Hub Location Problem Research Articles

Hub Network Design Problem with Capacity, Congestion, and Stochastic Demand Considerations

Our study introduces the hub network design problem with congestion, capacity, and stochastic demand considerations (HNDC), which generalizes the classical hub location problem in several directions. In particular, we extend state-of-the-art by integrating capacity acquisition decisions and congestion cost effect into the problem and allowing dynamic routing for origin-destination (OD) pairs. Connecting strategic and operational level decisions, HNDC jointly decides hub locations and capacity acquisitions by considering the expected routing and congestion costs. A path-based mixed-integer second-order cone programming (SOCP) formulation of the HNDC is proposed. We exploit SOCP duality results and propose an exact algorithm based on Benders decomposition and column generation to solve this challenging problem. We use a specific characterization of the capacity-feasible solutions to speed up the solution procedure and develop an efficient branch-and-cut algorithm to solve the master problem. We conduct extensive computational experiments to test the proposed approach’s performance and derive managerial insights based on realistic problem instances adapted from the literature. In particular, we found that including hub congestion costs, accounting for the uncertainty in demand, and whether the underlying network is complete or incomplete have a significant impact on hub network design and the resulting performance of the system. Funding: This work was supported by Türkiye Bilimsel ve Teknolojik Araştırma Kurumu [Grant 218M520]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2022.0112 .

A Hybridization Approach to Solve the Capacitated Asymmetric Allocation Hub Location Problem

This paper deals with a capacitated asymmetric allocation hub location problem (CAAHLP). We determine the number of hubs, the locations of hubs, and asymmetric allocation of non-hub nodes to hub with the objective of minimum total transportation costs satisfying the required service level. To solve the problem optimally, we present a 0-1 integer programming model and find an optimal solution using CPLEX. As the CAAHLP has impractically demanding for the large-sized problem, a solution method based on combined ant colony optimization algorithm and genetic algorithm is developed which solve hub location problem and node allocation problem respectively. We investigate performance of the proposed solution method through the comparative study. Key Words: Hub Location, Asymmetric Allocation, Ant Colony Optimization, Genetic Algorithm

A robust optimization model for dynamic virtual hub location problem under uncertainty using an M/M/C/K queuing model: two metaheuristic algorithms

A robust optimization model for dynamic virtual hub location problem under uncertainty using an M/M/C/K queuing model: two metaheuristic algorithms

Machine learning augmented approaches for hub location problems

Hub location problems are widely analyzed in fields of logistic and transportation industry for cost reduction. In this paper, a novel algorithm framework based on machine learning is proposed to improve solution quality of hub location problems for large-scale instances. First, a deep-learning based probabilistic hub-ranker (DLHr) is developed to determine the priority of nodes to be selected as hubs. Next, two node-ranking based approaches DL-CBS and DL-GVNS are developed to augment the DLHr for single allocation hub location problems. DL-CBS is an augment algorithm embedding DLHr-ranking into clustering-based potential hub sets algorithm (CBS) while DL-GVNS embeds DLHr-ranking into general variable neighborhood search (GVNS). The numerical results evidence that DLHr outperforms baselines on the node-ranking task and helps to identify potential hubs. Evaluation on a wide range of experiments shows that DL-CBS and DL-GVNS improve solution quality of single allocation hub location problems compared with vanilla CBS and GVNS, revealing DLHr ranking helps to boost the performance of traditional heuristics.

Modeling and Solving a Linear Integer Problem (PLNE) for the Optimal Localization of a Hub Air Transport in the WAEMU Zone

In this article, we propose a linear integer model for the optimal location of a hub for air traffic in the WAEMU zone. A hub represents for an airline a base where an essential part of its activities is concentrated. Its location must therefore be judiciously determined. The hub location problem is one of the new and promising areas of research in the field of location theory. In order to satisfy a demand, the location of the hub involves the movement of people, goods between origin destination pairs required. Hubs are applied to reduce the number of transport links between the origin and destination airports The proposed model minimizes the distances and takes into account the flow of passengers registered in the different airports and minimizes the total cost of the transfer via the hub airport. The simulations were made with the programming language Python.

The synchronized multi-commodity multi-service Transshipment-Hub Location Problem with cyclic schedules

The synchronized multi-commodity multi-service Transshipment-Hub Location Problem is a hub location problem variant faced by a logistics service provider operating in the context of synchromodal logistics. The provider must decide where and when to locate transshipment facilities in order to manage many customers’ origin–destination shipments with release and due dates while minimizing a total cost given by location costs, transportation costs, and penalties related to unmet time constraints. The considered synchromodal network involves different transportation modes (e.g., truck, rail, river and sea navigation) to perform long-haul shipments and the freight synchronization at facilities for transshipment operations. To the best of our knowledge, this variant has never been studied before. Considering a time horizon in which both transportation services and demand follow a cyclic pattern, we propose a time–space network representation of the problem and an ad-hoc embedding of the time-dependent parameters into the network topology and the arcs’ weight. This allows to model the flow synchronization required by the problem through a Mixed-Integer Linear Programming formulation with a simplified structure, similar to well-known hub location problems and avoiding complicating constraints for managing the time dimension. Through an extensive experimental campaign conducted over a large set of realistic instances, we present a computational and an economic analysis. In particular, we want to assess the potential benefits of implementing synchromodal logistics operations into long-haul supply-chains managed by large service providers. Since flexibility is one of the main features of synchromodality, we evaluate the impact on decisions and costs of different levels of flexibility regarding terminals’ operations and customers’ requirements.

An efficient model for the multiple allocation hub maximal covering problem

The hub location problem is one of the challenging subjects in location theory. This problem can benefit transportation, telecommunication or delivery systems, in which hub nodes are responsible for receiving, collecting and delivering commodities. This paper discusses the multiple allocation hub maximal covering problem (MAHMCP). In this problem, the flow of an origin–destination pair is transferred via multiple hubs such that the total flow covered by located hubs is maximized. We present a new model for the MAHMCP, which has a significantly smaller number of binary variables compared to previous models. The proposed model is theoretically stronger than past models, and an empirical study using the Australia Post (AP) dataset demonstrates its effectiveness. Our experiments show that the new formulation provides high-quality solutions and fast run times for instances up to 100 nodes.

Hub Location with Protection Under Interhub Link Failures

This paper introduces the hub location problem under interhub link failures, a hub location problem in which activated interhub links may fail with a given probability. Two different optimization models are studied, which construct hub backbone networks protected under interhub link disruptions by imposing that, for each commodity, an additional routing path exists besides its original routing path. Both models consider the minimization of the fixed costs of the activated hubs and interhub links plus the expected value of the routing costs of the original and alternative paths. The first model builds explicitly the alternative routing paths, whereas the second model guarantees that, for each commodity, at least one alternative path exists using a large set of connectivity constraints although the alternative paths are not built explicitly. The results of extensive computational testing allow us to analyze the performance of the two proposed models and to evaluate the extra cost required to design a robust backbone network under interhub link failures. The obtained results support the validity of the proposal. History: Accepted by David Alderson, Area Editor for Network Optimization: Algorithms & Application. Funding: The authors of this research acknowledge financial support by the Spanish Ministerio de Ciencia y Tecnología, Agencia Estatal de Investigación and Fondos Europeos de Desarrollo Regional (FEDER) via projects PID2020-114594GB-C21 and MTM2019-105824GB-I00. The authors also acknowledge partial support from projects FEDER-US-1256951, Junta de Andalucía P18-FR-422, P18-FR-2369, B-FQM-322-UGR20 (COXMOS), and NetmeetData: Ayudas Fundación BBVA a equipos de investigación científica 2019. The first author was partially supported by the IMAG-Maria de Maeztu grant [CEX2020-001105-M/AEI/10.13039/501100011033] and UE-NextGenerationEU (ayudas de movilidad para la recualificación del profesorado universitario). Supplemental Material: The online supplement is available at https://doi.org/10.1287/ijoc.2023.1296 .

ILS-based algorithms for the profit maximizing uncapacitated hub network design problem with multiple allocation

This study addresses a hub network design problem to maximize net profit. This problem considers an incomplete hub network with multiple allocation that does not impose capacity constraints, does not allow direct connections between non-hub nodes, and accepts the demand to be partially met, being satisfied only when profitable. To tackle this problem, which is NP-hard, we propose two heuristic algorithms based on the Iterated Local Search (ILS) metaheuristic, a standard ILS algorithm, and an Enhanced ILS algorithm, which increases the perturbation level only after a few unsuccessful attempts at improvement. Both algorithms use Random Variable Neighborhood Descent in the local search. Computational experiments were performed using benchmark instances for hub location problems, and statistical analyzes of the algorithms were presented. Numerical results confirm that both algorithms yield good-quality solutions with an acceptable runtime. In particular, the proposed algorithms obtain the optimal solution for most instances with up to 150 nodes, which have known optimal solutions. Furthermore, the proposed algorithms were able to handle instances with up to 500 nodes.

Multimodal Public Transit Network Design Method Based on Hub-and-Spoke Infrastructure

This paper presents a two-phase method for generating a hub-and-spoke network for a multimodal public transit network (MPTN). The first phase addresses the problem of clustering in MPTNs, which is a key operation in solving the hub location problem (HLP) in MPTN design. However, previous work often oversimplifies or neglects the clustering phase, so this study presents a spatial clustering algorithm that can process real urban MPTNs without reducing their size or dividing them into zones. The algorithm is tested on four large city datasets and compared with popular spatial clustering algorithms. In the second phase, a heuristic algorithm is presented that aims to maximize network coverage. The proposed method is tested using the MPTN of Greater London and the resulting hub-and-spoke network is compared with the Journey API provided by Transport for London. The results show that the total travel time is improved by 16.9% with a strict hubbing policy. Transportation planners can adapt the proposed method to their specific needs by changing the size and number of clusters using the cluster scaling factor ([Formula: see text]) parameter and including or excluding any criteria in the decision equations.

A GPU-Based Genetic Algorithm for the Multiple Allocation P-Hub Median Problem

As the sizes of realistic hub location problems increase as time goes on (reaching thousands of nodes currently) this makes such problems difficult to solve in a reasonable time using conventional computers. This study aims to show that such problems may be solved in a short computing time and with high-quality solutions using the computational power of the GPU (actually available in most personal computers). So, we present a GPU-based approach for the uncapacitated multiple allocations p-hub median problems. Our method identifies the nodes that are likely to be hubs in the optimal solution and improves them via a parallel genetic algorithm. The obtained GPU implementation reached within seconds the optimal or the best solutions for all the known benchmarks we had access to and solved larger instances up to 6000 nodes so far unsolved. Compared to this study, no other article dealing with hub location problems has presented results for instances as large.

Domestic flight network hub location problem under traffic disruption with sustainability provision

There are many models in the current literature used extensively for the last 20 years on hub location problems and collect-distributive network structures. A centrally hub located facility serves as the main distribution base and flows from other facilities are collected in this hub then distributed. This centralization approach and expansion of the operational network brings the advantage of economies of scale in these days. According to the airline companies, the flight network in form of a distributor increases the profit of airline companies and provides significant savings in costs. In this study, a new hub location problem as homogeneous multi allocation p-hub median problem is proposed and solved considering the effects of airplane types and characteristics on hub locations were investigated. The results showed that the constraints and parameters used in the developed model have a significant effect on hub site selection and assignment to the different flight routes of low-cost airline companies.

Multi-modal and multi-product hierarchical hub location problem with fuzzy demands

The hub location is a major problem in the systems with high dependence on the transportation of goods, information, and passengers between the constituent parts. The present study is aimed to introduce a multi-commodity multi-model hierarchical hub location problem with uncertain demand. Thus, it is estimated by intuitionistic fuzzy variables. The objective function in the present problem is to minimize the total transportation costs in the network to determine the optimal hub location, allocate non-hub nodes to the hubs and the ground hubs to the air hubs, and identify the type of vehicles required in each route. The model has a hierarchical structure consisting of a three-echelon network (i.e., central hubs, non-central hubs, and demand nodes) connected in the star-tour-star form. A four-index mathematical model was presented and solved by GAMS optimization software. The results indicated that the objective function (cost) has a descending trend with increasing the number of hubs which can be assigned to the decline in the transportation costs. The costs increased by a decrease in the maximum delivery time which could be due to the selection method of the transportation mode. In the multi-product case, the costs declined by increasing the number of hubs as these hubs decremented the network complexity. Regarding the NP-Hard nature of the hub problems, a genetic meta-heuristic algorithm was proposed in the MATLAB software to solve the large-scale problem. According to the results, this algorithm offered close-optimal solutions. Noteworthy, this study employed known AP datasets.

Reliable Liner Shipping Hub Location Problem Considering Hub Failure

Hub ports play an important role in reducing the number of container routes and saving the operating costs of liner companies. However, hub failures caused by uncertainties such as natural disasters may cause huge recovery costs. Considering the accidental failure probability of hub ports and the reallocation of feeder ports, a global reliable liner shipping hub location problem (RLSHLP) is studied. We use the k-means algorithm to divide the global shipping network into different communities and propose two mixed integer linear programs to determine the hub port of each community. Then Benders decomposition algorithm is applied to the global RLSHLP and compared with our method. Numerical experiments verify the effectiveness of our method and determine the optimal hub port location scheme considering hub failure.

A new formulation and branch-and-cut method for single-allocation hub location problems

A new compact formulation for uncapacitated single-allocation hub location problems with fewer variables than the previous Integer Linear Programming formulations in the literature is introduced. Our formulation works even with costs not based on distances and not satisfying triangle inequality. Moreover, costs can be given in aggregated or disaggregated way. Different families of valid inequalities that strengthen the formulation are developed and a branch-and-cut algorithm based on a relaxed version of the formulation is designed, whose restrictions are inserted in a cut generation procedure together with two sets of valid inequalities. The performance of the proposed methodology is tested on well-known hub location data sets and compared to the most recent and efficient exact algorithms for single-allocation hub location problems. Extensive computational results prove the efficiency of our methodology, that solves large-scale instances in very competitive times.

Adaptive distributionally robust hub location and routing problem with a third-party logistics strategy

In this paper, we study an essential and more realistic variant of the hub location-routing problem in which third-party logistics (3PL) are incorporated into a self-built distribution hub network. A two-stage mixed-integer programming model is developed to address the proposed hub location-routing problem with mixed logistical strategies. In the strategic stage, the hub location and allocation decisions are made before the realization of uncertain demands to minimize the total construction and transportation costs. In the operational stage, the managers make vehicle routing decisions with and without the 3PL strategy, and route planning is considered for multiple owned and 3PL vehicles on the basis of simultaneous pickup and delivery. We investigate the effects of uncertain factors on the network design of this framework, as the node demands are often unobservable or difficult to obtain accurately in practice. To address the inherent uncertainty of the problem, we propose an adaptive distributionally robust model by limiting uncertain demands to a specified ambiguity set. Moreover, we reformulate the proposed model into tractable robust counterpart forms under the ambiguity set with information about the support, mean and upper bounds on the dispersion. We design a genetic algorithm with local search to solve the reformulated model on a large scale. Finally, we conduct a case study for a leading retail enterprise in the Beijing–Tianjin–Hebei region to demonstrate the effectiveness and applicability of our model.

Surrogate-based optimization approach for capacitated hub location problem with uncertainty

CJ Logistics has started to consider opening single new hub facility to expand the current transportation network system. This naturally leads to formulating a research question “where should the new hub facility be located in South Korea to minimize total transportation cost of the network system operated by the company?”. This research aims to answer the question by proposing a surrogate-based optimization approach. In addition to finding an optimal location of the new hub facility, this research performs sensitivity analysis to study the correlation between hub capacity (i.e., the source of uncertainty) and transportation cost. The results indicate that (1) total transportation cost after the establishment of the new hub facility at the optimal location is reduced by approximately 14% compared to the current transportation network system and (2) the currently operated hub facility located in Daejeon has the greatest influence on total transportation cost; while the existing hub facilities located in Cheongwon, Yongin, and Gunpo have little impact on total transportation cost after the construction of the new hub facility. It is expected that the outcome of this research helps the company systematically manage the transportation network system when the new hub facility is constructed.

Modeling and Solving a Linear Integer Problem (PLNE) for the Optimal Localization of a Hub Air Transport in the WAEMU Zone

In this article, we propose a linear integer model for the optimal location of a hub for air traffic in the WAEMU zone. A hub represents for an airline a base where an essential part of its activities is concentrated. Its location must therefore be judiciously determined. The hub location problem is one of the new and promising areas of research in the field of location theory. In order to satisfy a demand, the location of the hub involves the movement of people, goods between origin destination pairs required. Hubs are applied to reduce the number of transport links between the origin and destination airports. The proposed model minimizes the distances and takes into account the flow of passengers registered in the different airports and minimizes the total cost of the transfer via the hub airport. The simulations were made with the programming language Python.

Scheduling of transportation fleet based on the customer’s priority in a hub location problem

Scheduling of transportation fleet based on the customer’s priority in a hub location problem

A parallel adaptive memory algorithm for the capacitated modular hub location problem

The capacitated modular hub location problem is a realistic variant of the popular hub location problem arising from the design of telecommunications networks. Given a set of demand nodes, the problem consists in selecting a subset of nodes to represent hubs and assigning the rest of the nodes to the hub nodes, such that the transportation cost is minimized while satisfying the capacity constraints. The adaptive memory algorithm is a hybrid evolutionary heuristic that uses a central memory to store blocks of solutions. At each iteration, the recombination operator uses these solution blocks to create an offspring solution. In this paper, we present a parallel adaptive memory algorithm for the capacitated modular hub location problem that stores both solution blocks and complete solutions in a shared memory for the creation of an offspring. Other distinguishing features of our proposed algorithm include specially designed recombination and mutation operators for search diversification, an effective tabu search procedure for search intensification, and parallel computing for global optimization. Extensive computational results on three well-known data sets of 170 benchmark instances show that the proposed algorithm competes very favorably with the state-of-the-art heuristics from the literature. In particular, it finds 115 improved best-known solutions (for more than 67% of the cases). Furthermore, we analyze the key algorithmic components and shed lights on their impact on the proposed algorithm.