The Elevator Dispatching Problem

In this paper, we formulate the elevator dispatching problem as a stochastic bilevel optimization problem, where a group of elevators serves a set of transportation requests. In the upper level, the requests are assigned to the elevators. In the lower level, the route for each elevator is solved separately. The lower level problem predicts the optimal system state for a finite planning horizon according to stochastic demand. The demand affects the cost of traveling, capacity constraints, and the upper level payoff function. To solve the problem in real time, we use a genetic algorithm to optimize the upper level assignments. In the lower level optimization, we use the certainty equivalent control scheme, where stochastic quantities are replaced by their expected values. Extensive numerical simulations carried out in this paper, together with commercial installations, verify the applicability of our new on-line optimization algorithm.