Hierarchical multilevel optimization with multiple-leaders multiple-followers setting and nonseparable objectives

¹ Department of Mathematics, Addis Ababa University, P.O.Box 1176, Addis Ababa, Ethiopia
² Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, P/Bag 16, Palapye, Botswana

^* Corresponding author: kassas@biust.ac.bw

Received: 1 November 2020
Accepted: 18 September 2021

Abstract

Hierarchical multilevel multi-leader multi-follower problems are non-cooperative decision problems in which multiple decision-makers of equal status in the upper-level and multiple decision-makers of equal status are involved at each of the lower-levels of the hierarchy. Much of solution methods proposed so far on the topic are either model specific which may work only for a particular sub-class of problems or are based on some strong assumptions and only for two level cases. In this paper, we have considered hierarchical multilevel multi-leader multi-follower problems in which the objective functions contain separable and non-separable terms (but the non-separable terms can be written as a factor of two functions, a function which depends on other level decision variables and a function which is common to all objectives across the same level) and shared constraint. We have proposed a solution algorithm to such problems by equivalent reformulation as a hierarchical multilevel problem involving single decision maker at all levels of the hierarchy. Then, we applied a multi-parametric algorithm to solve the resulting single leader single followers problem.