1 Dual cycle time modelling and design optimization for the bidirectional flow-rack AS/RS Mohammed A. Hamzaoui 1,2 , Zaki Sari 1,3 1 Manufacturing Engineering Laboratory of Tlemcen (MELT), 1 Higher School of Applied Sciences of Tlemcen, Algeria (ESSAT). 2 hamzaoui.mohammed.adel@gmail.com, 3 zaki_sari@yahoo.com Abstract The current dynamic economic context with very rapid changes, pushes economic players to always get up to speed, adapt and innovate to face the growing competition. Having efficient supply chains capable of absorbing the shocks of various fluctuations is a necessity. Storage warehouses are essential links in these latter, and improving their performance is the keystone through which the control of any supply chain must pass. The appearance of automated-storage/retrieval-systems (AS/RS) has made it possible to have the technological implements to achieve these ends. However, it is necessary to have mathematical tools that allow the effective and efficient use of these equipment in order to optimize their performances. In this paper, we develop mathematical models of dual cycle times for the bidirectional-flow-rack AS/RS. First, we develop models according to two approaches and then compare them to each other. Then we proceed to an optimization of the system's dimensions for minimum cycle times. This allowed us to extract approximate formulas of optimal dimensions according to the size of the system and its nominal load rate. Next, thanks to a numerical study we could deduce the optimal shape of the system for the two modelled cycle times as a function of the nominal load rate. Lastly, we proceeded to a throughput calculation thanks to the conducted study. This represents an indispensable tool for the upstream design and installation of the system in order to optimize its performances in steady state, which will have a direct positive impact on the supply chain performances. Keywords: Automated Storage/Retrieval Systems, Material Handling, Warehousing, Mathematical Models, Design Optimization. 1 Introduction and backgrounds Thanks to the development of information and communication technologies, internet of things and artificial intelligence, we have recently been able to move into Industry 4.0. This fourth industrial revolution is mainly based on the digitalization, information literacy and interconnectivity, which led to the modernization of all the production operations and related activities. Transportation, material handling and warehousing activities are highly concerned by this modernization journey, and numerous related equipment could recently see the light of day, among which, we can mention the automated storage/retrieval systems (AS/RS). These latter, in order to be used efficiently and effectively, are studied according to different angles and perspectives, while the key point to achieve flexible automated warehouse excellence is the combination of automated equipment, data collection technologies, and management solutions [1]. The addressed issues may be of a strategic, tactical or operational nature. When dealing with the strategic issues, the main related decisions have to be made before the system’s installation; therefore, tools for performance evaluation upstream of the system’s installation are required. Simulation and mathematical modelling are mainly used for this purpose. These different tools are generally developed for throughput evaluation and response time calculation, as well as to proceed to systems performance comparison, design optimization, energy consumption and usage cost evaluation. Concerning mathematical modelling, when applied to cycle time and throughput evaluation, specific mathematical formulas are developed. Bozer & White [2] were among the first ones who addressed the cycle time mathematical modelling problem. In their paper, they calculated different cycle time models for the unit- load AS/RS, and laid the groundwork for the two most used modelling approaches, the (1) discrete and the (2) continuous approaches. The discrete one provides precise mathematical models, but which are difficult to use