A Mixed-Integer Linear Programming Formulation for the Budget-Constrained Minimum Bottleneck Spanning Tree Problem with Node Upgrades

We investigate the Budget-Constrained Minimum Bottleneck Spanning Tree problem with Node Upgrades (BC-MBST-NU), a network design challenge that optimizes infrastructure investment to improve worst-case performance. By upgrading nodes to reduce the weights of adjacent edges, we seek a spanning tree that minimizes the maximum edge weight under a strict budget. We propose the first exact approach for this NP-hard problem, presenting a novel mixed-integer linear programming formulation. Our solution strategy is enhanced by a tailored primal heuristic for warm-starting the solver and a structural variable-fixing procedure that leverages the bottleneck objective to prune the search space effectively. Computational results on various instance scales show that the proposed methodology is robust, providing optimal solutions for small and medium instances and good-quality feasible solutions for large-scale networks within practical time limits.