A modification of the trilevel Kth-Best algorithm

Abstract

In this paper, we present a modification of the traditional linear trilevel Kth-Best algorithm. The proposed modified Kth-Best algorithm considers the linear trilevel programming problems in which the middle level and the lower level problems are unbounded or their objective functions areinconsistant. These cases are not considered in the trilevel Kth-Best algorithm proposed by Zhang etal. Moreover, we discuss some geometric properties of a linear trilevel programming problem whereineach decision maker might have his (her) own restrictions and the upper level objective function containlower level variables. Finally, a number of numerical examples are presented and the results are verifiedas well.

Keywords

• multilevel programming| trilevel programming| Kth-Best algorithm