Tri-level Multi-follower Decision-making in a Partial-cooperative Situation

Tri-level decision-making addresses compromises between interactive decision entities that are distributed throughout a three-level hierarchy. These decision entities are respectively termed as the top-level leader, the middle-level follower and the bottom-level follower. This paper considers a hi-level multi-follower (TLMF) decision problem where both cooperative and uncooperative relationships coexist between multiple followers at the same level. In this situation, followers share some decision variables with their counterparts and also control individual decision variables to achieve their respective goals; this is also known as partial-cooperative TLMF decision-making. To support this category of decision-making, this paper first presents a linear model to characterize the partial cooperative TLMF decision-making process. It then develops a vertex enumeration algorithm to obtain a solution to the resulting model. Lastly, we apply the proposed TLMF decision techniques to handle an inventory management problem in applications.