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

Abstract

An 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.

A literature review of smart warehouse operations management

“…Today, AS/RS has evolved into an efficient system with many variants, including AVS/RS (Lerher et al, 2021), SBS/RS (Zhao et al, 2020a;Yetkin Ekren and Akpunar, 2021), compact AS/RS (Hao et al, 2015;Xu et al, 2018;Kumawat and Roy, 2021), and puzzle-based storage and retrieval system (Mirzaei et al, 2017;Yalcin et al, 2019). The system configuration of AS/RS and its variants can be affected by many factors, such as the configuration of rack (Yetkin Ekren, 2017), aisle (Roy et al, 2015a;Manzini et al, 2016), cross-aisle (Tutam and White, 2019a), space (Derhami et al, 2019), tier (Tappia et al, 2017), shape (Tappia et al, 2017;Tutam and White, 2019b), depot (Gharehgozli et al, 2017;Gharehgozli et al, 2021), shuttles (Ha and Chae, 2019), and pick position (Liu et al, 2021). Some tactical policies Fig.…”

Technical note: A graphical approach to the analysis of travel times in an automated storage and retrieval system

“…Their work was extended by Scharfstein (1990) for a NSIT rack. Liu et al (2020) derived the PDF of travel time from a discrete or continuous random point to a random point, and to another discrete or continuous random point in a NSIT rack. In comparison to previous work, we introduced a graphical approach to derive the travel time PDF.…”