An analytical approach for a performance calculation of shuttle-based storage and retrieval systems

Abstract

This paper deals with a method for performance calculation of shuttle-based storage and retrieval systems (SBS/RS) with tier captive shuttles. A continuous time open queueing system with limited capacity approach is applied. The cycle times of shuttles and lifts can be used directly with their time distributions. These cycle times are determined by a discrete spatial value approach. The main novelty of this approach is the use of a time continuous queueing model to take the interactions between lifts and shuttles combined with a spatial discrete approach for the processes of lifts and shuttles into account. A comparison between the analytical approach and a discrete events simulation is presented to validate the developed model. The data used in this comparison to validate this approach was given by an European material handling provider. Finally, it will be outlined how the model can be used for designing SBS/RS, to meet given requirements.

Analytical model to estimate the performance of shuttle-based storage and retrieval systems with class-based storage policy

“…Existing research on tier-captive shuttle-systems with random storage assignment is substantial. Eder [2] asserted two possible ways of discussing SBS/RS: one using discrete event simulation (DES) and the other via an analytical approach to examine such systems. Nonetheless, there have been rare accounts discussing class-based storage policies in SBS/RS.…”

“…Kuo et al [10], for instance, discussed the use of a queueing network to investigate a SBS/RS with class-based storage. Such approach though was limited; although it was only able to calculate the waiting times within one handling cycle, the maximum throughput could not be extracted [2]. Ekren et al [6] presented an approach that treated, or rather, simulated class-based storage policies in SBS/RS.…”

“…Literature [2][3][4][5] describes the manner in which the system is closest to its real behavior. More importantly, Eder [2] additionally used a spatially discrete approximation, which likewise corresponds to reality. An overview of all existing literature on SBS/RS is presented in Table 1.…”

“…This is the reason for the research gap in analytical decision tools for determining the maximum throughput of SBS / RS with a class-based storage policy. This study specifically adopted and advanced the main idea in Eder [2] through consideration of several probability based approaches within the class-based storage policy.…”

“…1. A lift can be seen in front [13] Tier-captive Uniform QN Single deep No Ekren et al [6] Tier-captive Class-based SIM Single deep Yes Eder et al [3] Tier-captive Uniform SQLC Double deep Yes Eder et al [4] Tier-captive Uniform SQLC Single deep Yes Schloz et al [15] Tier-captive Class-based OPT Single deep No Eder et al [5] Tier-captive Uniform SQLC Single deep Yes Kriehn et al [9] Tier-captive Class-based SIM Single deep Yes Eder [2] Tier-captive Uniform SQLC Single deep Yes of each rack for totes transport from the input/output (I/O) point to the tier and back. Basically, these I/O points are located on the first tier in front of the lifts.…”