In this study, we consider the special case of the uncapacitated p-hub center problem, where the weight/flow matrix includes 0 entities. In some real life networks, such as airline networks, cargo networks etc., the zero flow might exist between certain demand points. Typically in airline networks, nobody travels from city i to city i. In the literature, the general assumption is that all entries of the weight/flow matrix are positive. Therefore, the optimal solution of the hub center problem might correspond to a path from origin to destination with a zero flow. In this study, we discuss the effects of zero flows on the optimal solution and modified the current formulation of the uncapacitated p-hub center problem in order to handle this case. We also analyze several scenarios under which the longest path should have enough volumes of flow in order to be involved in investment decisions. We present our computational results.
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