We propose a joint model that links the strategic level location and capacity decisions with the operational level routing and hub assignment decisions to solve hub network design problem with congestion and heterogeneous economics of scale. We also develop a novel flow-based mixed-integer second-order cone programming (MISOCP) formulation. We perform numerical experiments on a real-world data set to validate the efficiency of solving the MISOCP reformulation. The numerical studies yield observations can be used as guidelines in the design of transportation network for a logistics company.
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Xiaotong Liu (2024) studied this question.
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