. In the lower level, the original problem is reduced to several multi-trip heterogeneous vehicle routing problems by fixing the optimal production, inventory, and allocation decisions and clustering customers. A well-recognised metaheuristic, guided local search method, is adapted to solve the low-level routing problems. A real-world case study in the UK illustrates the applicability and effectiveness of the proposed optimisation framework.

Minimization of Sustainable-Cost Using Tabu Search for Single Depot Heterogeneous Vehicle Routing Problem with Time Windows

Minimization of Sustainable-Cost Using Tabu Search for Single Depot Heterogeneous Vehicle Routing Problem with Time Windows

A Branch and Price Algorithm for the Heterogeneous Fleet Multi-Depot Multi-Trip Vehicle Routing Problem with Time Windows

The multi-trip vehicle routing problem (MTVRP) extends the well-known VRP by allowing vehicles to perform several trips in a workday. The motivation arises from the new challenges in city logistics that push companies to use smaller and cleaner vehicles such as cargo bikes. With the integration of small vehicles into the fleet, many companies start to operate with a heterogeneous fleet and use multiple depots located in the city centers to reload the small vehicles. Inspired by these new challenges the companies face, we study the heterogeneous fleet multi-depot MTVRP with time windows under shared depot resources where small and large vehicles have different travel times in certain areas. We formulate this problem using workday variables and propose a branch and price algorithm that exhibits an enhanced performance by a new heuristic algorithm based on the reduction in the graph size. The proposed algorithm introduces a new way to compute the completion bounds using the iterative structure of the state-space augmenting algorithm and eliminates the need for solving a separate relaxation. We conduct experiments on modified small- and medium-size instances from Solomon’s benchmark set. The results of our computational experiments show that the proposed algorithm is very effective and can solve instances with up to 40 customers, three depots, and two types of vehicles.

Heterogeneous multi-depot collaborative vehicle routing problem

Collaborative vehicle routing of multiple logistics providers is an important component of horizontal logistic collaboration that generates economic and societal benefits. Existing research on collaborative vehicle routing is limited to the homogeneous setting where the logistics providers transport the same product. To better address the need of a general modeling framework and fast computational methods for the growth of collaboration among logistics providers carrying various products, we investigate a heterogeneous multi-depot collaborative vehicle routing problem (HMCVRP) in this paper. The key operational and computational challenge of realizing the collaborative route planning is to properly select transfer points for product transshipment between vehicles of different depots. We propose a Benders-based branch-and-cut algorithm with the technique of combinatorial Benders’ cuts to solve a mixed-integer programming formulation of HMCVRP. Numerical experiments indicate that the proposed algorithm significantly outperforms the CPLEX solver using the commonly adopted big-M transformation-based method. Additional computational study further reveals the importance of the locations of depots and having a well-designed cost savings allocation mechanism in practice.

A Genetic Algorithm for Solving Periodic Heterogeneous Vehicle Routing Problem

This paper addresses the periodic heterogeneous vehicle routing problem (PHVRP), an extension of the classical vehicle routing problems (VRP). This problem is known to be confined to various real-world instances where each customer's demand should be served within a specific time horizon and a maximum demand quantity that can be delivered at each visit. The heterogeneous capacitated vehicles are available to perform the services for each customer. This paper aims to minimize the total traveling time of routes for all vehicles over the time horizon so that the customers' demands can be delivered. Thus, a novel coding scheme is also proposed to directly convert a random sequence of integers into a feasible solution, which is then embedded into algorithms. Furthermore, this paper also compares the performance of the Genetic Algorithm (GA) with the particle swarm optimization algorithm (PSO). The numerical results of the experiments show that the proposed GA is superior to PSO. However, the computation time of PSO is faster than GA.

A heterogeneous vehicle routing problem with common carriers and time regulations: Mathematical formulation and a two-color ant colony search

This paper considers a heterogeneous vehicle routing problem with common carriers and time regulations implemented at a major logistics company and contributing to an estimated $160 M in savings. In our problem, the objective is to minimize the network costs by considering heterogeneous fleet routes, outsourcing options, time windows, and drivers’ layover regulations. This variant of the vehicle routing problems has many practical applications, particularly in the design of long-haul transportation and last-mile delivery services. The problem has received limited attention in the literature likely because addressing all the needed aspects are especially challenging. To solve the large-scale problem, our work develops a meta-heuristic called Red-Black Ant Colony System (RB-ACS), which solves the two problems: dedicated fleet routing and outsourcing decisions simultaneously. The savings by supporting improved bidding and outsourcing selected deliveries. We also present a compact mixed-integer formulation for this problem and introduce strong valid inequalities to strengthen branch and cut alternatives. Further, we describe our extensive computational experiments, demonstrate the capability of the proposed RB-ACS in solving large-scale problems and show the efficiency of the formulated math models.

The Heterogeneous Flexible Periodic Vehicle Routing Problem: Mathematical formulations and solution algorithms

The aim of this paper is to introduce the Flexible Periodic Vehicle Routing Problem with Heterogeneous Fleet, a variant of the Periodic Vehicle Routing Problem. Flexibility is introduced in service schedules and delivered quantities, heterogeneity comes from different vehicles capacities and speeds. Three Mixed-Integer Linear Programming formulations and a matheuristic, based on Kernel Search, are proposed. Computational tests are made to evaluate the performance of the three formulations and to assess the quality of the solutions provided by the matheuristic.

A new metaheuristic approach for the meat routing problem by considering heterogeneous fleet with time windows

Guided by a real case, this paper efficiently proposes a new metaheuristic algorithm based on Simulated Annealing to solve the Heterogeneous Vehicle Routing Problem with Time Windows to deliver fresh meat in urban environments. Our proposal generates an initial feasible solution using a hybrid heuristic based on the well-known Travelling Salesman Problem (TSP) solution and, subsequently, refining it through a Simulated Annealing (SA). We have tested the efficiency of the proposed approach in a company case study related to the planning of the transportation of a regional distribution center meat company to customers within the urban and rural perimeter of Bogotá, Colombia. The main goal is to reach a service level of 97% while reducing operational costs and several routes (used vehicles). The results show that the proposed approach finds better routes than the current ones regarding costs and service level within short computing times. The proposed scheme promises to solve the refrigerated vehicle routing problem.

Multi-Parking Lot and Shelter Heterogeneous Vehicle Routing Problem With Split Pickup Under Emergencies

The vehicle rescue process for individuals in residential areas in disaster scenarios is a typical vehicle routing problem (VRP). However, most studies do not consider the factor of individual mobility. In residential areas, there are two types of individuals: individuals with high mobility and individuals with low mobility, such as the elderly. To improve the evacuation efficiency, besides ordinary vehicles, special vehicles equipped with wheelchairs and volunteers are also in great need. Thus, evacuation vehicles should consist of a heterogeneous fleet. Vehicles depart from parking lots, arrive at residential areas to pick up individuals, and then transport them to shelters. In other words, the origin and destination are different, but they are viewed as the same in classical VRP. Each residential area can be served directly by vehicles departing from parking lots or by vehicles that have already served others, which means demands can be split. All these make the VRP in emergency rescue more complicated than classical VRP. Therefore, we propose an integer liner program model – multi-parking lot and shelter heterogeneous vehicle routing problem with split pickup (MPSHVRPSP) model, which includes matching constraints of individuals and vehicles to satisfy the demands of different types of individuals, and considers the selectivity of parking lots and shelters too. We provide a Tabu Search (TS) algorithm with diversification strategy to solve the model and ensure the high quality of solution. A lot of experiments are carried out on various instances. Our results show that MPSHVRPSP can be applied to efficient evacuation of complicated scenarios that satisfies the demands of all individuals in residential areas. Besides, it is more reasonable compared with classical VRP, and TS can also obtain a satisfactory solution in less time. Furthermore, sensitivity analysis is conducted on factors that may affect the result of objective function.