Two-worker blocking congestion model with walk speed m in a no-passing circular passage system

• Published in: European journal of operational research 2014-06, Vol.235 (3), p.687-696
• Main Author: Hong, Soondo
• Format: Article
• Language: English
• Subjects: Approximation; Blocking; Blocking congestion; Bucket brigade order picking; Circularity; Computer simulation; Congestion; Exact solutions; Facilities planning and design; Integer programming; Markov analysis; Mathematical analysis; Mathematical models; No-passing passage system; Order picking; Simulation; Stations; Studies; Walking
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2013.10.013

•Construct a blocking model traveling with walk speed m in a circular-aisle warehouse.•Derive a closed-form expression of two-worker blocking congestion.•Estimate the blocking congestion in a practical walk speed system.•Demonstrate the applicability to a bucket-brigade order picking situation. This paper introduces a blocking model and closed-form expression of two workers traveling with walk speed m (m=integer) in a no-passing circular-passage system of n stations and assuming n=m+2, 2m+2,…. We develop a Discrete-Timed Markov Chain (DTMC) model to capture the workers’ changes of walk, pick, and blocked states, and quantify the throughput loss from blocking congestion by deriving a steady state probability in a closed-form expression. We validate the model with a simulation study. Additional simulation comparisons show that the proposed throughput model gives a good approximation of a general-sized system of n stations (i.e., n>2), a practical walk speed system of real number m (i.e., m⩾1), and a bucket brigade order picking application.