This paper introduces the hub location problem with Bernoulli demands (HLPBD). The problem is a variant of capacitated stochastic hub location problems in which demands for transportation service are assumed to be Bernoulli random variables. We address the problem under single and multiple allocation settings, and for each case, a two-stage stochastic programming model is presented. Further, assuming a homogeneous demand probability, a closed-form expression for the recourse function is presented, and deterministic equivalent formulations are developed for the original stochastic problems. To solve large instances, exact solution algorithms based on Benders decomposition and Lagrangian relaxation are proposed. An extensive set of computational experiments on three well-known data sets is conducted to test the efficiency of the proposed models and solution algorithms, and also to evaluate the effect of different input parameters on the optimal solutions.
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