## 4 Development and Simulation of a Predictive S&OP Methodology
### Development of the Conceptual Model
#### 4.1.3 Definition of the S&OP Concept and Forecasting Techniques for Comparison  
The S&OP concept for classical approaches is defined based on:  
* Forecasts based on historical data;
* Sales plans based on forecasted values aggregated for a certain planning horizon;
* Operations plans defined by sales plans and the current system situation (the operations methods are the same as those for the predictive S&OP model);
* Demand pattern changes based on an analysis of historical data;
* The potential measures or investments to adapt capacities along the supply chain, which are not prepared or discussed with suppliers and/or distributors;  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Areas**} & \multirow{2}{*}{\begin{tabular}{c} **Expected Inefficiencies** \\ **Detected within the** \\ **Scenarios** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Cause of the** \\ **Inficiency** \\ \end{tabular} } & \multirow{2}{*}{**Potential Solutions**} & \multirow{2}{*}{
\begin{tabular}{c} **Simulation Model** \\ **Example** \\ \end{tabular} } \\ \hline \multirow{4}{*}{1} & \multirow{4}{*}{Procurement} & & & 1.1. New contract for & \\  & & & an increase in & & \\  & & 1.1. Lack of Quantity & 1.2. Time & & supplier’s capacity & 1.1. Supplier capacity \\  & & 1.2. Lack of Quality & 1.2. Time & & 1.2. Time horizon and & \\  & & 1.3. Delivery time or & constraints/stress & & specifications of & 1.2. Time horizon \\  & & 1.3. Delivery time or & factor & & procurement plans & 1.3. Lead time due to \\  & & & 1.3. Lead time & & & new consignment \\  & & & & & & stock \\  & & & & & producer ’s plant & \\ \hline \multirow{4}{*}{2} & \multirow{4}{*}{Production} & & & 2.1. Investments in & & \\  & & & & new equipment, & & \\  & & & 2.1. Production & outsourcing & & \\  & & & capacities & production & & \\  & & 2.2. Quantity, training, & 2.2. Personnel and /or motivation & & 2.2. Personnel acquisition, training, & \\  & & 2.3. Production lead & 2.3. Production lead & and leadership & 2.2. Quantity of & employees \\  & & 2.3. Storage limitations & time or storage & 2.3. Improvement of & 2.3. Investment in \\  & & 2.4. Lack of quality & 2.4. Existing & investments in new & & \\  & & equipment, time & intermediate storage & & \\  & & & constraints, or volume & & & 2.4. Volume leveling \\  & &The control limits for potential future decisions, which are not defined in advance.  
The demand forecasting methods applied to the S&OP concept for the classical approach are the moving average, the mean of previous \(n\) values [40], and linear regression appropriate for stable trend [37]. In the model, the single moving average (_SMA_) with \(n\) equal to ten, and the cumulative moving average (_CMA_) with \(n\) as a variable, are applied, where \(D(t)\) is the demand of the item. In addition, in the linear regression, \(a\) is the slope of the trend, and \(t_{trend}\) is the quantity of days since the trend demand pattern started, while \(b\) is the value when the demand pattern is initiated:  
\[SMA=F_{(t+1)}=\frac{1}{n}\sum_{t=t-(n+1)}^{t}D_{(t)} \tag{1}\]  
\[CMA=F_{(t+1)}=\frac{1}{n}\sum_{t=t-(n+1)}^{t}D_{(t)} \tag{2}\]  
\[F_{(t+1)}=a\cdot t_{trend}+b \tag{3}\]  
The classical approach uses one of the previous methods to forecast customer demand. The classical simulation model can change between different forecasting methods depending on the demand pattern and an analysis of the historical data. Moreover, it can detect outliers, forecast sporadic trends, extend the moving average, and detect seasonal demands.  
As in the predictive S&OP model, the classical simulation model prepares procurement, operations, and distribution plans based on the demand plan for the time horizon. Moreover, it can decide to invest in new capacities based on the expected gap between current capacities and future expected demand.