Routing Problem Research Articles

Mathematical Modelling Approaches for Integrated Single Machine Scheduling and Electric Vehicle Routing Problem

Mathematical Modelling Approaches for Integrated Single Machine Scheduling and Electric Vehicle Routing Problem

Multi-Criteria Framework for Routing on Access Land: A Case Study on Dartmoor National Park

Creating routes across open areas is challenging due to the absence of a defined routing network and the complexity of the environment, in which multiple criteria may affect route choice. In the context of urban environments, research has found Visibility and Spider-Grid subgraphs to be effective approaches that generate realistic routes. However, the case studies presented typically focus on plazas or parks with defined entry and exit points; little work has been carried out to date on creating routes across open areas in rural settings, which are complex environments with varying terrain and obstacles and undefined entry or exit points. To address this gap, this study proposes a method for routing across open areas based on a Spider-Grid subgraph using queen contiguity. The method leverages a Weighted Sum–Dijkstra’s algorithm to allow multiple criteria such as surface condition, total time, and gradient to be considered when creating routes. The method is tested on the problem of routing across two areas of Dartmoor National Park, United Kingdom. The generated routes are compared with benchmark algorithms and real paths created by users of the Ordnance Survey’s Maps App. The generated routes are found to be more realistic than those of the benchmark methods and closer to the real paths. Furthermore, the routes are able to bypass hazards and obstacles while still providing realistic and flexible routes to the user.

A hybrid multi-objective solution approach for a reliable truck-drone routing problem integrated with pickup and delivery services

ABSTRACT Humanitarian logistics aims to reduce the arrival time of relief goods and optimize services in disaster-affected regions. This paper introduces a multi-objective hybrid truck-drone routing problem with pickup and delivery services, considering reliability (MHTDRP-PD-R) to enhance relief operations within humanitarian logistics. The model is formulated as a mixed-integer linear programming problem with the simultaneous goals of minimizing transportation time and maximizing reliability through routing and inventory decisions made by multiple trucks and drones. An adaptive large neighborhood search (ALNS) algorithm, coupled with heuristic technique, is developed to tackle the problem. The ALNS algorithm refines initial solutions through destroy and repair operators, integrated with multi-objective optimization methods to create a unified objective function. Small and large-scale test problems are then employed to evaluate solution quality using multi-objective optimization. The calculation results show the superiority of the developed ALNS integrated with the ε-constraint method regarding the objective value and solution time.

Logistics Distribution Route Optimization With Time Windows Based on Multi-Agent Deep Reinforcement Learning

Multi-depot vehicle routing problem with time windows (MDVRPTW) is a valuable practical issue in urban logistics. However, heuristic methods may fail to generate high-quality solutions for massive problems instantly. Thus, this article presents a novel reinforcement learning algorithm integrated with a multi-head attention mechanism and a local search strategy to solve the problem efficiently. The routing optimization was regarded as a vehicle tour generation process and an encoder-decoder was used to generate routes for vehicles departing from different depots iteratively. A multi-head attention strategy was employed for mining complex spatiotemporal correlations within time windows in the encoder. Then, a decoder with multi-agent was designed to generate solutions by optimizing reward and observing transition state. Meanwhile, a local search strategy was employed to improve the quality of solutions. The experiments results demonstrate that the proposed method can significantly outperform traditional methods in effectiveness and robustness.

An integrated Bi-objective green vehicle routing and partial disassembly line problem for electronic waste: an industrial case study

ABSTRACT Today, serious environmental problems arise with overconsumption. The most effective way of protecting the environment is recycling. To obtain maximum benefit from the recycling activities depends on the effective and robust design of the disassembly lines. In addition, the distribution plan of products to be recycled is as important as the disassembly process. Therefore, this study includes the integrated optimization of the partial disassembly line balancing problem and the multi-objective green vehicle routing problem for the first time. The integrated problem is formulated as a Multi-Objective Mixed Integer Linear Programming. The model’s objectives consist of minimization of total CO2 emission and cost. The Pareto optimal solution set is found by solving this problem with the Augmented ℇ-Constraint Method. The model respectively determines (i) the total number of opened workstations in the disassembly center, (ii) optimal task assignments to workstations in disassembly centers and non-disassembled tasks, (iii) total workstation times and idle times of each workstation, (iv) optimal distribution routes for all vehicles. This study examines a case study in Turkey. To determine the best Pareto optimal solution for homogeneous and heterogeneous fleets, the integrated multi-criteria decision-making method consisting of EWM (Entropy Weight Method) and COPRAS (Complex Proportional Assessment) is used.

A Dynamic and Stochastic Cumulative Capacitated Vehicle Routing Problem

A Dynamic and Stochastic Cumulative Capacitated Vehicle Routing Problem

A hybrid metaheuristic to optimize electric first-mile feeder services with charging synchronization constraints and customer rejections

This paper addresses the on-demand meeting-point-based feeder electric bus routing and charging scheduling problem under charging synchronization constraints. The problem considered exhibits the structure of the location routing problem, which is more difficult to solve than many electric vehicle routing problems with capacitated charging stations. We propose to model the problem using a mixed-integer linear programming approach based on a layered graph structure. An efficient hybrid metaheuristic solution algorithm is proposed. A mixture of random and greedy partial charging scheduling strategies is used to find feasible charging schedules under the synchronization constraints. The algorithm is tested on instances with up to 100 customers and 49 bus stops/meeting points. The results show that the proposed algorithm provides near-optimal solutions within less one minute on average compared with the best solutions found by a mixed-integer linear programming solver set with a 4-hour computation time limit. A case study on a larger sized case with 1000 customers and 111 meeting points shows the proposed method is applicable to real-world situations.

Hybrid Artificial Bee Colony Algorithm with Variable Neighborhood Search for Capacitated Vehicle Routing Problem

Aiming at the capacitated vehicle routing problem, a hybrid integer programming model with goal of lowest path cost is constructed, and a hybrid artificial bee colony algorithm with variable neighborhood search based on the model and the characteristics of the CVRP problem is proposed to solve the problem. The hybrid algorithm integrates the artificial bee colony algorithm and the variable neighborhood search algorithm, embeds a multi-variable neighborhood operator in the local search link of the artificial bee colony to carry out iteration. And the operator contains targeted transformation operations on path nodes, strings, and sub paths to ensure the diversity of the bee population. In addition, a variable neighborhood perturbation strategy is used to strengthen the algorithm's ability to escape from local optima. The comparative analysis of the literature study set and its algorithm solution shows that the designed hybrid variable neighborhood artificial bee colony algorithm has strong global search ability and high solution accuracy, especially in solution stability. HABC-VNS can obtain 47 optimal solutions in 74 examples. The average minimum deviation of the optimal solution is 0.34%, and the average deviation of the average CVRP set is 0.57%. The overall performance is better than the algorithm in the comparative literature.

Fourth Party Logistics Routing Problem Under Uncertain Time and Random Demand

With the rapid development of the economy, the fourth party logistics (4PL) has become an indispensable part of economic development, and the path optimization is an important topic in the research of 4PL routing problem. This paper studies the fourth party logistics routing problem with random demand and uncertain transportation time and transfer time by considering the randomness and uncertainty of the environment. In order to solve the path optimization strategy that minimizes the total transportation cost, this paper establishes an uncertain random programming model under the constraints of the total transportation time, the carrying capacity of the logistics provider, the transfer capacity of the transfer station, and the demand of the distributor. Subsequently, this paper transforms the uncertain random programming model into an equivalent deterministic programming model based on the distribution functions of random demand and uncertain time, and verifies the effectiveness of the model through two examples. The results show that the uncertain random programming model can give a reasonable path optimization strategy.

Optimal Transportation Planning for a Do-It-Yourself Retailer with a Zone-Based Tariff

This article describes the development of a decision support tool for a Rich Vehicle Routing Problem (R-VRP) of a major European do-it-yourself (DIY) retailer. The tool enables more comprehensive and structured planning at the retailer and an average of 8% transportation cost savings, translating to total savings of more than € 1 million per year for this specific retailer compared with the status quo.

Multi-Objective Last-Mile Vehicle Routing Problem for Fresh Food E-Commerce: A Sustainable Perspective

Last-mile logistics poses a pivotal challenge for the sustainable prosperity of fresh food e-commerce. However, there has been insufficient research attention towards optimizing the last-mile vehicle routing from three sustainable dimensions simultaneously based on triple-bottom-line. To narrow this gap, this paper proposes a multi-objective last-mile vehicle routing model for fresh food e-commerce, which takes the three sustainable dimensions as independent objectives. The economic and environment objectives are minimizing the total cost and carbon emission, respectively. For social dimension, a nonlinear function is proposed based on the Prospect theory, which quantifies customers’ satisfaction when they perceive delivery time. Then the social objective is described as maximizing customers’ satisfaction. Subsequently, the model is solved by the nondominated sorting genetic algorithm II and validated by a numerical experiment. Based on the experiment results, this paper recommends that logistics enterprises should prioritize the trade-off among the three sustainable dimensions.

Optimizing School Bus Routes With Ant Colony Optimization: A Dynamic Approach To Sustainable Transportation Logistics

In response to the escalating demands of modern transportation and logistics within the educational sector, this paper presents a novel exploration of Ant Colony Optimization (ACO) applied to school bus routing, a complex subset of the Vehicle Routing Problem (VRP). Traditional methods of addressing VRPs have proven insufficient in navigating the intricate requirements and dynamic nature of routing challenges, necessitating the adoption of more sophisticated heuristic and metaheuristic strategies. By harnessing ACO, inspired by the path-finding capabilities of ants via pheromone trails, this study introduces an innovative approach to dynamically optimize school bus routes. This optimization not only aims for efficiency in routing but also emphasizes environmental considerations and cost reduction. This research extends beyond the theoretical framework of ACO, incorporating practical applications and simulations that reflect real-world conditions such as fluctuating student attendance and varying traffic patterns. Through a comprehensive analysis that includes the development of a Python-based ACO model, calculation of transition probabilities, and a simulation of routing strategies, we demonstrate the algorithm's robustness and versatility. Additionally, we address critical factors such as time windows and bus capacity constraints, underscoring the model's adaptability to the multifaceted dimensions of school bus routing. The findings from this study highlight the significant advantages of applying ACO to VRPs, showcasing notable improvements in route efficiency, fuel consumption, and overall logistical execution compared to conventional routing methods. This research not only contributes to the existing body of knowledge on VRPs and ACO but also sets the stage for future explorations into dynamic routing optimization. It opens avenues for integrating advanced predictive models and real-time data analysis, promising further enhancements in transportation logistics and the potential for broad application across various sectors.

Tailoring Evolutionary Algorithms to Solve the Multiobjective Location-Routing Problem for Biomass Waste Collection

Location-routing problems widely exist in logistics activities. For the biomass waste collection, there is a recognized need for novel models to locate the collection facilities and plan the vehicle routes. So far most location-routing models fall into the cost-driven-only category. However, comprehensive objectives are required in the specific context, such as time-dependent pollution and speed-and load-related emission. Furthermore, location-routing problems are hierarchical by nature, containing the facility location problems (strategic level) and the vehicle routing problems (tactical level). Existing studies in this field usually adopt computational intelligence methods directly without decomposing the problem. This can be inefficient especially when multiple objectives are applied. Motivated by these, we develop a novel multi-objective optimization model for the location-routing problem for biomass waste collection. To solve this model, we explore the way to tailor evolutionary algorithms to the hierarchical structure. We develop adapted versions of two commonly used evolutionary algorithms: the genetic algorithm and the ant colony optimization algorithm. For the genetic algorithm, we divide the population by the strategic level decisions, so that each subpopulation has a fixed location plan, breaking the location-routing problem down into many multi-depot vehicle routing problems. For the ant colony optimization, we use an additional pheromone vector to track the good decisions on the location level, and segregate the pheromones related to different satellite depots to avoid misleading information. Thus, the problem degenerates into vehicle routing problem. Experimental results show that our proposed methods have better performances on the location routing problem for biomass waste collection.

An exact method for a last-mile delivery routing problem with multiple deliverymen

The demand for efficient last-mile delivery systems in large cities creates an opportunity to develop innovative logistics schemes. In this paper, we study a problem in which each vehicle may travel with more than one deliveryman to serve multiple customers with a single stop of the vehicle, increasing the delivery efficiency. We extend the vehicle routing problem with time windows and multiple deliverymen by explicitly considering the deliveryman routes. We introduce the problem, formally define it with a formulation, propose valid inequalities, and develop a tailored branch-and-Benders-cut (BBC) algorithm to solve it. The BBC is capable of solving 89% of the instances to proven optimality in reasonable times, many of them of realistic sizes. Additionally, we show the benefits of evaluating the deliveryman routes considering a cost minimization perspective, and discuss relevant solutions for urban logistics problems that can help decrease congestion and emissions.

Low-latency Virtual Network function Scheduling Algorithm Based on Deep Reinforcement Learning

This paper addresses the problem of mapping, scheduling, and routing of virtual network functions (VNF) on a service function chain (SFC) that is sensitive to latency in a virtual network. A scheduling algorithm for VNF is proposed, which aims to minimize the SFC rejection rate while taking into account VNF mapping, scheduling, and traffic routing during the scheduling process. To achieve this goal, a Markov decision process (MDP)-based VNF scheduling model is established that guarantees SFC resource requirements are met. The model uses the D3QN (Dueling Double DQN) algorithm based on composite rules to select the SFC at each scheduling time point, and selects virtual nodes and routes using a routing optimization algorithm to minimize the SFC rejection rate. We compare our algorithm with the single rule, DQN and genetic algorithm, and the simulation results show that the proposed algorithm can reduce the rejection rate of SFC by approximately 8% compared to genetic algorithms.

Routing and Scheduling in Multigraphs With Time Constraints—A Memetic Approach for Airport Ground Movement

Routing and scheduling problems with increasingly realistic modelling approaches often entail the consideration of multiple objectives, time constraints, and modelling the system as a multigraph. This detailed modelling approach has increased computational complexity and may also lead to violation of the additivity property of the costs. In the worst scenario, increased complexity makes the problem intractable for exact algorithms. Even when the problem is solvable, exact algorithms may not provide solutions within the given time budget, and the found solutions are not guaranteed to be optimal due to the additivity property violation. Approximate solution methods become more suitable in this case. This paper focuses on one particular real-world application, the Airport Ground Movement Problem, where both time constraints and parallel arcs are involved. We introduce a novel Memetic Algorithm for Routing in Multigraphs with Time constraints (MARMT) and present a comprehensive study of its different variants based on diverse genetic representation methods. We propose a local search operator that enhances search efficiency and effectiveness. MARMT is tested on real data based on two airports of different sizes. Our results show that MARMT does not suffer from the non-additivity property problem as it outperforms the state-of-the-art exact algorithm when allowed to converge. When a time budget of 10 seconds is imposed on MARMT, it is able to provide solutions with quality comparable (within 1-5% degradation) to the ones given by the exact algorithm with respect to the aggregated objective values. MARMT can be adapted for other applications, such as train operations.

Modeling and Path-Following Control for Dubins Dynamics in Complex State Space

A path-following control design in the complex state space for the Dubins vehicle is proposed. The vehicle dynamics are modeled as a bilinear system of two complex ordinary differential equations with a scalar complex control input. The developed control solution represents a feedback linearizing proportional–integral–derivative servomechanism, with real valued control gains applied to complex valued tracking error components. The design is performed within the model reference control framework. It is applied to solving path-following and waypoint routing problems for curves with bounded curvature and vehicles with bounded speeds. The path-following controller regulates the system turn rate and the reference model speed. The vehicle speed dynamics are independently maintained as desired. In that regard, the developed control policy forces the system position to track a virtual target point defined by the reference model. Verifiable sufficient conditions are formulated to enable steering the Dubins vehicle along the designated routes in the presence of unknown bounded environmental disturbances, such as wind and gust. Application examples of the developed path-following control solution to waypoint routing guidance for unmanned aerial platforms are discussed.

First train timetabling and passenger transfer routing problems in urban rail transit networks

This paper incorporates the shortest passenger travel paths into the first train timetabling problem in urban rail transit networks. We first propose a path-based first train timetabling problem, which is formulated as a mixed-integer nonlinear programming model to reduce the travel time for passengers. To solve this model, we present a tailored branch-and-bound combined with the timetable-based Dijkstra algorithm. To further enhance the efficiency of the exact algorithm, we design a rolling time heuristic algorithm as a substitute for the branch-and-bound algorithm. Then, we proved that the rolling time heuristic combined with the timetable-based Dijkstra algorithm achieves 97.86% and 99.39% reductions in CPU time while sacrificing only 0.007% and 0.057% of optimality gap by two numerical experiments. Finally, the results based on two test networks with different structures demonstrate that the path-based first train timetabling model effectively improves passenger travel efficiency. Specifically, the travel times are reduced by 744 mins and 761 mins, while the transfer waiting times are reduced by 37.87% and 58.91% compared to the existing timetables. Moreover, the results also demonstrate that loop line networks will increase the difficulty of timetabling and lead to many passengers taking detours. To further enhance the efficiency of commuting for passengers who take the first train, URT operators may consider relaxing the limitations on the departure time of the depot stations.

An Integrated Temporal and Spatial Synchronization For Two-Echelon Vehicle Routing Problem in Waste Collection System

This paper presents a two-echelon vehicle routing problem (2E-VRP) with vehicle synchronization at meeting points for the reverse logistic network to collect waste in the urban area. Low-capacity vehicles are utilized to perform collection only in the inner part of the city because of restricted access and limited infrastructure to be expanded. While, high-capacity vehicles are used to transform waste from the border of the inner city to the recycling centers located outside of city. Vehicles of the first and second echelons visit each other at meeting points, which do not have storage capacity mainly because of environmental and social consequences of the transshipment of waste. The timing aspect plays a critical role at meeting points to ensure the reasonable sequence of operations. So, temporal synchronization, a critical aspect of 2E-VRP, is considered in this paper, as well as minimization of waiting time of vehicles in meeting points to avoid long dwelling time. Moreover, because the previous study of 2E-VRP has not dealt with space limitation of meeting points, this paper presents a 2E-VRP that incorporates temporal synchronization, waiting time, and temporal capacity simultaneously for the first time to address a more practical model. To solve the mentioned problem a set of capable and latest metaheuristics are proposed as well as the hybrid ones to probe their efficiency and reasonably construct high quality routes. Moreover, the impact of the temporal capacity is investigated compared to temporal synchronization without considering temporal capacity.

Case Article—Prescriptive Analytics for Entrepreneurial Growth: Data-Driven Strategic Decision Making at iParty Bangkok Co., Ltd.

This case centers around the dilemma faced by the female owner of a balloon decoration business: whether to outsource transportation of balloon arrangements to third-party providers or handle the transportation of some orders in house. The case illustrates a path to answering the strategic business question through solving a sequence of vehicle routing problems (VRPs) of increasing complexity. The focus of the case is not only on solving VRPs, but also on teaching a practical framework for (1) framing a business problem as a prescriptive analytics problem; (2) researching appropriate concepts, prior publications, and tools; (3) setting up an optimization problem formulation, estimating the necessary inputs, and obtaining a solution; (4) deciding on the appropriate level of formulation complexity needed; and (5) mapping the results from the models to a response to the original business question. Realistic data and Excel models and are provided. The case is appropriate for use in courses in optimization, operations research, and business analytics at either the advanced undergraduate or master’s/MBA level. Supplemental Material: The Teaching Note and supplemental data are available at https://www.informs.org/Publications/Subscribe/Access-Restricted-Materials .