Classical Vehicle Routing Problem Research Articles

Heterogeneous Multitype Fleet Green Vehicle Path Planning of Automated Guided Vehicle with Time Windows in Flexible Manufacturing System

In this study, we present and discuss a variant of the classical vehicle routing problem (VRP), namely the heterogeneous multitype fleet green automated guided vehicle (AGV) routing problem with time windows (HFGVRPTW) applied in the workshops of flexible manufacturing systems (FMS). Specifically, based on the analysis of AGV body structure and motion state, transport distance and energy consumption are selected as two optimization objectives. According to the characteristics and application context of the problem, this paper designs a hybrid genetic algorithm with large neighborhood search (GA-LNS) considering the farthest insertion heuristic. GA-LNS is improved by increasing the local search ability of genetic algorithm to enhance the solution optimal quality. Extensive computational experiments which are generated from Solomon’s benchmark instances and a real case of FMS are designed to evaluate and demonstrate the efficiency and effectiveness of the proposed model and algorithm. The experimental results reveal that compared with using the traditional homogeneous fleet, the heterogeneous multitype AGV fleet transportation mode has a huge energy-saving potential in workshop intralogistics.

The doubly open park-and-loop routing problem

The purpose of this paper is to introduce a highly efficient heuristic for the doubly open park-and-loop routing problem. This problem is an extension of the classical vehicle routing problem in which routes may involve a main tour that is completed using a vehicle and subtours that are carried out on foot after parking the vehicle. In addition, routes do not start and end at a central depot, but at customer locations. We propose a matheuristic based on a split procedure that generates high quality solutions fast. We present computational experiments on a set of real instances with up to 3,800 customers. We also illustrate the use of the matheuristic on a related problem called the vehicle routing problem with transportable resources, where the method is capable of finding 32/40 new best solutions.

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.

Coordinated routing system for fire detection by patrolling trucks with drones

Vehicle routing problem with drones (VRPD) is an extension of classical vehicle routing, which involves the usage of trucks and drones. Nowadays, bushfires are taken into account as a major global challenging subject. Indeed, forests are very vulnerable to fires, and the classical patrol systems cannot patrol all areas of the forest and pastures due to the difficult crossing of some routes.The literature survey demonstrated that the mathematical models are an efficient approach for planning forest and rangeland patrols. Drones and trucks are used in cooperation for forest monitoring in this study, with drones acting as an efficient and accurate means of monitoring routes that are impassable to ground vehicles. However, this novel approach deals with several substantial challenges, including limitation in the drone's battery and the routing problem in an integrated truck-drone system based on considering hard-to-reach areas and creating a trade-off between time and cost of the patrol process. These issues make significant differences between the proposed novel approach and the classical vehicle routing problem. Thus, it is essential to develop a comprehensive approach to resolve these crucial issues. The present study develops a multi-objective mathematical programming model as mixed-integer programming for simultaneous patrolling of trucks and drones. The augmented epsilon constraint (AEC) method has been considered to solve the two-objective mathematical programming model. Besides, Benders' decomposition (BD) algorithm has been employed to evaluate the achieved results in large-size problems. The performance of the BD algorithm has been confirmed in this study. The findings indicated that the proposed model efficiently protected the forest via monitoring all areas, including impassable areas where ground patrolling is impossible (e.g., the lack of roads due to dense vegetation). Also, it was proved that this system was a novel, cost-effective patrol, which prevents uncontrollable fires in the shortest possible time.

Branch-and-Price Approaches for Real-Time Vehicle Routing with Picking, Loading, and Soft Time Windows

We propose and evaluate branch-and-price approaches for vehicle routing problems with picking, loading, and soft time windows. This general type of vehicle routing problem is of particular relevance in the same-day delivery context, in which fast routing algorithms are required because of the commitment to real-time delivery in the presence of high customer order frequencies. To boost the performance of the branch-and-price algorithms, we introduce the new method of tree-compatible labeling with nondominance trees. This method represents cost functions by a fixed number of breakpoints and uses a specialized tree-based data structure to store Pareto-optimal labels. We prove the theoretical soundness of the new method and evaluate its performance numerically with respect to pricing, column generation, and branch-and-price. Our numerical results show that the method yields substantial performance gains. In particular, we show that, with the new method, branch-and-price is able to reliably generate within a few minutes close to optimal solutions for problem instances with 50 customers. By additional experiments with classic vehicle routing problems with hard time windows, we show that the performance gains of our method result from its ability to handle cost functions in the pricing step. Our approach is the first branch-and-price approach for vehicle routing with picking, loading, and soft time windows. As such, it represents an exact routing algorithm that is able to reliably satisfy the runtime requirements of real-time delivery services. Summary of Contribution: In this paper, we propose the first branch-and-price approaches for a general class of vehicle routing problems with picking, loading, and soft time windows. This problem class is of particular importance for real-time delivery services, for which customers expect to be served within only a few hours after their order has been placed. We provide a problem formulation that takes into account that short runtimes of routing algorithms are required, that the upper bounds of the customers’ time windows may be violated at a certain cost, and that a significant part of the delivery time window is consumed by picking orders from a warehouse and loading orders into vehicles. Solving the problem with branch-and-price requires the use of cost functions as elements of the labels in the pricing step. We propose a method that approximates these cost functions and leverages the computational performance of nondominance tree data structures for solving the pricing problem. We prove the theoretical soundness of this new method for exact branch-and-price, and we show numerically that the method leads to a significant performance increase of branch-and-price. The paper lies at the intersection of computing and operations research, in particular because our algorithms are designed to leverage the computational performance of advanced data structures for solving a combinatorial optimization problem.

Mathematical Model and Simulated Annealing Algorithm for the Two-Dimensional Loading Heterogeneous Fixed Fleet Vehicle Routing Problem

This paper addresses the two-dimensional loading heterogeneous fixed fleet vehicle routing problem, which is a complex and unstudied variant of the classical vehicle routing problem and has a wide range of applications in transportation and logistics fields. In this problem, each customer demands a set of rectangular two-dimensional items, and the objective is to find the minimum cost delivery routes for a limited set of vehicles with different capacities, fixed and variable operating costs, and rectangular two-dimensional loading surfaces. We formulate a mixed integer linear programming model to obtain optimal solutions for small-scale problems. To obtain solutions for large-scale problems, we develop an algorithm based on simulated annealing and local search, which uses a collection of packing heuristics to address the loading constraints, and we also propose three new heuristics. We conduct experiments on benchmark instances derived from the two-dimensional loading heterogeneous fleet vehicle routing problem. The results indicate that the proposed model correctly describes the problem and can solve small-scale problems, that the new packing heuristics are effective in improving the collection of packing heuristics, and that the proposed simulated annealing algorithm can find good solutions to large-scale problems within an acceptable computational time. Hence, it can be used by logistic companies using a heterogeneous fixed fleet in the integrated planning of vehicle loading and routing.

Improved NSGA-II to solve a novel multi-objective task allocation problem with collaborative tasks

From the perspective of practical application, a novel task allocation problem for multi-vehicle systems is proposed. The goal is to allocate an optimal route for each vehicle to execute tasks. The planning result is a comprehensive decision considering the influence of time windows, collaborative tasks, and recharging. This problem is represented as a new extension of the classical vehicle routing problem and a multi-objective integer programming mathematical model is established. The objective functions are the total completion time and total penalty costs. A solution strategy hybridizing non-dominated sorting genetic algorithm-II and variable neighborhood search is proposed, and a feasibility recovery strategy and the concept of the immigrant population are introduced. Finally, the simulation results show that the proposed algorithm can solve the problem effectively and is robust to different complexity scenarios. To illustrate concretely the optimization process, an instance is given in the last.

Vehicle routing problems over time: a survey

In vehicle routing problems (VRPs) the decisions to be taken concern the assignment of customers to vehicles and the sequencing of the customers assigned to each vehicle. Additional decisions may need to be jointly taken, depending on the specific problem setting. In this paper, after discussing the different kinds of decisions taken in different classes of VRPs, the class where the decision about when the routes start from the depot has to be taken is considered and the related literature is reviewed. This class of problems, that we call VRPs over time, includes the periodic routing problems, the inventory routing problems, the vehicle routing problems with release dates, and the multi-trip vehicle routing problems.

Tackling the rich vehicle routing problem with nature-inspired algorithms

In the last decades, the classical Vehicle Routing Problem (VRP), i.e., assigning a set of orders to vehicles and planning their routes has been intensively researched. As only the assignment of order to vehicles and their routes is already an NP-complete problem, the application of these algorithms in practice often fails to take into account the constraints and restrictions that apply in real-world applications, the so called rich VRP (rVRP) and are limited to single aspects. In this work, we incorporate the main relevant real-world constraints and requirements. We propose a two-stage strategy and a Timeline algorithm for time windows and pause times, and apply a Genetic Algorithm (GA) and Ant Colony Optimization (ACO) individually to the problem to find optimal solutions. Our evaluation of eight different problem instances against four state-of-the-art algorithms shows that our approach handles all given constraints in a reasonable time.

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.

A hybrid algorithm for time-dependent vehicle routing problem with soft time windows and stochastic factors

In order to meet the logistics and distribution requirements with poor actual traffic conditions, this paper considers adding soft time windows and stochastic factors (road traffic congestion, weather changes, etc.) based on classic vehicle routing problem. Firstly, we construct a time-dependent vehicle routing problem (TDVRP) with soft time windows model with the objective function of minimizing the total cost of distribution. A Hybrid Algorithm (HA) combining Sweep Algorithm (SA) and Improved Particle Swarm Optimization (IPSO) is developed to solve this model. Secondly, we compare IPSO with other algorithms through benchmark test functions and traditional vehicle routing problem cases. Finally, By applying HA to the modified Solomon benchmark test set, this paper compares HA with the existing solutions in the number of vehicles used, total transportation distance and total waiting time. Then experimental results manifest the practicability of HA.

The Vehicle Routing Problem with Fuzzy Payloads considering Fuel Consumption

ABSTRACT This paper considers the Vehicle Routing Problem (VRP) with fuzzy payloads with the aim to minimize two criteria: the travel distance and the fuel consumption. VRP with fuzzy payloads is an NP-hard problem, in which a fleet of vehicles with finite capacity leaves from a central depot empty of goods and has to serve a set of geographically dispersed customers associated with fuzzy payloads. Thus, an optimization approach based on a bi-objective Genetic Algorithm is developed that is integrated with fuzziness. This problem differentiates from the classic VRP, since it also considers the fuel consumption to reduce the energy consumption. The efficiency of the developed method is investigated and discussed through a set of test instances. The experimental results highlight the impact of both criteria on the resulted optimum solution and prove that increasing the uncertainty in customers’ collection quantities results in more costly solutions.

Planning sustainable routes: Economic, environmental and welfare concerns

We introduce a problem called the Sustainable Vehicle Routing Problem (SVRP) in which the sustainability notion is considered in terms of economic, environmental and social impacts. Inspired by real-world problems that large cargo companies face for their delivery decisions, we introduce a new facet to the classical vehicle routing problem by considering the welfare of all three stakeholders of the problem: an environmentally conscious company, the drivers, and the indistinguishable customers, as our setting assumes that all customers belong to the same delivery class. Thus, the proposed problem consists of three objective functions. The first one is to minimize the total fuel consumption and emission to represent the companies’ main economic and environmental concerns. The second one is to maximize total welfare of the drivers through a function that encourages equitable payment across drivers while encouraging low total driver cost and the third one is to maximize total welfare of the customers through a function that encourages fairness in terms of delivery times. The last two objectives are measured using slots for tour lengths and delivery times. We implement an efficient solution approach based on the ϵ-constraint scalarization to find the nondominated solutions of our triobjective optimization problem and present computational analysis that provide insights on the trade-off between the objectives. Our experiments demonstrate the potential of the suggested framework under the customer anonymity assumption to help decision makers make effective plans that all parties involved would give consent to.

Adaptive large neighborhood search for vehicle routing problems with transshipment facilities arising in city logistics

In this paper, we investigate vehicle routing problems with third-party transshipment facilities that arise in the context of city logistics. Contrary to classical vehicle routing problems, where each customer request is delivered directly to its destination, the problems considered in this paper feature the alternative possibility of delivering customer requests to third-party transshipment facilities, such as urban consolidation centers, for a fee. We present an adaptive large neighborhood search with an embedded random variable neighborhood descent as a local search component and a set-partitioning problem for the recombination of routes to solve various versions of the problem. Thereby, we consider location-dependent time windows as well as heterogeneous fleets and propose several new procedures that consider transshipment facilities within the components of our adaptive large neighborhood search. The proposed method is tested on benchmark instances from the literature as well as newly created benchmark instances. It shows promising results, leading to multiple improvements over existing algorithms from the literature. Moreover, a real-world study is presented to gain managerial insights on the impact of transshipment fees, order size, and heterogeneous fleets on the transshipment decisions.

Simplified Swarm Optimization for the Heterogeneous Fleet Vehicle Routing Problem with Time-Varying Continuous Speed Function

Transportation planning has been established as a key topic in the literature and practices of social production, especially in urban contexts. To consider traffic environment factors, more and more researchers are taking time-varying factors into account when scheduling their logistic activities. The time-dependent vehicle routing problem (TDVRP) is an extension of the classical Vehicle Routing Problem with Time Windows (VRPTW) by determining a set of optimal routes serving a set of customers within specific time windows. However, few of them use the continuous speed function to express the time-varying. In practice, many vehicle routing problems are addressed by a fleet of heterogeneous vehicles with different capacities and travel costs including fix costs and variable costs. In this study, a Heterogeneous Fleet Vehicle Routing Problem (HFPRP) Time-Varying Continuous Speed Function has been proposed. The objective is to minimize distribution costs, which contained fixed costs of acquiring and variable fuel costs. To address this problem, our research developed a mathematical model and proposed a Simplified Swarm Optimization (SSO) heuristic for HFVRP with Time-Varying Continuous Speed Function.

The min-cost parallel drone scheduling vehicle routing problem

Adopting unmanned aerial vehicles (UAV), also known as drones, into the last-mile-delivery sector and having them work alongside trucks with the aim of improving service quality and reducing the transportation cost gives rise to a new class of Vehicle Routing Problems (VRPs). In this paper, we introduce a new optimization problem called the min-cost Parallel Drone Scheduling Vehicle Routing Problem (PDSVRP). This problem is a variant of the well-known Parallel Drone Scheduling Traveling Salesman Problem (PDSTSP) recently introduced in the literature in which we allow multiple trucks and consider the objective of minimizing the total transportation costs. We formulate the problem as a Mixed Integer Linear Program and then develop a Ruin and Recreate (R&R) algorithm. Exploiting PDSVRP solution characteristics in an effective manner, our heuristic manages to introduce “sufficient” rooms to a solution via new removal operators during the ruin phase. It is expected to enhance the possibilities for improving solutions later in the recreate phase. Multiple experiments on a new set of randomly generated instances confirm the performance of our approach. To explore the benefits of drone delivery as well as the insight into the impact of related factors on the contribution of drones’ use to operational cost, a sensitivity analysis is conducted. We also adapt the proposed algorithm to solve the PDSTSP and validate it via benchmarks available in the literature. It is shown that our algorithm outperforms state-of-the-art algorithms in terms of solution quality. Out of 90 considered instances, it finds 26 new best known solutions.

The last-mile vehicle routing problem with delivery options

The ongoing rise in e-commerce comes along with an increasing number of first-time delivery failures due to the absence of the customer at the delivery location. Failed deliveries result in rework which in turn has a large impact on the carriers’ delivery cost. In the classical vehicle routing problem (VRP) with time windows, each customer request has only one location and one time window describing where and when shipments need to be delivered. In contrast, we introduce and analyze the vehicle routing problem with delivery options (VRPDO), in which some requests can be shipped to alternative locations with possibly different time windows. Furthermore, customers may prefer some delivery options. The carrier must then select, for each request, one delivery option such that the carriers’ overall cost is minimized and a given service level regarding customer preferences is achieved. Moreover, when delivery options share a common location, e.g., a locker, capacities must be respected when assigning shipments. To solve the VRPDO exactly, we present a new branch-price-and-cut algorithm. The associated pricing subproblem is a shortest-path problem with resource constraints that we solve with a bidirectional labeling algorithm on an auxiliary network. We focus on the comparison of two alternative modeling approaches for the auxiliary network and present optimal solutions for instances with up to 100 delivery options. Moreover, we provide 17 new optimal solutions for the benchmark set for the VRP with roaming delivery locations.

The in‐house logistics routing problem

AbstractIn this work, we consider the internal logistics processes in the car assembling company SEAT S.A (where SEAT is Sociedad Española de Automóviles de Turismo). We focus on the design of the supplying routes from the warehouse toward the workstations along a production line. The in‐house logistics routing problem (ILRP) can be seen as an extension of the classical vehicle routing problem considering special features such as long‐term fixed routes, unknown orders, backorders, and homogeneous fleet. To solve the ILRP, we propose an integer linear programming (ILP) model and a simulation‐based iterated local search (SimILS) algorithm. We conduct two computational experiments. The first experiment analyzes the methods' performance, and the second experiment compares the SimILS results with the current company's routes, considering real data provided by SEAT S.A. The results show that the SimILS provides the best overall results overcoming both the ILP approach and the current company's solution, leading to a significant improvement in the company's processes.

Optimal and heuristic algorithms for the multi-objective vehicle routing problem with drones for military surveillance operations

<p style='text-indent:20px;'>During military operations, obtaining information on remote battlefields is essential and recent advances in unmanned aerial vehicle technology have led to the use of drones to view battlefields. However, the use of drones in military operations introduces the new problem of determining travel routes for the drones. This type of problem is similar to the well-known classical vehicle routing problem, but the main difference is its objective function. For maintenance purposes, a minimized difference in travel distances is preferred. In addition, obtaining a shorter route in terms of travel distance is important. In this research, we propose a mathematical formulation and an optimal algorithm for the problem and suggest a simple heuristic to handle the large size instance of the problem. The computational results indicate that this algorithm can solve the real-scale instances of the problem, and the heuristic exhibits good performance even when the instance size of the problem is large.</p>

The electric location-routing problem with heterogeneous fleet: Formulation and Benders decomposition approach

In this paper, we focus on a problem that requires the location of recharging stations and the routing of electric vehicles in a goods distribution system. The goods are disseminated from a depot and distributed to the customers via a heterogeneous fleet of electric vehicles with limited capacity. Differently from the classical vehicle routing problem, the vehicles have battery restrictions that need to be recharged at some stations if a trip is longer than their range. The problem reduces to finding the optimal locations of the recharging stations and their number to minimize the total cost, which includes the routing cost, the recharging cost, and the fixed costs of opening stations and operating vehicles. We propose a novel mathematical formulation and an efficient Benders decomposition algorithm embedded into a two-phase general framework to solve this environmental logistics problem. Phase I solves a restricted problem to provide an upper bound for the original problem which is later solved in Phase II. Between the two phases, an intermediate processing procedure is introduced to reduce the computations of the Phase II problem. This is achieved by a combination of the Phase I upper bound and several lower bounds obtained via exploiting the underlying network structure. Our approach solves the problem in a general setting with non-identical stations and vehicles by allowing multiple visits to the stations and partial recharging. The computational study provides both managerial and methodological insights.