Morton E. O'Kelly

A quadratic integer program for the location of interacting hub facilities

Abstract This paper reports a new formulation of a general hub location model as a quadratic integer program. Non-convexity of the objective function makes the problem difficult. A variety of alternative solution strategies are discussed. Computational results from two simple heuristics are presented for the task of siting 2, 3 or 4 hubs to serve interactions between sets of 10, 15, 20 and 25 U.S. cities. The effects of different computational shortcuts are examined.

The Location of Interacting Hub Facilities

Hubs are central facilities which act as switching points in networks connecting a set of interacting nodes. This paper develops several location models for hubs. The one-hub siting problem is equivalent to a Weber least cost location model. An empirical example demonstrates the relevance of this model for an understanding of contemporary express delivery networks. A new model describing the location of two hubs in a plane yields several interesting pairs of hub location under different assumptions about scale effects on the interfacility linkage: generally as these scale effects increase the locations of the hubs move apart.

Tight linear programming relaxations of uncapacitated p-hub median problems

Abstract The problem of locating hub facilities and allocating non-hub nodes to those hubs arises frequently in the design of communication networks, airline passenger flow and parcel delivery networks. In this paper we consider uncapacitated multiple and single allocation p -hub median problems. We develop new mixed 0 1 linear formulations with tight linear programming relaxations. The approach is tested on a well known and heavily used benchmark data set of real-world problems with resulting LP relaxations ranging from 10010 to 391 250 variables and from 2 101 to 31 901 constraints, which proved to be difficult linear programs. Yet, this approach proved to be very effective: in almost all instances the linear programming solution was integer. In cases with fractional solutions, the integrality was achieved by adding a small partial set of integrality constraints. Therefore, we extended the range of optimally solvable instances of these NP-hard hub location problems, which have defied researchers for the last ten years. As an additional result for the single allocation case we were able to establish optimality of all heuristic solutions obtained via tabu search algorithm from a previous study. For the more difficult single allocation p -hub median problem we also used the best known heuristic solution as a guidance in adding integrality constraints. This novel linkage between optimal and heuristic solutions has a potential impact in a number of other problem settings, where efficient heuristic solutions exist and are probably, but not provably optimal.

THE HUB NETWORK DESIGN PROBLEM: A REVIEW AND SYNTHESIS.

Abstract Hubs, or central trans-shipment facilities, allow the construction of a network where large numbers of direct connections can be replaced with fewer, indirect connections. Hub-and-spoke configurations reduce and simplify network construction costs, centralize commodity handling and sorting, and allow carriers to take advantage of scale economies through consolidation of flows. Such networks have widespread application in transportation. This paper presents a structured review of research on the hub network design problem. Three critical design questions need to be considered: (a) are the nodes in the network assigned exclusively to a single hub? (b) are direct node-to-node linkages permitted to bypass the hub facilities? and, (c) are the hub facilities fully interconnected? The nature and difficulty of the hub network design problem depends on the analysts judgement with respect to these questions. We review analytical research papers, and give brief empirical examples of eight different network design protocols.

Hub location with flow economies of scale

A characteristic feature of hub and spoke networks is the bundling of flows on the interhub links. This agglomeration of flows leads to reduced travel costs across the interhub links. Current models of hub location do not adequately model the scale economies of flow that accrue due to the agglomeration of flows. This paper shows that current hub location models, by assuming flow-independent costs, not only miscalculate total network cost, but may also erroneously select optimal hub locations and allocations. The model presented in this paper more explicitly models the scale economies that are generated on the interhub links and in doing so provides a more reliable model representation of the reality of hub and spoke networks.

Twenty-Five Years of Hub Location Research

Last year was the 25th anniversary of two seminal transportation hub location publications, which appeared in 1986 in Transportation Science and Geographical Analysis. Though there are related hub location and network design articles that predate these works, the 1986 publications provided a key impetus for the growth of hub location as a distinct research area. This paper is not intended as a comprehensive review of hub location literature; rather, our goal is to reflect on the origins of hub location research, especially in transportation, and provide some commentary on the present status of the field. We provide insight into early motivations for analyzing hub location problems and describe linkages to problems in location analysis and network design. We also highlight some of the most recent research, discuss some shortcomings of hub location research and suggest promising directions for future effort.

Hub and spoke networks in air transportation : an analytical review

In this analytical review, the authors survey advances in the analysis of the hub location problem and its variants. In the course of the review, opportunities for enhanced analysis become apparent. The authors emphasize the most pressing areas for further research. They find that first, research needs to be devoted to developing more reliable heuristics for the multiple assignment model and its extensions, and second, that additional research is needed to understand the conditions under which the model will tend to have integer solutions. Research in this area will contribute to the solution of a longstanding puzzle in economics about the allocation of indivisible resources.

A geographer's analysis of hub-and-spoke networks☆

Abstract Hubs, as discussed in this paper, are special nodes that are part of a network , located in such a way as to facilitate connectivity between interacting places. Hubs are examined from the spatial organization viewpoint: that is, the linkages, hinterlands, and hierarchies formed by hub-and-spoke networks are described. Features of the hub-and-spoke system that make them different from basic facility location problems are emphasized. Special attention is paid to the contrasts between air passenger and air express freight applications. The paper discusses various broad types of models that are appropriate for network analysis. The paper includes a simulation exercise with a hypothetical network. The data are for interactions between 100 city pairs in the US, and the characteristic features of the hub network under three alternatives scenarios are developed. Although there is not a perfect correspondence between any of these models and the ‘reality’ of actual air freight and air passenger nets, a rudimentary matching is suggested. The single hub allocation model would be an especially inconvenient network for passengers, but might be ideal for regional freight or communications systems. The multiple assignment model has much less passenger inconvenience. While the network appears to be ideal for the passenger system, it seems to make a miscalculation about the nature of flow economies of scale. In the final model flows must be deliberately routed to make up economical bundles, and the incentives are stacked in favor of large flows.

Recent advances in accessibility research: Representation, methodology and applications

Abstract. In this article we examine recent advances in accessibility research and their implications for future studies. We base our discussion on three intersecting dimensions that are useful for evaluating the contribution of recent studies: representation, methodology and applications. Various examples are selected to show that research concerned with representation and methodological problem solving is often applied to issues of broad concern in policy and planning. It is, however, not clear that the simultaneous treatment of representation, methodological and application issues has ever been fully worked out. The questions raised in this article may serve as a foundation for addressing issues pertinent to accurate representation, improved model building, and more rigorous applications in accessibility research.

HUB NETWORK DESIGN WITH SINGLE AND MULTIPLE ALLOCATION: A COMPUTATIONAL STUDY

Abstract We present exact solutions for hub location models and discuss sensitivity of these solutions to the interhub discount factor. Both multiple and single hub allocations are considered. We employ a linearization that is smaller than any previously used, and we determine the number of variables and constraints. This formulation is used to make extensive computations. Specifically, we include runs for a standard test problem for 3 and 4 hubs, and n = 10, 15, 20 and 25 origins and destinations, although the case with 25 origins and destinations is still large enough to require us to present results for fewer parameter combinations than for the other cases. The results show that the integer-friendliness of the formulation depends on the value of α. A new result in this paper is a determination of the optimal number of hubs as the fixed costs and interhub discount factors change.