Editorial

New developments on hub location

Geometric branch-and-bound techniques are well-known solution algorithms for non-convex continuous global optimization problems with box constraints. Several approaches can be found in the literature differing mainly in the bounds used.

The aim of this paper is to extend geometric branch-and-bound methods to mixed integer optimization problems, i.e. to objective functions with some continuous and some integer variables. Mixed-integer non-linear and non-convex optimization problems are extremely hard, containing several classes of NP-hard problems as special cases. We identify for which type of mixed integer non-linear problems our method can be applied efficiently, derive several bounding operations and analyze their rates of convergence theoretically. Moreover, we show that the accuracy of any algorithm for solving the problem with fixed integer variables can be transferred to the mixed integer case.

Our results are demonstrated theoretically and experimentally using the truncated Weber problem and the p-median problem. For both problems we succeed in finding exact optimal solutions.

We propose a new hub location model defined by the minimization of costs. The main contribution of this work is to permit the analysis of a hub-and-spoke network operated under “decentralized management”. In this type of network, various transport companies act independently, and each makes its route choices according to its own criteria, which can include cost, time, frequency, security and other factors, including subjective ones. Therefore, due to the diversity of the various companies’ criteria, one can expect that between each origin–destination pair, a fraction of the flow will be carried through hubs and a fraction will be carried by the direct route. to resolve this problem, it becomes necessary to determine the probability that any network user will choose the hub route for each trip to be made (or for each load to be carried). We present an integer programming formulation, subject the new model to experiments with an intermodal general cargo network in Brazil and address questions regarding the solution of the problem in practice.