Electric Vehicle Routing Problem Research Articles

Dynamic electric vehicle routing problem considering mid-route recharging and new demand arrival using an improved memetic algorithm

With the widespread popularity of electric vehicles (EVs) in recent years, electric vehicle routing problem (EVRP) has received considerable attention from logistics management field. However, the real-world logistics and transportation system is always time-varying, such as new customer demand arrives dynamically. This dynamic transportation environment poses a great deal of challenges upon the decision-making of EVRP since the mid-route recharging of EVs has to be considered to meet the dynamic arrival of new customer demand due to the limited battery capacity. Therefore, a dynamic EVRP (DEVRP) with mid-route recharging and new demand arrival is investigated in this study. A mathematical model considering both recharging and routing decision-makings is developed, and then an improved memetic algorithm (IMA) with adaptive local search and economical random immigrant strategy is proposed. Four peer algorithms are used to test the performance of the proposed IMA on numerous extended benchmarks. It is observed that IMA can be treated as a more effective solution tool to achieve a better routing plan as well as the improved energy efficiency of EVs.

An efficient optimization algorithm for electric vehicle routing problem

AbstractThere has been a steady increase in the prevalence of electric vehicles (EVs) (electric cars) in the transportation industry. The limited range of EVs and the lack of charging facilities make it harder to gain widespread adoption of the EV service. Several optimisation algorithms for EV routes have not yet resolved the problems of trip time and travel cost. The study provides a Bat optimisation technique to reduce trip time and costs while taking into account customer service requests and EV charging schedules. Taking into account battery capacity, charging duration, and delivery/pickup needs, the suggested method may determine the optimal path to supercharger stations. To demonstrate its effectiveness, it is compared to other state‐of‐the‐art algorithms across a variety of benchmark cases.

A multi-compartment electric vehicle routing problem with time windows and temperature and humidity settings for perishable product delivery

Perishable product delivery has been a notable challenge due to the nature of perishability and high customer expectations. Recently, emerging technologies such as electric and multi-compartment vehicles have been applied to facilitate perishable product deliveries with less deterioration and carbon emissions. Accordingly, new management problems are placed including setting environmental conditions of compartments, routing and scheduling the recharging of vehicles. To deal with these difficulties, we introduce the multi-compartment electric vehicle routing problem with time windows and temperature and humidity settings (MCEVRP-th). A mathematical formulation is proposed, and a hybrid adaptive large neighborhood search and tabu search heuristic (ALNS/TS), which allows generating infeasible solutions, is developed. Extensive experiments assess the performance of the proposed algorithm based on the modified benchmark and real-world instances, and several management insights are derived.

A branch-cut-and-price algorithm for the time-dependent electric vehicle routing problem with time windows

The adoption of electric vehicles (EVs) within last-mile deliveries is considered one of the key transformations towards more sustainable logistics. The inclusion of EVs introduces new operational constraints to the models such as a restricted driving range and the possibility to perform recharges en route. The discharge of the typical batteries is complex and depends on several variables, including the vehicle travel speed, but most of the approaches assume that the energy consumption depends only on the distance traveled. This becomes relevant in different logistics contexts, such as last-mile distrubtion in large cities and mid-haul logistics in retail, where traffic congestion affects severely the travel speeds. In this paper, we introduce a general version of the Time-Dependent Electric Vehicle Routing Problem with Time Windows (TDEVRPTW), which incorporates the time-dependent nature of the transportation network both in terms of travel times and the energy consumption. We propose a unifying framework to integrate other critical variable times arising during the operations previously studied in the literature, such as the time-dependent waiting times and non-linear charging times. We propose a state of the art branch-cut-and-price (BCP) algorithm. Based on extensive computational experiments, we show that the approach is very effective solving instances with up to 100 customers with different time dependent configurations. From a managerial standpoint, our experiments indicate that neglecting the travel speeds can affect the quality of the solutions obtained, where up to 40 percent of the infeasibilities induced by neglecting the time dependency can be caused by exceeding the battery capacity.

Optimization Model for Electric Vehicle Routing Problem with Two Charging Options

The use of electric vehicles recently is an alternative way to lower pollutants and the emissions of carbon dioxide resulting from the usage of motor vehicle fuel oil. The limited battery capacity of this electric vehicle is a problem for its users. Vehicle routing problem (VRP) is a problem of integer programming and combinatorial optimization that is frequently used in planning and decision-making processes. One application of this issue is to find the best path for delivering items from a corporation to customers. VRP problems are frequently utilized in order to reduce internal expenditure. Model optimization in this paper uses two rehcarging options, recharging and swapping battery. The purpose of this paper is to present a VRP optimization model for electric vehicle routing problems to find the best route option that minimizes the total of the fees for fixed vehicles, transit, charging, battery changing, and waiting.

A mat‐heuristics approach for electric vehicle route optimization under multiple recharging options and time‐of‐use energy prices

SummaryTraveling has contributed a lot to the evolution of mankind. Today, electric vehicles (EVs) are being preferred due to their greater efficiency, comfort, and environment‐friendly qualities. The EVs' contribution to future mobility is projected to rise exponentially in years to come. To make this innovative technology more successful, there is a dire need to install a sufficient number of charging stations (CSs). As the EVs are limited by their cruising range, they require multiple recharging to cover long distances (especially in the case of logistics delivery services). Thus, there is a great need to develop an efficient and cost‐effective EV route optimization approach considering multiple recharging options and time‐of‐use (ToU) energy prices. In this regard, a novel mat‐heuristic approach named (firefly with ant colony algorithm) has been proposed to solve the problem of EVRPTW (electric vehicle routing problem with time windows) incorporating detailed modeling of multiple charging flexibility (i.e., battery swapping, partial recharge, and different charging levels) and ToU energy prices. Our proposed approach aims to minimize the total cost of traveling, which is highly influenced by the cost of recharging. Ant colony algorithm (ACA) serves as the basic optimization framework in the proposed approach, while the firefly approach explores hitherto unexplored solution space and avoids local optima. The computation performance of the proposed approach is compared with existing state‐of‐the‐art similar domain approaches such as variable neighborhood search (VNS) and ant colony optimization using local search (ACO‐LS) which has average deviation of nearly 20%–25% from with optimal solution achieved by the proposed . The proposed approach yields a near‐optimal solution with a faster convergence rate (approximately 50%) compared to other existing approaches. Moreover, the multiple recharging options modeled in our proposed approach justify their significance in terms of cost‐effectiveness for most scenarios.

The time-dependent electric vehicle routing problem with drone and synchronized mobile battery swapping

Logistics enterprises are moving towards high efficiency and green. As an emerging technology, unmanned aerial vehicle (UAV, also known as drone) is very useful to cope with flexible and fast delivery. Electric vehicles (EVs), as new energy vehicles, are the technical support for green logistics development. This paper considers the last-mile delivery system in which a fleet of homogeneous EVs, equipped with a UAV each, serve a set of customers, and meanwhile battery swapping vehicles (BSVs) offer mobile battery swapping service for EVs. A mixed integer programming (MIP) model is formulated to minimize the sum of depreciation cost, driver wages and energy consumption cost of EVs, UAVs, and BSVs, by considering the nonlinear energy consumption of each vehicle, time-dependent speeds of EVs and BSVs and monetary time value on depreciation cost. A large neighborhood search algorithm based on Q-learning (LNS-QL) is designed in which Q-learning is used to select a combination of tailored destroy and repair operators to solve three sub-problems, (1) the UAV multi-visit problem, (2) the EV and UAV synchronized scheduling problem, (3) the EV and BSV synchronized mobile battery swapping problem. Besides, this paper also designs Lagrangian relaxation algorithm for comparison with LNS-QL. Extensive experiments verify the correctness of the model by testing small-scale instances. Further analysis demonstrates the accuracy and stability of LNS-QL on medium and large-scale instances as well as computational time and verifies the effectiveness of the mobile battery swapping mode in the cooperative delivery system of EVs and UAVs. Actual cases analyze the characteristics of EV delivery from the cost and emissions perspectives by comparing with FV delivery.

An improved matheuristic for solving the electric vehicle routing problem with time windows and synchronized mobile charging/battery swapping

The shift towards low-emission vehicles in transportation activities, electric vehicles (EVs) in particular, has accelerated lately due to the growing concerns in modern societies regarding greenhouse gas emissions and climate change. Delivery companies have started using EVs in their fleets to reduce their dependency on fossil fuels and improve their carbon footprints. However, range anxiety, long recharge durations and insufficient recharging infrastructure still restrain the wider adoption of EVs in the sector. As a remedy, battery swapping vans (BSVs) were proposed in the literature to supply energy to EVs at points of need and the arising problem was referred to as the Electric Vehicle Routing Problem with Time Windows and Synchronized Mobile Battery Swapping (EVRPTW-SMBS). However, the use of BSVs is limited to small commercial vehicles. In this study, we generalize the problem and present the Electric Vehicle Routing Problem with Time Windows and Mobile Charging Stations (EVRPTW-MCS). In this problem, EVs serve the customers within their time windows and electric trucks/vans are employed to recharge or swap their batteries at selected customer locations during their visits. The objective is to minimize the total operational cost with the minimum fleet size. First, we present the mathematical model of the EVRPTW-MCS. Next, we propose a matheuristic approach that combines the Variable Neighborhood Search with exact method to solve it. Then, we perform an extensive numerical study to validate the performance of the proposed approach and present new best solutions for two related problems in the literature. We also investigate the potential benefits of utilizing MCSs and provide several trade-off analyses. Finally, we provide a case study based on real data to present managerial insights.

A hybrid simulated annealing and variable neighborhood search algorithm for the close-open electric vehicle routing problem

AbstractElectric Vehicles (EVs) are the future of transportation, but due to their battery and charging technology they cannot yet directly replace traditional vehicles. Nonetheless, EVs are a great option for city-logistics, due to the small distances and their zero local emissions. In this paper, a novel variant of the Electric Vehicle Routing Problem (EVRP), called Close-Open EVRP (COEVRP), is presented. It considers ending EV trips at Charging Stations, as opposed to other EVRP variants that only allow for en-route charging. This new variant follows a traditional routing scheme, allowing EVs to recharge only at the end of their route. The objective is to minimize energy consumption, as well as the number of vehicles. The energy consumption function takes into account the weight of the transported items. A mathematical formulation for the problem is presented and small instances were solved using a commercial solver. To solve larger instances, a hybrid metaheuristic combining Simulated Annealing and Variable Neighborhood Search algorithm was employed and thoroughly tested.

Electric Vehicle Routing Problem With Variable Vehicle Speed and Soft Time Windows for Perishable Product Delivery

This work studies perishable products’ distribution using electric commercial vehicles (ECVs). Extra energy is consumed for refrigeration to keep such products from deteriorating, which shortens the limited driving range of ECVs. Besides charging at public recharging stations, their travel speed can be adjusted to improve their driving range and decrease distribution cost. We propose an Electric Vehicle Routing problem with variable vehicle speed and soft time windows for perishable products (EVRP-VS). An energy consumption rate function of refrigerated ECVs during driving is introduced into the problem. The function considers refrigeration and has a nonlinear relationship with ECV speed and weight. As long as the carriage is not empty, the vehicle needs refrigeration during driving and during its stay at customers and stations. A mathematical programming model is developed for EVRP-VS, to minimize total distribution cost, including vehicle cost, power cost, refrigeration cost, and penalty cost due to delayed delivery. An adaptive hybrid ant colony optimization (AHACO) with a two-stage speed optimization strategy is proposed to solve EVRP-VS. In the first stage, local speed optimization is used to optimize the speed of each ant (ECV) in each transfer step. In the second one, global speed optimization further optimizes the speed for each fixed route constructed by ants. AHACO is applied to many problem instances. Experimental results show that it can effectively solve EVRP-VS in comparison with CPLEX and other meta-heuristics.

A Collection of Literature Review on Vehicle Routing Problem and Reflections

As a variation of vehicle routing problem whose objective is to determine the subset of nodes to be visited, and the order in which they should be visited, in order to maximize the profit collected within a given time, team orienteering problem has received a lot of attention in the last decades. With the growing interest in the logistics community in using electric vehicles as an alternative to conventional fuel vehicles, academic research on electric vehicle problem is increasing. However, there is still a paucity of research on the use of electric vehicles in team orienteering problem. This paper reviews the existing literature on electric vehicle routing problems and team orienteering problems to identify the feasibility of innovations that propose the use of electric vehicles to replace conventional fuel vehicles in team orienteering problems to complete deliveries, and briefly outlines future research plans.

ELECTRIC VEHICLE ROUTING PROBLEM USING ADAPTIVE SIMULATED ANNEALING

Road transport is a major CO2 emission contributor globally. To tackle the challenge of reducing world carbon emissions, alternative technologies for the automobile industry are widely researched. The automotive industry has started to shift from Internal combustion engine (ICE) vehicles to electric vehicles (EVs), where EVs are the future of the automotive industry in terms of reducing greenhouse gas emissions and air pollution. EV manufacturers are continuously looking for opportunities to optimize the supply chain processes, aiming for supply chain resilience. In this study, we present an Electric Vehicle Routing Problem (EVRP) to achieve the best decision, which is an extension of the traditional Vehicle routing problem (VRP) which in particular finding the shortest route for electric vehicles. The objective function is to find the best travel route that minimizes travel distance. Each route serves a set of customer nodes that starts and ends at a given depot node. We take battery capacity and charging stations as the constraints. In addition, the use of homogenous fleets and single depot are considered in this paper. A hybrid metaheuristic approach is used to find the best solution with the Adaptive Simulated Annealing algorithm. The use of adaptive in simulated annealing generates a higher probability of finding the best operators, which results in better solutions. A comparison of results from various metaheuristic methods is also presented in this paper to get the best method for the EVRP based on a benchmark dataset. This paper ends with recommendations for creating a routing plan that is resilient to disruptions to distribution.

A hybrid metaheuristic approach for solving a bi-objective capacitated electric vehicle routing problem with time windows and partial recharging

PurposeThe vehicle routing problem (VRP) has been widely investigated during last decades to reduce logistics costs and improve service level. In addition, many researchers have realized the importance of green logistic system design in decreasing environmental pollution and achieving sustainable development.Design/methodology/approachIn this paper, a bi-objective mathematical model is developed for the capacitated electric VRP with time windows and partial recharge. The first objective deals with minimizing the route to reduce the costs related to vehicles, while the second objective minimizes the delay of arrival vehicles to depots based on the soft time window. A hybrid metaheuristic algorithm including non-dominated sorting genetic algorithm (NSGA-II) and teaching-learning-based optimization (TLBO), called NSGA-II-TLBO, is proposed for solving this problem. The Taguchi method is used to adjust the parameters of algorithms. Several numerical instances in different sizes are solved and the performance of the proposed algorithm is compared to NSGA-II and multi-objective simulated annealing (MOSA) as two well-known algorithms based on the five indexes including time, mean ideal distance (MID), diversity, spacing and the Rate of Achievement to two objectives Simultaneously (RAS).FindingsThe results demonstrate that the hybrid algorithm outperforms terms of spacing and RAS indexes with p-value <0.04. However, MOSA and NSGA-II algorithms have better performance in terms of central processing unit (CPU) time index. In addition, there is no meaningful difference between the algorithms in terms of MID and diversity indexes. Finally, the impacts of changing the parameters of the model on the results are investigated by performing sensitivity analysis.Originality/valueIn this research, an environment-friendly transportation system is addressed by presenting a bi-objective mathematical model for the routing problem of an electric capacitated vehicle considering the time windows with the possibility of recharging.

A new approach based on hybrid ant colony optimization-artificial bee colony algorithm for multi-objective electric vehicle routing problems

In real-life, routing plans try to optimize multiple objectives without relying on just one. So, this paper introduces three multi-objective electric vehicle routing problems (MOEVRP) that consider different charging strategies and electric vehicle (EV) charger types while optimizing five conflicting objectives: a total minimization cost of recharging, the number of vehicles required, a total travel distance, load-dependent energy consumption, and the total number of charging stations required. We develop a new hierarchical approach consisting of two phases: a Hybrid Ant Colony Optimization (HACO) and an Artificial Bee Colony Algorithm (ABCA). In the first phase, an initial solution is obtained using a HACO that integrates local search algorithms and simulated annealing (SA) to reduce the solution time. Then in the second phase, the problem is solved using an ABCA considering the initial solution obtained from the first phase. Using the proposed HACO-ABCA as the search engine, two posteriors’ methods, namely the weighted-sum method (WSM) and the conic method (CM), are applied to scalarize the five objectives. The effectiveness of the proposed hierarchical approach is examined on well-known test-based instances and obtained the best new results in most instances. Additionally, the proposed solution is applied to a real-life case study. The results show that multi-objective traditional methods give more effective results than multi-objective evolutionary algorithms, regardless of the MOEVRP problem type. We can also conclude that the partial recharge and multiple recharge technology options can significantly improve the route decisions of logistic companies.

A matheuristic for the electric vehicle routing problem with time windows and a realistic energy consumption model

We address an Electric Vehicle Routing Problem with Time Windows (E-VRPTW) considering several real-like factors in the energy consumption model, e.g., the payload and the vehicle speed. We model E-VRPTW as a Mixed Integer Linear Program (MILP) where the speeds of vehicles are continuous variables that can vary between a minimum and a maximum value. Moreover, the proposed MILP formulation is cloneless since it allows using more than once the same recharging station without introducing dummy copies of it. To efficiently solve large-sized instances of the problem, we design a Random Kernel Search (RKS) matheuristic approach, based on the cloneless MILP formulation, that in turn exploits another matheuristic, called Random k-Degree Search (RkDS), to generate an initial feasible solution. We compare the results produced by a MILP solver using the MILP formulation with the ones obtained by the RKS on instances up to 100 customers derived from the benchmark instances of E-VRPTW. We show that the proposed matheuristic outperforms the cloneless MILP formulation on the medium/large-sized instances and also that it is robust, being not significantly sensitive to the values of the parameters used by the RkDS to generate the initial solution and to the initial time limit for the restricted MILP models.

Electric Vehicle Routing Problem with Fuzzy Time Windows using Genetic Algorithm and Tabu Search

&#x0D; &#x0D; &#x0D; &#x0D; The distribution of goods becomes a very calculated thing in the economic aspect, especially in the case of wide and complex distribution. The greater the range of distribution of goods, the more precise, fast, and accurate calculations are needed. Specifically, the calculation of the distribution required starts from mileage, total travel time, customer satisfaction level based on customer time windows, and operational costs. Vehicle Routing Problem (VRP) is a solution to the problem of distributing goods from the depot to its customers. This study aims to determine the optimal route. The methods used for VRP optimization are the Genetic Algorithm (GA) and Tabu Search (TS) methods. Fuzzy logic is used to provide leeway on the limitations of the time windows parameters, thus providing a time tolerance in the event of early arrival of the vehicle or delay in delivery. Data processing using the GA-TS combination was carried out as many as two types of trials, namely trials with the same dataset ten times and trials with various types of datasets ten times. The results of the first trial fitness value on E-VRPFTW average increased by 14.39% compared to the results of the E-VRPTW fitness value that did not use fuzzy. The results of the second trial also experienced an average increase of 8.49% compared to the results of the E-VRPTW fitness value that did not use fuzzy. Therefore, the addition of fuzzy logic has an effect in determining the optimum route of E-VRPTW.&#x0D; &#x0D; &#x0D; &#x0D;

Customer-oriented multi-objective optimization on a novel collaborative multi-heterogeneous-depot electric vehicle routing problem with mixed time windows

With the increasing demand for express delivery and enhancement of sustainable logistics, the collaborative multi-depot delivery based on electric vehicles has gradually attracted the attention of logistics industry. However, most of the existing studies assumed that the products required by different customers could be delivered from any homogeneous depot, ignoring the limitations in facilities and environment of depots in reality. Thus, this study proposed a novel collaborative multi-heterogeneous-depot electric vehicle routing problem with mixed time windows and battery swapping, which not only involves the multi-heterogeneous-depot to meet different customer demands, but also considers the constraints of mixed time windows to ensure timely delivery. Furthermore, a customer-oriented multi-objective optimization model minimizing both travel costs and time window penalty costs is proposed to effectively improve both delivery efficiency and customer satisfaction. To solve this model, an extended non-dominated sorting genetic algorithm-II is proposed. This combines a new coding scheme, a new initial population generation method, three crossover operators, three mutation operators, and a particular local search strategy to improve the performance of the algorithm. Experiments were conducted to verify the effectiveness of the proposed algorithm in solving the proposed model.

How to achieve sustainable distribution in the fast fashion industry? An electric vehicle solution under the "vehicle-battery separation" mode.

Exploring sustainable urban distribution based on electric vehicles is crucial given the rise in global greenhouse gas emissions, especially for fast fashion industries with extremely high distribution frequencies. However, most studies have overlooked the impact of deep discharge on the distribution route scheme, and few studies fit the characteristics of the fast fashion industry. As a result, this study presents a novel electric vehicle routing problem considering deep discharge model (EVRP-DD) for distribution route optimization, which fully considers deep discharge under the emerging mode of vehicle-battery separation. The characteristics of fashion consumers and products were also integrated into the model, such as consumer satisfaction and 3D loading constraints. To solve this complex programming problem, a sophisticated hybrid ant colony optimization (HACO) algorithm was designed by combining the advantages of ACO and A-star algorithms. Using real-life data, the experimental results verify the effectiveness and superiority of the proposed solution. EVRP-DD achieved reduced driving distance, total distribution cost, and deep discharge distance. HACO can enhance the computation speed and reduce the total distribution cost compared with the two conventional algorithms. The proposed solution showed excellent flexibility and could effectively adjust the optimal route scheme according to the ever-changing external environment. Thus, it can be concluded that this solution is a powerful tool for enterprises to achieve sustainable distribution. This study has realized theoretical innovation in sustainable distribution under the new mode of vehicle-battery separation, and its successful application in the fast fashion industry reflects its valuable application value.

Delivery routing problem of pure electric vehicle with multi-objective pick-up and delivery integration.

With the growth of people's environmental awareness and the encouragement of government policies, the use of electric vehicles in logistics distribution is gradually increasing. In order to solve the dual demand of customers' simultaneous pick-up and delivery in the "last kilometer logistics", an electric vehicle routing problem with simultaneous pick-up and delivery and time window (EVRPSPDTW) is considered from the perspective of multi-objective distribution in this paper. Firstly, a decision-making model based on distribution cost and power consumption function is established. In this model, distribution cost includes transportation cost, vehicle use cost, penalty cost of not arriving on time and charging cost. Power consumption function is the energy loss caused by air resistance, tire rolling friction and transmission system. Secondly, a multi-objective genetic algorithm (NSGA-II) optimization solution with fast nondominated ranking and elite strategy is designed, and in view of the shortcomings of traditional NSGA-II, it is proposed to complete population initialization through greedy algorithm and random rules, introduce adaptive cross-mutation strategy in the chromosome crossing and mutation stage, and design three different neighborhood operators in mutation operation based on variant fitness function. Finally, the sensitivity analysis of traffic congestion coefficient further proves the effectiveness of the proposed model and the improved algorithm.

Collaborative multidepot electric vehicle routing problem with time windows and shared charging stations

Logistics distribution using electric vehicles (EVs) is gradually becoming popular in urban logistics networks with the promise of carbon peak and carbon neutrality. A collaborative mechanism among multiple depots can effectively increase the efficiency and sustainability of a logistics network. Sharing charging stations (CSs) is presented as a critical strategy to improve the efficiency of logistics networks and facilitate collaboration further. Solving a collaborative multidepot EV routing problem with time windows and shared charging stations (CMEVRPTW-SCS) involves centralized transportation services among multiple depots, coordinated delivery services among multiple depots and the charging needs of EVs. A bi-objective nonlinear programming model for CMEVRPTW-SCS is formulated to minimize the total operating cost and number of EVs, wherein the operating cost contains transportation costs among depots and vehicle routing costs in each depot. Gaussian mixture clustering algorithm is developed to cluster customers and assign them to depots probabilistically to reduce the computational complexity, and an improved multi-objective genetic algorithm with tabu search (IMOGA-TS) is designed to optimize the EV routes and charging locations in CMEVRPTW-SCS. With the combination of local and global searches and the improvement of solutions at each iteration by TS, the proposed hybrid algorithm can significantly accelerate the efficient exploration of optimal solutions. The comparative results of the IMOGA-TS with multi-objective genetic algorithm, non-dominated sorting genetic algorithm-II and multi-objective harmony search algorithm show the superiority of the proposed algorithm in solving CMEVRPTW-SCS. Then, a Shapley value model based on game theoretical methods is proposed to find the best profit allocation scheme. A real-world case study of CMEVRPTW-SCS in Chongqing City, China is conducted, and three scenarios of various collaborative alliances and 11 schemes with and without shared CSs are further discussed. The experimental results show that the proposed methods are of practical significance in reducing operating costs, improving transportation efficiency, and achieving sustainable operation in EV-based logistics distribution networks.