  This work studies the effect of hub congestion and time-sensitive demand on a
hub-and-spoke location/allocation system. The Hub Location with Congestion and
Time-sensitive Demand Problem is introduced, which combines these two main
characteristics. On the one hand, hubs can be activated at several service
levels, each of them characterized by a maximum capacity, expressed as the
amount of flow that may circulate through the hub, which is associated with a
hub transit time. On the other hand, alternative levels are available for
served commodities, where each demand level is characterized by its amount of
demand, unit revenue, and maximum service time. In this problem the efficiency
of a hub-and-spoke system is given by the maximum net profit it may produce. To
the best of our knowledge this is the first work where hub congestion and
time-sensitive demand are jointly considered. Two alternative mixed-integer
linear programming formulations are proposed. They include a new set of
constraints, which are necessary to guarantee the consistency of the obtained
solutions under the presence of the capacity-type constraints derived from hub
service levels and served demand levels. The efficiency of the formulations is
analyzed through a set of computational experiments. The results of the
computational experiments allow to study the structure of the obtained
solutions and to analyze how the different parameters affect them.
