Model, Solution Concept and the Kth-Best Algorithm for Linear Tri-level Programming

Tri-level programming deals with hierarchical optimization problems in which the toplevel decision maker attempts to optimize his or her objective, but subjects it to a set of constraints and the reactions of decision makers at the middle-level and bottom-level. The middle-level’s decision is at the same time influenced by the reactions of the bottom decision maker. To describe and solve this complex issue, this paper first proposes a trilevel programming model and a set of linear tri-level programming (LTLP) solution concepts. It then presents a Kth-best algorithm to solve the linear tri-level programming problems. Finally, a case-based example further illustrates the proposed model, solution concept and algorithm.