Capacity analysis of sequential zone picking systems

Jelmer van der Gaast, M.B.M. de Koster, I.J.B.F. Adan, J.A.C. Resing

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Abstract

This paper develops a capacity model for sequential zone picking systems. These systems are popular internal transport and order picking systems, due to their scalability, flexibility, high-throughput ability, and fit-for-use for a wide range of products and order profiles. The major disadvantage of such systems is congestion and blocking under heavy use, leading to long order throughput times. To reduce blocking and congestion, most systems use the block-and-recirculate protocol to dynamically manage workload. In this paper, the various elements of the system, such as conveyor lanes and pick zones, are modeled as a multi-class block-and-recirculate queueing network with capacity constraints on subnetworks. Due to this blocking protocol, the stationary distribution of the queueing network is highly intractable.
We propose an approximation method based on jump-over blocking. Multi-class jump-over queueing networks admit a product-form stationary distribution
and can be efficiently evaluated by Mean Value Analysis (MVA) and Norton's theorem. This method can be applied during the design phase of sequential zone picking systems to determine the number of segments, number and length of zones, buffer capacities, and storage allocation of products to zones, to meet performance targets.
For a wide range of parameters, the results show that the relative error in the system throughput is typically less than 1% compared to simulation.
Original languageEnglish
Pages (from-to)161-179
Number of pages19
JournalOperations Research
Volume68
Issue number1
Early online date21 Nov 2019
DOIs
Publication statusPublished - 1 Jan 2020

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Keywords

  • Logistics
  • Material handling
  • Queueing theory
  • Warehousing

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