The purpose of this two-part study is to investigate the operation problem of single-car
elevator systems with destination hall call registration. Destination hall call registration is
such a system in which passengers register their destination floors at elevator halls before
boarding the car, while in the ordinary systems passengers specify only the directions of
their destination floors at elevator halls and register destination floors after boarding the car.
In this part of the study, we formulate the operation problem as a dynamic optimization …

In this study we consider the elevator operation problem of single-car elevator systems with
destination hall call registration. In this part we construct a branch-and-bound algorithm to
solve the dynamic operation optimization problem formulated in the first part. To calculate
lower bounds of the subproblems generated in the course of the branch-and-bound
algorithm, we first relax some of the constraints of the subproblems and decompose the
relaxed subproblems into three parts. Then, we apply the Lagrangian relaxation method to …