Location-routing Problem Research Articles

A mixed integer linear programming model for designing a green closed-loop supply chain network considering location-routing problem

In today's business environment, reusing the products could result in a great deal of supply chains cost reductions. Additionally, environmental regulations and customers' increasing expectations leave companies no choice but applying the return policy. In this regard, designing a supply chain network incorporating the reverse flow can provide environmental requirements in addition to economic objectives. In this paper, a new mixed integer linear programming (MILP) model is developed for a closed-loop supply chain network (CLSCN) design. The proposed model is multi-period and multi-product that covers facility location and routing of heterogeneous vehicle fleets, simultaneously. The efficiency of the model is validated based on a real case in production and distribution chain of automotive spare parts manufacturing company in Iran. Managerial insights are gained through the numerical results.

A mixed integer linear programming model for designing a green closed-loop supply chain network considering location-routing problem

A mixed integer linear programming model for designing a green closed-loop supply chain network considering location-routing problem

Routing optimization of the emergency supplies distribution vehicles using NSGA-II algorithm: a case study

In recent years, emergencies, including natural disasters and other public disasters, have seriously threatened the lives and property security of people all over the world. In order to save more people’s lives and reduce the losses caused by disasters, many researchers have carried out intensive study on the distribution of emergency supplies. This paper first studies Location-Routing Problem(LRP) of alternative logistics centers and material demand points, and constructs a multi-objective integer programming model based on the actual situation. The model consists of two objectives: (1) the minimum total transportation time; (2) the maximum total emergency material satisfaction. Then an algorithm is introduced to solve the above model: NSGA-II. Finally, the emergency materials distribution in Hubei Province is taken as an example to verify the applicability and effectiveness of the above method and the models.

A Hybrid Heuristic Based on a Particle Swarm Algorithm to Solve the Capacitated Location-Routing Problem With Fuzzy Demands

In this paper, the capacitated location-routing problem with fuzzy demands (CLRP-FD) is considered, which simultaneously solves two problems: locating the facilities and designing the vehicle routes among the established facilities and customers. In the CLRP-FD, the capacities of the employed vehicles and established facilities cannot exceed, and the demands of the customers are assumed to be triangular fuzzy variables. To model the CLRP-FD, a fuzzy chance constrained programming approach is designed using fuzzy credibility theory. To solve this problem, a hybrid particle swarm optimization (HPSO) algorithm, which includes a stochastic simulation and a local search strategy based on the variable neighborhood search algorithm, is proposed. Finally, the influence of the value of the dispatcher preference index ( DPI ) on the total distribution cost is analyzed by conducting numerical experiments. To evaluate the efficiency of the proposed HPSO and the performance of the CLRP-FD model, the results obtained using the HPSO were compared with their corresponding lower bound provided using the CPLEX solver. Moreover, we also evaluated the performance of HPSO through computational experiments on some well-known benchmark CLRP instances. The numerical results show that the proposed HPSO is competitive, and can give a satisfactory solution in a reasonable amount of time.

DESIGNING A LOGISTIC NETWORK FOR HOSPITAL WASTE MANAGEMENT: A BENDERS DECOMPOSITION ALGORITHM

Healthcare wastes are produced from all medical and therapeutic activities in hospitals and healthcare centres. Around 15-20% of these wastes are classified as infectious wastes that could be hazardous. Therefore, an effective approach is required for handling costs and environmental issues. In this paper, a bi-objective Mixed-Integer Linear Programming (MILP) model is presented for logistics of infectious and non-infectious wastes. The proposed bi-objective model aims to minimize network costs and the risk of exposure to contamination. In this respect, a multi-stage network consisting of hospitals, recycling centres, treatment centres, disposal centres, mainly covering the location-routing problem, is considered. To deal with computational complexity of the proposed model, a Benders Decomposition Algorithm (BDA) has been employed. The researchers were faced with two important questions: (1) whether the proposed model can be applied to real-world scenarios or not, and (2) how efficient is the proposed algorithm in solving standard test problems and real-world cases. To answer these questions, the outputs of the BDA have been compared with the optimal solutions provided by the CPLEX software. The results imply that the BDA has been able to achieve optimal solutions in less computation times. Moreover, the proposed model and algorithm have been applied to a real-world study in Alborz Province of Iran. The outputs demonstrate that the proposed model and algorithm can yield applicable solutions for the case study which have been approved by experts. The proposed model can be extended by considering compatibility of wastes in storage.

A novel approach based on heuristics and a neural network to solve a capacitated location routing problem

In this work, we describe a method to solve the capacitated location-routing problem (CLRP) to minimize the delivery distance for a vehicle. The CLRP consists of locating depots, assigning each customer to one depot, and determining routes. The objective is to minimize the cost (distance). In the locating problem, we use a self-organizing map (SOM) to determine the depots and assign customers to depots. The SOM is an unsupervised learning method with two layers and has proven effective in several research areas, such as clustering. In the routing problem, we use the Clarke and Wright technique to determine routes. In the present work, we propose an improvement of the capacitated self-organizing map (CSOM) to optimize the location of depots and the Or-Opt algorithm to ameliorate the routes obtained by Clarke and Write (CSOM&CW). The numerical results show that the proposed method can meet many benchmarks of small and medium instances. Computational results assess the higher performance of our approach and demonstrate its efficiency in solving large-size instances.

Bi-objective optimization approaches to many-to-many hub location routing with distance balancing and hard time window

This study addresses a many-to-many hub location-routing problem where the best-found locations of hubs and the best-found tours for each hub are determined with simultaneous pickup and delivery within the hard time window. To find practical solutions, the hubs and transportation fleet have constrained capacity, in which every node can be serviced by multiple allocations with the hard time window and limited tour length. First, a bi-objective optimization model is proposed to balance travel costs among different routes and to minimize the total sum of fixed costs of locating hubs, the costs of handling, traveling, assigning, and transportation costs. The problem is then solved using an augmented e-constraint technique for small to medium size instances of the problem. Due to the NP-hardness nature of the problem, the proposed multi-objective optimization model is solved by a multi-objective imperialist competitive algorithm (MOICA). To show the superior performance of the MOICA, the solutions are compared with those obtained by the non-dominated sorting genetic algorithm (NSGA-II). For the large-scale problem instances, the comparative results indicate that the MOICA can indeed provide better Pareto optimal solutions compared to NSGA-II for the large-scale problem instances.

The location routing problem using electric vehicles with constrained distance

The introduction of Electric Vehicles (EVs) in modern fleets facilitates a shift towards greener road transportation practices. However, the driving ranges of EVs are limited by the duration of their batteries, which raises some operational challenges. This paper discusses the Location Routing Problem with a Constrained Distance (LRPCD), which is a natural extension of the Location Routing Problem when EVs are utilized. A fast multi-start heuristic and a metaheuristic are proposed to solve the LRPCD. The former combines biased-randomization techniques with the well-known Tillman’s heuristic for the Multi-Depot Vehicle Routing Problem. The latter incorporates the biased-randomized approach into the Variable Neighborhood Search (VNS) framework. A series of computational experiments show that the multi-start heuristic is able to generate good-quality solutions in just a few seconds, while the biased-rendomized VNS metaheuristic provides higher-quality solutions by employing more computational time.

Local search algorithm for solving periodic location routing problem

This study examines the problem of facility location and vehicle routes determination in supply chain system periodically. The problem is determining the location and route to meet the supply of commodity to the power plant that taken from the case of an electricity company in Indonesia. In this study, the problem is called Periodic Location Routing Problem (PLRP). Periodic Location Routing Problem is a non-polynomial hard problem (NP-hard), if locations considered is increase, the computation time used is increasing exponentially. Therefore, to solve a large-scale of this problem, a local search algorithm is proposed. Local search is a very simple metaheuristic algorithm. To explore the solution space for the problem, this algorithm will use the relocation operator. The results of computational experiments from 10 instances indicate that the results of the solution have a small standard deviation with short computing time in less than 2 hours.

Location-Routing Optimization with Split Demand for Customer Self-Pickup via Data Analysis and Heuristics Search

Customer self-pickup, offered as an option at most distribution centers, can provide flexible service times and save operational costs. Customers can either choose to self-pickup their demand or to have it delivered by a traditional way. At each customer point, the delivery demand is split, with the amount depending on the service and personal characteristics. In this situation, how to efficiently locate distribution centers and route deliveries becomes a vital problem for express companies that has not been studied in the literature. In this paper, for the first time, we propose a mathematical programming model for optimizing the location-routing problem with split demand (LRP-SD), together with a delivery ratio analysis model to predict self-pickup and delivery demand. To adapt the model to real-world cases, two heuristics as used in large-scale simulation-based optimization are devised and implemented. One is biogeography-based optimization (BBO) for solution speed, and the other is an adaptive large neighborhood search (ALNS) for solution quality. The two algorithms are compared using real data from a Shanghai-based express delivery company.

A variable neighbourhood decomposition search approach applied to a global liner shipping network using a hub-and-spoke with sub-hub structure

This paper presents a new concept for a hub-and-spoke network structure, called “sub-hub”, applied to global operations of liner shipping. Hub-and-spoke networks are widely used in transportation due to the economy of scale offered to the demands between hubs. However, efficient network structures require more than an economy of scale with regard to transport costs. This study therefore, aims to demonstrate that lower transport costs are achievable by a hub-and-spoke with sub-hub structure because the economy of scale this model provides is combined with shorter alternative paths. A short sea operation in liner shipping is a circular route at cluster level (the hub and its allocated spokes). A deep sea operation functions as a direct connection between hubs. A sub-hub is an intersection point between two regional (cluster) routes, thereby allowing the transshipment of goods, for certain demands, without using hub nodes. Hubs and sub-hubs are selected between the existing ports (nodes), and installation costs are not included for these models. A cutting plane approach was implemented. Although the computation results of the models, which are classified as hub location-routing problems, were compared on small instances, a Variable Neighbourhood Decomposition Search (VNDS) was implemented to test large instances.

An Effective Variable Neighborhood Search with Perturbation for Location-Routing Problem

Location-Routing Problem (LRP) is a challenging problem in logistics, which combines two types of decision: facility location and vehicle routing. In this paper, we focus on LRP with multiple capacitated depots and one uncapacitated vehicle per depot, which has practical applications such as mail delivery and waste collection. We propose a simple iterated variable neighborhood search with an effective perturbation strategy to solve the LRP variant. The experiments show that the algorithm is efficient and can compute better solutions than previous algorithms on tested instances.

The bi-objective periodic closed loop network design problem

Reverse supply chains are becoming a crucial part of retail supply chains given the recent reforms in the consumers’ rights and the regulations by governments. This has motivated companies around the world to adopt zero-landfill goals and move towards circular economy to retain the product’s value during its whole life cycle. However, designing an efficient closed loop supply chain is a challenging undertaking as it presents a set of unique challenges, mainly owing to the need to handle pickups and deliveries at the same time and the necessity to meet the customer requirements within a certain time limit. In this paper, we model this problem as a bi-objective periodic location routing problem with simultaneous pickup and delivery as well as time windows and examine the performance of two procedures, namely NSGA-II and NRGA, to solve it. The goal is to find the best locations for a set of depots, allocation of customers to these depots, allocation of customers to service days and the optimal routes to be taken by a set of homogeneous vehicles to minimise the total cost and to minimise the overall violation from the customers’ defined time limits. Our results show that while there is not a significant difference between the two algorithms in terms of diversity and number of solutions generated, NSGA-II outperforms NRGA when it comes to spacing and runtime.

A simheuristic algorithm for the capacitated location routing problem with stochastic demands

ABSTRACT The capacitated location routing problem (CLRP) integrates a facility location problem with a multi-depot vehicle routing problem. We consider the CLRP with stochastic demands, whose specific values are only revealed upon reaching each customer. The main goal is to minimise the expected costs of: (i) opening facilities, (ii) using a fleet of vehicles, (iii) executing a routing plan, and (iv) applying corrective actions. The latter are required whenever a route failure occurs due to unexpected high demands. We propose a simheuristic algorithm hybridizing simulation with an iterated local search metaheuristic, aimed at: (i) proposing a safety-stock policy to diminish the likelihood of route failure; and, (ii) estimating the expected cost and the reliability of each “elite” solution. We assess our approach on classical CLRP benchmarks, which are later extended to consider demand uncertainty. Finally, we also discuss the effects of the safety-stock policy on costs and reliability.

A bi-objective transportation-location arc routing problem

ABSTRACT Location and routing problems belong to well-known optimization ones, whose combinations have merged as a location-routing problem (LRP). Arc routing has recently become a popular interest of researchers. Accordingly, the location-arc routing problem (LARP) is defined. This paper deals with a location-arc routing problem when there are transportation decisions from suppliers to established depots (TLARP). It is addressed by developing a bi-objective mathematical model to optimize the total costs and makespan. An augmented ε-constraint algorithm is employed to find the true Pareto solutions. Then two meta-heuristics are considered: non-dominated sorting genetic algorithm II (NSGA-II) and multi-objective late acceptance hill-climbing (MOLAHC) algorithm. There are four heuristics regarding NSGA-II, its combination with MOLAHC, and having/not having a local search (LS). Results demonstrate that NSGA-II+LS is the best and hybrid+LS is the second best heuristics while the solving time of hybrid+LS is significantly less than the time of NSGA-II+LS.

A Sustainable Multimodal Transport System: The Two-Echelon Location-Routing Problem with Consolidation in the Euro–China Expressway

Sustainable development of transport systems is a common topic of concern and effort in multiple countries, in which reducing carbon emissions is one of the core goals. Multimodal transport is an effective way to achieve carbon emission reduction and to efficiently utilize transport resources. The intercontinental transport system, represented by the Euro–China Expressway, is a prominent exploration that has recently received attention, which promotes the sustainable development of transport between countries and carbon emission reduction. In the intercontinental multimodal transport system, the reasonable connection of roads and railways, especially the optimization of consolidation, is an important link which affects the system’s carbon emissions. This paper focuses on the consolidation of sustainable multimodal transport and summarizes the multimodal transport two-echelon location-routing problem with consolidation (MT-2E-LRP-C). We aim to solve multimodal consolidation optimization problem, especially locations of multimodal station, by routing of highway and railway. We propose a two-layer mixed integer linear problem (MILP) model, which highlights the consolidation of roads and railways, focuses on road and rail transport connections, and optimizes road routes and railway schemes. To validate the MT-2E-LRP-C model, we design a series of random instances for different quantities of nodes. In order to solve large-scale instances and realistic transport problems, we propose a hybrid differential evolution algorithm, which decomposes the problem into a railway layer and a highway layer for heuristic algorithm solving. Furthermore, the MILP model and algorithm are tested by small-scale random instances, and the hybrid differential evolution algorithm is solved for the large-scale random instances. Finally, we solve the realist instance from the Euro–China Expressway to develop instructive conclusions.

Designing a Multi-Objective Three-Stage Location-Routing Model for Humanitarian Logistic Planning under Uncertainty

Natural and technological disasters threaten human life all around the world significantly and impose many damages and losses on them. The current study introduces a multi-objective three-stage location-routing problem in designing an efficient and timely distribution plan in the response phase of a possible earthquake. This problem considers uncertainty in parameters such as demands, access to routes, time and cost of travels, and the number of available vehicles. Accordingly, a three-stage stochastic programming approach is applied to deal with the uncertainties. The objective functions of the proposed problem include minimizing the unsatisfied demands, minimizing the arriving times, and minimizing the relief operations costs. A modified algorithm of the improved version of the augmented e-constraint method, which finds Pareto-optimal solutions in less computational time, is presented to solve the proposed multi-objective mixed-integer linear programming model. To validate the model and evaluate the performance of the methods several test problems are generated and solved by them. The computational results show the satisfactory performance of the proposed methods and effectiveness of the proposed model for delivery of relief commodities in the affected areas.

Unmanned Aerial Vehicle Location Routing Problem With Charging Stations for Belt Conveyor Inspection System in the Mining Industry

Technological advances have opened up the possibility of using unmanned aerial vehicles (UAVs) in diverse environments. The mining industry has been looking for solutions to handle periodic inspections of the belt conveyors that transport iron ore. The state of the art indicates the use of UAVs for this task as an attractive, low-cost and safe alternative, allowing for a significant increase in security. A new concise mixed-integer linear programming (MILP) model is developed to address UAV routing and charging station planning for belt conveyor inspection. We conduct computational tests covering a real conveyor belt system in Brazil to validate the model in practical applications. The loading terminal possesses approximately 120 km of belt conveyors, leading to 230 inspection points. Instances of different sizes were generated by randomly sampling a subset of these points and using two different drone specifications. The results show that the new optimization modeling satisfies the problem requirements and is a significant contribution to the automation of inspection in the mining industry.

A novel hybrid genetic algorithm for the location routing problem with tight capacity constraints

Location routing problem (LRP) is a popular and challenging topic in the field of logistic systems. LRP needs to address the depot location problem and vehicle routing problem at the same time. Till now, different LRP variants have been formulated to better meet realistic requirements. In this study, we focus on the capacitated LRP (CLRP) with tight capacity constraint on both depots and vehicles. To cope with the tight constraints, a hybrid genetic algorithm (HGA) is developed to search not only feasible solution space but also infeasible solution space. The proposed HGA combines the wide exploration capacity of GA, and the fast exploitation capacity of neighbourhood local search. To evolve GA for CLRP, solutions are represented by sets and sequences, and accordingly, a multi-sequence-based crossover is designed for the offspring generation. Moreover, a population management scheme is designed to facilitate GA’s evolution. Experiments are conducted on two benchmark sets and the results show that HGA is quite competitive with existing well-known CLRP algorithms on the classical instances. Furthermore, HGA is able to obtain quite a number of new best solutions on the real-life-like instances with tighter constraints.

A two-echelon location-routing problem with synchronisation

Motivated by an actual problem of a national postal service company, we introduce and define a new two-echelon location-routing problem (2E-LRP). The 2E-LRP is defined in a two-echelon distribution system where products are transported from origins to destinations through intermediate facilities. A major question that arises in a two-echelon distribution system is how to synchronise the flows of the two echelons at intermediate facilities. The synchronisation is important due to limited storage space or waiting times for transshipments at the intermediate facilities. In our new 2E-LRP, the activities in the two echelons are organised into two waves; a delivery wave, where products are sent from the primary facility to the customers through the intermediate facilities, and a following pickup wave, where the flow of products is reversed. The model only considers temporal constraints, assuming that capacities are never binding; the vehicles are always large enough given the constraints on time. As a solution approach, we propose a decomposition-based heuristic. Besides the solution approach, we propose data-driven schemes for use in combination with the model and we provide the computational results for different sets of instances.