# Simulation

Simulation means the analysis of time dynamic processes using computer-aided experiments. This may be the spread of a contagious disease, the flow of material through a production system or the time evolution of a specified share prices. If you want to explore such systems to find out dependencies or to make predictions, one has to carry out extensive experiments, which are expensive and slow. Often such experiments fail because you can not manipulate the real system or there is insufficient time to carry out the many investigations. The aim of the simulation is to abstract the real processes by a mathematical model and transfer the experiments to the model. Since the model using a computer is realized numerically, the experiments can be carried out quickly, cost effectively and safely. What in nature takes days and years, can be adjusted in this way in a few seconds or minutes. The results are data that may need to be evaluated using statistical procedures.

## Example: Capacity planning by simulation

When re-planning a production line by the factory planning two successive process steps which are to be accommodated in different halls which are connected with each other by a driverless transport system were provided. The capacity calculation showed that one could accomplish the transport with three vehicles. Despite the high utilization of the transport system of approximately 97%, the management initially did not wanted to approve any additional vehicles because of the high cost of the vehicles and the difficult financial situation during the start of the new product. On the contrary, the management was pleased to use the transport system as efficient, especially since downtime for maintenance and repair ware already taken into account in the static calculation.

However, the simulation showed that an additional vehicle would pay for itself after one year because due to the high utilization of the vehicles in the initial case a disproportionately high storage space had to be provided at the end of the first state (see chart). The storage space would have been a significant cost factor due to the capital intensive storage components and also because of the high capital commitment by waiting workpieces, which would have been out of proportion to the acquisition and maintenance costs of an additional vehicle (see table). So if one had only relyed on the static calculation, the total cost would have been about twice as high.

### Profitability analysis

3 Vehicle 4 Vehicle 5 Vehicle
Utilization 97% 73% 58%
Acquisition cost 75.000 € 100.000 € 125.000 €
Storage space 100.000 € 11.000 € 8.000 €
Capital commitment(*) 240.000 € 26.000 € 20.000 €
Maintenance 30.000 € 40.000 € 50.000 €
Total costs 445.000 € 177.000 € 203.000 €

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