Analytical computation of sojourn time distributions in large-scale conveyer systemsAnalysis of the impact of material flow control policies on the material flow system

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In the planning and dimensioning of complex, networked material handling systems, functionality, layout and facilities were set. The respective intralogistical system should produce a certain logistic performance. Modern logistic systems focus on a time-accurate material supply with short lead times. The logistic performance consists not only of reaching a specific transport or sort amount per time (throughput), but also of ensuring the settlement of orders within a preset time (lead time). The mean values used in the rough planning phase do not suffice here as concrete individual values can sometimes be a multiple of that.The current project phase developed an analysis tool (called Material Flow Analyzer). Time-discrete analytical models form the basis of the analysis tool. In contrast to classical (continuous) analytical models, discrete time models provide not only mean values but also about the probability or likelihood that particular characteristics are achieved (so-called quantiles). This includes waiting times, turnaround and required buffer sizes, for which results can be determined only by means of elaborate simulation experiments. With the Material Flow Analyzer there is a tool available which can calculate required ratios such as utilization, but also probability distributions of lead times and buffer allocations, quickly and without elaborate simulation in not known accuracy.It became evident that control strategies based on material flow node can only inadequately covered by correction factors. For a precise determination of the time they must be modeled explicitly. The amended main material flow node includes crossing elements and storage/retrieval machines.The developed test environment by systematically made tests and calculations show that the time-discrete calculation method has a good agreement with the expected values. The tests systematically carried out by the developed test environment and comparative calculations certify a good correspondence with the values to be expected to the time-discrete analyses. For this reason, it can be assumed that results in some non-trivial network topologies are not owed this new calculation method, but other, already known, hardly quantifiable effects like correlation are responsible.The goal for the continuation of the research project is therefore in addition to the further development of calculation methods to make more detailed and systematic studies with the 'Material Flow Analyzer' tool, to explore different effects such as control strategies or formation, effect and propagation of correlation in time-discrete models of complex material flow systems.