Location-routing Problem Research Articles

A simple hyper-heuristic approach for a variant of many-to-many hub location-routing problem

A simple hyper-heuristic approach for a variant of many-to-many hub location-routing problem

Two-echelon multi-period location routing problem with shared transportation resource

Solving a two-echelon multi-period location routing problem (2E-MPLRP) involves facility location selection and two-echelon vehicle routing optimization. Based on the periodic time characteristics of logistics facilities and customers, the optimal solutions provide periodic location decisions and vehicle routing schemes simultaneously in each service period of the planning horizon. Transportation resource configuration is tweaked by enabling resource sharing across multiple service periods to maximize resource utilization in the context of growing emphasis on sustainable development. A bi-objective mathematical model is developed to formulate the 2E-MPLRP to obtain the minimum total operating cost and number of vehicles. A two-stage hybrid algorithm including three-dimensional (3D) k-means clustering and multi-objective improved particle swarm optimization (MOIPSO) algorithm is proposed to solve the 2E-MPLRP. The 3D k-means clustering algorithm is adapted to assign customers to distribution centers (DCs) to receive service in multiple service periods, and the MOIPSO algorithm is then designed to optimize the vehicle routes and find the Pareto optimal solutions. With an external repository strategy and a rapidly decreasing mutation strategy incorporated in the iterative process, the proposed hybrid algorithm performs well in expanding the particles’ searching region and achieving robust optimal results. An algorithm comparison demonstrates the superiority of the proposed hybrid algorithm over other existing algorithms. A real-world case study of 2E-MPLRP in Chongqing, China is conducted, and results show that the proposed model and algorithm are of practical significance in minimizing operating cost, improving transportation efficiency, and contributing to sustainable two-echelon logistics network operations.

Two-Echelon Location-Routing Problem with Time Windows and Transportation Resource Sharing

In this work, a two-echelon location-routing problem with time windows and transportation resource sharing (2E-LRPTWTRS) is solved by selecting facility locations and optimizing two-echelon vehicle routes. The optimal solutions improve the efficiency of a logistics network based on the geographical distribution and service time windows of logistics facilities and customers. Furthermore, resource utilization is maximized by enabling resource sharing strategies within and among different logistics facilities simultaneously. The 2E-LRPTWTRS is formulated as a biobjective optimization model, and obtaining the smallest number of required delivery vehicles and the minimum total operating cost are the two objective functions. A two-stage hybrid algorithm composed of k-means clustering and extended multiobjective particle swarm optimization algorithm is proposed for 2E-LRPTWTRS optimization. A self-adaptive mechanism of flight parameters is introduced and adopted during the iterative process to balance the evolution of particles and improve the efficiency of the two-stage hybrid algorithm. Moreover, 20 small-scale instances are used for an algorithm comparison with multiobjective genetic algorithm and nondominated sorting genetic algorithm-II, and the solutions demonstrate the superiority of the proposed algorithm in optimizing logistics networks. The proposed optimization model and hybrid algorithm are tested by employing a real-world case of 2E-LRPTWTRS in Chongqing, China, and the optimization results verify the positive role of the developed model and algorithm in improving logistics efficiency, reducing operating cost, and saving transportation resources in the operations of two-echelon logistics networks.

The Location Routing Problem of the Car-Sharing System with Autonomous Electric Vehicles

Car-sharing, electrification, and autonomous driving are greatly revolutionizing the future of the transportation system. This study proposes a location routing problem for the car-sharing system with autonomous electric vehicles to determine optimal station location and vehicle routing, where each station is both a depot and a charging station. A mathematical model is formulated and then extended to three variants, while simultaneously considering different recharging and service options. The proposed mixed-integer nonlinear models are separately solved by general algebraic modeling system (GAMS) and genetic algorithm (GA), and the efficiency of the GA is demonstrated. The comparative experimental results of instances are presented, and the benefits of allowing partial recharge are obtained. More significant savings in cost can be achieved if partial service is simultaneously allowed. Furthermore, the trade-off between the operator’s interests and the interests of users, as well as the operator’s immediate profits and future profits, are explored through sensitivity analysis.

Deploying autonomous mobile lockers in a two-echelon parcel operation

In this study, Autonomous Mobile Lockers (AMLs) are introduced into current city logistics networks to reduce traffic congestion and save cost. The proposed system consists of couriers working with AMLs that visit the couriers in the field and transfer parcels between the couriers and the depot. Couriers can continue their tours without having to make repeated returns to the depot. At the same time, the AMLs can enlarge the coverage of each depot and allow a reduction in the number of depots, saving on rent. We propose a mixed integer programming model to solve the AML-Courier 2-Echelon Location Routing Problem in order to determine the tours of AMLs and couriers. We adapt and modify a hybrid Clark and Wright heuristic, the performance of which is examined for larger problem sizes, and introduce an enhanced version to improve the routes constructed. The results show the efficiency of the proposed heuristics for large problem sizes in terms of solution quality and execution time. Finally, the sensitivity of the best found solutions to some important parameters is analysed and a comparison with a single-echelon model made to establish the benefit of AML use.

Multi-period two-echelon location routing problem for disaster waste clean-up

Waste clean-up after a disaster is one of the most critical tasks in the response stage of disaster management. We develop a model to minimise the cost and duration of disaster waste clean-up considering using Temporary Disaster Waste Management Sites (TDWMSs), which can store and process waste before it is sent to the final disposal sites. The problem that arises can be seen as a Multi-Period Two-echelon Location Routing Problem (MP-2ELRP) in which the main decisions are the location of the TDWMSs and the routing of vehicles in both echelons. In this paper, we propose both a mixed-integer program and a Genetic Algorithm (GA) to model and solve the problem. Computational tests indicate: (i) the performance of proposed GA is robust; (ii) the use of TDWMSs can reduce both total waste clean-up cost and duration; and (iii) the capacities of TDWMSs have a significant impact on the total waste clean-up time and duration.

Capacitated location routing problem with simultaneous pickup and delivery under the risk of disruption

This paper develops a new mathematical model to study a location-routing problem with simultaneous pickup and delivery under the risk of disruption. A remarkable number of previous studies have assumed that network components (e.g., routes, production factories, depots, etc.) are always available and can permanently serve the customers. This assumption is no longer valid when the network faces disruptions such as flood, earthquake, tsunami, terrorist attacks and workers strike. In case of any disruption in the network, tremendous cost is imposed on the stockholders. Incorporating disruption in the design phase of the network will alleviate the impact of these disasters and let the network resist disruption. In this study, a mixed integer programming (MIP) model is proposed that formulates a reliable capacitated location-routing problem with simultaneous pickup and delivery (RCLRP-SPD) services in supply chain distribution network. The objective function attempts to minimize the sum of location cost of depots, routing cost of vehicles and cost of unfulfilled demand of customers. Since the model is NP-Hard, three meta-heuristics are tailored for large-sized instances and the results show the outperformance of hybrid algorithms comparing to classic genetic algorithm. Finally, the obtained results are discussed and the paper is concluded.

Pareto-based grouping meta-heuristic algorithm for humanitarian relief logistics with multistate network reliability

This article considers a biobjective location-routing problem to deliver relief resources to the victims affected by a disaster under uncertainty in demand, transportation infrastructure, and travel time. Since transportation networks are exposed to a considerable level of uncertainty, choosing the reliable path for relief goods to be transmitted to the affected areas ensures the arrival of these supplies. For the first time, route reliability is calculated based on the multistate theory, and the universal generating function technique is used for network reliability assessment. The problem is formulated as a multiperiod robust biobjective mixed-integer programming model. Two objective functions are considered: (a) decreasing the sum of arrival times of relief vehicles at the demand nodes for delivering aids to the affected areas, and (b) increasing the minimum route reliability for all the serving vehicles. A novel multiobjective grouping algorithm is proposed to obtain the Pareto-optimal solutions of the problem. Then, its performance is compared with two other multiobjective grouping algorithms. To evaluate the solution method, the algorithms are implemented on various test problems and compared statistically. A case study is presented to illustrate the potential applicability of our model. Additionally, to determine the effect of the changes in the main parameters of the problem on the value of objective functions, the sensitivity analyses are performed and the managerial insights are given.

Multiobjective Multiple Neighborhood Search Algorithms for Multiobjective Fleet Size and Mix Location-Routing Problem With Time Windows

This paper introduces a multiobjective fleet size and mix location-routing problem with time windows and designs a set of real-world benchmark instances. Then, two versions of multiobjective multiple neighborhood search algorithms based on decomposition and vector angle are developed for solving the problem. In the proposed algorithms, three different kinds of neighborhood search operators, including general local search, objective-specific local search, and large neighborhood search, are carefully designed and combined in a synergistic manner. The experimental results show the effectiveness of the proposed algorithms. Relationships between different objectives in this multiobjective problem are also discussed.

A bi-level model and memetic algorithm for arc interdiction location-routing problem

This paper investigates arc interdiction location-routing problem (AI-LRP), a new variant of the classical LRP. There are two decision-makers with dissimilar perceptions of the problem, making efforts to achieve their contradictory yet interconnected targets. While the interdictor develops a plan to disrupt products flow in a distribution network, the distributor strives to mitigate the effects of disruption and to deliver goods to customers at minimal risk and cost in the interdicted network. The impacts they have on one another are formulated as a bi-level programming model, with the interdictor taking decisions at the upper level. This problem has wide applications in reality, including distribution of particular goods such as money, precious metals, hazardous materials, and even prisoners that may need security measures. To solve the problem, an efficient memetic algorithm (EMA) with a dynamic local search is proposed. The efficiency of the developed EMA is demonstrated by comparing its performance with a few LRP algorithms published in the literature as well as with a commercial solver. A cost–benefit analysis, along with a case study in maritime transportation, is conducted to provide managerial insights. The results from numerical experiments show that when more budgets are allocated to interdiction and the distributor estimates the interdictor's parameters with less accuracy, AI-LRP is capable of formulating close-to-real-life cases under information asymmetry more effectively.

An approach based on Clustering AH and VND for Supply Chain Management

In this work, we present a new approach to solve the Capacitated Location-Routing Problem (CLRP). The aim of this method is to determine the depot locations, to assign customers to facilities and to define routes for each depot to serve the associated clients. The proposed approach contains two phases, which are the constructive phase and the improvement phase. In the first phase, we select the depots to be opened, allocate the customers to open depots using a Hierarchical Ascendant (HA) method and we solve the vehicle routing problem for each depot using Sweep algorithm. In the second phase, we apply a Variable Neighborhood Descent (VND) with three structures in order to optimize the cost obtained by the first phase. Two sets of well-known instances from the literature are used to evaluate the performance of this method, and the numerical results obtained are compared with the experimental results of other methods. Results show that our method is competitive with respect to the best-known solutions (BKSs) and demonstrate its efficiency in comparison with other approaches.

Location‐routing problem: a classification of recent research

AbstractThe location‐routing problem (LRP) and its variants have been studied extensively over the past few years. The number of articles has grown more than ever, since the last surveys. Therefore, this study aims to perform a review of recent LRP research from 222 academic literature published from 2014 to 2019. The analysis of publication intensity, problem characteristics, solution methods, and application areas was executed to draw the state‐of‐the‐art of LRP research. As the main contributions to this study, a new taxonomy was proposed to capture some recently emerging issues in LRP and some suggestions for future research were listed and discussed.

The electric location-routing problem with heterogeneous fleet: Formulation and Benders decomposition approach

In this paper, we focus on a problem that requires the location of recharging stations and the routing of electric vehicles in a goods distribution system. The goods are disseminated from a depot and distributed to the customers via a heterogeneous fleet of electric vehicles with limited capacity. Differently from the classical vehicle routing problem, the vehicles have battery restrictions that need to be recharged at some stations if a trip is longer than their range. The problem reduces to finding the optimal locations of the recharging stations and their number to minimize the total cost, which includes the routing cost, the recharging cost, and the fixed costs of opening stations and operating vehicles. We propose a novel mathematical formulation and an efficient Benders decomposition algorithm embedded into a two-phase general framework to solve this environmental logistics problem. Phase I solves a restricted problem to provide an upper bound for the original problem which is later solved in Phase II. Between the two phases, an intermediate processing procedure is introduced to reduce the computations of the Phase II problem. This is achieved by a combination of the Phase I upper bound and several lower bounds obtained via exploiting the underlying network structure. Our approach solves the problem in a general setting with non-identical stations and vehicles by allowing multiple visits to the stations and partial recharging. The computational study provides both managerial and methodological insights.

A column-and-constraint generation algorithm for two-stage stochastic programming problems

This paper presents a column-and-constraint generation algorithm for two-stage stochastic programming problems. A distinctive feature of the algorithm is that it does not assume fixed recourse and as a consequence the values and dimensions of the recourse matrix can be uncertain. The proposed algorithm contains multi-cut (partial) Benders decomposition and the deterministic equivalent model as special cases and can be used to trade-off computational speed and memory requirements. The algorithm outperforms multi-cut (partial) Benders decomposition in computational time and the deterministic equivalent model in memory requirements for a maintenance location routing problem. In addition, for instances with a large number of scenarios, the algorithm outperforms the deterministic equivalent model in both computational time and memory requirements. Furthermore, we present an adaptive relative tolerance for instances for which the solution time of the master problem is the bottleneck and the slave problems can be solved relatively efficiently. The adaptive relative tolerance is large in early iterations and converges to zero for the final iteration(s) of the algorithm. The combination of this relative adaptive tolerance with the proposed algorithm decreases the computational time of our instances even further.

Combining Heuristics with Simulation and Fuzzy Logic to Solve a Flexible-Size Location Routing Problem under Uncertainty

The location routing problem integrates both a facility location and a vehicle routing problem. Each of these problems are NP-hard in nature, which justifies the use of heuristic-based algorithms when dealing with large-scale instances that need to be solved in reasonable computing times. This paper discusses a realistic variant of the problem that considers facilities of different sizes and two types of uncertainty conditions. In particular, we assume that some customers’ demands are stochastic, while others follow a fuzzy pattern. An iterated local search metaheuristic is integrated with simulation and fuzzy logic to solve the aforementioned problem, and a series of computational experiments are run to illustrate the potential of the proposed algorithm.

Retracted: The HSABA for Emergency Location-Routing Problem

Retracted: The HSABA for Emergency Location-Routing Problem

Design of the Distribution Network for a “Collect-on- Delivery” Company in a Metropolitan Context using Simulated Annealing with Path Relinking

Parcel delivery service by collect-on-delivery (COD, a.k.a. cash-on-delivery) companies is a new distribution mode in China. The design of the distribution network of a COD company in urban areas is of great importance and a relatively new research direction. In this paper, we aim to model this distribution n etwork as a two-echelon location routing problem (2E-LRP) and propose a novel efficient optimization algorithm by combining simula ted annealing (SA) and path relinking (PR) to solve this NP combinatorial optimization problem. The experimental results are reported for 84 test problems from Nguyen's, Prodhon's, and Sterle 's benchmark. They indicate that the proposed SA-PR algorithm is competitive with other existing state-of-art algorithms for 2E-LRP from the perspectives of both quality of solution and computational time. Therefore, SA-PR is an effective metaheuristic to solve 2E-LRP problems, i.e., design distribution network of a COD company in a metropolitan context.

A Branch & Cut algorithm for the prize-collecting capacitated location routing problem

The Capacitated location routing problem (CLRP) is the combination of two well-studied problems in Operations Research: the capacitated facility location problem (CFLP) and the multiple depots vehicle routing problem (MDVRP). Given a set of available locations and a fleet of vehicles, the aim is to determine a set of depots to open and routes of the vehicles to satisfy the customers demands. The objective of the CLRP is to minimize the total cost, that is the cost of the opened depots, the fixed cost of the vehicles and the cost of the routes while satisfying vehicle and depot capacity constraints. In this work the prize-collecting capacitated location routing problem (PC-CLRP), a new variant of the CLRP is presented. In this case it is possible to leave some customers unvisited and if a customer is visited it gives a gain. The objective is to maximize the overall benefit. A two-index formulation for the PC-CLRP and a Branch & Cut algorithm based on this model are proposed. Valid inequalities for the CLRP are adapted for the PC-CLRP. Also new valid inequalities and optimality cuts are proposed together with their corresponding separation algorithms. A hierarchical branching strategy is also included. The initial solution was provided by an Ant Colony Algorithm. The algorithm is tested on a set of instances specially designed for the new problem. Computational results showed very promising. We also compare the performance of the algorithm with recent work for CLRP on instances from the literature.

Multiobjective location-routing problem of relief commodities with reliability.

The applicability and efficiency of location-routing problems for relief commodities motivate several researchers to develop optimization models and algorithms with regards to real-world cases. This study by presenting a multiobjective mixed integer mathematical model for the location-routing of the medical relief problem at the time of a disaster, proposes a new extension to this applicable model with reliability considerations. The proposed model focuses on the location of temporary relief centers and delivers the pharmaceutical commodities to centers at the shortest possible time with reliability assurance. The model includes three simultaneous objectives of minimizing response time, minimizing operational costs, and maximizing the reliability of the transportation network. As far as we know, this study firstly optimizes these three objectives simultaneously. Another novelty is to add the uncertainty of the problem. In this regard, the inherent uncertainty is formulated by a scenario-based approach. Considering the multiobjectiveness of the proposed model, the Epsilon constraint method as a solution algorithm has been used to solve the model. Results are tested for numerical examples via different scenarios. The results represent the excellent performance of the model to minimize the costs and to increase the reliability for the proposed location-routing problem of relief commodities.

Application of a Bilevel Programming Model in Disposal Site Selection for Hazardous Waste

In this study, a bilevel programming model is proposed for a multiple decision-subject location-routing problem of hazardous waste (HW) under a fuzzy random environment to select the best HW dispos...