Stochastic analysis of an automated storage and retrieval system with multiple in‐the‐aisle pick positions

Abstract

AbstractAn automated storage and retrieval system with multiple in‐the‐aisle pick positions (MIAPP‐AS/RS) is often used to support case‐picking occurring at floor and mezzanine levels. In this paper, the replenishment process is modeled as an M/G/1/N/N queueing problem in which the aisle‐captive AS/R machine is the server and pick positions requiring replenishments are customers. Four scenarios are considered: finite population with dedicated storage, finite population with random storage, infinite population with dedicated storage and infinite population with random storage. The corresponding probability density functions (PDFs) for travel time are derived using a Chebyshev travel metric. For the finite population case, PDFs are derived using a novel method based on contour lines; the contour‐line‐based method can be used to derive PDFs for similar problems. From queueing and simulation results, the robustness of the M/G/1/N/N queueing model is demonstrated, allowing it to be applied in analyzing an MIAPP‐AS/RS case‐picking operation when interarrival times of replenishment requests are not exponentially distributed and heterogeneous customers are present. Dedicated‐ and random‐storage policies for reserve storage are compared and conditions favoring each policy are provided. A case study demonstrates how queueing results can be applied in designing an MIAPP‐AS/RS.