Online-optimization of multi-elevator transport systems with reoptimization algorithms based on set-partitioning models

Authors:
Philipp Friese;Jörg Rambau
Affiliations:
Department of Optimization, Zuse Institute Berlin, Germany;Department of Mathematics, University of Bayreuth, Germany
Venue:
Discrete Applied Mathematics - Special issue: Traces of the Latin American conference on combinatorics, graphs and applications: a selection of papers from LACGA 2004, Santiago, Chile
Year:
2006

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Abstract

We develop and experimentally compare policies for the control of a system of k elevators with capacity one in a transport environment with l 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.