On the single-assignment p-hub center problem

Abstract

We study the computational aspects of the single-assignment p-hub center problem on the basis of a basic model and a new model. The new model's performance is substantially better in CPU time than dierent linearizations of the basic model. We also prove the NP-Hardness of the problem. Ó 2000 Elsevier Science B.V. All rights reserved.Keywords: Hub location; Modeling; Complexity Hub location problems arise when it is desirable to consolidate and disseminate¯ows at certain centralized locations called hubs. Typical applications arise in airline passenger travel (Toh and Higgins, 1985), cargo delivery (Kuby and Gray, 1993), and message delivery in computer communication networks (Klincewicz, 1998).The existing studies in the literature on hub location have almost exclusively focused on the p-hub median problem which involves the minimization of the total cost. The case with p 1Y 2 is posed by O'Kelly (1986) and the case for general p is formulated as a quadratic binary program by O'Kelly (1987). Dierent linearizations of the basic model of O'Kelly (1987) are investigated by Aykin (1995), Campbell (1994), Campbell (1996, Krishnamoorthy (1996, 1998), Skorin-Kapov et al. (1996).Our focus in this paper is on the minimax criterion which is essentially unstudied in the literature. The minimax criterion is traditionally used in location applications to minimize the adverse effects of worst case scenarios in providing emergency service. In hub location, even though emergency service protection does not seem to be an issue, the minimax criterion is still important from the viewpoint of minimizing the maximum dissatisfaction of passengers in air travel and minimizing the worst case delivery time in cargo delivery systems. The latter case is particularly important for delivery of perishable or time sensitive items.The literature on hub location under the minimax criterion is restricted to two papers. The

An Efficient Imperialism Competitive Algorithm for a Reliable Hub Covering Location Problem

“…Then, Campbell [13] presented a first linearization of O'Kelly [12] model. After that, the majority papers in this scope focus on linearization of O'Kelly's model [12] and solving procedure to minimize total transportation cost (e.g., [14]- [18]). Many different types of HLP were introduced by Campbell [14], such as phub median, p-hub center and p-hub covering.…”

“…The emanated flows between non-hub nodes and hub nodes, and between hub nodes are calculated by (18) and (19), respectively:…”

A robust decision-making approach for p-hub median location problems based on two-stage stochastic programming and mean-variance theory: a real case study

“…Due to the fact that the p-hub median location problem is NP hard [24], solving RM1, which is a mixed integer nonlinear program, is more difficult, especially in large-scale problems. To overcome this issue, the relaxed mixed integer nonlinear programming, called RM2, is presented to determine risk aversion coefficient.…”

Release Time Scheduling and Hub Location for Next-Day Delivery

“…Hamacher et al (2004), Labbé and Yaman (2004), Labbé et al (2005), and Marin et al (2006) Canovas et al (2007), Cunha and Silva (2007), Chen (2007), and Silva and Cunha (2009). Kara and Tansel (2000) and Ernst et al (2009) give integer programming formulations for the p-hub center problem. Pamuk and Sepil (2001) and Meyer et al (2009) propose heuristic algorithms, and Baumgartner (2003) derives valid inequalities and gives a branch-and-cut algorithm.…”