## 3 Analysis Model Proposal, Testing, and Results
### The Importance of Synchronising Stocks and Prices across Sales Channels  
According to the studies carried out when there is a permanent synchronization between the prices that a seller practices on various e-commerce platforms, the degree of customer satisfaction is high because the customer has the possibility to choose a desired product according to the purchase price, see Table 1. This procedure saves a lot of time wasted in operationalization; automatic price updating between several sales channels can be achieved by uploading product feeds, which contain at least one product identification code and, through matching logic between them, can automatically update prices on all sales channels without the need for manual adjustment and operator intervention. This information is extracted from the automation market in Romania, specifically through the Ecap and Syncap SaaS solutions. \begin{table}
\begin{tabular}{c} \hline \hline \multicolumn{1}{c}{**Identification of Variables**} \\ \hline \(P_{i}=\text{Product price }i\text{ by sales channel }j\) \\ \(P_{sync}=\text{Synchronised product pricing }i\) \\ \(T_{m}=\text{The time required to manually adjust prices on a sales channel}\) \\ \(T_{a}=\text{The time required to automatically update prices on a sales channel}\) \\ \(N=\text{Number of products}\) \\ \(C_{m}=\text{Operational cost of manual adjustment}\) \\ \(C_{a}=\text{Operational cost of automatic update}\) \\ \(S=\text{Customer satisfaction (score on a scale of 1 to 10)}\) \\ \(\Delta\text{S}=\text{Increased customer satisfaction due to price synchronization}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mathematical conversion model highlighting the importance of price automation and scaling in e-commerce. Therefore, we can highlight the method by which the degree of accuracy in saving time is identified through automation procedures, these being identification through Formulas (1)-(3):  
\[T_{Total_{manual}}=N\times T_{m} \tag{1}\]  
\[T_{Total_{automatic}}=N\times T_{a} \tag{2}\]  
\[T_{Save}=T_{Total_{manual}}-T_{Total_{automatic}} \tag{3}\]  
When discussing how we can reduce costs through automation we must also consider the following aspects in Formulas (4)-(6):  
\[C_{Total_{manual}}=N\times C_{m} \tag{4}\]  
\[T_{Total_{automatic}}=N\times C_{a} \tag{5}\]  
\[C_{Save}=T_{Total_{manual}}-C_{Total_{automatic}} \tag{6}\]  
These aspects should not be neglected, which include the degree of customer satisfaction, around which all of these aspects revolve in Formulas (7) and (8):  
\[S_{manual}=S \tag{7}\]  
\[S_{automate}=S+\Delta S \tag{8}\]  
The application of the model can be taken on an individual case and can be presented in the form where the number of products \(N\) = 1000, and for manual price adjustment by an operator we have a time of the form \(T_{m}=5\) min, and the time required for the automatic updating of prices will be discussed in terms of \(T_{a}=0.1\) min. When we consider the operational costs of manual adjustments the form of applying the model, it will be of the form \(C_{m}=0.5\) USD/product, and the cost of operationalization and automation will be of the form \(C_{a}=0.1\) USD/product, with a probabilistic degree of customer satisfaction of the form \(S=7\), and the increase in the degree of satisfaction through price synchronization is represented by \(\Delta S=2\), see Table 2.  
To further extrapolate what was highlighted, both in the study and in the economic model generated by this automation modality, an identical situation was generated by analyzing the exposure for 1000 products, 5000 products, 10,000 products, 20,000 products, 30,000 products, 40,000 products, and 50,000 products, this flow being extremely common and covering every customer pattern that an automation solution can have, including data that were exposed using Ecap and Syncap reports. Having this information, the necessary correlations were made to highlight the different variables, and depending on the number of products, to clearly show how much automation impacts an online store.