## 4 Impact of the Centralization Strategy on the Effectiveness of the Distribution  
The regression model can then be used to simulate the cost-effectiveness of using a storage strategy. Calculations using this model were carried out for three hypothetical products from the following industries: food, electronics, and clothing; various standard deviations of demand, and two distributions of demand: Gaussian and Gamma. First, calculations were carried out, the purpose of which was to check to what extent the results coincided with the results obtained using the \"Square Root\" formula (Tables 4 and 5 and Figures 2 and 3). The starting point is a decentralized system with nine warehouses. \begin{table}
\begin{tabular}{c c c c c} \hline  & \(R^{2}\) & \(F\) & \(p\)-Value & \(d\) Durbin–Watson \\ \hline The Gaussian distribution & 0.905694 & 978.1901 & \textless{}0.00001 & 1.9013 \\ \hline The Gamma distribution & 0.840391 & 663.1129 & \textless{}0.00001 & 1.8976 \\ \hline Source: own calculations. & & & & \\ \end{tabular}
\end{table} 
Table 3: Verification of the regression model. In both distributions, even with small standard deviations (15% of the average demand), the levels of safety stocks calculated using the regression model decreased significantly with the reduction of the number of warehouses. However, the greater benefits of centralization are in the Gamma distribution. In the Gaussian distribution, the safety stock in one central warehouse is 50.1% of the stock in a system consisting of nine warehouses. In the case of the Gamma distribution, this stock drops to 12.8%. Even greater differences are visible when the sales fluctuations are greater (the standard deviation is 30% of the average demand). In the case of Gauss, the stock is only 80.71% (thus, the benefits of centralization are smaller here). In the Gamma distribution, with greater fluctuations in demand, the benefits are also smaller, but are still greater than in the case of Gauss, because the safety stock in the central warehouse is 32.8% of the inventory in the decentralized system. The results of the calculations of the safety stock level obtained by the regression model (RM) were then compared with the results calculated using the \"Square Root Formula\" (SRF). In the case of the normal distribution with small fluctuations in sales (15% of average demand), the inventory levels calculated using both methods are very similar, although the differences between the two become larger with fewer warehouses. Inventory levels already vary significantly with greater volatility in demand (30% of average demand). Therefore, it could be concluded that perhaps the Square Root Formula could be used to calculate the level of the safety margin after some modification of this formula, which would take into consideration the demand volatility. However, the results were completely different when the Gamma distribution was in demand. The results obtained with both methods are most similar to each other, not with small changes in scale (and therefore unlike in Gauss), but with large changes in sales (Table 5 and Figure 3). Moreover, with large deviations, the results for Gamma are more similar to each other than for Gauss, which may give rise to a supposition that the \"Square Root law\" was perhaps developed for this type of demand. This issue should be the subject of further research. The calculated inventory levels can then be used to calculate the total cost of distribution using the following formula:  
\[\text{Cd}=\text{Ctw}+\text{Ci}+\text{Cw}+\text{Cls}+\text{Ctc}\]  
where:  
Cd--The total costs of distribution;  
Ctw--Transport costs to warehouses;  
Ci--Inventory costs;  
Figure 3: Levels of stocks—simulation vs. “Square Root Formula” (Gamma distribution). Cw--Warehousing costs;  
Cls--The costs of lost sales;  
Ctc--Transport costs from warehouses to customers.