a hierarchical multi-period approach to integrated facility location and network design problem

This study addresses an integrated problem of hierarchical facility location and network design, which involves multiple decisions about the opening of facilities and network links at various levels. we introduce a novel multi-period model that integrates these problems, taking into account budgetary constraints and addressing the specific challenge of optimizing hierarchical upgrades for urban centers and transportation network links within each time period. the aim is to determine the optimal upgrade levels for urban centers and transportation network links in each time period, subject to a predefined budget. the proposed model is formulated as a mixed-integer linear programming problem. to solve the developed model, we employ a heuristic algorithm that combines simulated annealing with different neighborhood structures and fix-and-optimize strategies. the efficiency of the proposed algorithm is demonstrated through various instances, showing superior performance compared to the cplex solver, especially for larger problem instances. furthermore, we illustrate the practical utility of this model in real-world decision-making processes, underscoring its efficacy. by addressing these factors, the proposed model provides valuable insights for organizational managers and planners.