## 4 Design and Simulation of the Conceptual Model for Capacity Planning of an OEM Plant
### Design of a Generic Conceptual Model Development Applying the VSM
Forecasting models: There are three methods in requirements planning: demand-driven or deterministic, stochastic, and heuristic. Each forecasting method is adequate for a certain demand pattern, as shown in Figure 2[15]. As mentioned above, one important characteristic of the viable system model is its ability to adapt its demand forecasting. As a consequence, it is able to detect demand pattern changes after it starts forecasting with another method or with the same method but with different parameters. The approach tries to respond as quickly as possible to demand transformations. In so doing, the model can detect fake changes, which would be worthwhile due to its fast reaction capability. The VSM model recognizes the following patterns, and it forecasts them with the forecasting methods listed:  
* Trend: with regression analysis. * Trend plus sporadic: with regression analysis plus an average sporadic quantity per day. * Sporadic: the sum of outliers is divided by their frequency to obtain the average demand per day. * Steady: with the cumulative moving average method. * Steady plus sporadic: with the cumulative moving average method plus an average sporadic quantity per day. * Seasonal: with the cumulative moving average method (however, this is not the appropriate forecast method in terms of accuracy for this kind of demand pattern). The system is able to detect the following changes by analyzing historical demand data:  
* From steady to steady with a lower/higher mean;
* From steady to steady with a lower/higher standard deviation;
* From steady to steady plus a positive/negative sporadic pattern;
* From steady to an increasing/decreasing trend;
* From trend to trend plus a positive/negative sporadic pattern;
* From trend to steady;
* From trend to seasonal;  
Figure 2: Use suitability of forecasting methods [15]. * From a sporadic pattern to another sporadic pattern. All of these changes are controlled by the variable called \"demand reactivity\". This variable affects all of the control limits for the changes described above. When the value of this variable is higher, then the VSM simulation model detects more changes in demand with less accuracy but reacts before real changes occur in the demand pattern. Each of these changes has a lower and an upper control limit. These limits are fixed using a statistical approach that assumes the forecasting parameters have a normal distribution. It can be seen as a hypothesis test. We use the first type of detection (from steady to steady with a lower/higher mean) as an illustrative example. If the mean of the last 10 days (the sample) for the customer is lower/higher than the mean that is used for forecasting (the population) minus/plus one standard deviation, then a new steady pattern is created with a lower/higher mean, because, with a high percentage, the last 10 values are not a sample of the population (the last demand pattern). * H\({}_{0}\) = the mean is the same as before: the null hypothesis is accepted when mean of the last 10 values is within the control limits that are the mean plus/minus one standard deviation. * H\({}_{1}\) = the mean is higher/lower: one of the alternative hypotheses is accepted if the mean of the last 10 values is not within the control limits. As was explained in the first detection case, the other changes are tracked using the same methodology. Capacity planning: This has an influence on the decision on the number of shifts, the number of employees, and new investments, each of which has a certain delay until its implementation. The conceptual model compares, for each period of time, the gap between demand and available capacity. Based on it and on the demand planning, which is based on a forecasting method and a statistical analysis, the following measures are considered in the conceptual model:  
* Adjust the number of employees in order to produce more in the same number of shifts. * Adjust the number of shifts, as well as working hours, on weekends or holidays.