Profit-maximizing hub network design with hub congestion and time-sensitive demands

Resumen

Hub location is an active research area, as shown by the frequentliterature reviews [2, 4]. Current topics of interest include extensions ofearlier models like, for instance, incorporating capacity selection and/orcongestion [3, 5], explicitly considering sensitive demands [6], or movingfrom cost minimization to profit maximization [1].To the best of our knowledge, no previous studies jointly consider theabove three modelling aspects. Our contribution is to formulate andsolve a profit-maximizing hub network design problem that incorporatessimultaneously hub congestion, time-sensitive demands through stepwise functions, where service paths with one or two stops are allowed.A stepwise function on transportation times is used to model demand.Hub congestion is expressed in terms of transit times at the hubs, whichare also modelled as a stepwise function. A profit is obtained from captured demand, while costs include fixed setup cost for enabling hubs and inter-hub edges, as well as the usual transportation costs. We develop a set of conditions to either fix variables or add additional constraints to the formulation. Families of valid inequalities are also presented together with their separation procedures. These allow us to improve the LP bound of our formulation, decreasing the computationaltime required. Preliminary results are encouraging.