On Optimistic and Pessimistic Bilevel Optimization Models for Demand Response Management

This paper investigates bilevel optimization models for demand response management, and highlights the often overlooked consequences of a common modeling assumption in field. That is, overwhelming majority existing research deals with so-called optimistic variant problem where, case multiple optimal consumption schedules consumer (follower), chooses an schedule that is most favorable electricity retailer (leader). However, this usually illegitimate practice; as result, consumers may easily deviate from their expected behavior during realization, suffers significant losses. One way out to solve pessimistic instead, where prepares least responses consumers. The main contribution exact procedure solving problem. First, key properties solutions are formally proven efficiently solvable special cases identified. Then, detailed investigation variants presented. It demonstrated set typically contains various equal follower, but bring radically different profits leader. reduces slightly perturbed data. A numerical study shows solution perform poorly practice, while gives very close highest profit can be achieved theoretically. To best authors’ knowledge, first propose approach