Location-routing Problem Research Articles

A bi-objective location-routing problem for infectious waste reverse logistics during a pandemic

A bi-objective location-routing problem for infectious waste reverse logistics during a pandemic

Optimization of Location-Routing for Multi-Vehicle Combinations with Capacity Constraints Based on Binary Equilibrium Optimizers

The Location-Routing Problem (LRP) becomes a more intricate subject when the limits of capacities of vehicles and warehouses are considered, which is an NP-hard problem. Moreover, as the number of vehicles increases, the solution to LRP is exacerbated because of the complexity of transportation and the combination of routes. To solve the problem, this paper proposed a Discrete Assembly Combination-Delivery (DACA) strategy based on, the Binary Equilibrium Optimizer (BiEO) algorithm, in addition, this paper also proposes a mixed-integer linear programming model for the problem of this paper. Our primary objective is to address both the route optimization problem and the assembly group sum problem concurrently. Our BiEO algorithm was designed as discrete in decision space to meet the requirements of the LRP represented by the DACA strategy catering to the multi-vehicle LRP scenario. The efficacy of the BiEO algorithm with the DACA strategy is demonstrated. through empirical analysis utilizing authentic data from Changchun City, China, Remarkably, the experiments reveal that the BiEO algorithm outperforms conventional methods, specifically GA, PSO, and DE algorithms, resulting in reduced costs. Notably, the results show the DACA strategy enables the simultaneous optimization of the LRP and the vehicle routing problem (VRP), ultimately leading to cost reduction. This innovative algorithm proficiently tackles both the assembly group sum and route optimization problems intrinsic to multi-level LRP instances.

Planning decentralized battery-swapping recharging facilities for e-bike sharing systems

E-bike sharing has been embraced as a sustainable transportation mode, and its success hinges on efficient recharging facility planning. While battery-swapping technology has emerged as a promising solution for refueling shared e-bikes, the efficient recharging of swapped batteries remains understudied. This study explores two battery-swapping recharging modes, namely, centralized charging (CC) and decentralized swapping (DS). Specifically, a multi-decentralized swapping (M-DS) mode is introduced to incorporate multiple recharging sites within each service area, aiming to enhance recharging efficiency. A general modeling framework is proposed to simulate battery-swapping demand based on available bike-sharing data and optimize facility planning and routes across various recharging modes. The optimization model is formulated into a location-routing problem, addressed by a customized meta-heuristic algorithm. A case study conducted in Shenzhen, China, demonstrates the model’s ability to jointly determine optimal facility locations, facility types, and operational strategies. The results indicate significant efficiency enhancement achieved by M-DS, offering both cost savings and improved e-bike availability. Further scenario analysis reveals the flexibility and cost-effectiveness of M-DS, thereby supporting small-scale e-bike sharing services and facilitating the expansion of access to environment-friendly transportation. This study contributes to facility planning for electric micromobility and provides practical insights for industry practitioners.

An Artificial Physarum polycephalum Colony for the Electric Location-Routing Problem

Electric vehicles invented for environmental sustainability are prone to adverse impacts on environmental sustainability due to the location and construction of their charging facilities. In this article, an artificial Physarum polycephalum colony is proposed to solve the novel challenging problem. First, the electric location-routing problem is established as a multi-objective network panning model with electric constraints to provide the optimal charging infrastructure layout, electric vehicle maintenance costs, and traffic conditions. The electric facility location problem and vehicle routing problem are integrated by integer programming, which considers the total distance, total time, total cost, total number of electric vehicles, and order fill rate. Second, an artificial Physarum polycephalum colony is introduced to solve the complex electric location-routing problem and includes the two basic operations of expansion and contraction. In the expansion operation, the optimal parent individuals will generate more offspring individuals, so as to expand the population size. In the contraction operation, only individuals with high fitness will be selected to survive through a merge sorting algorithm, resulting in a decrease in population size to the initial value. Through the iterative computing of the two main operations, the proposed artificial Physarum polycephalum colony can finally find the optimal solution to the objective function. Third, a benchmark test is designed for the electric location-routing problem by extracting the real road network from Tokyo, and the experimental results prove the effectiveness and applicability of this work.

Waste collection routing: a survey on problems and methods

Waste collection is a vital service performed all over the world, which heavily relies on vehicle routing. Due to regulations and local conditions, the problems and their characteristics often differ greatly. This literature survey aims to review the current state of the art overlap in waste collection and vehicle routing literature. The most notable papers are categorized according to their underlying problem type, examined and brought into relation based on their common problem characteristics. The problem types comprise general, node and arc routing problems, with vehicle routing problems being the most common, followed by arc and location routing problems. Besides the use of intermediate facilities, which is naturally very common in waste collection literature, the authors point out other interesting characteristics found in the literature and in practical problems, such as uncertain demand, personnel planning aspects, alternative collection systems or vehicle types, and characteristics related to risk or sustainability. Additionally, the authors highlight prominent scopes and objectives as well as recent developments in this area. Overall, this survey provides a selective overview and calls attention to research gaps and possible future research directions.

Hazardous materials facility siting optimization and ranking: A transportation risk mitigation framework

Hazardous material transportation problems have widely been studied in the past especially in the context of routing, scheduling, and network design problems. Yet, the combined hazardous material facility location-routing problem has not been studied adequately. We emphasize that locating a hazardous material facility is a rich process, and a good site can mitigate the potential transportation risk beforehand. A methodological framework is proposed which allows evaluation and ranking of potential sites based on hierarchical relationship utilities. The proposed method attempts to improve the risk functions and applies a stochastic analysis to measure the risk, which relaxes some assumptions in deterministic analysis, and is more realistic while avoiding overestimation of the risk. The study covers multi-objective optimization considering the decision-makers’ preferences on network segments and risk to the population and water bodies. Potential hazardous material facility sites’ rank is determined by the probability of optimality and one-to-one relationship utilities with the points of interests. Results show that the proposed stochastic analysis offers more flexibility to select and rank the potential sites.

Unmanned aerial vehicle service network design for urban monitoring

This study examines the multi-depot location-routing problems of unmanned aerial vehicles (UAVs) for urban monitoring (MDLRP-UM). MDLRP-UM arises in various practical applications, including daily police patrols in urban residential areas, forest fire patrols, urban infrastructure status monitoring and data collection, traffic flow monitoring at important intersections, and monitoring of urban temperature and humidity, among others. These diverse applications can be modeled as a general mixed-integer quadratically constrained problem (MIQCP), where we jointly plan the service routes of the UAVs, the frequency on each route, and the location of the depots to minimize the total cost. To solve the proposed problem, we decompose it into a master problem and sub-problems. We then propose an iterative algorithm (termed as “Frequency-Time-Frequency Strategy”) to solve the sub-problems, which is to find the optimal frequency and corresponding single service time for a given single route. The “Frequency-Time-Frequency Strategy” is further nested within a tailored adaptive large neighborhood search (ALNS) based heuristic algorithm to solve the master problem. The efficiency and effectiveness of the proposed solution method are demonstrated by a series of numerical studies.

An exact algorithm for Two-Echelon Location-Routing problem with simultaneous pickup and delivery

This study considers an extension of the two-Echelon Location-Routing Problem (2E-LRP) namely two-Echelon Location-Routing Problem with Simultaneous Pickup and Delivery (2E-LRPSPD). A Mixed Integer Programming (MIP) formulation is developed and strengthened by the use of valid inequalities to solve the 2E-LRPSPD, and then a Branch and Cut-based exact algorithm (B&C) is presented. To improve the upper bounds, Iterated Local Search and Variable Neighborhood Search-based metaheuristic algorithms, namely, ILS-VNS and VNS, are developed and embedded into the B&C. Computational results, conducted on instances produced from the literature, demonstrate that the B&C yields tight lower and upper bounds, and also is capable of solving some instances optimally with up to 50 customers and 10 satellites in a reasonable time. Furthermore, sensitivity analysis reveals that the heuristic approaches and an increase in the runtime limit assist the algorithm to reach tight the upper bounds, whereas the number of potential depots does not have any effect on the performance of the algorithm. Besides, further computational analysis on the 2E-LRPSPD with a single depot, which is studied in the literature, shows that the B&C improves some best-known solutions while proving the optimality of some instances. Finally, the B&C is applied to a two-echelon supermarket distribution system in Türkiye. The computational results show that simultaneous pickup and delivery operations, as well as depot location decisions are critical elements to consider in the design of cost-effective distribution networks.

Volleyball premier league algorithm with ACO and ALNS for simultaneous pickup–delivery location routing problem

The reverse logistics problem, which involves customer returns and incurs high additional logistics costs, has become a topic of increasing interest. This problem is modeled as the location routing problem with simultaneous pickup and delivery under time constraints (LRPSPDTW), which is a more complex version of the location routing problem (LRP). Previous studies have shown that existing algorithms are unable to provide satisfactory solution accuracy for this problem. In order to address this, a novel algorithm called the hybrid volleyball premier league (HVPL) algorithm is proposed. Drawing inspiration from the competition mechanism of the original volleyball premier league (VPL) algorithm, the HVPL algorithm incorporates adaptive large neighborhood search (ALNS) and improved ant colony optimization (ACO) as sub-algorithms, allowing them to work together synergistically and strike a balance between exploration and exploitation. The learning and elimination phases of the VPL algorithm have been redesigned to enhance convergence speed. Furthermore, the Bellman’s algorithm has been enhanced to determine depot locations and construct vehicle paths for the solution. Prior to solving the LRPSPDTW problem, benchmark testing was conducted using 35 latest benchmark functions. Experimental results and Friedman mean rank test demonstrated that HVPL exhibits superior exploration and exploitation capabilities. HVPL was subsequently tested on 66 instances based on the modified Solomon’s benchmark and the NEO research group benchmarks, and the results showcased its outperformance over other methods in the majority of cases.

Designing the Location–Routing Problem for a Cold Supply Chain Considering the COVID-19 Disaster

In this study, a location routing problem (LRP) model was considered for the distribution network of multiple perishable food items in a cold supply chain (CSC) where vehicles can refuel at gas stations during light of the COVID-19 disaster. Fuel consumption is assumed to vary depending on the cargo transported between nodes when using a non-standard fuel fleet. The problem was formulated as a mixed-integer linear programming (MILP) model to reduce the production of carbon dioxide (CO2). The model was validated using several numerical examples which were solved using the software, LINGO 17.0. The results show that fuel consumption could be reduced in this case. Due to the complexity of the problem, genetically simulated annealing algorithms were developed to solve the actual size problems, and their performance was also evaluated.

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

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

Multi-echelon sustainable reverse logistics network design with incentive mechanism for eco-packages

With the pollution caused by express packaging waste, eco-packages are being commonly used to promote a green supply chain. However, extant research has yet to address the efficacious reverse logistics network design problem while considering both economic and environmental consumption in the recycling process. In this study, a multi-echelon reverse logistics network is designed to collect eco-packages from customers, instead of door-to-door recycling by couriers. This study aims to solve the capacity location-routing problem in a reverse logistics network integrated with the incentive mechanism for customers, which is regarded as NP-hard. To avoid the combinatorial explosion, a multi-objective hybrid genetic algorithm-tabu search (MOHGATS) is developed to reduce search space and improve search speed by changing search strategies. Computational experiments are conducted to verify the proposed model and algorithm based on several test instances and a real-world case study. The impacts of the quantity of eco-packages, the incentive costs for customers, and the quantity and capacity of recycling stations on the reverse logistics network are explored from both economic and environmental perspectives, providing a reference for practical operation and promotion of eco-packages on a large scale.

A Decision-Making Model to Determine Dynamic Facility Locations for a Disaster Logistic Planning Problem Using Deep Learning

Disaster logistics management is vital in planning and organizing humanitarian assistance distribution. The planning problem faces challenges, such as coordinating the allocation and distribution of essential resources while considering the severity of the disaster, population density, and accessibility. This study proposes an optimized disaster relief management model, including distribution center placement, demand point prediction, prohibited route mapping, and efficient relief goods distribution. A dynamic model predicts the location of post-disaster distribution centers using the K-Means method based on impacted demand points’ positions. Artificial Neural Networks (ANN) aid in predicting assistance requests around formed distribution centers. The forbidden route model maps permitted and prohibited routes while considering constraints to enhance relief supply distribution efficacy. The objective function aims to minimize both cost and time in post-disaster aid distribution. The model deep location routing problem (DLRP) effectively handles mixed nonlinear multi-objective programming, choosing the best forbidden routes. The combination of these models provides a comprehensive framework for optimizing disaster relief management, resulting in more effective and responsive disaster handling. Numerical examples show the model’s effectiveness in solving complex humanitarian logistics problems with lower computation time, which is crucial for quick decision making during disasters.

Soft computing for hazardous waste routing in Malaysia: a review

<span lang="EN-US">Nowadays, a significant number of researchers are focusing on utilizing soft computing approaches to address the issue of scheduling in applications concerned with hazardous waste management. In Malaysia, there is thoughtless awareness of the management of hazardous waste, even though the production of wastes in hazardous domains at the industrial and domestic levels has been rising lately. According to previous research findings, the location routing problem (LRP) can be designated as one of the models closer to the actual situation, evaluating the most suitable and optimal location for establishing facilities and utilizing transportation for pick-up and distribution. Recent studies have <span>focused on enhancing the LRP model, and its methodologies approach to solve the waste management problem in hazardous domains. In this paper, a comprehensive review of the better promising and practicable mathematical model of LRP and its methodology approach is discussed, as well as an analysis of the publishing pattern and the trend of research over the preceding five years and more, as retrieved from the web of science (WoS) database. In conclusion, this research is significant in ensuring the effectiveness of reliable mathematical model development and suitable methodologies in the future for solving hazardous waste management</span> problems.</span>

Robust Bi-Level Optimization for Maritime Emergency Materials Distribution in Uncertain Decision-Making Environments

Maritime emergency materials distribution is a key aspect of maritime emergency responses. To effectively deal with the challenges brought by the uncertainty of the maritime transport environment, the multi-agent joint decision-making location-routing problem of maritime emergency materials distribution (MEMD-LRP) under an uncertain decision-making environment is studied. First, two robust bi-level optimization models of MEMD-LRP are constructed based on the effect of the uncertainty of the ship’s sailing time and demand of emergency materials at the accident point, respectively, on the premise of considering the rescue time window and priority of emergency materials distribution. Secondly, with the help of robust optimization theory and duality theory, the robust optimization models are transformed into robust equivalent models that are easy to solve. Finally, a hybrid algorithm based on the ant colony and tabu search (ACO-TS) algorithm solves multiple sets of numerical cases based on the case design of the Bohai Sea area, and analyzes the influence of uncertain parameters on the decision making of MEMD-LRP. The study of MEMD-LRP under uncertain decision-making environments using bi-level programming and robust optimization methods can help decision makers at different levels of the maritime emergency logistics system formulate emergency material reserve locations and emergency material distribution schemes that can effectively deal with the uncertainty in maritime emergencies.

A branch-and-cut algorithm for the one-commodity pickup and delivery location routing problem

This paper introduces a new problem that combines characteristics of the Location and Routing Problem and the One-commodity Pickup and Delivery Traveling Salesman Problem. We are given a set of customers that provide or demand given amounts of a product, and a set of potential facility locations that can be opened or not in order to give service to the customers. Each facility has an opening cost and is the depot of a vehicle with capacity Q. The problem consists in deciding which facilities to open, assigning customers to open facilities, and designing the routes that connect each facility with its customers. The objective is to minimize the sum of the cost of the routes and the facilities. This NP-hard problem has not been previously studied. We propose for it two mathematical formulations, compare them, and present a branch-and-cut algorithm able to solve instances with up to 100 nodes.

The drone latency location routing problem under uncertainty

This paper addresses a location routing problem arising in the last-mile drone delivery context, where drones are used to deliver small packages to a set of customers. Each drone is launched from a fulfillment center to serve multiple customers on a single trip. The goal is to find the optimal subset of fulfillment centers to use as drone launching and landing platforms and the optimal drone routes with the aim of minimizing the sum of customers’ waiting times. We study the problem under two realistic assumptions. First, the drone energy consumption is a nonlinear function of the drone load that varies along the route, as parcels are delivered. Second, the drone flight time is not deterministically known. To hedge against drone flight time uncertainty, we adopt a robust optimization approach. Due to the complex nature of the problem, which turns out to be a nonlinear mixed-integer problem, we design an exact method based on a tailored efficient Branch & Check algorithm that uses customized no-good cuts. The computational experiments show the validity of the proposed model and the promising performance of the exact method. Moreover, we present a case study on last-mile parcel delivery in Turin, Italy, providing insights into the advantages of a drone-based delivery system.

A branch-and-price method for a two-echelon location routing problem with recommended satellites

In city logistics, the two-echelon location routing problem is crucial in coordinating resources and radiating nodes, enabling the efficient planning of relay stations and vehicle distribution routes. However, with the expansion of distribution scopes and changes in urban development, fixed relay stations may not be able to adapt to the evolving network demand structure, leading to reduced efficiency. This paper proposes a two-echelon location routing problem with recommended satellites (2E-LRPRS) to address this issue. These satellites are chosen from the customer set and can be reoptimized to enhance the network's adaptability. A mixed-integer linear program (MILP) is formulated to minimize the distribution cost of the two-echelon network. To solve this problem, a column-generation algorithm (CG) is proposed, which decomposes the original problem into a linear relaxation main problem and a series of two-stage shortest-path subproblems with resource constraints. The branch-and-pricing algorithm (B&P) is then designed to obtain the integer solution. The experimental results demonstrate that the proposed B&P is significantly more efficient and effective than the MILP solver - Cplex. Furthermore, by selecting relay stations from customers, the recommended satellites can be flexibly adjusted based on the locations and demands of distribution customers, leading to an average operating cost savings of 8.43%.

Joint impacts of ambient temperature, path flexibility, and hybrid fleet on energy-conserving supply chain network

The increasing urban logistics transportation activities hugely impact the economy and environment. This paper investigates the combined impact of ambient temperature, path flexibility, and hybrid fleet on the economy and environment in urban logistics. The proposed problem is a variant of the location-routing problem (LRP) named dual-mode energy-conserving LRP (DMECLRP) that handles the combination of three types of decisions: the location of depots, the design of the distribution routes, and the location of charging stations (CSs) and battery swapping stations (BSSs). The objective is to minimize the total cost, including the daily fixed costs of operating depots, the cost of renting vehicles and depreciation, driver compensation, and the routing costs, where the latter can be defined concerning the cost of the consumed energy and CO2 emissions. Due to the NP-hardness of the problem, this paper presents a Q-learning-based hyper-heuristic (QLHH) algorithm to address the DMECLRP. The QLHH employs a Q-learning approach to select appropriate heuristics through its search process and simulated annealing to determine the acceptance of solutions. Results show that the proposed algorithm is effective, providing competitive results for LRP benchmark instances within reasonable computing time, and the proposed model can effectively reduce logistics costs, energy consumption, and CO2 emissions. Extensive analyses are carried out to empirically assess the effect of ambient temperature, path flexibility, and hybrid fleet on key performance indicators, including energy consumption, carbon emissions, and operational costs. Several managerial insights are provided.

Accelerating Two-Phase Multiobjective Evolutionary Algorithm for Electric Location-Routing Problems

Electric location-routing problem is a challenging problem consisting of the optimization of electric vehicle routing and charging facility location, simultaneously. Existing algorithms generally adopt the two-phase search strategy to alternately optimize the routing and the location. However, they are usually criticized for the inefficiency as the problem scale increases. In order to improve the search efficiency in each phase, we propose an accelerating two-phase multiobjective evolutionary algorithm, where the learning method is used to mine the useful information from the historical search process to generate the high-quality routing and location offspring. To be specific, in the routing optimization phase, an interpolation method is developed to extract the frequent visiting orders existing in the historical best solutions. These frequent visiting orders are used to create potential routing offspring that can accelerate the convergence toward the optimal solutions. In the location optimization phase, a surrogate model is used to approximatively represent the relationship from routing to location, which can directly output a promising location scheme for a given routing offspring and thus reduce the optimization time. Experimental results on different scales of test instances demonstrate the competitiveness of the proposed algorithm in comparison with several state of-the-art algorithms, including four widely used heuristic algorithms and two multiobjective evolutionary algorithms.