Hub network design problem in the presence of disruptions

The main issue in p-hub median problem is locating hub facilities and allocating spokes to those hubs in order to minimize the total transportation cost. However hub facilities may fail occasionally due to some disruptions which could lead to excessive costs. One of the most effective ways to hedge against disruptions especially intentional disruptions is designing more reliable hub networks. In this paper, we formulate the multiple allocation p-hub median problem under intentional disruptions by a bi-level model with two objective functions at the upper level and a single objective at the lower level. In this model, the leader aims at identifying the location of hubs so that minimize normal and worst-case transportation costs. Worst-case scenario is modeled in the lower level where the follower’s objective is to identify the hubs that if lost, it would mostly increase the transportation cost. We develop two multi-objective metaheuristics based on simulated annealing and tabu search to solve the problem. Computational results indicate the viability and effectiveness of the proposed algorithms for exploring the non-dominated solutions.     

Spatial Analysis of Single Allocation Hub Location Problems

Hubs are special facilities that serve as switching, transshipment and sorting nodes in many-to-many distribution systems. Flow is consolidated at hubs to exploit economies of scale and to reduce transportation costs between hubs. In this article, we first identify general features of optimal hub locations for single allocation hub location problems based on only the fundamental problem data (demand for travel and spatial locations). We then exploit this knowledge to develop a straightforward heuristic methodology based on spatial proximity of nodes, dispersion and measures of node importance to delineate subsets of nodes likely to contain optimal hubs. We then develop constraints for these subsets for use in mathematical programming formulations to solve hub location problems. Our methodology can also help narrow an organization’s focus to concentrate on more detailed and qualitative analyses of promising potential hub locations. Results document the value of including both demand magnitude and centrality in measuring node importance and the relevant tradeoffs in solution quality and time.     

A tabu-search based heuristic for the hub covering problem over incomplete hub networks

Hub location problems deal with finding the location of hub facilities and with the allocation of demand nodes to these located hub facilities. In this paper, we study the single allocation hub covering problem over incomplete hub networks and propose an integer programming formulation to this end. The aim of our model is to find the location of hubs, the hub links to be established between the located hubs, and the allocation of non-hub nodes to the located hub nodes such that the travel time between any origin–destination pair is within a given time bound. We present an efficient heuristic based on tabu search and test the performance of our heuristic on the CAB data set and on the Turkish network.     

Endogenous Effects of Hubbing on Flow Intensities

Location of hub facilities and the allocation decisions in transport networks endogenously affect both the flow intensities and the transportation costs. Since the introduction of the hub location problem to the operations research literature in mid-1980s, many researchers investigated different ways of modelling the effects of hub facilities on the transportation costs. On the other hand, there has been very limited research on their effect on the flow intensities. This study proposes a new approach, inspired by the Bass diffusion model, to forecast the change in the demand patterns generated at different locations as a result of the placement of new hubs. This new model is used in the context of the uncapacitated single allocation p-hub median problem to investigate the effects of endogenous attraction, caused by the spatial interaction of present hubs, on future hub location decisions. Computational results indicate that the location and allocation decisions may be greatly affected when these forecasts are taken into account in the selection of future hub locations.     

The q-Ad Hoc Hub Location Problem for Multi-modal Networks

This research proposes a spatial optimization problem over a multi-modal transportation network, termed the q-Ad-hoc hub location problem (AHLP), to utilize alternative hubs in an ad-hoc manner in the wake of a hub outage. The model aims to reorganize the spatial structure of disrupted networks: unaffected hubs are utilized as ad-hoc hubs through which alternative routes connect supply and demand nodes. As a case study, the AHLP is applied to a multi-modal freight transport system connecting international destinations with the United States. The models are utilized to establish a new ranking methodology for critical infrastructure by combining metrics capturing nodal criticality and network resilience and recuperability. The results show that the AHLP is both an effective and practical recovery approach for a hub network to respond to the potential disruptions of hubs and a novel methodology for ranking critical infrastructure.     

Heuristics for the capacitated modular hub location problem

In this paper we study the hub location problem, where the goal is to identify an optimal subset of facilities (hubs) to minimize the transportation cost while satisfying certain capacity constraints. In particular, we target the single assignment version, in which each node in the transportation network is assigned to only one hub to route its traffic. We consider here a realistic variant introduced previously, in which the capacity of edges between hubs is increased in a modular way. This reflects the practical situation in air traffic where the number of flights between two locations implies a capacity in terms of number of passengers. Then, the capacity can be increased in a modular way, as a factor of the number of flights. We propose heuristic methods to obtain high-quality solutions in short computing times. Specifically, we implement memory structures to create advanced search methods and compare them with previous heuristics on a set of benchmark instances. Memory structures have been widely implemented in the context of the tabu search methodology, usually embedded in local search algorithms. In this paper we explore an alternative design in which the constructive method is enhanced with frequency information and the local search is coupled with a path relinking post-processing. Statistical tests confirm the superiority of our proposal with respect to previous developments.     

Uncapacitated single and multiple allocation p-hub center problems

The hub median problem is to locate hub facilities in a network and to allocate non-hub nodes to hub nodes such that the total transportation cost is minimized. In the hub center problem, the main objective is one of minimizing the maximum distance/cost between origin destination pairs. In this paper, we study uncapacitated hub center problems with either single or multiple allocation. Both problems are proved to be NP-hard. We even show that the problem of finding an optimal single allocation with respect to a given set of hubs is already NP-hard. We present integer programming formulations for both problems and propose a branch-and-bound approach for solving the multiple allocation case. Numerical results are reported which show that the new formulations are superior to previous ones.     

Routing and scheduling decisions in the hierarchical hub location problem

Hubs are facilities that consolidate and disseminate flow in many-to-many distribution systems. The hub location problem considers decisions that include the locations of hubs in a network and the allocations of demand (non-hub) nodes to these hubs. We propose a hierarchical multimodal hub network structure, and based on this network, we define a hub covering problem with a service time bound. The hierarchical network consists of three layers in which we consider a ring-star-star (RSS) network. This multimodal network may have different types of vehicles in each layer. For the proposed problem, we present and strengthen a mathematical model with some variable fixing rules and valid inequalities. Also, we develop a heuristic solution algorithm based on the subgradient approach to solve the problem in more reasonable times. We conduct the computational analysis over the Turkish network and the CAB data sets.     

Benders decomposition for the uncapacitated multiple allocation hub location problem

In telecommunication and transportation systems, the uncapacitated multiple allocation hub location problem (UMAHLP) arises when we must flow commodities or information between several origin–destination pairs. Instead of establishing a direct node to node connection from an origin to its destination, the flows are concentrated with others at facilities called hubs. These flows are transported on links established between hubs, being then splitted and delivered to its final destination. Systems with this sort of topology are named hub-and-spoke (HS) systems or hub-and-spoke networks. They are designed to exploit the scale economies attainable through the shared use of high capacity links between hubs. Therefore, the problem is to find the least expensive HS network, selecting hubs and assigning traffic to them, given the demands between each origin–destination pair and the respective transportation costs. In the present paper, we present efficient Benders decomposition algorithms based on a well known formulation to tackle the UMAHLP. We have been able to solve some large instances, considered ‘out of reach’ of other exact methods in reasonable time.     

A model for a reliable single allocation hub network design under massive disruption

Hub facilities may fail to operate in networks because of accidental failures such as natural disasters. In this paper, a quadratic model was presented for a reliable single allocation hub network under massive random failure of hub facilities which more than one hub may be disrupted in a route. It determines the location of the hub facilities and the primal allocation of non-hub nodes. It also determines the backup allocation in case of failure of the primal hub. First, a new lexicographic form of a bi-objective quadratic model is presented where the first objective maximizes served demands or equivalently, minimizes lost flows and the second objective minimizes total cost under a to massive disruption in the network. Then, by adding a structure-based constraint, the model is transformed to a single objective one. A linearization technique reported in the literature is applied on the quadratic model to convert it into classic linear zero–one mixed integer model while enhancing it by finding tighter bounds. The tight bounds’ technique is compared with other techniques in terms of computational time and its better performance was approved in some problem instances. Finally, due to the NP-hardness of the problem, an iterated local search algorithm was developed to solve large sized instances in a reasonable computational time and the computational results confirm the efficiency of the proposed heuristic, ILS can solve all CAB and IAD data set instances in less than 15 and 24 seconds, respectively. Moreover, the proposed model was compared with the classical hub network using a network performance measure, and the results show the increased efficiency of the model.     

Multi-product Capacitated Single-Allocation Hub Location Problems: Formulations and Inequalities

In this paper we extend the classical capacitated single-allocation hub location problem by considering that multiple products are to be shipped through the network. We propose a unified modeling framework for the situation in which no more than one hub can be located in each node. In particular, we consider the case in which all hubs are dedicated to handling a single-product as well as the case in which all hubs can handle all products. The objective is to minimize the total cost, which includes setup costs for the hubs, setup costs for each product in each hub and flow routing costs. Hubs are assumed to be capacitated. For this problem several models are proposed which are based on existing formulations for the (single-product) capacitated single-allocation hub location problem. Additionally, several classes of inequalities are proposed in order to strengthen the models in terms of the lower bound provided by the linear relaxation. We report results of a set of computational experiments conducted to test the proposed models and their enhancements.     

Capacitated single allocation hub location problem—A bi-criteria approach

A different approach to the capacitated single allocation hub location problem is presented. Instead of using capacity constraints to limit the amount of flow that can be received by the hubs, we introduce a second objective function to the model (besides the traditional cost minimizing function), that tries to minimize the time to process the flow entering the hubs. Two bi-criteria single allocation hub location problems are presented: in a first model, total time is considered as the second criteria and, in a second model, the maximum service time for the hubs is minimized. To generate non-dominated solutions an interactive decision-aid approach developed for bi-criteria integer linear programming problems is used. Both bi-criteria models are tested on a set of instances, analyzing the corresponding non-dominated solutions set and studying the reasonableness of the hubs flow charge for these non-dominated solutions. The increased information provided by the non-dominated solutions of the bi-criteria model when compared to the unique solution given by the capacitated hub location model is highlighted.     

Trading hubs construction in electricity markets using evolutionary algorithms

The trading hubs construction problem for electricity markets under locational marginal prices is considered. Given historical prices for all nodes of the electricity grid and for all market participants over a sufficiently long period of time, the problem is to choose a required number of node clusters (hubs) and to assign market participants to hubs so as to minimize the deviation of hub prices from the prices of participants under certain constraints. In view of problem complexity, two evolutionary algorithms are proposed: a genetic algorithm and a hybrid local search heuristic. It is proved that the proposed genetic algorithm converges to optimum almost surely. The algorithms are tested and compared on the real-life data. The structure of the fitness landscapes is analyzed using multiple restarts of the local search and the behavior of the evolutionary algorithms is explained on the basis of this analysis.     

Robust and fuzzy goal programming optimization approaches for a novel multi-objective hub location-allocation problem: A supply chain overview

In this paper, a novel multi-objective mathematical model is developed to solve a capacitated single-allocation hub location problem with a supply chain overview. Three mathematical models with various objective functions are developed. The objective functions are to minimize: (a) total transportation and installation costs, (b) weighted sum of service times in the hubs to produce and transfer commodities and the tardiness and earliness times of the flows including raw materials and finished goods, and (c) total greenhouse gas emitted by transportation modes and plants located in the hubs. To come closer to reality, some of the parameters of the proposed mathematical model are regarded as uncertain parameters, and a robust approach is used to solve the given problem. Furthermore, two methods, namely fuzzy multi-objective goal programming (FMOGP) and the Torabi and Hassini's (TH) method are used to solve the multi-objective mathematical model. Finally, the concluding part presents the comparison of the obtained results.     

Capacitated single-allocation hub location model for a flood relief distribution network

In disaster management, the logistics for disaster relief must deal with uncontrolled variables, including transportation difficulties, limited resources, and demand variations. In this work, an optimization model based on the capacitated single-allocation hub location problem is proposed to determine an optimal location of flood relief facilities with the advantage of economies of scale to transport commodities during a disaster. The objective is to minimize the total transportation cost, which depends on the flood severity. The travel time is bounded to ensure that survival packages will be delivered to victims in a reasonable time. Owing to complexity of the problem, a hybrid algorithm is developed based on a variable neighborhood search and tabu search (VNS-TS). The computational results show that the VNS found the optimal solutions within a 2% gap, while the proposed VNS-TS found the optimal solution with a 0% gap. A case study of severe flooding in Thailand is presented with consideration of related parameters such as water level, hub capacity, and discount factors. Sensitivity analyses on the number of flows, discount factors, capacity, and bound length are provided. The results indicated that demand variation has an impact on the transportation cost, number of hubs, and route patterns.     

A two‐stage hub location method for air transportation in Brazil

During the past decade, the Brazilian air passenger market has been growing at impressive rates suggesting the need for rationalization and the consistent use of the hub‐and‐spoke configuration. This research considers 135 airports, mostly extremely small, and the aim is to identify regional hubs that would accumulate traffic and feed a predefined restricted number of major hubs. The proposed approach is divided into two phases: the first phase considers all 135 existing commercial airports and using the p‐median problem identifies p airports that would play the role of regional hubs, and the second phase considers a problem with these p airports and solves the q‐hub location problem. Both phases are sequentially solved by the software AIMMS 3.9. The research has broad implications consistent with the publicized efforts to improve management practices, support a larger number of commercial airports, and face the expected peak demand in the upcoming international events. Given the growth in the air passenger market in Brazil, both phases may be seen as two independent objectives.     

Models and solution methods for the uncapacitated r‐allocation p‐hub equitable center problem

Hub networks are commonly used in telecommunications and logistics to connect origins to destinations in situations where a direct connection between each origin–destination (o‐d) pair is impractical or too costly. Hubs serve as switching points to consolidate and route traffic in order to realize economies of scale. The main decisions associated with hub‐network problems include (1) determining the number of hubs (p), (2) selecting the p‐nodes in the network that will serve as hubs, (3) allocating non‐hub nodes (terminals) to up to r‐hubs, and (4) routing the pairwise o‐d traffic. Typically, hub location problems include all four decisions while hub allocation problems assume that the value of p is given. In the hub median problem, the objective is to minimize total cost, while in the hub center problem the objective is to minimize the maximum cost between origin–destination pairs. We study the uncapacitated (i.e., links with unlimited capacity) r‐allocation p‐hub equitable center problem (with) and explore alternative models and solution procedures.     

A genetic algorithm for the uncapacitated single allocation planar hub location problem

Given a set of n interacting points in a network, the hub location problem determines location of the hubs (transfer points) and assigns spokes (origin and destination points) to hubs so as to minimize the total transportation cost. In this study, we deal with the uncapacitated single allocation planar hub location problem (PHLP). In this problem, all flow between pairs of spokes goes through hubs, capacities of hubs are infinite, they can be located anywhere on the plane and are fully connected, and each spoke must be assigned to only one hub. We propose a mathematical formulation and a genetic algorithm (PHLGA) to solve PHLP in reasonable time. We test PHLGA on simulated and real life data sets. We compare our results with optimal solution and analyze results for special cases of PHLP for which the solution behavior can be predicted. Moreover, PHLGA results for the AP and CAB data set are compared with other heuristics.     

Uncapacitated single allocation p-hub maximal covering problem

The hub location problem is to find a set of hub nodes on the network, where logistics transportation via the hubs is encouraged because of the cost or distance savings. Each node that has a specified amount of demands can be connected to one of p hubs. The uncapacitated single allocation p-hub maximal covering problem is to maximize the logistics covered, where the logistics of demand is said to be covered if the distance between two nodes is less than or equal to the specified range in consideration of the distance savings between hubs. The aim of our model is to locate the hub, and to allocate non-hub nodes to the located hub nodes; the hub can maximize the demand covered by deadline traveling time. It is presented an integer programming formulation for the new hub covering model, and a computational study based on several instances derived from the CAB (Civil Aeronautics Board) data set. Two heuristics, distance based allocation and volume based allocation methods, are suggested with a computational experiment on the CAB data set. Performances of heuristics are evaluated, and it is shown that good solutions are found in a relatively reasonable computation time for most of instances.     

Hybrid simulation models for spare parts supply chain considering 3D printing capabilities

In the era of Industry 4.0, 3D printing unlocks a wide array of solutions to rapidly-produce spare parts for maintenance operations. In this research, we propose a hybrid simulation approach, combining agent-based and discrete event simulation methods, to investigate how the adoption of 3D printing technologies to manufacture spare parts for maintenance operations will improve operational efficiency and effectiveness. Specifically, our framework is applied to the United States Navy’s fighter jet maintenance operations to study various network configurations, where 3D printing facilities may be centralized, decentralized, or hub configured. System performance in terms of the total cost, timeliness of delivery, and vulnerability under disruptions such as cyber-attacks and emergencies are evaluated. Lastly, the impact of 3D printing technological advancements on operational performance is investigated to obtain managerial insights.