A Method for Solving Some Class of Multilevel Multi-leader Multi-follower Programming Problems

Addis B. Zewde, Semu Mitiku Kassa

Research output: Contribution to conferencePaper

Abstract

Multiple leaders with multiple followers games serve as an important model in game theory with many applications in economics, engineering, operations research and other fields. In this paper, we have reformulated a multilevel multi-leader multiple follower (MLMLMF) programming problem into an equivalent multilevel single-leader multiple follower (MLSLMF) programming problem by introducing a suppositional (or dummy) leader. If the resulting MLSLMF programming problem consist of separable terms and parameterized common terms across all the followers, then the problem is transformed into an equivalent multilevel programs having a single leader and single follower at each level of the hierarchy. The proposed solution approach can solve multilevel multi-leader multi-follower problems whose objective values in both levels have common, but having different positive weights of, nonseparable terms.
Original languageEnglish
Pages589–599
DOIs
Publication statusPublished - 2020

Fingerprint

Follower
Programming
Economics
Game theory
Operations research

Cite this

@conference{c806086b925f4ecaafd291bcda5aa918,
title = "A Method for Solving Some Class of Multilevel Multi-leader Multi-follower Programming Problems",
abstract = "Multiple leaders with multiple followers games serve as an important model in game theory with many applications in economics, engineering, operations research and other fields. In this paper, we have reformulated a multilevel multi-leader multiple follower (MLMLMF) programming problem into an equivalent multilevel single-leader multiple follower (MLSLMF) programming problem by introducing a suppositional (or dummy) leader. If the resulting MLSLMF programming problem consist of separable terms and parameterized common terms across all the followers, then the problem is transformed into an equivalent multilevel programs having a single leader and single follower at each level of the hierarchy. The proposed solution approach can solve multilevel multi-leader multi-follower problems whose objective values in both levels have common, but having different positive weights of, nonseparable terms.",
author = "Zewde, {Addis B.} and Kassa, {Semu Mitiku}",
year = "2020",
doi = "10.1007/978-3-030-21803-4_59",
language = "English",
pages = "589–599",

}

A Method for Solving Some Class of Multilevel Multi-leader Multi-follower Programming Problems. / Zewde, Addis B.; Kassa, Semu Mitiku.

2020. 589–599.

Research output: Contribution to conferencePaper

TY - CONF

T1 - A Method for Solving Some Class of Multilevel Multi-leader Multi-follower Programming Problems

AU - Zewde, Addis B.

AU - Kassa, Semu Mitiku

PY - 2020

Y1 - 2020

N2 - Multiple leaders with multiple followers games serve as an important model in game theory with many applications in economics, engineering, operations research and other fields. In this paper, we have reformulated a multilevel multi-leader multiple follower (MLMLMF) programming problem into an equivalent multilevel single-leader multiple follower (MLSLMF) programming problem by introducing a suppositional (or dummy) leader. If the resulting MLSLMF programming problem consist of separable terms and parameterized common terms across all the followers, then the problem is transformed into an equivalent multilevel programs having a single leader and single follower at each level of the hierarchy. The proposed solution approach can solve multilevel multi-leader multi-follower problems whose objective values in both levels have common, but having different positive weights of, nonseparable terms.

AB - Multiple leaders with multiple followers games serve as an important model in game theory with many applications in economics, engineering, operations research and other fields. In this paper, we have reformulated a multilevel multi-leader multiple follower (MLMLMF) programming problem into an equivalent multilevel single-leader multiple follower (MLSLMF) programming problem by introducing a suppositional (or dummy) leader. If the resulting MLSLMF programming problem consist of separable terms and parameterized common terms across all the followers, then the problem is transformed into an equivalent multilevel programs having a single leader and single follower at each level of the hierarchy. The proposed solution approach can solve multilevel multi-leader multi-follower problems whose objective values in both levels have common, but having different positive weights of, nonseparable terms.

U2 - 10.1007/978-3-030-21803-4_59

DO - 10.1007/978-3-030-21803-4_59

M3 - Paper

SP - 589

EP - 599

ER -