Integrating goal programming, Kuhn–Tucker conditions, and penalty function approaches to solve linear bi-level programming problems

Bi-level programming, a tool for modeling decentralized decisions, consists of the objective(s) of the leader at its first level and the follower(s) at the second level. Three level programming results when the second level itself is a bi-level programming which helps us develop the idea of bi-level programming to multi-level programs with any number of levels. In this paper, we integrate goal programming (GP), Karush–Kuhn–Tucker conditions and Penalty Function approaches to solve linear bi-level programming problems.