A further research on Stochastic Single-Allocation Hub LocationProblem

Resumen

The Hub Location Problem (HLP) has been addressed by a wide community of operationsresearchers due to its practical relevance. Many reviews about location problems show theextensive activity in this field and the applications of these problems, see [1], [2] and [3],among others.Most studies on the HLPs are focused on models where the input parameters are assumedto be fixed and known. However, in most real-life problems, parameters such as demands,transportation costs, capacity of hubs, et cetera are subject to variation due to a varietyof factors such as population shifts, economic, environmental and political circumstances,quality of the provided services, et cetera. Hence, some information required for planning isnot available a priori, and the associated uncertainties are only resolved once the system isconstructed and the hubs are installed.This work deals with a Single-Allocation Hub Location Problem (SAHLP) where the amountof product sent between origins and destinations, the transportation costs and the capacitiesof the hubs, are uncertain and modelled using random variables with realization only afterthe hubs are selected. Different scenarios are considered (with their probabilities) and twodecisions have to be made: i) the location of the hubs (this location does not change from onescenario to another), and ii) the allocation of each origin/destination to these hubs in orderto minimize the expected overall costs of the system. This is a realistic practice because thehubs are located before knowing the real scenario and the allocations are determined when theactual parameters are realized. This is motivated by the necessity of the network operators to quickly react to the changes in overall system performance by adjusting the assignments ofthe origins/destinations to the hubs when the uncertainty is realized. A compact integer programming formulation is proposed for the stochastic SAHLP with three variants: uncapacitated, capacitated and ?-hub problem. Valid inequalities are developed to reinforce the formulation and added in a branch-and-cut procedure.