## 4 Design and Simulation of the Conceptual Model for Capacity Planning of an OEM Plant
### Simulation of a Specific Model for the Case Study of an Automotive Plant  
The following assumptions were made:  
* Time restrictions: Firstly, the modeler must define a time horizon and units of time. It is easy to carry out this step by asking to what extent the simulation should be considered. In the case of the study, it was decided to simulate four working years to evaluate influences in the medium and long term. The simulation was performed with 1000 time periods, each representing one producing day counting in total for four years of production. * Production capacity has a maximum of 600 units per day in three shifts at the beginning of the simulation. During the simulation, two investment options were considered: an increase of 100 units per day or an increase of 200 units per day. Both models assessed the same requirements for initiating one or the other investment. The difference between the viable system model and the nonviable system model was the lead time of the decision-making process. * Viable system model: the decision-making process takes 10 days. * Nonviable system model: the decision-making process takes 100 days. * Demand characteristics and forecast: The model makes different forecasts using two methods, i.e., moving average and linear regression: Moving average: the simple moving average (SMA) is the non-weighted mean of the previous \(n\) data [16]. In the nonviable system model, it is calculated as the average for the last 10 days (\(n=10\)). As the VSM is able to detect demand changes over time, all demand values were taken into account for the forecast until a new demand pattern was registered. Therefore, the formula of the cumulative moving average was applied. Linear regression: The regression analysis method is usually applicable to a steady course of a time series or a stable trend [16]. In the model, it is only used for trend demand patterns, when using only one leading indicator and the time since the trend demand pattern was detected. As a result, a simple linear regression can be defined as follows: \[\text{F}_{\text{j}}\left(\text{t}\right)=\text{demand forecast for customer j at time t}=\alpha\times\text{t}_{\text{trend}}+\beta,\] where \(\alpha\) is the slope, \(\text{t}_{\text{trend}}\) is the time since the trend demand pattern was detected, and \(\beta\) is the value at the time when the trend demand pattern was detected. * The existing car model is in a mature stage with stable demand and provides 1000 euros/car of margin. The new model is in the process of being launched and provides 2000 euros/car. These values were used to calculate profits. If there is loss in volume, it is assumed that the new model will have the loss in volume due to unknown future demand. * The simulation model considers sales loss starting from a customer order lead time greater than 60 days. * A product is a finished product after it leaves the production facility. * The warehouses have no stock limitation. * There is no transport limitation (or limitation to the number of trucks) between the different stages. * A steady supply of materials for the production process is provided. * The available stock, as well as the number of products, is known at every moment of the transport process. * Order information along the supply chain is available. * Data on historical demand are available for both models one day after the demand. * Operational adjustments allow for changing the shift model with a one-third increase in the capacity per extra shift with a maximum of three shifts. Moreover, a higher number of employees in an existing shift provide a flexibility of 10% to existing production capacities. * Production is 50% make-to-stock and 50% make-to-order. * Production consists of a process that begins with steel stamping and ends with final revision. The plants in the process are shown in Figure 3 and listed below. * Press shop 1: a nominal capacity of 300 units per day. * Bodywork shop 1: a nominal capacity of 300 units per day. * Press shop 2: a nominal capacity of 300 units per day.