Hub location in air cargo transportation: A case study Hakan Oktal * , Asuman Ozger Avionics Department, Faculty of Aerospace Sciences, Anadolu University, _ Ikieylul Kampusu, 26470 Eskisehir, Turkey Keywords: Air cargo transportation Hub and spoke networks Multiple hub location abstract This paper models constrained choices when establishing cargo hub and spoke networks. A mixed integer linear programming model is developed introducing additional constraints to the traditional model of uncapacitated multiple allocation hub location problem and empirically tested. The tests suggest that aircraft range and trip cost, runway availability and cargo traffic continuity of an airport are major factors affecting hub locations along with the costs of airline movements. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction Hub systems require different network designs based upon their particular characteristics. Here we introduce the sectorial charac- teristics of air transportation into the traditional uncapacitated multiple allocation hub location problem (UMAHLP) and develop a new mixed integer linear programming model. In most of the studies on air transportation applications of hub location problem (HLP), little attention has been given to the value and the components of cost; and in particular direct operating cost (DOC), total operating cost (TOC), fixed and variable costs for aircraft are generally not considered in any detail or with consis- tency (e.g. Lin et al., 2003; Yang, 2009). Here we explore the effects of the new constraints and the sectorial characteristics of air transportation on HLP. These constraints can also be used in different fields such as road trans- portation, computer networks etc. The model developed, by including the new constraints, is tested using two data sets. 2. The model Our analysis involves modified Ebery et al.’s (2000) multiple allocation version of the capacitated hub location problem (the “EA Model”) by including additional constraints (the “New Model”). In both models, the capacity constraint is removed and the objective function 1 is used under the constraints 2e11 for the New Model and constraints 2e6, 10 and 11 for the EA Model. min X i˛N " X k˛N CT ik Z ik þ X k˛N X l˛N aCT kl Y i kl þ X l˛N X j˛N CT lj Y i lj # þ X k F k H k (1) subject to X k˛N Z ik ¼ X j W ij (2) X l˛N X i ij ¼ W ij ci; j˛N (3) X l˛N Y i kl þ X j˛N X i kj  X l˛N Y i lk  Z ik ¼ 0 ci; k˛N (4) Z ik  O i $H k ci; k˛N (5) X i lj  W ij $H l ci; j; l˛N (6) d ik $H k  S ci; k (7) T $H k  Wa ðm;kÞ cm; k (8) H k  RA k ck (9) H k ˛f0; 1g ck (10) X i lj ; Y i kl ; Z ik  0 ci; j; k; l˛N (11) where; N is the set of nodes, W ij  0 is the flow from the origin i to the destination j for all, CT ij is the unit trip cost from i to j, RA k is the appropriateness of node k to be a hub, F k is the fixed hub cost of node k, S is the maximum link distance, T is the minimum required traffic flow of node k, Wa (m,k) is the flow of node k in time period m and a is the interhub discount factor. The decision variables used are given likewise: H k ¼ 1 if node k is a hub and * Corresponding author. Tel.: þ90 5322853572; fax: þ90 2223221619. E-mail address: hoktal@anadolu.edu.tr (H. Oktal). Contents lists available at SciVerse ScienceDirect Journal of Air Transport Management journal homepage: www.elsevier.com/locate/jairtraman 0969-6997/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jairtraman.2012.10.009 Journal of Air Transport Management 27 (2013) 1e4