This paper presents analytical travel time model for the computation of travel (cycle) time for shuttlebased storage and retrieval systems (in continuation SBS/RS). The proposed model considers the operating characteristics of the elevators lifting table and the shuttle carrier, such as acceleration and deceleration and the maximum velocity. Assuming uniform distributed storage rack locations and using the probability theory, the expressions of the cumulative distribution functions with which the mean travel time is calculated, have been determined. The proposed model enables the calculation of the mean travel (cycle) time for the single and dual command cycles, from which the performance of SBS/ RS can be evaluated. The approximation model and a simulation model of SBS/RS have been used to compare the performances of the proposed analytical travel time model. The analysis shows that regarding all examined types of SBS/RS, the results of proposed analytical travel time model for SBS/RS correlate with the results of simulation models of SBS/RS.

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In this paper a simulation analysis of an automated single-tray Vertical Lift Module (VLM) system is presented. Compared to other well-known warehouse systems, a VLM system can provide moderate throughput capacity and lower investment cost. The objective of the study is to investigate benefits of a single-tray VLM system design in terms of reducing transactions' mean cycle time, which results in increased throughput of the system. Performance of the single-tray VLM is evaluated regarding alternative design configurations and the velocity profiles.The results show that single-tray VLM systems are effective and may serve as guideline for warehouse designers in designing a new or improving an existing automated warehouse system.

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