Vehicle Routing Research Articles

An evaluation of common modeling choices for the vehicle routing problem with stochastic demands

We investigate three common modeling choices for the vehicle routing problem with stochastic demands: (i) the total expected demand of customers on a route may not exceed the capacity of the vehicle, (ii) the number of routes is fixed, and (iii) demand is distributed with a support that contains negative-valued realizations. We prove that modeling choices (i) and (ii) result in an arbitrarily large increase of the optimal objective value in the worst case. Additionally, we provide lower and upper bounds on the change of the optimal objective value following from (iii) in case the actual distribution of demand is censored, truncated or folded. We also evaluate the consequences of these choices numerically, by employing a state-of-the-art integer L-shaped method to solve the vehicle routing problem with stochastic demands to optimality, which we modify to deal with the alternative choices. We find that restricting the expected demand of a route to the vehicle’s capacity has a limited effect on the optimal objective value for most, but not all, benchmark instances from the literature, while drastically reducing the computation times of the integer L-shaped method. When restricting the number of routes, a similar effect occurs when the total expected demand on a route is not restricted. Otherwise, the computation time decreases only slightly, and even increases for some benchmark instances. For instances from the literature, despite admitting negative realizations, the normal distributions used to model demand are an adequate approximation for censored, truncated and folded normal distributions that have nonnegative supports.

An exact method for the two-echelon split-delivery vehicle routing problem for liquefied natural gas delivery with the boil-off phenomenon

In this paper we investigate a two-echelon vehicle routing problem for liquefied natural gas (LNG) delivery to determine how to transport LNG from an overseas production terminal to a set of import terminals by vessels, and transport the LNG from the import terminals to a set of filling stations either by tanker trucks or bunker barges. Some important features of this problem are that part of LNG will be evaporated during delivery and split deliveries are allowed at both import terminals and filling stations, which render the problem more intractable than those considered in most of the existing two-echelon vehicle routing studies. The objective is to find the optimal first-echelon and second-echelon delivery schemes to minimize the sum of the routing cost and boil-off cost. To solve the problem, we develop a customized branch-and-price-and-cut (BPC) algorithm incorporating a specialized labeling algorithm tailored to address the issues of LNG evaporation and split deliveries in solving the challenging pricing subproblems. To speed up the solution algorithm, we introduce some heuristic pricing strategies to quickly solve the pricing subproblems, and explore the (strong) k-path inequalities and subset-row inequalities to tighten the lower bound obtained by column generation. We conduct extensive numerical studies on simulation instances and a case study of LNG delivery in region along the Yangtze river, China to verify the effectiveness of the model and proposed algorithm. The numerical results demonstrate that our algorithm significantly outperforms CPLEX and the existing BPC algorithm on related topic, confirm the superiority of our integrated two-echelon solution method over its sequential solution counterpart, and illustrate that the locations of the production terminal and import terminals are highly related to the solution performance.

Optimal Launch Manifesting for Space Freight Forwarders

This paper proposes a novel framework to optimize a launch vehicle manifesting plan for small satellites from the perspective of a space freight forwarder. The forwarder in space logistics coordinates individual shipment orders from the launch customers and launch service providers like a freight forwarder in ground logistics does. An optimal launch manifesting problem is formulated as a variant of the vehicle routing problem involving the decisions on carriers, launch strategies (dedicated or multi-payload), launch dates, and satellite deployment sequences. A solution procedure based on the column generation method is proposed to address the challenges associated with the large-scale combinatorial optimization problem. A case study demonstrates the effectiveness of the proposed framework and solution procedure.

Application of Metaheuristics for Multi-Trip Capacitated Vehicle Routing Problem with Time Window

Abstract This study focuses on the delivery routing problem faced by a transport company located in Phuket, Thailand. The goal of this study is to find a daily optimum route in order to minimize the total transportation cost, which comprises fixed costs associated with vehicle rental and variable costs calculated based on factors of travel distance, fuel prices, and fuel consumption. The complexity of this problem is compounded by the fact that customer demand often exceeds a vehicle capacity, in terms of weight and volume. In addition, delivery must be made within specific time windows. To tackle this issue, the delivery routing problem is classified as a multi-trip capacitated vehicle routing problem with time window (MTCVRPTW). Since the problem is NP-hard, an application of metaheuristic is more practical to determine the delivery routing of the company within a reasonable computing time. In this study, Particle Swarm Optimization (PSO) and Differential Evolution (DE) algorithm are applied to solve MTCVRPTW. The numerical results show that DE provides better solution quality compared to those obtained from PSO and company current practices.

The set team orienteering problem

We introduce the Set Team Orienteering Problem (STOP), a generalised variant of the Set Orienteering Problem (SOP), in which customer locations are split into multiple clusters (or groups). Each cluster is associated with a profit that can be gained only if at least one customer from the cluster is visited. There is a fleet of homogeneous vehicles at a depot, and each vehicle has a limited travel time. The goal of the STOP is to find a set of feasible vehicle routes to collect the maximum profit. We first formulate the problem as a Mixed Integer Linear Programming (MILP) to mathematically describe it. A branch-and-price (B&P) algorithm is then developed to solve the problem to optimality. To deal with large instances, we propose a Large Neighbourhood Search (LNS), which relies on problem-tailored solution representation, removal, and insertion operators. Multiple experiments on newly generated instances confirm the performance of our approaches. Remarkably, when tested on the SOP using benchmarks available in the literature, our B&P method achieves optimality in 61.9% of these instances. This is the first time such a large number of SOP instances are solved to optimality. Our LNS outperforms existing algorithms proposed to solve the SOP in terms of solution quality. Out of 612 considered instances, it improves 40 best-known solutions.

PENYELESAIAN CAPACITATED VEHICLE ROUTING PROBLEM PADA PENDISTRIBUSIAN AIR GALLON MENGGUNAKAN ALGORITMA KOLONI LEBAH

Distribution is one of the problems in the business and industrial world, for example the problem of delivering supplies of raw materials and other goods to several customers, where the delivery must be carried out exactly once by one or more vehicles to each customer with a certain capacity. In its development, this problem was formulated as the Capacitated Vehicle Routing Problem (CVRP). Based on the definition, CVRP is one of the most common variations of the Vehicle Routing Problem (VRP) problem to determine the optimal route with the addition of constraints in the form of homogeneous vehicle capacity. Here, we discussed the CVRP problem of the distribution route for Pak Nurrofiq's gallons of water from the depot to its customers in the Taman Sei Raya Complex, Serdam Asri Complex and Kapuas Mas Complex. The aim of this research is to create a mathematical model for the CVRP problem in the distribution of Pak Nurrofiq's drinking water and solve it using the bee colony algorithm. The bee colony algorithm is a metaheuristic algorithm based on the behavior of honey bees in searching for food sources. The research results show that the case of gallon water distribution was successfully implemented into CVRP and completed using the bee colony algorithm, 4 routes were obtained with a total distance of all routes, namely 9,068 km.

An alternating direction multiplier method with variable neighborhood search for electric vehicle routing problem with time windows and battery swapping stations

This paper studies a real-world electric vehicle routing problem (EVRP). Specifically, it is an EVRP with time windows and battery swapping stations (EVRP_TWBSS). The EVRP_TWBSS considers the routing of electric vehicles (EVs), the determination of each electric vehicle’s battery level, and the selection of battery swapping stations. The criterion of EVRP_TWBSS is to minimize the operating costs. To simplify the structure of model, a time-discrete and multi-commodity flow model based on extended state-space-time network (TMFM_ESSTN) is established. Meanwhile, an alternating direction multiplier method with variable neighborhood search (ADMM_VNS) is presented to address the TMFM_ESSTN. In ADMM_VNS, the augmented lagrangian relaxation (ALR) model constructed from the TMFM_ESSTN is decomposed and linearized to a series of least cost vehicle routing subproblems through the linear augmented lagrangian relaxation (LALR) decomposed technique. Then, each subproblem is iteratively solved by using the dynamic programming and two special designed VNS strategies in ADMM_VNS iterative framework. The solution’s quality can be controlled to a certain extent through monitoring the gap between the lower and upper bounds obtained after each iteration. Test results on instances with different scales and a real-world instance based on partial road network in Kunming City demonstrate that ADMM_VNS can achieve smaller gaps and better solutions than several state-of-the-art algorithms. In which, ADMM_VNS can reduce the optimal gap by up to 2.27 % compared to the other state-of-the-art algorithms in small-scale instances. The gap of ADMM_VNS is calculated based on the lower bound and the upper bound in the large-scale instances and the real-world instance are 10.36 % and 1.57 %, respectively.

A Non-Linear Optimization Model for the Multi-Depot Multi-Supplier Vehicle Routing Problem with Relaxed Time Windows

A Non-Linear Optimization Model for the Multi-Depot Multi-Supplier Vehicle Routing Problem with Relaxed Time Windows

Determining Book Distribution Routes by Implementing Vehicle Routing Problems Using Excel Solver at Gunadarma University

Gunadarma University operates multiple campuses, each equipped with its own library. To ensure equitable access to newly acquired titles, it is imperative that these materials are disseminated across all campus libraries. So, when a new book title is added, this book must also be owned by the library at each campus location. In this research, book distribution routes with the shortest distance and time will be determined using the Vehicle Routing Problem (VRP) method with Excel Solver. Gunadarma University has a central library which is the starting point for distributing books to other campuses. The central university library serves as the distribution hub, from which books are dispatched to seven additional campus locations. Simulation results using Excel Solver showed that the shortest route for sending books to seven library locations on the Gunadarma University campus using one vehicle was a distance of 137.14 km in 3 hours 12 minutes. This optimized route yielded substantial cost savings, amounting to a 12.5% reduction compared to previous distribution practices.

Leveraging AI automated emergency response with natural language processing: Enhancing real-time decision making and communication

Artificial Intelligence (AI) and Natural Language Processing (NLP) technologies play an essential role in the ongoing development and advancements of emergency response systems. This paper explores the new opportunities and possibilities offered by the incorporation of AI-driven automated emergency response systems, and the benefits of using NLP to increase the efficiency of human language processing and communication in real time. Using case studies and applications, we analyse how integrating AI and NLP technologies can reduce response times, improve situational awareness and coordination between emergency services. We then explore how AI-driven models can be used to predict natural disasters, optimise emergency vehicle routes and identify areas of need in real time through the analysis of social media and emergency communications via NLP. However, we also discuss the issues that come with implementing these technologies, such as data-privacy challenges, technical limitations and the need for sustained retraining of AI systems. The conclusions of this research indicate that continued collaboration between stakeholders is necessary to overcome these barriers, and that substantial innovation is needed to maximise the potential of AI and NLP technologies in emergency management.

Optimizing the organization of the first mile in agri-food supply chains with a heterogeneous fleet using a mixed-integer linear model

Consumers are increasingly demanding high-quality food, which presents significant challenges for agricultural supply chains. While the majority of research in the agri-food sector has concentrated on optimizing logistics costs and meeting demand by focusing on minimizing the last mile, the complexity of the first mile in the agricultural supply chain has been less explored. Farmers must efficiently manage the harvesting process and the transportation of harvested produce to consolidation centers to ensure the delivery of high-quality products. This paper addresses this research gap by introducing a mixed-integer programming model that leverages vehicle routing problem concepts to optimize the logistics processes involved in transporting harvested products from various fields to a central depot. The primary objective is to minimize total logistics costs associated with visiting different fields during a pick-up round using multiple vehicles. The model has been applied to a case study involving an agricultural cooperative in Greece as part of the European BBTWINS project, which aims to enhance agri-food value chain digitalization for improved resource efficiency. The results demonstrate that organizing the first mile of the agri-food supply chain with a cooled vehicle for pick-up rounds can reduce logistics costs by up to 40% compared to the current practices.

Advancements in Multi-Objective Mathematical Programming Models and Solution Approaches for Sustainable Waste Management Practices in Vehicle Routing Problem: A Systematic Literature Review

In recent years, the integration of sustainable principles into the Vehicle Routing Problem (VRP) for efficient waste management has gained significant attention. This paper provides an overview of advancements in multi-objective mathematical programming (MP) models and the optimization techniques for sustainable waste management practices within the VRP framework. Sustainable waste management practices in the context of the VRP involve optimizing routes and schedules aim to reduce the environmental impact of waste collection. It investigates the integration of multi-objectives with sustainability criteria, including social, economic, and environmental considerations. Furthermore, it surveys various optimization methodologies applied in waste management to enhance efficiency and sustainability practices. The Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement was employed as a formal systematic review guideline for data gathering. Data was obtained from studies conducted between 2017 and 2023. The analysis included a total of 18 papers from online sources and databases. Based on the literature review, it has been observed that the majority of the research focused on employing Mixed-Integer Linear Programming (MILP) models to tackle the optimization problem for waste management. The literature survey demonstrated significant contributions in computational performance, cost-effectiveness, operational efficiency, and utilization of real-world data by improving the solution approaches, aiming to prioritize economic, social, and environmentally friendly solutions. The paper aims to serve as a convenient reference for researchers and practitioners seeking information on using the MP model and solution approaches to optimize VRP for waste management.

The Impact of Variable Ambient Temperatures on the Energy Efficiency and Performance of Electric Vehicles during Waste Collection

The market for electric cars (EVs) is growing quickly, which has led to a diversity of models and significant technological advancements, particularly in the areas of energy management, charging, range, and batteries. A thorough analysis of the scientific literature was conducted to determine the operational and technical parameters of EVs’ performance and energy efficiency, as well as the factors that influence them. This article addresses the knowledge gap on the analysis of ambient temperature-related parameters’ effects on electric garbage trucks operating in particular urban traffic conditions for selective waste collection. To optimize vehicle routes, a computational model based on the Vehicle Routing Problem was used, including the Ant Colony Optimization algorithm, considering not only the load capacity of garbage trucks but also their driving range, depending on the ambient temperature. The results show that the median value of collected bulky waste for electric waste collection vans, depending on the ambient temperature, per route is 7.1 kg/km and 220 kg/h. At a temperature of −10 °C, the number of points served by EVs is 40–64% of the number of points served by conventional vehicles. Waste collection using EVs can be carried out over short distances of up to 150 km, which constitutes 95% of the optimized routes in the analyzed case study. The research contributed to the optimal and energy-efficient use of EVs in variable temperature conditions.

Problem size reduction methods for large CVRPs

We solve the Capacitated Vehicle Routing Problem (CVRP) by introducing a novel approach to problem size reduction. We propose the generation of short sequences of nodes called “sections”, which effectively act as single nodes in a reduced CVRP that is faster and easier to solve. Three section generation methods are compared, and the trade-off between solution quality and computation time savings is evaluated. We show that reduced problem sizes of up to around 60 percent of the original problem size, result in only modest decreases in solution quality, but allow for significant reductions of computation time, regardless of the optimization algorithm used. Our findings highlight the potential benefits of problem aggregation and size reduction for large-scale CVRPs and suggest opportunities for further improving aggregation methods.

Swarm intelligence and nature inspired algorithms for solving vehicle routing problems: a survey

Swarm intelligence and nature inspired algorithms for solving vehicle routing problems: a survey

Towards greener city logistics: an application of agile routing algorithms to optimize the distribution of micro-hubs in Barcelona

The COVID-19 pandemic accelerated the shift towards online shopping, reshaping consumer habits and intensifying the impact on urban freight distribution. This disruption exacerbated traffic congestion and parking shortages in cities, underscoring the need for sustainable distribution models. The European Union's common transport policy advocates for innovative UFD approaches that promote intermodal transportation, reduce traffic, and optimize cargo loads. Our study addresses these challenges by proposing an agile routing algorithm for an alternative UFD model in Barcelona. This model suggests strategically located micro-hubs selected from a set of railway facilities, markets, shopping centers, district buildings, pickup points, post offices, and parking lots (1057 points in total). It also promotes intermodality through cargo bikes and electric vans. The study has two main objectives: (i) to identify a network of intermodal micro-hubs for the efficient delivery of parcels in Barcelona and (ii) to develop an agile routing algorithm to optimize their location. The algorithm generates adaptive distribution plans considering micro-hub operating costs and vehicle routing costs, and using heuristic and machine learning methods enhanced by parallelization techniques. It swiftly produces high-quality routing plans based on transportation infrastructure, transportation modes, and delivery locations. The algorithm adapts dynamically and employs multi-objective techniques to establish the Pareto frontier for each plan. Real-world testing in Barcelona, using actual data has shown promising results, providing potential scenarios to reduce CO2 emissions and improve delivery times. As such, this research offers an innovative and sustainable approach to UFD, that will contribute significantly to a greener future for cities.

Koordinasi Dinas Perhubungan dan Kepolisian dalam Meningkatkan Ketertiban Berlalu Lintas di Kabupaten Malang

Indonesia is a country with a large number of land transportation users and it is necessary to organize strategies so that it runs well in order to maintain safe and secure traffic. It is hoped that the coordination carried out by the transportation service and the police will have a big impact on traffic order in Malang Regency. The aim of this research is to find out how traffic order is coordinated in Malang Regency, the method used is a case study based on interviews. The results of this research show that the communication process is direct when transportation service officers are in the field, the communication process uses Handy talkie technology, communication from this tool for one direction and one purpose. The competency of participants from the transportation service is more technical, such as checking the condition of vehicle tires, lights and wheel position, understanding vehicle routes in the district, while from the police, it is understanding legal regulations and procedures for implementing enforcement. According to the agreement and commitment, the Transportation Service has limited authority and can only carry out technical matters regarding the condition of vehicles, while the authority of the Police is to take action, therefore there is a need for coordination between the two. Determination of an agreement regarding coordination when there is an activity that requires a number of parties, a formal letter will be written based on the applicable regulations. Coordination incentives show that the implementation of tasks has been coordinated. If a violation occurs, there will be no sanctions but what has been agreed is that responsibility will return to the respective agencies. Due to feedback, the communication process is sometimes long, so the time needed to carry out traffic operations also increases.

An interaction-enhanced co-evolutionary algorithm for electric vehicle routing optimization

Recently, the electric vehicle routing problem (EVRP) has emerged as a significant challenge in the transportation field. Unlike traditional vehicle routing problems, EVRP requires optimizing not only the customer route but also the charging scheme. This implies that routes must be planned while considering the availability of charging stations, and charging decisions must be made based on the specific route structure. Although the dual-population-based co-evolutionary algorithm (DPCA) has been proposed to address this coupling relationship, there is still room for further performance improvement. Therefore, this paper proposes an interaction-enhanced co-evolutionary algorithm (IECA) that facilitates a more effective collaborative search between routing and charging optimizations. For routing optimization, we propose an improved ant colony optimization method with a novel pheromone update approach to generate diverse route solutions. Specifically, we utilize information from the charging population to guide the pheromone update process. In contrast to DPCA, which solely relies on the best solution, we establish interaction among multiple solutions from both the routing and charging populations, which can better contribute the information interaction between two populations. Furthermore, we devise a novel population update strategy that enhances the selection of promising solutions. Experimental results validate the effectiveness of the proposed algorithm by demonstrating its ability to avoid local optima. Moreover, it achieves a reduction of approximately 4% in the average route distance across two public test suites. The source code is available at https://github.com/ShouLiang-Z/IECA.

Pickup and delivery problem with electric vehicles and time windows considering queues

The electric vehicle, as a green and sustainable technology, has gained tremendous development and application recently in the logistics distribution system. However, the increasing workload and limited infrastructure capacity pose challenges for electric vehicles in the pickup and delivery operating system, including task allocation, electric vehicle routing, and queue scheduling. To address these issues, this paper introduces a pickup and delivery problem with electric vehicles and time windows considering queues, which considers queue scheduling for multiple electric vehicles when operating at the same site. A novel mixed integer linear programming model is proposed to minimize the cost of travel distance and queue time. An adaptive hybrid neighborhood search algorithm is developed to solve the moderately large-scale problem. Experimental results demonstrate the effectiveness of the model and adaptive hybrid neighborhood search algorithm. The competitive performance of the developed algorithm is further confirmed by finding 9 new best solutions for the pickup and delivery problem with electric vehicles and time windows benchmark instances. Moreover, the results and sensitivity analysis of objective weight costs highlight the impact and importance of considering queues in the studied problem and obtain some management insights.

Municipal solid waste management using electric vehicle by variable neighbourhood search algorithm

Efficient solid waste management is essential for addressing the multifaceted challenges associated with waste disposal, including environmental, economic, technical, and social aspects. Municipal solid waste management (MSWM) incurs significant costs and contributes to environmental pollution primarily due to the collection process. This research presents a comprehensive case study that focuses on optimising the routing of electric vehicles for solid waste collection. Specifically, it addresses the Half-Open Time-Dependent Multi-Depot Electric Vehicle Routing Problem considering Battery Recharging and Swapping (HOTDMDEVRPBRS) in the context of waste collection. This problem aims to optimise the routes taken by electric vehicles across multiple depots, considering constraints such as limited battery capacity, multiple technologies for recharging battery capacity, the impact of truckload on energy consumption, and time-dependent travel times. To tackle this problem, we propose a highly efficient Variable Neighborhood Search (VNS) meta-heuristic algorithm, which outperforms the Simulated Annealing (SA) approach. The proposed algorithm achieves an average improvement of 11.88% in solution quality and reduces execution time by 73% for last-mile delivery. We evaluate the effectiveness of the proposed approach using real-world data from New York's recycling management system. The findings of this study emphasise the potential for enhancing solution quality and operational efficiency in solid waste management.