Capacitated Location-routing Problem Research Articles

Integrated strategic and tactical design of multi-echelon city distribution systems with vehicles synchronization: A case of the Greater Montréal area

The sharp increase in e-commerce volume drives the explosive demand growth for urban parcel delivery. Consequently, more and more logistics service providers (LSP) are moving toward establishing more distribution centres in customers' vicinity within metropolitan areas to ensure fast deliveries to online shoppers and reduce costs. Such LSP seeks to optimize the design of their multi-echelon distribution systems by finding the best satellite locations and vehicle routing solutions. However, since satellites have limited parking and no storage spaces, synchronizing the vehicles' arrival times at these facilities and minimizing their waiting times to be loaded/unloaded are essential in designing multi-echelon distribution systems. This study proposes a new Two Echelons Location Routing problem (2E-LRP) model that incorporates vehicles' temporal synchronization at satellites through minimization and setting of a maximum duration to the second echelon vehicle's waiting times, which had not until now been dealt with in 2E-LRP literature. The 2E-LRP new extension is called Two-Echelon Capacitated Location Routing Problem with Vehicles Synchronization (2E-CLRPVS), and the Binary Variable Fixing (BVF) method is proposed to solve it. To assess the validity and applicability of the 2E-CLRPVS model and the efficiency and robustness of the proposed solving method, we conducted computational experiments for a network with up to 99 customers and 5 five satellites based on data from the Great Montreal area in Canada. We also conducted an extensive sensitivity analysis of some critical parameters of the problem to provide some interesting managerial insights regarding multi-echelon urban distribution network design decision-making.

A conceptually simple algorithm for the capacitated location-routing problem

Location-routing problems (LRPs) jointly optimize the location of depots and the routing of vehicles. The most studied LRP variant, the capacitated LRP (CLRP), has been addressed by a large number of metaheuristic approaches. These methods often decompose the problem into a location stage to determine a promising depot configuration and a routing stage, in which a vehicle-routing problem is solved to assess the quality of the previously determined depot configuration. Unfortunately, the CLRP literature does not shed much light on the important question which algorithmic features have the biggest influence on the solution quality and runtime of such heuristics. The purpose of this paper is to propose a conceptually simple (yet reasonably effective) heuristic for the CLRP and to provide some insights on the design of successful metaheuristics for this problem. Our algorithm is a hybrid combining (i) a GRASP phase that uses a variable neighborhood descent for local improvement in the location stage, and (ii) a variable neighborhood search in the routing stage. We analyze the impact of the algorithmic components on solution quality and runtime. In addition, we find that the suboptimal routing solutions used to assess the quality of the investigated depot configurations in tendency lead to depot configurations with too many open depots. We propose a depot configuration refinement phase that alleviates this drawback, and we show that this algorithmic component significantly contributes to the solution quality of our method, enabling it to provide reasonable results in comparison to the state-of-the-art methods from the literature.

Development of a robust multi-objective model for green capacitated location-routing under crisis conditions

Location-Routing Problem (LRP) is a strategic supply chain design problem aimed at meeting customer demands. LRPs involve selecting one or more depot sites from a set of potential locations and determining the best routes to connect them to demand points. With the rising awareness about the environmental impacts of transportation over the past years, the use of green logistics to mitigate these impacts has become increasingly important. To compensate for a gap in the literature, this paper presents a robust bi-objective mixed-integer linear programming (MILP) model for the green capacitated location-routing problem (G-CLRP) with demand uncertainty and the possibility of failure in depots and routes. The final result of this Robust Multi-Objective Model is to set up the depots and select the routes that offer the highest reliability (Maximizing network service) while imposing the lowest cost and environmental pollution. A Nondominated Sorting Genetic Algorithm (NSGA-II) is used to solve the large-sized instances of the modeled problem. The paper also provides a numerical analysis and a sensitivity analysis of the solutions of the model.

The two-echelon stochastic multi-period capacitated location-routing problem

Given the emergence of two-echelon distribution systems in several practical contexts, this paper tackles, at the strategic level, a distribution network design problem under uncertainty. This problem is defined as the two-echelon stochastic multi-period capacitated location-routing problem (2E-SM-CLRP). It considers a network partitioned into two capacitated distribution echelons: each echelon involves a specific location-assignment-transportation schema that must cope with the future demand. It aims to decide the number and location of warehousing/storage platforms (WPs) and distribution/fulfillment platforms (DPs), and on the capacity allocated from first echelon to second echelon platforms. In the second echelon, the goal is to construct vehicle routes that visit ship-to locations (SLs) from operating distribution platforms under a stochastic and time-varying demand and varying costs. This problem is modeled as a two-stage stochastic program with integer recourse, where the first-stage includes location and capacity decisions to be fixed at each period over the planning horizon, while routing decisions of the second echelon are determined in the recourse problem. We propose a logic-based Benders decomposition approach to solve this model. In the proposed approach, the location and capacity decisions are taken by solving the Benders master problem. After these first-stage decisions are fixed, the resulting sub-problem is a capacitated vehicle-routing problem with capacitated multiple depots (CVRP-CMD) that is solved by a branch-cut-and-price algorithm. Computational experiments show that instances of realistic size can be solved optimally within a reasonable time and provide relevant managerial insights on the impact of the stochastic and multi-period settings on the 2E-CLRP.

Multi-depot green capacitated location routing problem considering uncertainty and in-facility queuing

Nowadays, designing a framework for an environmentally-friendly waste collection network is of higher importance due to population growth. This study presents a multi-depot green capacitated location routing problem (MGCLRP) considering the time window and in-facility queuing under uncertainty. A scenario-based robust optimization is employed to deal with demand and travelling time uncertainties. Moreover, the M/M/c queuing system calculates the expected total wait time at a recycling center. As a solution method, we develop an algorithm to find the optimal number of potential locations and use this optimal number to find the main objectives of the problem. Then, two versions of NSGA-III, enhanced by greedy initializations, are proposed to solve the large-scale instances. The obtained results show the superiority of the proposed NSGA-III over the simple version of this algorithm. Finally, we investigate the applicability of the given model in a practical case study for Tehran. • Designing a Green Capacitated Location Routing Problem Considering Uncertainty and In-Facility Queuing. • Applying a scenario-based robust optimization method to manage the uncertainty. • Proposing two hybrid metaheuristic algorithms to efficiently solve the problem.

The sorted-waste capacitated location routing problem with queuing time: A cross-entropy and simulated-annealing-based hyper-heuristic algorithm

Waste sorting is an imperative and significant issue in China, of which sorted-waste collection and transportation are indispensable parts. Despite its vital yet practical significance, few studies research mathematical models or algorithms of waste collection and transportation from the perspective of waste sorting. To address this issue, we extend a novel transportation model for the waste management system, namely, capacitated location routing problem with queuing time (CLRPQT) and design a cross-entropy and simulated-annealing based hyper-heuristic algorithm (CE-SAHH) for it. The main idea of this paper is three-fold: (1) As a particular property of this problem, source nodes cannot but need to be served by more than one vehicle that causes queuing time between a heterogeneous fleet of vehicles, which is novel in terms of the proposed model; (2) For the methodological contribution, a character encoding scheme, new decoding procedure, and local search strategy are designed embedded in the proposed method; (3) An integration of simulated annealing strategy and the cross-entropy-based hyper-heuristic algorithm is developed to overcome the combinatorial optimization problem with a more complex solution of this study. Finally, the results and analysis of three numeric experiments on benchmark datasets, new instances of CLRPQT, and simulation data in Shanghai, China, verify the effectiveness and universality of the proposed model and method.

Multi-objective sustainable capacitated location routing problem formulation in sustainable supply-chain management

Conflicting sustainability dimensions are considered in a multi-objective formulation, focusing on the capacitated location routing problem (CLRP). The proposed sustainable version (S-CLRP) addresses the location of facilities, the routing of vehicles, the balance of the working load among drivers, and the environmental impact of operations due to the emission of greenhouse gases. In this work, both a mixed integer linear programming model solved using the goal attainment method and an approximated method based on iterated local search (ILS) and decomposition (ILS/D) are proposed. The results show the generation of non-dominated fronts with adequate dispersion and convergence characteristics with which supply-chain decision-makers can evaluate the impact of their decisions on the financial, environmental and social dimensions of their operations.

Heuristic algorithm based on Ant Colony Optimization for the Capacitated Location-Routing problem with Homogeneous Fleet

This paper considers the Capacitated Location-Routing Problem with Homogeneous Fleet (CLRP). The objective is to minimize the sum of the open depots' costs, the costs for the used vehicles, and the costs associated with the distances traveled. A metaheuristic algorithm of two phases for the CLRP is proposed. In the first phase, customers establish the clusters to be subsequently heuristically assigned to the depots. In the second phase, the initial routes are improved using an algorithm based on Ant Colony. The obtained results show the efficiency of the proposed approach.

A multiobjective model for the green capacitated location-routing problem considering drivers' satisfaction and time window with uncertain demand.

Location-routing problem is a combination of facility location problem and vehicle routing problem. Numerous logistics problems have been extended to investigate greenhouse issues and costs related to the environmental impact of transportation activities. The green capacitated locating-routing problem (LRP) seeks to find the best places to establish facilities and simultaneously design routes to satisfy customers' stochastic demand with minimum total operating costs and total emitted carbon dioxide. In this paper, features that make the problem more practical are: considering time windows for customers and drivers, assuming city traffic congestion to calculate travel time along the edges, and dealing with capacitated warehouses and vehicles. The main novelty of this study is to combine the mentioned features and consider the problem closer to the real-world case uses. A mixed-integer programming model has been developed and scenario production method is used to solve this stochastic model. Since the problem belongs to the class of NP-hard problems, a combination of the progressive hedging algorithm (PHA) and genetic algorithm (GA) is considered to solve large-scale problems. It is the first time, as per our knowledge, that this combination is implemented on a green capacitated location routing problem (G-CLPR) and resulted in satisfactory solutions. Nondominating sorting genetic algorithm II (NSGA-II) and epsilon constraints methods are used to face with the bi-objective problem. Finally, sensitivity analysis is performed on the problem's input parameters and the efficiency of the proposed method is measured. Comparing the results of the proposed solution approach with those of the exact method indicates that the solution approach is computationally efficient in finding promising solutions.

An Augmented Variable Neighborhood Search to Solve the Capacitated Location-Routing Problem

In this paper we proposed a new variable neighborhood search (VNS) for solving the location- routing problem with considering capacitated depots and vehicles. A set of capacitated vehicles, a set of depots with restricted capacities, and associated opening costs, and a set of customers with deterministic demands are given. The problem aims to determine the depots to be opened, fleet assignment to each depot, and the routes to be performed to satisfy the demand of the customers. The objective is to minimize the total costs of the open depots, the setup cost associated with the used vehicles, and transportation cost. We proposed a new VNS which is augmented with a probabilistic acceptance criterion as well as a set of efficient local searches. The computational results implemented on four well-known data sets demonstrate that the proposed algorithm is competitive with other well- known algorithms while reaching many best-known solutions and updating six best new results with reasonable computational time. Conclusions and future research avenues close the paper.

An Augmented Variable Neighborhood Search to Solve the Capacitated Location-Routing Problem

In this paper we proposed a new variable neighborhood search (VNS) for solving the location- routing problem with considering capacitated depots and vehicles. A set of capacitated vehicles, a set of depots with restricted capacities, and associated opening costs, and a set of customers with deterministic demands are given. The problem aims to determine the depots to be opened, fleet assignment to each depot, and the routes to be performed to satisfy the demand of the customers. The objective is to minimize the total costs of the open depots, the setup cost associated with the used vehicles, and transportation cost. We proposed a new VNS which is augmented with a probabilistic acceptance criterion as well as a set of efficient local searches. The computational results implemented on four well-known data sets demonstrate that the proposed algorithm is competitive with other well- known algorithms while reaching many best-known solutions and updating six best new results with reasonable computational time. Conclusions and future research avenues close the paper.

Incorporating fuel delivery in network design for hydrogen fueling stations: Formulation and two metaheuristic approaches

This study extends the fueling station location problem to consider interdependencies with fuel delivery. Specifically, we present a new variant of the bi-objective capacitated location routing problem (bi-objective CLRP), flow capturing location problem with fuel delivery (FCLP-FD), to simultaneously determine the location of hydrogen fueling stations (HFSs) and routing decisions for hydrogen delivery trucks. The FCLP-FD is proposed to overcome barriers to the deployment of HFSs. The HFS network is determined while maximizing the fueling demand flow captured and minimizing the total daily cost. The metaheuristic algorithm of adaptive large neighborhood search (ALNS) was developed, and its performance on solving bi-objective optimization problems was tested and compared with the genetic algorithm (GA). The developed model and algorithms were applied to a case study in Bourgogne-Franche-Comté, France. Results show that the model improved the understanding of decision-makers about various components within the HFS network and provides useful managerial insights regarding the role of fleet composition and physical forms of hydrogen. In terms of algorithm performance, the GA was faster than ALNS for all the tested instances; however, ALNS is characterized by a better average gap, which is the differences between the obtained Pareto front (generated by ALNS) and the optimal one (generated using IBM ILOG CPLEX Optimization Studio).

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.

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.

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.

Solving the multi-level location routing problem considering the environmental impact using a hybrid metaheuristic

The multi-level location routing problem (MLLRP) is an extension of the capacitated location routing problem (CLRP). MLLRPs are considered a class of combinatorial optimization problems that arise in transportation applications, such as agricultural logistic planning. Along with concerns regarding the environmental harmfulness, recent studies have considered “green” logistics. This paper addressed a low environmental impact model for MLLRP by considering characteristics, emissions, and traffic congestion that have not appeared in the recent literature. The mathematical model was formulated to deal with a reverse flow problem, which was a real case that occurs in Thailand agriculture. We developed a hybrid metaheuristic algorithm to solve the MLLRP by integrating a variable neighborhood search (VNS) with an adaptive large neighborhood search (ALNS). The experimental results shown that the hybrid algorithm had clear advantages in the time consumption and quality of the solution. The extended study indicated that the proposed algorithm obtained competitive results compared with the previously published methods. The proposed practice is useful not only for the agricultural industry but also for other industries.

A hybrid adaptive large neighbourhood search algorithm for the capacitated location routing problem

This paper proposes a new hybrid metaheuristic algorithm that is composed of the adaptive large neighbourhood search (ALNS) and the variable neighbourhood search (VNS) algorithms to tackle the location routing problem (LRP) with capacity constraints. The rationale of the proposed hybrid metaheuristic algorithm is to enhance the performance of the ALNS algorithm by incorporating the VNS algorithm as an elitist local search. Therefore, the diversification and intensification strategies of the proposed hybrid metaheuristic algorithm are realized via the ALNS and VNS algorithms, respectively. The performance evaluation tests of the proposed hybrid metaheuristic algorithm are performed on the three classical LRP benchmark sets taken from the related literature, and the obtained results are compared against some of the formerly proposed and published methods in terms of solution quality. Computational results indicate that the proposed hybrid metaheuristic algorithm has a satisfactory performance in solving the LRP instances and is a competitive algorithm.

Designing multi-tier, multi-service-level, and multi-modal last-mile distribution networks for omni-channel operations

The fast and dynamic evolution of e-retailing is driving structural changes in the way companies are reaching the urban consumer. Companies are offering faster delivery services, deploying collection-and-delivery points and multi-echelon distribution networks with a range of facility types, diversifying last-mile transportation modes with new types of vehicles and contracting third-party and crowd-sourcing-based transportation. In this paper, we propose an integrated modeling framework for strategic last-mile design of three-tiered multi-modal networks in omni-channel environment, with customer demand differentiated according to multiple time-differentiated delivery services and multiple product-exchange alternatives. In order to apply this framework in a large-scale demand setting and capture the granularity of customer demand and distribution network features, we extend the route cost estimation formulae from the literature and incorporate them in a three-echelon capacitated location-routing problem that optimizes the configuration of distribution networks in an integrated way. Through a number of numerical experiments, we show the impact of the diversified customer demand and the novel distribution network features on the overall network performance and demonstrate the economic benefit of an integrated approach. A real-world case study, inspired by the ongoing operations of a major omni-channel retailer in São Paulo, Brazil, serves to illustrate the real-world impact of our work.

Variable neighborhood strategy adaptive search for solving green 2-echelon location routing problem

This paper presents the green 2-echelon location routing problem (G2ELRP) which is a variant of the capacitated location-routing problem (CLRP) and the 2-echelon location routing problem (2ELRP), in that it deals with the collection problem for which routing decisions at both levels are required. The G2ELRP aims to minimize the total fuel consumption depending on the distance and the road conditions in both echelons. In the G2ELRP, that a customer can be served more than once is considered as a new constraint. Due to its complexity, the G2ELRP requires a complex problem formulation. A new variable neighborhood strategy adaptive search (VaNSAS) algorithm as a solution approach is introduced to solve the problem. The computational results indicate that the VaNSAS algorithm efficiently solves the case study problem and outperforms all other proposed heuristics. The G2ELRP model saved fuel cost by 3.71% over the traditional LRP. This demonstrates that the proposed VaNSAS is very efficient and not only useful for decreasing costs of rubber logistics, but also for application to other related agro-industries.

Evolutionary Hyperheuristics for Location-Routing Problem with Simultaneous Pickup and Delivery

This paper presents an evolution-based hyperheuristic (EHH) for addressing the capacitated location-routing problem (CLRP) and one of its more practicable variants, namely, CLRP with simultaneous pickup and delivery (CLRPSPD), which are significant and NP-hard model in the complex logistics system. The proposed approaches manage a pool of low-level heuristics (LLH), implementing a set of simple, cheap, and knowledge-poor operators such as “shift” and “swap” to guide the search. Quantum (QS), ant (AS), and particle-inspired (PS) high-level learning strategies (HLH) are developed as evolutionary selection strategies (ESs) to improve the performance of the hyperheuristic framework. Meanwhile, random permutation (RP), tabu search (TS), and fitness rate rank-based multiarmed bandit (FRR-MAB) are also introduced as baselines for comparisons. We evaluated pairings of nine different selection strategies and four acceptance mechanisms and monitored the performance of the first four outstanding pairs in 36 pairs by solving three sets of benchmark instances from the literature. Experimental results show that the proposed approaches outperform most fine-tuned bespoke state-of-the-art approaches in the literature, and PS-AM and AS-AM perform better when compared to the rest of the pairs in terms of obtaining a good trade-off of solution quality and computing time.