A modification of the trilevel Kth-Best algorithm

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 are inconsistant. These cases are not considered in the trilevel Kth-Best algorithm proposed by Zhang et al. Moreover, we discuss some geometric properties of a linear trilevel programming problem wherein each decision maker might have his (her) own restrictions and the upper level objective function contain lower level variables. Finally, a number of numerical examples are presented and the results are verified as well.