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Published in:
2018 | OriginalPaper | Chapter
Markov Models for System Throughput Analysis in Warehouse Design
Authors : Anja Heßler, Christoph Schwindt
Published in: Operations Research Proceedings 2016
Publisher: Springer International Publishing
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Abstract
In this paper we study the problem of computing the expected cycle time of a storage and retrieval system executing single-command cycles and being operated according to the closest open location rule. Assuming that the arrivals of the storage and the retrieval orders at the storage follow independent Poisson processes, we first consider the case of homogeneous inventory and develop closed-form expressions for the steady-state probabilities of a given storage location being selected for storage or retrieval. The approach is then generalized to storages with multiple stock keeping units. Comparing our results with estimation formulas from industry standards shows that the latter tend to significantly underestimate the maximum throughput of storage and retrieval systems.