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.     

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.     

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.     

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.     

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.     

A branch-and-cut algorithm for two-level survivable network design problems

This paper approaches the problem of designing a two-level network protected against single-edge failures. The problem simultaneously decides on the partition of the set of nodes into terminals and hubs, the connection of the hubs through a backbone network (first network level), and the assignment of terminals to hubs and their connection through access networks (second network level). We consider two survivable structures in both network levels. One structure is a two-edge connected network, and the other structure is a ring. There is a limit on the number of nodes in each access network, and there are fixed costs associated with the hubs and the access and backbone links. The aim of the problem is to minimize the total cost. We give integer programming formulations and valid inequalities for the different versions of the problem, solve them using a branch-and-cut algorithm, and discuss computational results. Some of the new inequalities can be used also to solve other problems in the literature, like the plant cycle location problem and the hub location routing problem.     

Star p-hub median problem with modular arc capacities

We consider the hub location problem, where p hubs are chosen from a given set of nodes, each nonhub node is connected to exactly one hub and each hub is connected to a central hub. Links are installed on the arcs of the resulting network to route the traffic. The aim is to find the hub locations and the connections to minimize the link installation cost. We propose two formulations and a heuristic algorithm to solve this problem. The heuristic is based on Lagrangian relaxation and local search. We present computational results where formulations are compared and the quality of the heuristic solutions are tested.     

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.     

Airline network design and hub location problems

Due to the popularity of hub-and-spoke networks in the airline and telecommunication industries, there has been a growing interest in hub location problems and related routing policies. In this paper, we introduce flow-based models for designing capacitated networks and routing policies. No a priori hub-and-spoke structure is assumed. The resulting networks may suggest the presence of “hubs”, if cost efficient. The network design problem is concerned with the operation of a single airline with a fixed share of the market. We present three basic integer linear programming models, each corresponding to a different service policy. Due to the difficulty of solving (even small) instances of these problems to optimality, we propose heuristic schemes based on mathematical programming. The procedure is applied and analyzed on several test problems consisting of up to 39 U.S. cities. We provide comments and partial recommendations on the use of hubs in the resulting network structures.     

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.     

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.     

枢纽成本约束下的零担物流轴辐式网络设计

针对考虑枢纽建造成本和货物流的不确定的枢纽新建方案问题,引入全寿命周期理论,建立以轴辐式运营网络总成本最小化为目标的混合整数线性规划模型,并提出改进的最大最小后悔值的不确定性决策方法。通过算例来分析投资年限、枢纽干线折扣系数和不确定枢纽建造成本对零担物流（LTL）轴辐式网络的设计的影响。实验结果表明, 采用改进的不确定性决策方法得到的最优方案的运营成本比5个场景的运营成本平均降低了2.17%,表明基于改进的最大最小后悔值的不确定性决策方法,能够降低整个零担物流轴辐式运营网络总成本。     

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 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.     

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.     

Path relinking approach for multiple allocation hub maximal covering problem

We consider the multiple allocation hub maximal covering problem (MAHMCP): Considering a serviced O–D flow was required to reach the destination optionally passing through one or two hubs in a limited time, cost or distance, what is the optimal way to locate p hubs to maximize the serviced flows? By designing a new model for the MAHMCP, we provide an evolutionary approach based on path relinking. The Computational experience of an AP data set was presented. And a special application on hub airports location of Chinese aerial freight flows between 82 cities in 2002 was introduced.     

Star p-hub center problem and star p-hub median problem with bounded path lengths

We consider two problems that arise in designing two-level star networks taking into account service quality considerations. Given a set of nodes with pairwise traffic demand and a central hub, we select p hubs and connect them to the central hub with direct links and then we connect each nonhub node to a hub. This results in a star/star network. In the first problem, called the Star p-hub Center Problem, we would like to minimize the length of the longest path in the resulting network. In the second problem, Star p-hub Median Problem with Bounded Path Lengths, the aim is to minimize the total routing cost subject to upper bound constraints on the path lengths. We propose formulations for these problems and report the outcomes of a computational study where we compare the performances of our formulations.     

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.     

Hub location in backbone/tributary network design: a review

A common architecture for a communications network consists of tributary networks, which connect nodes to hubs, and a backbone network, which interconnects the hubs. Often, because of the size of the problem or the nature of the application, the design of the backbone network and the tributary networks are considered independently. However, in many cases, it is desirable or necessary to treat backbone and tributary design as an integrated problem, in which a key decision is the choice of hub locations. We provide a review of earlier algorithmic work on this integrated problem, drawing from the literature on facility location, network design, telecommunications, computer systems and transportation. Certain key issues in modeling hub location problems in the particular context of communications networks are discussed, and possible avenues for future work are proposed.     

Designing tributary networks with multiple ring families

Advances in telecommunication technology result in improved service, but can also lead to difficult and challenging network design problems. For example, networks in which nodes are connected by rings of optical fiber can now be used to provide rapid service restoration in the event of a failure. However, as a result, network designers are faced with the new problem of designing networks based on topological ring structures. In this paper, we consider the particular case of tributary network design. In a tributary network, a group of nodes are connected to a hub node, which is used as a point of interconnection with other parts of the network. For a particular network architecture, we describe an algorithm to determine how many topological ring structures are required, and which nodes should be included on each. We highlight connections between this problem and problems in vehicle routing.A common architecture for a telecommunications network consists of several tributary (often called access) networks, which connect locations to hubs, and a backbone network, which interconnects the hubs. This paper describes a heuristic approach for designing tributary networks based on self-healing rings (SHRs). The tributary network consists of multiple ring families, and each of those is comprised of one or more SHRs, called “stacked” rings. The SHRs in a given ring family are routed over the same cycle of optical fiber cables, but each SHR serves only a subset of the locations along the cycle. Each demand location is assigned to a single SHR on one of the ring families, whereas the hub is assigned to all SHRs on all ring families. A link that is used by some ring family incurs a fixed cost plus a variable cost per SHR associated with that family. Each SHR is constrained by the demand volume it can handle and by the number of locations it can serve. This tributary ring network design problem can be viewed as a complex version of a vehicle routing problem with a single-depot andmultiple vehicles. Our algorithm is initiated with numerous ring families. It then attempts to merge these families, while ensuring that savings are realized in terms of the sum of fixed and variable costs.