Improving Fleet Size Estimation for Factory Logistics Under Demand, Speed, and Efficiency Uncertainty

<ns3:p> In material handling systems, estimating the required fleet size of automated guided vehicles (AGVs) is a significant task when designing processes to ensure efficient demand fulfillment. Analytic fleet size estimation methods typically assume that key input variables – such as AGV speed, loading / unloading times, material transportation demand between stations, efficiency and availability coefficients – are deterministic averages, overlooking the variability found inherent in real-world operational conditions. In contrast, we investigate the potential benefits of modeling key parameters as random variables with known means and variances, to account for this uncertainty. The core of the method lies in expanding functions of random variables in terms of deviations from their mean values. Taking expectations, the expansions are expressed in terms of the central moments and mixed moments. The process is facilitated by the introduction of two linear operators, which streamline the development of the method. We thus derive second-order approximations for the expected value and variance of the required number of AGVs, providing more accurate and reliable fleet size estimates. The effectiveness of this approach is demonstrated through Monte Carlo simulations, comparing the results with empirical data from several case studies. The method has been implemented in the "Agent Optimization" software system, developed as part of the <ns3:italic>Grow your manufacturing business (Better Factory)</ns3:italic> Horizon 2020 project. </ns3:p>