Multifollower Trilevel Decision Making Models and System

In a trilevel hierarchical decision problem, the objectives and variables of each decision entity at one level are controlled, in part, by the decision entities at other levels. The choice of values for the decision variables at each level may influence the decisions made at other levels, and may thereby improve/reduce the objective for each level. When multiple decision entities are involved at the middle and bottom levels of a trilevel decision problem, the top-level entity´s decision will be affected, not only by these followers´ individual reactions, but also by the relationships between them. We call this problem a multifollower trilevel (MFTL) decision. This paper firstly defines and analyzes various kinds of relationships between decision entities in an MFTL decision problem. We then propose an MFTL decision making framework, in which 64 standard MFTL decision situations and their possible combinations are identified. To model these MFTL decision situations, we developed an innovative decision entity-relationship diagram (DERD) approach. We also established a general model for MFTL decision making and a set of standard MFTL decision models using trilevel programming. A trilevel decision support system (TLDSS) software has also been developed to transfer a DERD into a programming model. Finally, a case study illustrates typical MFTL decision making models and their development, using both DERD and programming approaches.