Delivery Vehicle Routing Research Articles

Electric delivery vehicle routing problem optimization model with time-varying traffic congestion

In order to plan a reasonable scheme for the fleet travel and minimize the energy consumption of electric vehicles during traffic congestion periods, while relieving the mileage anxiety of delivery personnel, the pure electric delivery vehicle routing problem considering time-varying traffic congestion was studied. Firstly , a novel mixed integer programming model (TD-EVRP) is established to step for its extended model of EVRP, which especially characterizes the time-varying traffic congestion state and measures the energy consumption of electric delivery vehicles. This model also refines its constraints including customer time window, vehicle load, and vehicle charging requirements. Secondly, a traffic congestion avoidance strategy is introduced into the model, which allows vehicles to park and charge at customer points during peak traffic periods in order to actively avoid unnecessary energy consumption caused by traffic congestion. Finally, the improved ant colony algorithm is designed to acquire the optimal solution.

Pickup and Delivery Vehicle Routing Problem with Hybrid Missions and Third-Party Vehicle Rentals: A Case Study of Animal Feed Industry

The vehicle routing problem for small and medium-sized animal feed manufacturers is a complex challenge because each transport route can vary significantly between delivering products to customers and picking up raw materials to return to the factory. Currently, businesses lack well-planned management for utilizing a limited number of trucks. As a result, they often incur additional costs by relying on third-party vehicle rentals. This research aims to reduce transportation costs for small and medium-sized animal feed manufacturers by solving a formulated mixed-integer linear programming (MILP) model, using experimental data that accurately reflects the actual problems faced. The MILP model results help reduce transportation costs by up to 18.5% compared to current practices by optimizing route sequences and incorporating the use of third-party vehicle rentals. This also serves as a guideline for reducing transportation costs in other similar industries.

A heuristic with a performance guarantee for the commodity constrained split delivery vehicle routing problem

AbstractThe commodity constrained split delivery vehicle routing problem (C‐SDVRP) is a routing problem where customer demands are composed of multiple commodities. A fleet of capacitated vehicles must serve customer demands in a way that minimizes the total routing costs. Vehicles can transport any set of commodities and customers are allowed to be visited multiple times. However, the demand for a single commodity must be delivered by one vehicle only. In this work, we developed a heuristic with a performance guarantee to solve the C‐SDVRP. The proposed heuristic is based on a set covering formulation, where the exponentially‐many variables correspond to routes. First, a subset of the variables is obtained by solving the linear relaxation of the formulation by means of a column generation approach which embeds a new pricing heuristic aimed to reduce the computational time. Solving the linear relaxation gives a valid lower bound used as a performance guarantee for the heuristic. Then, we devise a restricted master heuristic to provide good upper bounds: the formulation is restricted to the subset of variables found so far and solved as an integer program with a commercial solver. A local search based on a mathematical programming operator is applied to improve the solution. We test the heuristic algorithm on benchmark instances from the literature. The comparison with the state‐of‐the‐art heuristics for solving the C‐SDVRP shows that our approach significantly improves the solution time, while keeping a comparable solution quality and improving some best‐known solutions. In addition, our approach is able to solve large instances with 100 customers and six commodities, and also provides very good quality lower bounds. Furthermore, an instance of the C‐SDVRP can be transformed into a CVRP instance by simply duplicating each customer as many times as the requested commodities and by assigning as demand the demand of the single commodity. Hence, we compare heuristics for the C‐SDVRP against the state‐of‐the‐art heuristic for the Capacitated Vehicle Routing Problem (CVRP). The latter approach revealed to have the best performance. However, our approach provides solutions of comparable quality and has the interest of providing a performance guarantee.

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.

Improved Ant Colony Algorithm for the Split Delivery Vehicle Routing Problem

The split delivery vehicle routing problem (SDVRP) is a classic combinatorial optimization problem, which is usually solved using a heuristic algorithm. The ant colony optimization algorithm is an excellent heuristic algorithm that has been successfully applied to solve various practical problems, and it has achieved good results. However, in the existing ant colony optimization algorithms, there are issues with weak targeting of different customer selection strategies, difficulty in balancing convergence speed and global search ability, and a predisposition to become trapped in local optima. To solve these problems, this paper proposes an improved ant colony algorithm (IACA). First, in terms of customer point selection, the initial customer and noninitial customer selection strategies are proposed for different customers, and the adaptive selection threshold is designed. Second, in terms of pheromone processing, an initial pheromone distribution method based on a greedy strategy, a pheromone backtracking mechanism, and an adaptive pheromone volatile factor are proposed. Finally, based on the 2-opt local search method, vehicle path self-search and intervehicle path search are proposed to further improve the quality of the solution. This paper tests the performance of the IACA on datasets of different scales. The experimental results show that compared with the clustering algorithm, artificial bee colony algorithm, particle swarm optimization algorithm, traditional ant colony algorithm, and other algorithms, the IACA can achieve more competitive results. Specifically, compared to the path length calculated by other algorithms, the path length calculated by IACA decreased by an average of 1.58%, 4.28%, and 3.64% in small, medium, and large-scale tests, respectively.

Estimating optimal split delivery vehicle routing problem solution values

This paper explores the application of linear regression models to estimate the optimal solution value (i.e., the sum of tour lengths) for the Split Delivery Vehicle Routing Problem (SDVRP). We present novel models that integrate topological features along with the mean and standard deviation of feasible solution values, achieving an impressive accuracy with an error margin of approximately 3%. To obtain random feasible solutions for the SDVRP quickly, we propose a modified Clarke & Wright algorithm with split delivery (MCWSD). Our results demonstrate the potential of extending our earlier work to more complex routing problems, highlighting the importance of incorporating diverse features to obtain accurate approximations.

Logistics distribution route optimization of electric vehicles based on distributed intelligent system

Abstract The data management system of health cloud authentication plays an important role in the optimization of logistics vehicle routing. It can not only help logistics vehicles choose the best distribution path, but also save time and cost and improve economic efficiency. At present, logistics has not yet formed a complete service system. High distribution costs and low distribution efficiency limit the development of the entire logistics. The reduction of logistics costs and the improvement of distribution efficiency have become the top priorities of the society. The optimization of the distribution route is the key to cost saving and distribution logistics. It is particularly important to study and optimize the distribution route, because the distribution route affects the logistics transportation efficiency and the loss cost during transportation. Therefore, this paper adjusted the scheduling system of logistics vehicles through a distributed intelligent system, and optimized the path of logistics vehicles according to the improved genetic algorithm, thereby reducing the transportation cost of logistics and improving the efficiency of logistics distribution. This article first explains the definition, classification, and main components of the delivery vehicle routing problem. Then, using cloud authentication path optimization, a distributed intelligent system is constructed. Finally, an improved ant colony algorithm is used to analyze and study the distance constraints of vehicles. By improving the ant colony algorithm, it can be seen that the optimized path pheromone concentration and the optimized sub-function have gradually increased with time. The mean pheromone concentration was 40 %, and the seventh day was 15 % higher than the first. The mean value of the optimized subfunction was 0.34 %, and the seventh day was 20 % higher than the first. The distribution cost and distribution efficiency of the optimized logistics vehicle distribution path were much higher than those of the traditional logistics distribution path. Moreover, the distribution cost of the logistics distribution path was 9 % lower than the traditional one, and the distribution efficiency was 13 % higher. The average smoothness of the optimized logistics path is about 90 %, and the seventh day is 11 % higher than the first day. The average fitness of the optimized logistics path is 88 %, and the seventh day is 14 % higher than the first day. In a word, the data management system can uniformly schedule logistics vehicles and improve the efficiency of distribution.

Research on Dynamic Takeout Delivery Vehicle Routing Problem under Time-Varying Subdivision Road Network

For the dynamic takeout delivery vehicle routing problem, which faces fluctuating order demand and time-varying speeds, this study presents a novel approach. We analyze the time distribution of takeout orders and apply a Receding Horizon Control (RHC) strategy to convert the dynamic challenge into a static one. The driving speed of delivery vehicles on different roads at different times is determined based on the subdivision criteria of the urban road network and a traffic congestion measurement method. We propose a dynamic takeout delivery vehicle routing optimization model and a time-varying subdivision road network is established to minimize the total delivery cost. We validated the model through simulation examples. The optimization results show that the total distribution cost is reduced after considering the time-varying subdivision road network, with the penalty cost decreasing by 39%. It is evident that considering the subdivision of the road network can enhance order delivery efficiency and optimize the overall dining experience. The sensitivity analysis of various parameters reveals that the delivery platform must appropriately determine the time domain and allocate the number of delivery personnel based on order scale to avoid escalating delivery costs. These findings provide theoretical guidance for vehicle routing planning in the context of delivery platforms.

The last-mile delivery vehicle routing problem with handling cost in the front warehouse mode

This paper aims to investigate the vehicle routing problem faced by a logistics service provider that performs the last-mile delivery of large household appliances under the front warehouse mode for multiple enterprises. We formulate the problem as a new variant of the pickup and delivery problem and present a mixed integer programming model for it. To solve this problem heuristically, the neighborhood structures with newly proposed move operators are explored within a variable neighborhood search (VNS) and a randomized tabu thresholding (RTT). Experiments on small instances clearly indicate the effectiveness of the two heuristic methods. The comparative results on large-scale instances show that RTT performs relatively better than VNS. In addition, through comparison with computational results of algorithms from the literature, RTT proves good ability to solve a related problem. Furthermore, we introduce a sample case to explore the benefit of FWM for last-mile delivery and to discuss the impact of inventory in front warehouses, handling cost, and split delivery on the solution.

Research on a Joint Distribution Vehicle Routing Problem Considering Simultaneous Pick-Up and Delivery under the Background of Carbon Trading

In order to explore the positive impact of the joint distribution model on the reduction in logistics costs in small-scale logistics enterprises, considering the demand on enterprises for simultaneous pick-up and delivery, as well as the cost of carbon emissions, this study considers the vehicle routing problem of simultaneous pick-up and delivery under a joint distribution model. First of all, an independent distribution model and a joint distribution model including fixed transportation, variable transportation, time penalty, and carbon emissions costs are established; second, by adding the self-adaption cross-mutation probability and the destruction and repair mechanism in the large-scale neighborhood search algorithm, the genetic algorithm is improved to adapt to the solution of the model in this paper, and the effectiveness of the improved algorithm is verified and analyzed. It is found that the improved genetic algorithm is more advantageous than the original algorithm for solving the problems of both models designed in this paper. Finally, the improved genetic algorithm is used to solve the two models, and the results are compared and analyzed. It is found that the joint distribution model can reduce the total cost by 6.61% and the carbon emissions cost by 5.73%. Additionally, the impact of the carbon trading mechanism on the simultaneous pick-up and delivery vehicle routing problem under the joint distribution model is further explored. The results of this study prove that enterprises can effectively reduce costs, improve profits, reduce carbon emissions, and promote the sustainable development of logistics enterprises under the condition of joint distribution.

An exact algorithm for unpaired pickup and delivery vehicle routing problem with multiple commodities and multiple visits

This paper addresses a new multi-commodity unpaired pickup and delivery vehicle routing problem in which each vehicle is allowed to visit each customer more than once for both pickup and delivery of each commodity. It is a complex variant of the classical capacitated vehicle routing problem and comes from resource transfer among different plants in a distributed manufacturing environment. Notably, the pairing decisions of pickup and delivery for each commodity and the routing decisions among customers are interdependent, and they need to be made simultaneously and collaboratively. Firstly, a mixed integer programming model is developed, and then new valid inequalities are derived to improve the linear programming relaxation. Afterwards, a branch-and-cut algorithm is proposed by exploring different branching strategies and tailored separation algorithms. Computational results based on real-case instances from an automobile manufacturing company demonstrate that the costs are considerably reduced by considering the multiple visits compared to the single visit of each customer. In addition, our proposed branch-and-cut algorithm outperforms a manual solution method adopted by the company in practice and two solution methods in the literature. Furthermore, two adaptations of our branch-and-cut algorithm also perform better than two state-of-the-art algorithms in solving two closely-related problems in terms of solution quality and computation time. Sensitivity analyses with respect to vehicle capacity, vehicle duration, and vehicle speed are conducted to derive several valuable managerial insights.

Penyelesaian Split Delivery VRP dengan Ant Colony Optimization (Studi Kasus: Pengiriman Produk di PT Sinarmas Distribusi Nusantara)

PT Sinarmar Distribusi distributes its products to all Distribution Center (DC) every day. Currently PT Sinarmas Distribution Nusantara uses a predetermined route every day using Colt Diesel Double vehicles with maximum transport capacity of 500 cartons. Currently the number of products carried by each vehicle never reaches its maximum carrying capacity. PT Sinarmas Distribusi Nusantara wants vehicle transport capacity to be used optimally. This route problem at PT Sinarmas Distribusi Nusantara can be defined as Split Delivery Vehicle Routing Problem (SDVRP). Ant Colony Optimization (ACO) is a metaheuristic that can be used to solve SDVRP. By using ACO the resulting route is always shorter than the current route and the number of vehicles used is smaller.

Mathematical Models for Disassembly Line Balancing and Pickup - Delivery Vehicle Routing Problem

Mathematical Models for Disassembly Line Balancing and Pickup - Delivery Vehicle Routing Problem

The split delivery vehicle routing problem with time windows and three-dimensional loading constraints

The split delivery vehicle routing problem with time windows and three-dimensional loading constraints

Solution of green simultaneous pickup and delivery vehicle routing problem with time window using metaheuristic methods

Araç rotalama problemi, merkezi bir depodan farklı koordinatlarda yer alan müşterilere belirli kapasiteye sahip araçlarla yapılacak dağıtım için en kısa dağıtım rotasının belirlendiği bütünleşik bir optimizasyon problemidir. Artan çevresel duyarlılık ve problemin gerçek hayata daha uygun hale getirilmesi için zaman, eş zamanlı toplama ve dağıtım, rota uzunluğu, çoklu depo, teslimat bölme, yakıt tüketimi ve karbon emisyonu gibi kısıtlar probleme eklenerek yeni varyantlar ortaya konmuştur. Bu çalışmada, çevresel duyarlılığın ön plana çıktığı yeşil araç rotalama problemi, zaman pencereli ve eş zamanlı topla dağıt araç rotalama problemleri bütünleşik olarak ele alınmaktadır. Bu noktada, toplama ve dağıtım talepleri, siparişlerin teslim zamanları ve dağıtım esnasında sürdürülebilirliğin sağlanabilmesi için çevresel faktörler de önemli bir etken olarak göz önüne alınmıştır. Çalışma kapsamında Yeşil Zaman Pencereli ve Eş Zamanlı Topla Dağıt Araç Rotalama Problemi (YZPETDARP) için yeni karma tamsayılı doğrusal olmayan matematiksel model oluşturulmuş, belirli şartlar altında model doğrusallaştırılarak farklı yöntemler ile çözüm aranmıştır. YZPETPARP’nin çözümü için metasezgisel arama algoritmaları olan Genetik Algoritma (GA) ve Ağırlıklı Süperpozisyon Çekim Algoritması (ASÇA) önerilmiş, literatürdeki ilgili veriler entegre edilerek test verileri oluşturulmuştur. Deneysel çalışmalar sonucunda çözüm uygunluk değeri ve çözüm süresi bakımından GA ile daha iyi sonuçlara ulaşılmış, or-opt sezgiseli ile entegre edilen ASÇA ise GA ile elde edilen sonuçlara yakın ve tatmin edici sonuçlar vermiştir.

A multi-day waste collection and transportation problem with selective collection and split delivery

This paper addresses a multi-day waste collection and transportation problem with selective collection and split delivery (MDWCTP-SCSD). Rather than emptying waste according to a fixed schedule, garbage trucks only visit community waste collection sites whose waste level reaches a predetermined threshold, reducing collection costs but increasing overflow risk. Collection sites likely to overflow the next day if unvisited today are also selected for preventive collection. Split delivery is permitted. The MDWCTP-SCSD is formulated as a mixed integer linear programming model. To solve this NP-hard problem, a heuristic combining variable neighborhood search and simulated annealing is proposed. In addition to classical operators, three new operators are developed to handle split delivery. Experiments demonstrate the proposed algorithm is competitive in solving two split delivery vehicle routing benchmark sets; outperforms CPLEX in solving small-scale instances within an hour; and quickly solves large-scale instances with high quality. Noteworthy findings indicate fleet costs and size can be reduced by approximately 50% if only visiting sites whose waste level reaches 80%.

Cloud‐fog assisted human tracing and disaster evacuation framework

AbstractMany kinds of natural hazards and man‐made calamities have occurred in recent years, each of which has left a huge number of victims and has been challenging to deal with. The solution is an effective evacuation planning system, which is gaining the interest of governments, academic institutions, and industries all across the world. This study focuses on quick and organized evacuation from densely populated areas during disasters to decrease damage successfully. This research proposes a fog‐cloud‐assisted effective disaster evacuation framework. The data accumulation layer uses IoT, mobile networks, and GPS technologies to collect environmental and location‐based data to track the inhabitants. The fog layer is utilized for (i) disaster event detection and (ii) human tracing and crowd density analysis. A cloud layer makes it easier for an evacuation algorithm to produce an evacuation map that will point evacuees to the exit while computing a quick and safe path utilizing environmental and inhabitant information gathered from the fog. The findings reveal that the performance of Model A surpasses the split delivery vehicle routing problem model with the minimum demand of vehicles and with improvement of 38.1% average. Also, A* takes less time (18.3 s) than other state‐of‐the‐art techniques to find the best optimal route for evacuation. Implementation and performance analysis demonstrate the efficiency and effectiveness of the proposed framework.

Solving a Continent-Scale Inventory Routing Problem at Renault

This paper is the fruit of a partnership with Renault. Their reverse logistic requires solving a continent-scale multiattribute inventory routing problem (IRP). With an average of 30 commodities, 16 depots, and 600 customers spread across a continent, our instances are orders of magnitude larger than those in the literature. Existing algorithms do not scale, so we propose a large neighborhood search (LNS). To make it work, (1) we generalize existing split delivery vehicle routing problems and IRP neighborhoods to this context, (2) we turn a state-of-the-art matheuristic for medium-scale IRP into a large neighborhood, and (3) we introduce two novel perturbations: the reinsertion of a customer and that of a commodity into the IRP solution. We also derive a new lower bound based on a flow relaxation. In order to stimulate the research on large-scale IRP, we introduce a library of industrial instances. We benchmark our algorithms on these instances and make our code open source. Extensive numerical experiments highlight the relevance of each component of our LNS. Funding: This work was supported by Renault Group. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0342 .

Last mile delivery routing problem using autonomous electric vehicles

This paper presents a study on the application of Autonomous Delivery Vehicles (ADVs) in last-mile delivery for urban logistics. Specifically, we focus on a routing problem using multi-stop ADVs, with the goal of minimizing route and vehicle usage costs while satisfying several constraints associated with load and battery capacities, maximum route duration for ADVs, and maximum walking distance for customers. We refer to this problem as the Autonomous Delivery Vehicle Routing Problem (ADVRP) and present its mixed-integer linear programming formulation. Due to the NP-hardness of the problem, we propose a two-phase metaheuristic approach that first clusters customers and determines stopping locations for the ADVs, followed by a phase that determines the optimal routes for the ADVs using hybrid variable neighborhood search and simulated annealing. To evaluate our proposed solution methodology, we conduct computational experiments on various related Vehicle Routing Problems (VRPs) from the literature and newly generated ADVRP instances. The results show that the proposed two-phase metaheuristic approach can produce high-quality solutions with minimal computational effort while outperforming an exact solver in 26 medium- and large-sized instances of ADVRP and reaching optimal solutions in most VRP instances and related problems. Furthermore, we conduct sensitivity analyses on selected problem parameters and present a case study in Istanbul, Turkey to provide managerial insights for implementing ADVs in urban logistics.

A New Family of Route Formulations for Split Delivery Vehicle Routing Problems

We propose a new family of formulations with route-based variables for the split delivery vehicle routing problem with and without time windows. Each formulation in this family is characterized by the maximum number of different demand quantities that can be delivered to a customer during a vehicle visit. As opposed to previous formulations in the literature, the exact delivery quantities are not always explicitly known in this new family. The validity of these formulations is ensured by an exponential set of nonrobust constraints. Additionally, we explore a property of optimal solutions that enables us to determine a minimum delivery quantity based on customer demand and vehicle capacity, and this number is often greater than one. We use this property to reduce the number of possible delivery quantities in our formulations, improving the solution times of the computationally strongest formulation in the family. Furthermore, we propose new variants of nonrobust cutting planes that strengthen the formulations, namely limited-memory subset-row covering inequalities and limited-memory strong k-path inequalities. Finally, we develop a branch-cut-and-price (BCP) algorithm to solve our formulations enriched with the proposed valid inequalities, which resorts to state-of-the-art algorithmic enhancements. We show how to effectively manage the nonrobust cuts when solving the pricing problem that dynamically generates route variables. Numerical results indicate that our formulations and BCP algorithm establish new state-of-the-art results for the variant with time windows, as many benchmark instances with 50 and 100 customers are solved to optimality for the first time. Several instances of the variant without time windows are solved to proven optimality for the first time. Funding: This work was supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grants 306033/2019-4, 313220/2020-4, and 314088/2021-0], the Région Nouvelle Aquitaine, France [Grant AAPR2020A-2020-8601810], the Agence Nationale de la Recherche [Grant ANR-20-CE40-0021-01], the Fundação de Amparo à Pesquisa do Estado de São Paulo [Grants 13/07375-0, 16/01860-1, and 19/23596-2], and the Paraíba State Research Foundation [Grants 261/2020 and 041/2023]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0085 .