Location-routing Problem Research Articles

A risk-averse latency location-routing problem with stochastic travel times

In this paper, a latency location-routing problem with stochastic travel times is investigated. The problem is cast as a two-stage stochastic program. The ex-ante decision comprises the location of the depots. The ex-post decision regards the routing, which adapts to the observed travel times. A risk-averse decision-maker is assumed, which is conveyed by adopting the latency CVaRα as the objective function. The problem is formulated mathematically. An efficient multi-start variable neighborhood search algorithm is proposed for tackling the problem when uncertainty is captured by a finite set of scenarios. This procedure is then embedded into a sampling mechanism so that realistic instances of the problem can be tackled, namely when the travel times are represented by random vectors with an infinite support. An extensive computational analysis is conducted to assess the methodological developments proposed and the relevance of capturing uncertainty in the problem. Additional insights include the impact of the risk level in the solutions.

A two-phase adaptive large neighborhood search algorithm for the electric location routing problem with range anxiety

In response to environmental pollution and global warming, electric vehicles (EVs) have been widely applied in supply chain, and lots of researches have been focused on the electric location routing problem (ELRP) to optimize the location of battery-swapping stations (BSSs). However, few studies have simultaneously considered the EV’s collaborative behavior and range anxiety in ELRP. Therefore, this study focuses on formulating an ELRP with battery-swapping stations considering both collaborative behavior and range anxiety. The model takes into account the collaboration between the supply and demand sides to share supply chain resources effectively. The detour probability function is employed to handle the uncertainty caused by drivers’ range anxiety during the trip, which can be evaluated through a proposed range anxiety function. In addition, a new two-dimensional matrix-based solution representation is proposed to explore ELRP optimal solutions intuitively and efficiently. To solve the proposed model effectively, a two-phase adaptive large neighborhood search (TALNS) algorithm that integrates the adaptive large neighborhood search (ALNS) algorithm and the extended binary particle swarm optimization (EBPSO) algorithm is proposed. In the EBPSO algorithm, a new position update mechanism and local search strategy are used to strengthen the local search ability. In the ALNS algorithm, multiple destroy and repair operators are developed for the proposed model. Further, to validate the effectiveness and performance of the proposed algorithm, comparison experiments with the Gurobi optimizer and other baseline heuristic algorithms are conducted.

Multi-period emergency facility location-routing problems under uncertainty and risk aversion

This paper addresses a multi-period emergency facility location-routing problem, in which the uncertainties in material demands and transportation time, as well as dynamic inventory replenishment and carryover are incorporated in the design of multi-level emergency logistics networks. To measure the risks stemming from uncertain transportation time, mean-CVaR method is used. Then, a risk-averse stochastic programming model for the presented problem is formulated to minimize the total rescue time of the network. Moreover, a genetic algorithm is developed to solve the proposed model. Extensive numerical experiments including the randomly generated instances and a case study on the Wenchuan earthquake in China are conducted to verify the effectiveness of the presented model and algorithm. Experimental results show that the genetic algorithm significantly performs better than the Gurobi solver in terms of both solution quality and solution time.

Optimizing Drone Delivery Paths from Shared Bases: A Location-Routing Problem with Realistic Energy Constraints

Recently, Amazon patented fulfillment centers for drones on a large scale in densely populated areas. A network of such shared centers can be used for landing and launching drones as an alternative to the traditional private bases in near future. This paper studies how a user of such a shared delivery infrastructure can optimally determine the required bases among the existing bases to perform her delivery tasks. To this end, a location-routing problem is studied where the problem determines the drone launching centers and their routes to deliver parcels. A realistic energy function is used that incorporates the effect of load weight for calculating energy consumption in all flight phases including take-off, level flight, hovering, and landing. Although the energy consumption is nonlinear, the problem is formulated as a mixed-integer linear programming model and strengthened by valid inequalities and a pre-processing algorithm that enables us to solve instances with up to 100 customers using off-the-shelf optimization solvers. Moreover, a heuristic method is presented to solve instances with up to 200 customers. Results indicate the importance of incorporating the load-dependent energy formula in contrast to using fixed flight duration constraints for drones. The value of allowing multiple visits on each trip versus only simple back-and-forth trips is also assessed. The advantage of using an integrated location-routing approach is shown over the sequential approach in which the locations of bases are decided first and the routes are constructed next. Moreover, to manage future demand uncertainty, the model is extended for the case that a number of demand scenarios are given.

Designing a sustainable delivery network with parcel locker systems as collection and transfer points

Collection and delivery points, both attended and fully automated, have emerged as a popular solution in last-mile delivery. They offer not only operational advantages for the delivery company but also present a pathway to mitigating the negative environmental impact of parcel delivery operations. In this study, we explore a new approach, where parcel locker systems have a dual role: as collection points for customers and as transfer points for the delivery company. We introduce a variant of the Location-Routing Problem, optimizing the strategic location and capacity size of parcel locker systems as well as the delivery routes from those points. We develop an efficient branch-and-price algorithm and apply it to a real-life case study that focuses on the design of a delivery network with parcel lockers in a residential neighborhood in the city of Groningen, the Netherlands. Our case study findings underscore that the dual role of parcel locker systems considerably reduces the travel distance of delivery vehicles, is well-suited to deal with potential future increase in demand for parcel collection, and reduces the likelihood of customers traveling to parcel locker by car.

Design of a reverse logistics network for medical waste considering location and routing decisions

Medical waste generated in healthcare facilities is categorized as hazardous due to its infectious, toxic, or radioactive properties, posing substantial risks to human health and the environment. This research proposes a bi-objective Mixed-Integer Linear Programming model for designing reverse logistics networks that enable both economical and safe medical waste management. Said model determines optimal quantity, depot locations, and routes for transporting waste from its generating points (hospitals) to the treatment and disposal sites (depots).This research addresses a bi-objective location routing problem, with multiple depots, time windows, capacity constraints, and variated waste types, across a multi-period horizon. It is innovative because no previous works have successfully dealt with such a combination of pragmatic features. The Location Routing Problem is an already well-known NP-Hard problem, with the additional aforementioned features further adding to its complexity. Thus, a genetic algorithm to solve large-sized realistic instances within reasonable computing times had been developed.Numerical experiments considered 20 random instances contrasting exact and approximate solution approaches. Also, a medical waste collection case study of a public hospital network in Atlántico Department, Colombia, delivering a Pareto frontier solution set, was introduced. The results demonstrated the efficacy of the proposed genetic algorithm in successfully addressing small instances of the problem, delivering outcomes comparable to the Mixed-Integer Linear Programming model. Furthermore, it yields good-quality solutions in a reduced computational time for larger instances deemed unfeasible for the Mixed-Integer Linear Programming model.This article contributes to both scientific literature and practitioners by presenting a decision-making tool designed to address the medical waste reverse logistics challenge under realistic scenarios. It approaches the issue from a bi-objective standpoint, jointly considering economic factors and biomedical safety. Additionally, the article introduces realistic and pertinent assumptions that have not been explored in previous literature.

Risk-averse distributionally robust optimization for construction waste reverse logistics with a joint chance constraint

The uncertainty of the amount of construction and demolition waste (CDW) generation affects the CDW reverse logistics network service level. We investigate a CDW reverse logistics network location-routing problem considering uncertainties. To minimize the total social cost, a two-stage risk-averse distributionally robust optimization model is developed, which aims to optimize the location and number of CDW disposal facilities and the CDW transportation scheme. We introduce the mean-conditional value at risk measure and a joint chance constraint into our model to consider the government’s risk aversion. The above model is approximated as a standard second-order cone programming model (SOCP) considering a special case. To exactly solve the SOCP, we design an outer approximation algorithm. Several performance tests and a case study are proposed, and sensitivity analysis provides helpful managerial insights.

From operational to strategic modelling: A continuous multi-scale approach for last-mile analysis

Supply chain planning requires decision-making at all levels, especially in the new normal of intervened supply networks. The integration of strategic network design and operational routing decisions has been widely studied in the literature as the location-routing problem (LRP). However, the LRP does not consider the differences in the planning horizon of each sub-problem, nor have geospatial elements been included in the distribution of demand. This paper aims to redesign the conceptual modelling of the last mile to inform strategic network design problems. A continuous multi-scale approach (CMA) is proposed by taking elements from the districting problem (DP) and continuous approximation (CA). This approach includes stochastic demand in the analysis and the effects of time windows and failed deliveries. The validation of CMA in a case of rural parcel deliveries in Belgium shows an estimate of the distance travelled similar to traditional routing algorithms in scenarios with high demand density. Likewise, the effects of time windows on the spatial configuration of multi-scale districting are explored. This approach provides insights for decision-making in strategic and tactical planning, such as sonification, differentiated services to satisfy consumer preferences, and fleet management. The limitations of the CMA lie in its implementation in purely operational scenarios since it does not offer detailed routing information. Subsequent research aims to exploit the potential of strategic last-mile modelling with effective integration into network design problems.

An Optimization Method for Location-Routing of Cruise Ship Cabin Materials Considering Obstacle Blocking Effects

This study examines the challenges related to the storage and distribution of cabin materials on board during the construction of cruise ships. The construction process of cruise ships involves the assembly of various cabin materials, which are temporarily stored and transported in a complex deck environment with multiple obstacles. These processes can be viewed as location-routing problems (LRPs). However, existing solutions for LRPs do not account for the obstacles commonly encountered in deck environments. Therefore, this paper introduces a new variant of LRPs, termed as the BE-LRP (blocking environment location-routing problem). Initially, by considering the optimization objectives of minimizing the distribution distance and the number of vehicles required, the paper develops an optimization model for the location-routing of on-board materials while taking obstacles into consideration. Subsequently, a method for estimating blocked distances is proposed. This method utilizes Gaussian process regression to predict blocked distances and enables the rapid estimation of distances obstructed by obstacles between different destinations. Lastly, a hybrid obstacle blocking distance processing HO-NSGAII algorithm is formulated to address the BE-LRP. Experimental comparisons demonstrate that the distribution scheme derived from this research method does not necessitate modifications to the delivery distance when compared to the traditional NSGAII algorithm, and better aligns with the actual deck conditions. With an equivalent number of delivery vehicles, the scheme results in shorter delivery distances. The delivery distance can be reduced by 3–17% under varying circumstances. These findings are advantageous for enhancing the efficiency of cruise ship construction and mitigating the impact of warehousing and distribution on construction progress.

Optimal allocation and route design for station-based drone inspection of large-scale facilities

The utilization of drones to conduct inspections on industrial electricity facilities, including large-sized wind turbines and power transmission towers, has recently received significant attention, mainly due to its potential to enhance inspection efficiency and save maintenance costs. Motivated by the advantages of drones for facility inspection, we present a novel station-based drone inspection problem (SDIP) for large-scale facilities. The objective of SDIP is to determine the locations of multiple homogeneous automatic battery swap stations (ABSSs) equipped with drones, assign facility inspection tasks to the ABSSs with operation duration constraints, and design drone inspection routes with battery capacity constraints, such that minimize the sum of fixed ABSS costs and drone travel costs. The SDIP can be regarded as a variant of the location-routing problem, which is NP-hard and difficult to solve optimally. To obtain the optimal solution of SDIP efficiently, we firstly formulate this problem into an arc based formulation and a route based formulation, and then develop a logic-based Benders decomposition (LBBD) algorithm to solve it. The SDIP is decomposed into a master problem (MP) and a set of subproblems (SPs). The MP is solved by a branch-and-cut (BC) procedure. Once a feasible integer solution is found, the linear relaxation of SPs are solved by a stabilized column generation to generate Benders cuts. If the cost of all the SPs’ optimal LP solutions plus the cost of the MP’s solution is less that current best cost, the SPs are exactly solved by a Branch-and-Price (BP) algorithm to generate the logic cuts. The numerical results on five scales of randomly generated instances validate the effectiveness of the LBBD algorithm. Specifically, the LBBD can solve all small- and middle-sized instances, and seven out of ten large-sized instances in 1000 s. Furthermore, we conduct a sensitivity analysis by varying the attributes of ABSSs and drones, and provide valuable managerial insights for large-scale facility inspection.

An enhanced Modelling approach for warehouse sharing platform system designing problem

With the increasing importance of sustainability, warehouse sharing arises as a possible way to improve the logistics system efficiency. This paper studied the warehouse sharing platform systems (WSPS) and proposed an enhanced modelling approach for the WSPS design problem (WSPSDP) using the multi-allocation hub location routing problem framework. New elements, such as inter-warehouse transportation and multi-allocation scheme, were considered compared to the existing WSPS model. Then, an adaptive large neighbourhood decomposition search heuristic was applied to solve our problem. Computational experiments were conducted on different-sized instances to compare the WSPS model without inter-warehouse transportation (WSPSDP-WI) and the WSPS model with single-allocation scheme (WSPSDP-SA). The results suggested that our proposed WSPSDP model is more cost-efficient than the existing WSPS models, reducing 15.38% and 1.43% operation costs compared to the WSPSDP-WI and WSPSDP-SA models. Finally, our proposed WSPSDP model also has the potential to promote the utilisation of existing cheap idle warehouses.

Multi-Period Profit-Oriented Location Routing Problem in Multi-User Warehouses with Backordering and Order Acceptance: A Relax-Fix-Optimize Heuristic

Multi-Period Profit-Oriented Location Routing Problem in Multi-User Warehouses with Backordering and Order Acceptance: A Relax-Fix-Optimize Heuristic

A Novel Exact and Heuristic Solution for the Periodic Location-Routing Problem Applied to Waste Collection

A Novel Exact and Heuristic Solution for the Periodic Location-Routing Problem Applied to Waste Collection

The Two-Echelon for Meat Products Location-Routing Problem with Picking Up and Delivery by Using Constraint Programming

The Two-Echelon for Meat Products Location-Routing Problem with Picking Up and Delivery by Using Constraint Programming

A reinforcement learning guided hybrid evolutionary algorithm for the latency location routing problem

The latency location routing problem integrates the facility location problem and the multi-depot cumulative capacitated vehicle routing problem. This problem involves making simultaneous decisions about depot locations and vehicle routes to serve customers while aiming to minimize the sum of waiting (arriving) times for all customers. To address this computationally challenging problem, we propose a reinforcement learning guided hybrid evolutionary algorithm following the framework of the memetic algorithm. The proposed algorithm relies on a diversity-enhanced multi-parent edge assembly crossover to build promising offspring and a reinforcement learning guided variable neighborhood descent to determine the exploration order of multiple neighborhoods. Additionally, strategic oscillation is used to achieve a balanced exploration of both feasible and infeasible solutions. The competitiveness of the algorithm against state-of-the-art methods is demonstrated by experimental results on the three sets of 76 popular instances, including 51 improved best solutions (new upper bounds) for the 59 instances with unknown optima and equal best results for the remaining instances. We also conduct additional experiments to shed light on the key components of the algorithm.

A Bi-objective location-routing model for the healthcare waste management in the era of logistics 4.0 under uncertainty

The purpose of this study is to apply Industry 4.0-based technologies to improve the management of infectious healthcare waste considering location-routing problem and population risk under uncertainty. To achieve this, a decision support system is developed and implemented utilizing a bi-objective mixed-integer linear programming (MILP) model. The bi-objective MILP model improves the performance of the healthcare waste management by applying Industry 4.0 technologies, including electric autonomous vehicles, information sharing system, internet of things (IoT), Global Navigation Satellite System (GNSS), and RFID-tagged waste bags. We develop a multi-objective solution approach by integrating the lexicographic and TH methods. The validity of the model has been established through its implementation in seven hospitals in the city of Karaj, Iran. The results denoted significant improvements in waste collection efficiency, route optimization, and the reduction of contamination risks.

Location-Routing Problem for Integrated Supply Chain Network Design with First and Last Mile: A Critical Literature Review

Location-Routing Problem for Integrated Supply Chain Network Design with First and Last Mile: A Critical Literature Review

Location-routing optimization problem for electric vehicle charging stations in an uncertain transportation network: An adaptive co-evolutionary clustering algorithm

The rapid growth of Electric Vehicles (EVs) has led to issues such as insufficient and unevenly distributed charging stations, posing an increasingly severe challenge. This not only means higher economic and time costs for EV users traveling to charging stations, but also indicates that EVs need to incur additional energy consumption. To address these challenges, this paper first establishes an extended space-time-state network to describe the temporal variability and uncertainty of the traffic environment. Secondly, considering the impact of the energy consumption incurred by EVs traveling to charging stations (CSs) on the layout of CSs, a co-evolutionary optimization model of the location-routing problem is proposed. To solve the model, a two-stage Adaptive Co-evolutionary Clustering Algorithm (ACECA) integrating an adaptive clustering framework and a co-evolutionary mechanism is designed. Finally, the experiment results indicate that there exists a game between a short-term economic investment and long-term benefits of energy conservation and emission reduction. Moreover, ACECA demonstrates stronger solution performance and robustness compared to other algorithms, with the resulting CS location schemes showing superior advantages in energy conservation and in cost saving for users. The research findings can provide theoretical support for the planning of charging station locations for electric vehicles.

Location-Routing Optimization for Two-Echelon Cold Chain Logistics of Front Warehouses Based on a Hybrid Ant Colony Algorithm

Diverse demands have promoted the rapid development of the cold chain logistics industry. In the paper, a novel approach for calculating the comprehensive carbon emission cost was proposed and the front warehouse mode was analyzed under the background of energy conservation and emission reduction. To solve the two-echelon low-carbon location-routing problem (2E-LCLRP), a mathematical model considering operating cost, total transportation cost, fixed cost, refrigeration cost, cargo damage cost, and comprehensive carbon emission cost was proposed to determine the minimum total cost. A hybrid ant colony optimization (HACO) algorithm based on an elbow rule and an improved ant colony optimization (IACO) algorithm was proposed to solve the 2E-LCLRP. According to the elbow rule, the optimal number of front warehouses was determined and an IACO algorithm was then designed to optimize vehicle routes. An adaptive hybrid selection strategy and an optimized pheromone update mechanism were integrated into the HACO algorithm to accelerate convergence and obtain global optimal solutions. The proposed model and algorithm were verified through the case study of the 2E-LCLRP in Nanjing, China. The HACO algorithm outperformed the original ant colony optimization (ACO) algorithm in terms of convergence rate and solution quality. This study provides significant insights for enhancing heuristic algorithms as well as valuable research methods. Furthermore, the results can help cold chain logistics companies in balancing economic costs and environmental benefits and address cold chain distribution of agricultural products.

Sustainable location-routing problem for medical waste management using electric vehicles

The sustainable management of medical waste is essential for environmental protection and public health safety, contributing to urban development and societal well-being. This study focuses on the medical waste Location-Routing Problem with Electric Vehicles (EVs), aiming to mitigate infection risk while providing cost-effective and energy-efficient logistics solutions. It encompasses diverse elements such as disposal location selection, vehicle scheduling, recharge strategies, time windows, working duration, and load-dependent energy consumption. To tackle this complex problem, we introduce an Evolutionary Decomposition-based Adapted Large Neighborhood Search algorithm (E-ALNS/D), which surpasses existing methods such as MOEA/D-HGS, MOEA/D-LNS, MPGA, and NSGAII-LNS across various urban settings. Empirical analysis and a case study reveal opportunities for enhancing medical waste management with EVs. Key findings show that optimizing service times, adopting fast-charging infrastructure, and strategically placing temporary disposal facilities in response to unforeseen demand spikes significantly reduce energy consumption, lower infection risk, and cut charging cost. Furthermore, selecting peripheral over central disposal locations better minimizes infection risks. This research offers valuable insights for decision-makers in EV-based medical waste management, emphasizing the need to balance public health, environmental sustainability, and economic efficiency. Our methodology paves the way for future research in sustainable medical waste management with EVs.