Karush–Kuhn–Tucker transformation approach to multi-level linear programming problems

We have considered a multi-level linear programming problem, namely three-level linear programming problem and applied Karush–Kuhn–Tucker (KKT) transformation method to obtain the solution of the system. In the KKT transformation method, the lower level decision making problem is converted into the constraints of the higher level decision making problem. We have taken into account the non-negativity constraints at the initial stages of derivation i.e. in the formulation of the Lagrangian function.