## 4 Design and Simulation of the Conceptual Model for Capacity Planning of an OEM Plant
### Simulation Results for the Case Study of an Automotive Plant  
Before the results from the model were extracted and interpreted, a formal validation was performed. According to [PERSON], there are 12 possible methods for validating system dynamics models [17]. There are three that are relevant to our models; one of them is the extreme-value test, which we used in this paper. An application of this method proved that the model's response is plausible when taking extreme values for different input parameters. Some basic physical laws should be examined, for example, when there are no employees, the model's output should not able to meet the demand. For both models, the same input and output variables were chosen in order to analyze  
Figure 4: The four demand scenarios for the new car model (own elaboration). and validate the models. These input variables are nominal capacity and customer demand. From the variation in these variables, the following can be expected in order for the results to be logical and the model to be validated:  
* For a lower nominal capacity (units per day), the customer order lead time, volume loss, and capacity utilization must be higher, and the total number of units delivered to customers must be lower, as shown in Figure 5. The red lines indicate the lower nominal capacity, and the blue ones indicate the higher nominal capacity. * For a lower customer demand (units per day), the customer order lead time, volume loss, capacity utilization, and total number of units delivered to customers must be lower. After the validation, the results for the four demand scenarios were extracted for the selected key performance indicators. In the first scenario, the VSM produced better results for all relevant indicators as it can be seen in Table 1, although the nonviable system model increased its capacity by 200 units per day. As this decision was made with a delay in comparison to the viable system model, the total number of delivered units was almost 5000 units lower and the capacity utilization was 12% lower. Moreover, the viable system model generated a profit of 1021 million euros, whereas the nonviable system model generated a profit of 1012 million euros, which is nine million euros less. In addition, the VSM was able to generate savings of one million euros. For both scenarios, the return on investment (ROI) was positive at the moment the decision was made. The value was the same; however, the VSM achieved this ROI with an investment value that was 30 million euros less due to a lower increase in capacities than the nonviable system model. As the decision was made later, the customer order lead time was almost 10 days longer in the nonviable system model. Therefore, from the comparison of the models, the results show that the VSM would be selected as desirable in this demand scenario due to its combination of a low investment and a low cost and its highly efficient deployment (lead time, service level, and capacity utilization). Figure 5: Results of the validation for nominal capacity using the extreme-value test (own elaboration). In the second scenario, the VSM also produced better results for all relevant indicators as shown in Table 2, although, as in the first scenario, the nonviable system model increased its capacity by 200 units per day. As this decision was made with a delay in comparison to the viable system model, the total number of delivered units was nearly 5000 units lower, and the capacity utilization was almost 12% lower. Moreover, the viable system model generated a profit of 934 million euros, whereas the nonviable system model generated a profit of 925 million euros, which is nine million euros less. In addition, the VSM was able to generate savings of 3.5 million euros. For both scenarios, the return on investment was positive at the moment the decision was made. The ROI in the VSM was 13.4 million euros higher than that in the nonviable system model and it was achieved with an investment that was 30 million euros less.