A reformulation strategy for mixed-integer linear bi-level programming problems

Bi-level programming has been used widely to model interactions between hierarchical decision-making problems, and their solution is challenging, especially when the lower-level problem contains discrete decisions. The of such mixed-integer linear bi-level problems typically need decomposition, approximation or heuristic-based strategies which either require high computational effort cannot guarantee a global optimal solution. To overcome these issues, this paper proposes two-step reformulation strategy in first part consists reformulating inner into nonlinear one, while second step well-known Karush-Kuhn-Tucker conditions for are formulated. This results that can be solved with optimiser. numerical benefits proposed demonstrated by solving five examples from literature.