reliable hierarchical multimodal hub location problem: models and lagrangian relaxation algorithm

Hub facility location problems involve the establishment of strategic hub facilities and the allocation of demand nodes to them. meanwhile, with the emergence of new transport and distribution networks with multi-level structures, the design of such networks has evolved. the diversity of transportation system has added multimodality to these problems. considering the strategic nature and long-term implications of decisionmaking in this eld, the decisions shall be of high reliability. the present study is an attempt to consider the reliability of communication paths in proportion to the volume of transactions through them while covering all of the above-mentioned issues in hub location problems at the same time. incorporating hierarchical characteristics of the problem into the model, one can obtain a signicantly enhanced model in terms of multimodality and reliability. a lagrangian solution method was developed considering the strategic level of the problem and the importance of the solution accuracy. the model was then validated in terms of time and quality.