Partially-shared pessimistic bilevel multi-follower programming: concept, algorithm, and application

Abstract

When multiple followers are involved in a bilevel programming problem, the leader’s decision will be affected by the reactions of these followers. For actual problems, the leader in general cannot obtain complete information from the followers so that he may be risk-averse. Then he would need a safety margin to bound the damage resulting from the undesirable selections of the followers. This situation is called a pessimistic bilevel multi-follower (PBLMF) programming problem. This research considers a partially-shared linear PBLMF programming in which there is a partially-shared variable among the followers. The concept and solution algorithm of such a problem are developed. As an illustration, the partially-shared linear PBLMF programming model is applied to a company making venture investments.