Multi-follower tri-level decision making with uncooperative followers

© 2014 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. Multi-follower tri-level (MFTL) decision making addresses compromises among three interacting decision units within a hierarchical system of which multiple followers are involved in two lower-level units. The leader’s decision is affected not only by reactions of the followers but also by various relationships among them. The uncooperative relationship is the most basic situation in MFTL decision cases where multiple followers at the same level make individual decisions without any information exchange or share among them. To support such a MFTL decision, this paper firstly proposes a general model for the decision problem and then develops an extreme-point search algorithm based on bi-level Kth-Best approach to solve the model. Finally, a numerical experiment illustrates the decision model and procedures of the extreme-point search algorithm