Penalty function approach to linear trilevel programming

In this paper, we study a trilevel decision-making situation in which decisionmaker 1 selects an action, within a specified constraint set, then decisionmaker 2 selects an action within a constraint set determined by the action of decisionmaker 2, and finally decisionmaker 3 selects an action within a constraint set determined by the actions of decisionmakers 1 and 2. Each decisionmaker has an objective function to be optimized within the imposed constraint set. Bard (Ref. 1) presents a five-step algorithm for solving this problem. This paper presents an alternative approach to the key first step of that algorithm, which has some qualitative advantages over it.