## 4 Impact of the Centralization Strategy on the Effectiveness of the Distribution
The costs shown should be calculated as following:  
Ci = Average inventory level \(\times\) Cost of maintaining inventories \(\times\) Unit cost of production;  
Cw = Average inventory level \(\times\) Unit cost of warehousing;  
Cls = Sales price \(\times\) Sales volume \(\times\) (100%-Level of Service);  
Ctc = Transport performance [tkm/year] \(\times\) Freight rate [EUR/tkm] \(\times\) Distance. Average inventory level = Cycle Stock + Safety Stock + Excess Stock. The parameters used in the calculations are presented in Tables 6 and 7. The results of the calculations for Gaussian are presented in Tables 8 and 9 and Figures 4-9. Figure 5: Impact of the number of warehouses and distances of deliveries on the total costs of distribution (Gamma distribution, agriculture products). Figure 6: Impact of the number of warehouses and distances of deliveries on the total costs of distribution (Gaussian distribution, electronics products). Figure 7: Impact of the number of warehouses and distances of deliveries on the total costs of distribution (Gamma distribution, electronics products). A slightly greater impact on sales volatility is visible in the case of electronic products. The optimal number of warehouses is also four, regardless of the size of demand fluctuations, but only in the case of the Gaussian distribution. In the case of the Gamma distribution, the optimal size of the warehouses is smaller and, moreover, the influence of the demand fluctuations is visible; the optimal number of warehouses is three for 15% of the standard deviation and two for larger deviations (30%). The cost impact of choosing a storage strategy is also greater, which may be influenced by the greater value of electronic products. The largest cost differences are visible in the case of clothing; moreover, in the case of these products, the most profitable strategy is centralization. In the case of Gauss, the optimal number of warehouses is three when the sales fluctuations are small and two when the sales fluctuations are larger. In the case of Gamma, these are two and one, respectively. The results may seem surprising to some extent. It could be expected that the most favorable centralization strategy would be the most advantageous for the most expensive (electronic) products. Meanwhile, this strategy has turned out to be beneficial for clothing. However, these results can be interpreted quite easily. The total costs of distribution are  
Figure 8: Impact of the number of warehouses and distances of deliveries on the total costs of distribution (Gaussian distribution, garments). Figure 9: Impact of the number of warehouses and distances of deliveries on the total costs of distribution (Gamma distribution, garments). influenced not only by the value of goods, but also by cargo parameters that affect the costs of storage and transport. The simulations also took into consideration the impact of the presence of excess inventories resulting from incorrect sales forecasts. If we assume that the excess inventory for one central warehouse is 15% of inventories and for nine warehouses, 100%, then in all variants of the type of probability distribution and sales fluctuations, the results obtained by both methods are very similar. Therefore, it can be hypothesized that the Square Root Formula was developed for a situation where, in the case of decentralization of storage, excess stocks increased to a large extent. The model, after modification, can also be used to calculate external costs, both transport and storage (Table 10). If the external costs of storage for nine warehouses account for 50% of the external costs of transport, the total costs of the centralization strategy would be the lowest in the case of the Gamma distribution, regardless of the fluctuations in demand (Tables 11 and 12). According to the latest studies, external transport costs are even lower--[51], so the cost-effectiveness of the centralized warehousing would be even higher when taking into consideration the external costs.