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.     

考虑港口拥堵因素的沿海海运网络优化

沿海运输权制度是沿海运输是否保留给本国船舶或者向外国籍船舶开放的制度。港口拥堵主要发生在海运网络的枢纽港上。通过考虑沿海运输权和港口拥堵对轴辐式海运网络加以优化,以海运网络内货物运输总成本最小化为目标函数,构建一个小规模整数规划模型。从欧亚航线覆盖的主要地区中选取10个港口组成海运网络进行算例分析,并使用CPLEX软件进行求解,研究结果表明,通过考虑枢纽港间货物运输的规模经济效应和产生的拥堵成本,可合理地确定枢纽港的位置;若允许沿海捎带,外资航运企业将会改变货物中转的港口。     

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.     

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.     

A branch-and-cut algorithm for the hub location and routing problem

We study the hub location and routing problem where we decide on the location of hubs, the allocation of nodes to hubs, and the routing among the nodes allocated to the same hubs, with the aim of minimizing the total transportation cost. Each hub has one vehicle that visits all the nodes assigned to it on a cycle. We propose a mixed integer programming formulation for this problem and strengthen it with valid inequalities. We devise separation routines for these inequalities and develop a branch-and-cut algorithm which is tested on CAB and AP instances from the literature. The results show that the formulation is strong and the branch-and-cut algorithm is able to solve instances with up to 50 nodes.     

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.     

Multiple allocation hub-and-spoke network design under hub congestion

The multiple allocation hub-and-spoke network design under hub congestion problem is addressed in this paper. A non-linear mixed integer programming formulation is proposed, modeling the congestion as a convex cost function. A generalized Benders decomposition algorithm has been deployed and has successfully solved standard data set instances up to 81 nodes. The proposed algorithm has also outperformed a commercial leading edge non-linear integer programming package. The main contribution of this work is to establish a compromise between the transportation cost savings induced by the economies of scale exploitation and the costs associated with the congestion effects.     

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.     

Routing Traffic at Hub Facilities

Flows arriving at a hub or a transshipment facility may need to be switched from one path to another to complete their journey. These transfer aspects of hub and spoke systems are widely recognized as a hindrance to efficient completion of transit trips. For example, time-consuming delays at transfer points for bus passengers are a major reason for poor levels of service between some nodes when the origin and destination are on different network lines. Such transfers also arise in multimodal interaction systems. This paper outlines a simple notation and analytical framework for optimizing flows within a hub (i.e. at nodes with transfers) and discusses several variants of the problem. This paper addresses prototype models for the efficient allocation of resources to facilitate the operation of interactions at the hub. The paper is primarily a conceptual and methodological overview, but well-recognized existing optimization models are suggested as being useful for some of the related tasks. Small numerical examples are used to illustrate some of the ideas.     

Solving the p-hub Median Problem Under Intentional Disruptions Using Simulated Annealing

Hubs are special facilities designed to act as switching, transshipment and sorting points in various distribution systems. Since hub facilities concentrate and consolidate flows, disruptions at hubs could have large effects on the performance of a hub network. In this paper, we have formulated the multiple allocation p-hub median problem under intentional disruptions as a bi-level game model. In this model, the follower’s objective is to identify those hubs the loss of which would most diminish service efficiency. Moreover, the leader’s objective is to identify the set of hubs to locate in order to minimize expected transportation cost while taking normal and failure conditions into account. We have applied two algorithms based on simulated annealing to solve the defined problem. In addition, the algorithms have been calibrated using the Taguchi method. Computational experiments on different instances indicate that the proposed algorithms would be efficient in practice.     

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 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.     

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.     

An interactive possibilistic programming approach for a multi-objective hub location problem: Economic and environmental design

This paper presents a new multi-objective mathematical model for a multi-modal hub location problem under a possibilistic-stochastic uncertainty. The presented model aims to minimize the total transportation and traffic noise pollution costs. Furthermore, it aims to minimize the maximum transportation time between origin-destination nodes to ensure a high probability of meeting the service guarantee. In order to cope with the uncertainties and the multi-objective model, we propose a two-phase approach, including fuzzy interactive multi-objective programming approach and an efficient method based on the Me measure. Due to the NP-hardness of the presented model, two meta-heuristic algorithms, namely hybrid differential evolution and hybrid imperialist competitive algorithm, are developed. Furthermore, a number of sensitivity analyses are provided to demonstrate the effectiveness of the presented model. Finally, the foregoing meta-heuristics are compared together through different comparison metrics.     

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.     

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.     

Aggregation in hub location problems

Because of their widespread use in real-world transportation situations, hub location models have been extensively studied in the last two decades. Many types of hub location problems are NP-hard and remain unmanageable when the number of nodes exceeds 200. We present a way to tackle large-sized problems using aggregation, explore the resulting error, and show how to reduce it. Furthermore, we develop a heuristic based on aggregation for k-hub center problems and present computational results.     

多分配枢纽站集覆盖问题的随机p- 鲁棒优化模型及算法

枢纽站选址是轴辐式网络优化设计的重要问题,枢纽站覆盖则是该问题的一个类型.考虑枢纽站建站成本和节点间运输距离的不确定性,结合随机优化和鲁棒优化方法,建立了完备轴辐式网络中多分配枢纽站集覆盖问题的随机-鲁棒优化模型;采用二进制编码,对量子粒子群算法进行改进,加入免疫思想,设计了免疫量子粒子群求解算法.最后通过算例对模型进行仿真计算,结果表明了该模型及算法的可行性和有效性.     

New simple and efficient heuristics for the uncapacitated single allocation hub location problem

Hub-and-spoke networks are widely studied in the area of location theory. They arise in several contexts, including passenger airlines, postal and parcel delivery, and computer and telecommunication networks. Hub location problems usually involve three simultaneous decisions to be made: the optimal number of hub nodes, their locations and the allocation of the non-hub nodes to the hubs. In the uncapacitated single allocation hub location problem (USAHLP) hub nodes have no capacity constraints and non-hub nodes must be assigned to only one hub. In this paper, we propose three variants of a simple and efficient multi-start tabu search heuristic as well as a two-stage integrated tabu search heuristic to solve this problem. With multi-start heuristics, several different initial solutions are constructed and then improved by tabu search, while in the two-stage integrated heuristic tabu search is applied to improve both the locational and allocational part of the problem. Computational experiments using typical benchmark problems (Civil Aeronautics Board (CAB) and Australian Post (AP) data sets) as well as new and modified instances show that our approaches consistently return the optimal or best-known results in very short CPU times, thus allowing the possibility of efficiently solving larger instances of the USAHLP than those found in the literature. We also report the integer optimal solutions for all 80 CAB data set instances and the 12 AP instances up to 100 nodes, as well as for the corresponding new generated AP instances with reduced fixed costs.     

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.