We develop and experimentally compare policies for the control of a system
of k elevators with capacity one in a transport environment with ` floors, an idealized
version of a pallet elevator system in a large distribution center of the Herlitz PBS AG
in Falkensee. Each elevator in the idealized system has an individual waiting queue of
infinite capacity. On each floor, requests arrive over time in global waiting queues of
infinite capacity. The goal is to find a policy that, without any knowledge about future
requests, assigns an elevator to each request and a schedule to each elevator so that certain
expected cost functions (e.g., the average or the maximal flow times) are minimized. We
show that a reoptimization policy for minimizing average squared waiting times can be
implemented to run in real-time (1 s) using dynamic column generation. Moreover, in
discrete event simulations with Poisson input it outperforms other commonly used policies
like multi-server variants of greedy and nearest neighbor.