Classical Vehicle Routing Problem Research Articles

Mathematical Model for Multi Depot Simultaneously Pick Up and Delivery Vehicle Routing Problem with Stochastic Pick Up Demand

In classical vehicle routing problem (VRP), customer demands are known with certainty. On the other hand, in real life problems, customer demands may change over time. Therefore, in the classical VRP, the assumption that customer demands are stochastic should be taken into account. In order to meet the demands of the customers faster and to reduce the fuel consumption and carbon emissions, the companies meet the distribution and collection demands of the customers simultaneously. Customers' distribution requirements can be predicted, but it is impossible to predict in advance the product requirements they will send for recycling. Hence in this study, a mathematical programming model is developed for the multi-depot simultaneously pick up and delivery vehicle routing problem, under the assumption that customers' picking demands are stochastic. However, There are non-linear constraints in the developed model. Thereby firstly the stochastic model is linearized, and then the effectiveness of the model is analyzed. The efficiency of the linearized model is determined by creating test problems.

Research on vehicle path planning of automated guided vehicle with simultaneous pickup and delivery with mixed time windows

AbstractThe authors investigate new Automated Guided Vehicle (AGV) Routing Problem with Simultaneous Pickup and Delivery with Mixed Time Windows (VRPSPDMTW) in smart workshops, a variation of the classic Vehicle Routing Problem (VRP). A mixed time window vehicle routing model was developed for simultaneous deliveries. This model reduces the cost of AGVs used and distribution cost, along with time window penalties. To address this complex challenge, a Hybrid Adaptive Genetic Algorithm using Variable Neighbourhood Search (AGA‐VNS) is proposed. This algorithm enhances the genetic algorithm's local search capabilities while preserving solution diversity, thereby improving both efficiency and quality of solutions. Comprehensive computational experiments are conducted, which include both VRPSPDTW test benchmark and real‐world smart factory instance studies. The outcomes reveal that the AGA‐VNS algorithm outperforms both professional solver software and advanced heuristic methods significantly. Moreover, the newly developed mixed time window model is more aligned with the requirements of real‐world production processes compared to the traditional time window model. Thus, this research not only presents novel insights into the domain of vehicle routing problems but also demonstrates its significant applicability and potential in the background of intelligent workshops.

Optimisation of Multi-Type Logistics UAV Scheduling under High Demand

At present, interest in the application of unmanned aerial vehicles (UAV) for delivery is growing. A new “multi-type of UAV collaborative delivery” mode has been proposed. Through a combination of large, medium and small UAVs, the delivery capabilities of the UAV logistics system are significantly improved. Sometimes there is high demand, resulting in planned delivery routes that are no longer feasible, and even cause a shortage of distribution centre capacity and drones. This study explores logistics delivery strategies to solve problems caused by high demand. In this study, a multitype and multidistribution UAV model was established with the objective of minimising the total cost of distribution by considering factors such as the UAV energy consumption, load and distribution centre conditions. An improved ant colony algorithm was designed and its effectiveness was verified through the variability of the calculation time and multiple calculation results of different-scale examples. Finally, the classic vehicle routing problem (VRP) case is used in three scenarios to analyse the UAV scheduling optimisation problem. The results indicate that assisted delivery can reduce costs by 3% while ensuring delivery timeliness. The results of this study can provide guidance and benchmarks for the application of UAVs in urban logistics delivery systems.

A note on “A unified solution framework for multi-attribute vehicle routing problems”

In this note, the authors propose correcting one erroneous formula from [Vidal, T., Crainic, T. G., Gendreau, M., & Prins, C. (2014). A unified solution framework for multi-attribute vehicle routing problems. European Journal of Operational Research, 234(3), 658–673] in charge of lunch breaks. In the original paper, the authors propose to compute several attribute values from the solution of a vehicle routing problem; like the earliest and latest starting time for sequences of customers to visit. The computed values allow us to quickly evaluate the feasibility and the marginal cost of some neighbor solutions. Several variants of the class of vehicle routing problems can be addressed using this approach. In the case of drivers’ lunch break scheduling, the proposed formula combines optimistic values for the earliest and the latest completion times of the sequence of customers to visit. Using these values to evaluate neighbor solutions, may conclude that unfeasible solutions are feasible, or underestimate the completion time of a driver’s route. In this note, we describe a counter-example to identify the error in the formula. We also adapt the formula to the correct result.

A unified exact approach for a broad class of vehicle routing problems with simultaneous pickup and delivery

The vehicle routing problem (VRP) with simultaneous pickup and delivery (VRPSPD) is a classical combinatorial optimization problem in which one aims at determining least-cost routes, starting and ending at the depot, while simultaneously meeting the pickup and delivery demands of geographically dispersed customers in a single visit, and without violating the capacity of the vehicle. In this work, we propose a unified branch-cut-and-price (BCP) algorithm to solve ten variants of the problem, considering not only the standard version but also those including additional attributes such as a heterogeneous fleet of vehicles, time windows, route duration, multiple depots, and location decisions. The resulting problem that generalizes all of these variants can be formulated as a heterogeneous location routing problem with simultaneous pickup and delivery and time windows (HLRPSPDTW), for which we propose a compact formulation to serve as the basis for an extended formulation associated with the BCP approach. The proposed exact method includes many of the features developed in recent years, such as a bucket graph-based labeling algorithm, rank-1 cuts with limited memory, and dynamic ng-sets. Extensive computational experiments were performed on more than 550 benchmark instances and our algorithm was capable of obtaining a number of new optimal solutions, as well as improved lower bounds, for all variants addressed in this paper.

A hybrid approach to solve a raw material collecting vehicle routing problem

PurposeThe purpose of this study is to formulate a new class of vehicle routing problem with an objective to minimise the total cost of raw material collection and derive a new approach to solve optimization problems. This study can help to select the optimum number of suppliers based on cost.Design/methodology/approachTo model the raw material vehicle routing problem, a mixed integer linear programming (MILP) problem is formulated. An interesting phenomenon added to the proposed problem is that there is no compulsion to visit all suppliers. To guarantee the demand of semiconductor industry, all visited suppliers should reach a given raw material capacity requirement. To solve the proposed model, the authors developed a novel hybrid approach that is a combination of block and edge recombination approaches. To avoid bias, the authors compare the results of the proposed methodology with other known approaches, such as genetic algorithms (GAs) and ant colony optimisation (ACO).FindingsThe findings indicate that the proposed model can be useful in industries, where multiple suppliers are used. The proposed hybrid approach provides a better sequence of suppliers compared to other heuristic techniques.Research limitations/implicationsThe data used in the proposed model is generated based on previous literature. The problem derives from the assumption that semiconductor industries use a variety of raw materials.Practical implicationsThis study provides a new model and approach that can help practitioners and policymakers select suppliers based on their logistics costs.Originality/valueThis study provides two important contributions in the context of the supply chain. First, it provides a new variant of the vehicle routing problem in consideration of raw material collection; and second, it provides a new approach to solving optimisation problems.

Research on Green Vehicle Path Planning of AGVs with Simultaneous Pickup and Delivery in Intelligent Workshop

In this study, we present and discuss a variant of the classic vehicle routing problem (VRP), the green automated guided vehicle (AGV) routing problem, which involves simultaneous pickup and delivery with time windows (GVRPSPDTW) in an intelligent workshop. The research object is AGV energy consumption. First, we conduct a comprehensive analysis of the mechanical forces present during AGV transportation and evaluate the overall operational efficiency of the workshop. Then, we construct a green vehicle path planning model to minimize the energy consumption during AGV transportation and the standby period. Hence, the problems considered in this study are modeled based on asymmetry, making the problem solving more complex. We also design a hybrid differential evolution algorithm based on large neighborhood search (DE-LNS) to increase the local search ability of the algorithm. To enhance the optimal quality of solutions, we design an adaptive scaling factor and use the squirrel migration operator to optimize the population. Last, extensive computational experiments, which are generated from the VRPSPDTW instances set and a real case of an intelligent workshop, are designed to evaluate and demonstrate the efficiency and effectiveness of the proposed model and algorithm. The experimental results show that DE-LNS yields competitive results, compared to advanced heuristic algorithms. The effectiveness and applicability of the proposed algorithm are verified. Additionally, the proposed model demonstrates significant energy-saving potential in workshop logistics. It can optimize energy consumption by 15.3% compared with the traditional VRPSPDTW model. Consequently, the model proposed in this research carries substantial implications for minimizing total energy consumption costs and exhibits promising prospects for real-world application in intelligent workshops.

A new MILP formulation for the flying sidekick traveling salesman problem

AbstractNowadays, truck‐and‐drone problems represent one of the most studied classes of vehicle routing problems. The Flying Sidekick Traveling Salesman Problem (FS‐TSP) is the first optimization problem defined in this class. Since its definition, several variants have been proposed differing for the side constraints related to the operating conditions and for the structure of the hybrid truck‐and‐drone delivery system. However, regardless the specific problem under investigation, determining the optimal solution of most of these routing problems is a very challenging task, due to the vehicle synchronization issue. On this basis, this work provides a new arc‐based integer linear programming formulation for the FS‐TSP. The solution of such formulation required the development of a branch‐and‐cut solution approach based on new families of valid inequalities and variable fixing strategies. We tested the proposed approach on different sets of benchmark instances. The experimentation shows that the proposed method is competitive or outperforms the state‐of‐the‐art approaches, providing either the optimal solution or improved bounds for several instances unsolved before.

An adaptive large neighborhood search based approach for the vehicle routing problem with zone-based pricing

In the classical vehicle routing problems, the objective function is usually to minimize the transportation cost without considering the pricing decision-making. However, in some practical applications, such as riding-share services and fast-food delivery services, logistics companies aim to maximize profits, involving decision-making issues closely related to the pricing and route planning. This paper designs an adaptive large neighborhood search (ALNS) based approach to solve a vehicle routing problem with zone-based pricing (VRPZ). In the studied problem, the customers in the same zone share the same price for transportation, and each customer could accept or reject the price given by the logistics company. On the one hand, a too-high pricing strategy may reduce the number of served customers; on the other hand, a too-low pricing strategy may result in low earnings for logistics companies. VRPZ optimizes the routing planning and seeks an appropriate pricing strategy to maximize the total profit, which is the difference value of total earnings and costs. Considering that the studied problem is a computational challenge, we have developed an algorithm incorporating the local search into ALNS, particularly nested with two varying pricing operators: price++ and price−−, to solve the problem. The proposed algorithm has been compared with pure ALNS, variable neighborhood search (VNS) and Simulated Annealing (SA) by solving 472 benchmark instances in the published work. The compared results, which are validated by the statistic tests, highlight the efficiency and effectiveness of the proposed algorithm. To our best knowledge, this is the first heuristic to achieve a good performance in solving the benchmark instances. This study is significant for the retail industry to find a reasonable logistics pricing strategy and improve operational efficiency, as well as lays a foundation for developing a decision support system.

Drones Routing with Stochastic Demand

Motivated by the increasing number of drones used for package delivery, we first study the problem of Multiple drOne collaborative Routing dEsign (MORE) in this article. That is, given a fixed number of drones and customers, determining the delivery trip for drones under capacity constraint with stochastic demand for customers such that the overall expected traveling cost is minimized. To address the MORE problem, we first prove that MORE falls into the realm of the classical vehicle routing problem with stochastic demand and then propose an effective algorithm for MORE. Next, we have a scheme of resplitting customers into different individual delivery trips while the stochastic demands are determined. Moreover, we consider a variety of MORE, MORE-TW, and design an effective algorithm to address it. We conduct simulation experiments for MORE to verify our theoretical findings. The results show that our algorithm outperforms other comparison algorithms by at least 79.60%.

Optimal delivery route planning for a fleet of heterogeneous drones: A rescheduling-based genetic algorithm approach

The past decade has witnessed the rapid growth of pilot studies and the adoption of drone-assisted delivery by many e-commerce companies. In practice, delivery companies usually assemble fleets of drones consisting of heterogeneous configurations to satisfy various customer package demands, and this calls for in-depth research on how to deliver packages via drones efficiently. In this study, we extend the classic vehicle routing problem (VRP) by optimally scheduling the operations in a package depot center with a fleet of drones with different capacities, speeds, and maximum flight ranges. The drones travel multiple sorties to serve customers nearby. We formulate this problem as a mixed integer programming (MIP) model that minimizes the total delivery time for a set of packages. Due to the NP-hardness of the problem, we first develop a FIFO-based genetic algorithm (FBGA) to solve the problem. In anticipation of multiple trips, we further propose a modified, rescheduling-based genetic algorithm (RBGA) that incorporates a small-scale routing-planning optimization model that “reschedules” drone operations at the end of drone sorties, with the objective of minimizing the completion time. The RBGA features the combination of the knapsack problem, the shortest path problem, and a scheduling problem, from which near-optimal delivery plans are obtained for the fleet of drones. We conduct extensive numerical experiments with different numbers of customers and drones to evaluate the performance of the algorithms. The results suggest that compared with MIP, the proposed algorithms solve the problem efficiently for the testing instances, particularly for large instances that MIP fails to solve in time, indicating the practicality of the proposed methods for real-world implementations.

Cement Transport Vehicle Routing with a Hybrid Sine Cosine Optimization Algorithm

This study will solve the classical vehicle routing problem, the goal is to generate k trips with the shortest distance for h customers with predetermined locations and needs.. The proposed solution to the classical vehicle routing problem is a hybrid sine cosine algorithm. The sine cosine algorithm is hybridized with the grey wolf optimizer, which is used in combination with the methods of tournament selection, opposition learning, and the mutation and crossover method to build the optimal routing plan for the means of transporting cement. To demonstrate the advantages of the developed hybrid sine cosine algorithm, this algorithm is evaluated and compared with modern algorithms such as sine cosine algorithm, dragonfly algorithm, grey wolf optimizer, ant lion optimizer, particle swarm optimization, modified hybrid particle swarm optimization, genetic algorithm, and the double-population genetic algorithm in case studies. The hybrid sine cos algorithm gives optimal results in these cases because it balances mining and exploration. Thus, the results of this study indicate that managers can use the developed hybrid sine cosine algorithm to create optimal vehicle routing plans to reduce transportation distances.

An improved genetic algorithm for solving the multi-objective vehicle routing problem with environmental considerations

In recent years, the negative impacts of neglecting the environment, particularly global warming caused by greenhouse gases, have gained attention. Many countries and organizations are taking steps to reduce their greenhouse gas emissions and promote sustainable practices. In this paper, we aim to address the gap in the classical Vehicle Routing Problem (VRP) by taking into consideration the environmental effects of vehicles. To find a balance between cost-efficiency and environmental impact, we propose a Hybrid Genetic Algorithm (HGA) to address the Dynamic Vehicle Routing Problem with Time Windows (DVRPTW) and a heterogeneous fleet, taking into account new orders that arrive dynamically during the routing process. This approach takes into consideration the environmental effects of the solutions by optimizing the number and type/size of vehicles used to fulfill both static and dynamic orders. The goal is to provide a solution that is both cost-effective and environmentally friendly, addressing the issue of over-exploitation of energy and atmospheric pollution that threaten our ecological environment. Computational results prove that the hybridization of a genetic algorithm with a greedy algorithm can find high-quality solutions in a reasonable run time.

An adaptive ant colony algorithm for crowdsourcing multi-depot vehicle routing problem with time windows

Logistics distribution faces difficulties such as increasing delivery demands, demanding delivery time and lower delivery costs. However, the routing optimization for logistic distribution is not a simple vehicle routing problem (VRP). This study focuses on crowdsourcing multi-depot vehicle routing problem with time windows (MDVRPTW) problem, permitting one crowdsourcing driver to deliver multiple customers, which has not been covered yet. To quickly distribute many delivery tasks within a certain time, this paper proposes a two-stage MDVRPTW framework. The first stage is the division stage in which a k-means algorithm based on the elbow method is used to transform the multi-depot problem into several single-depot problems. Then a crowdsourcing VRPTW model is developed, which is a mixed-integer linear programming model. The second stage is the optimization stage, for which an adaptive ant colony (ADACO) algorithm is proposed to determine the most reasonable distribution routes for each distribution center. Solomons classic VRP data is then used to validate the models’ effectiveness, with the results confirming that the crowdsourcing MDVRPTW strategy could save 10.02% costs than traditional MDVRPTW strategy. By comparison, the ADACO algorithm could significantly improve the ACO’s weakness of falling into a local optimum, and would be more suitable for solving large-scale vehicle routing problems than the GUROBI solver.

Periodic Vehicle Routing Problem with Driver Consistency and service time optimization

The Periodic Vehicle Routing Problem with Driver Consistency is an extension of the classic Vehicle Routing Problem in which routes for several vehicles have to be determined over a time horizon of several days. Each customer has an associated set of possible visit schedules and must be visited always by the same vehicle. In this paper, we study a variant of the PVRP-DC in which, in addition to routes and visit schedules, service times of customers have to be determined in order to maximize the utility of the service to the company. We call this problem the Periodic Vehicle Routing Problem with Driver Consistency and Service Time Optimization. We present a mixed-integer linear programming formulation for the problem, propose three branch-and-cut methods to solve it, two of which are based on Benders reformulations, and report computational results on benchmark instances with different features.

Dynamic scheduling of home care patients to medical providers

Home care provides personalized medical care and social support to patients within their own homes. Our work proposes a dynamic scheduling framework to assist in the assignment of health practitioners (HPs) to patients who arrive stochastically over time and are heterogeneous with respect to their health requirements, service duration, and region of residence. We model the decision of which patients to assign to HPs as a discrete‐time, rolling‐horizon, infinite‐stage Markov decision process. Due to the curse of dimensionality and the combinatorial structure associated with an HP's travel, we propose an approximate dynamic programming (ADP) approach based on a one‐step policy improvement heuristic. Four policies are investigated: The first two prioritize HP fairness by balancing service and travel times, respectively, while the other two are based on fluid approximations of the system. We show that the first fluid model is optimal if the number of patient arrivals is sufficiently large while the second performs better experimentally; both approaches leverage pricing and decomposition strategies. We compare our framework to more commonly implemented policies—constrained versions of the classical vehicle routing problem—in a simulation study using data collected from a Canadian home care provider. We show that, in contrast to these approaches, by accounting for future uncertainty, substantial cost savings can be obtained while a fewer number of referrals are rejected. We also find that well‐performing policies assign patients to HPs operating within a small set of adjacent regions while considering the number of periods that a patient requires care for. Otherwise, HP workload may not be appropriately balanced over the long‐term even if travel time is minimized.

Population-Based Iterated Local Search Approach for Dynamic Vehicle Routing Problems

This article addresses the dynamic vehicle routing problem (DVRP). DVRP is a challenging variation of the classic vehicle routing problem in which some customers are not known in advance. The objective is to incorporate new customers into the schedule as they become known while still attempting to minimize the cost of serving all customers without violating the problem constraints. This work proposes an effective population-based approach that integrates various algorithmic components to address DVRP. The approach combines a local search algorithm with various evolutionary operators (crossover and mutation) in an adaptive manner. To promote diversity, the proposed approach utilizes a population of solutions and uses a quality-and-diversity strategy to retain only promising solutions. The well-known 21 DVRP benchmark instances are utilized to test the performance of the proposed approach. An experimental comparison is carried out to assess the contribution of the integrated components. Results demonstrate that the integrated components significantly improve search performance. It is also shown that the proposed approach produces new best results for several instances when compared with the best methods reported in the literature. Note to Practitioners—This work deals with dynamic vehicle routing problems (DVRPs). In DVRP, only limited information is available at the start, and new information is revealed over time. It proposes an effective hybrid approach to tackle this problem. The proposed approach combines evolutionary operators and a local search approach in an adaptive manner to exploit the benefits of each algorithmic component. The proposed approach produces several new best-known solutions. The experimental results demonstrate that the proposed approach is very effective in dealing with DVRP and can help decision-makers in designing best-routing solutions.

A Biobjective Vehicle Routing Problem with Stochastic Demand and Split Deliveries

This study addresses a biobjective vehicle routing problem with stochastic demand and split deliveries. Apart from minimizing the total travel cost that is widely considered in classical vehicle routing problems, we aim to balance the workload of all routes. A recourse policy for paired vehicles that allows the distribution service to fail once and meet part of the demand of customers first is provided. To solve the proposed biobjective vehicle routing problem, an adaptive large neighborhood search embedded with an improved optimization method is developed. The objective value is calculated based on the normalized values of two goals using the improved weighted sum approach. To evaluate the proposed optimization model and corresponding algorithm, some experiments modified from Solomon’s instances are conducted. Computational results show that the performance of the proposed heuristic approach is effective.

Distribution Path Optimization by an Improved Genetic Algorithm Combined with a Divide-and-Conquer Strategy

The multivehicle routing problem (MVRP) is a variation of the classical vehicle routing problem (VRP). The MVRP is to find a set of routes by multiple vehicles that serve multiple customers at a minimal total cost while the travelling-time delay due to traffic congestion is tolerated. It is an NP problem and is conventionally solved by metaheuristics such as evolutionary algorithms. For the MVRP in a distribution network, we propose an optimal distribution path optimization method that is composed of a distribution sequence search stage and a distribution path search stage that exploits a divide-and-conquer strategy, inspired by the idea of dynamic programming. Several optimization objectives subject to constraints are defined. The search for the optimal solution of the number of distribution vehicles, distribution sequence, and path is implemented by using an improved genetic algorithm (GA), which is characterized by an operation for preprocessing infeasible solutions, an elitist’s strategy, a sequence-related two-point crossover operator, and a reversion mutation operator. The improved GA outperforms the simple GA in terms of total cost, route topology, and route feasibility. The proposed method can help to reduce costs and increase efficiency for logistics and transportation enterprises and can also be used for flow-shop scheduling by manufacturing enterprises.

Branch-and-cut-and-price for the Electric Vehicle Routing Problem with Time Windows, Piecewise-Linear Recharging and Capacitated Recharging Stations

The Electric Vehicle Routing Problem with Time Windows, Piecewise-Linear Recharging and Capacitated Recharging Stations aims to design minimum-cost routes for a fleet of electric vehicles subject to intra-route and inter-route constraints. Every vehicle is equipped with a rechargeable battery that depletes while it transports goods along its route. A vehicle must detour to a recharging station to recharge before draining its battery. To approximate a real recharging process, the amount of energy restored is modeled as a piecewise-linear function of the time spent recharging. Furthermore, each station has a small number of chargers, and hence, when and where a vehicle can recharge must be scheduled around the availability of a charger. This interaction between vehicles does not appear in classical vehicle routing problems and motivates the development of new methods that can exploit the joint routing and scheduling structure. This paper proposes a branch-and-cut-and-price algorithm that designates the routing to integer programming using Dantzig–Wolfe decomposition and the scheduling to constraint programming using logic-based Benders decomposition. Experimental results indicate that this hybrid method solves 34% of the instances with 100 customers.