The design of material flow and production systems plays a decisive role for the achievable performance and thus also for their economic efficiency. This requires stable and robust production processes with efficient material and information flows. However, stochastic events, such as machine failures, complicate the quantitative analysis of the processes, which is necessary as a basis for decisions for an efficient design.
At the beginning of the planning phase for a new material flow or production system, there is a large number of potential system configurations that need to be analyzed with regard to various key performance indicators. The planner's task is to identify the alternative that best meets both quantitative and qualitative targets. The quantitative methods of the performance evaluation of material flow and production systems are classified in the literature based on the degree of detail and the required computing time into continuous time queueing theory, discrete time queueing theory and simulation.
We use both analytical and simulation-based stochastic models to evaluate the performance of material flow and production systems. A special focus is on the discrete time queueing theory. This has the advantage over the continuous time queueing theory that the existing data, for example processing times, can be used directly and do not have to be approximated by contin-uous distributions. In addition, the discrete time queueing theory is not limited to the calcula-tion of expected values when determining key performance indicators, such as the sojourn time of an order, instead the complete probability distributions can be determined. The fast and ac-curate numerical calculation of key performance indicators in material flow and production sys-tems with the help of discrete-time queueing theory closes the gap between (often inaccurate) purely analytical considerations and (always complex) simulation investigations. In the detailed planning of material flow and production systems, however, the simulation of the system is usually essential. We can draw on extensive experience in the field of material flow and production simulation, e.g. with the simulation software Anylogic or Plant Simulation.
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