Modeling uncertain passenger arrivals in the elevator dispatching problem with destination control

An Elevator Group Control System (EGCS) assigns an elevator of a group to each passenger transportation request by solving a snapshot optimization problem, the Elevator Dispatching Problem (EDP). In the destination control, passengers register their destination floors in the elevator lobbies, after which the EGCS completes the assignment at once and is not allowed to change it later. Therefore, the EDP is formulated as a stochastic optimal control problem, where uncertain future passenger arrivals are modeled by a Poisson and a geometric Poisson process. The EDP is considered as a certainty equivalent controller in which the uncertain quantities are replaced by their expected values, and as a robust controller in which they take multiple values according to risk scenarios. Numerical experiments show that the expectations do not accurately predict EDP variables. The modeling with the geometric Poisson process results in better forecasting accuracy than with the Poisson process and many scenarios that closely match the realizations of the variables. Hence, the scenarios can be used as a basis for a robust EDP which simultaneously minimizes a passenger service quality criterion and its variation due to uncertain demand.