## 2 Literature Review
### Square Root Formula Limitations  
The relationship between the level of safety stocks and the number of warehouses in the distribution network reflects the \"The Square Root Law\", which is presented in the form of the following mathematical formula [9; 10]:  
\[X_{2}=X_{1}\cdot\sqrt{\frac{n_{2}}{n_{1}}}\]  
\(n_{1}=\) number of existing facilities;  
\(n_{2}=\) number of future facilities;  
\(X_{1}=\) existing inventory;  
\(X_{2}=\) future inventory.  
Since the level of the customer service is included (measured by the availability of inventory), this means that it can also be used to evaluate the impact of warehouse centralization policies on the level of logistics customer service.  
However, in the scientific literature, one can find a critical approach to the applicability of the mentioned formula. Considering the different economic sectors, the obtainedoutcomes are highly varied. In the work of [PERSON] and [PERSON] [34], it was shown that the formula does not perform well in companies in the manufacturing sector and does better in companies in the trading sector. Additionally, another paper by this author [35] shows that it overestimates the savings that result from centralizing warehouses.  
First of all, the formula allows the calculation of the level of safety stocks before and after centralization. On the other hand, in some papers, there is a suggestion that cyclical stock and safety stock can be considered together [31; 33; 36; 37] and that a significant aspect for the effective application of this approach is transportation: the quality and the cost of transportation service [38].  
In addition, warehouses may accumulate excess inventory that results from erroneous forecasts, and the ability to adjust to actual demand may be higher in the case of centralization strategies.  
Some authors note that the minimization of the external costs could be aided by a minimal number of warehouses, in the sense of using less of certain resources such as energy [39]. This impact is not clear. The operation of big and extremely high-tech warehouses can result in a growing consumption of energy (heating or cooling, lighting, air conditioning) and growing CO\({}_{2}\) emission [40]. However, this impact also depends on certain properties of the building, e.g., the number of doors and windows, insulation, and efficacy of the heating and cooling system, as well as external factors such as properties of stored goods and outside temperature [41], the technology used [42], the parameters of the used equipment (motor power, energy consumption), and also the operating mode, e.g., the speed of movement in the warehouse and the organization of work in the warehouse [43].  
Current analyses show that about 10% of global carbon emissions come from logistics supply chains. The significant lighting, cooling,+ or heating energy required in storage accounts for almost 21% of the total logistics costs. According to a study, the total electricity consumption of warehouse facilities has decreased from 1976 to 2017, influenced by technological developments that resulted in the production of green equipment (e.g., air-circulation, lighting or ventilation systems, etc.) [44].  
The reduction of energy consumption is considered to be the most important factor for reducing external storage costs, which can be achieved, for example, by using the appropriate equipment in the picking area [45; 46; 47].  
[PERSON] [1] developed a simulation model of the total costs of centralization strategies in both micro (enterprise) and macro (external costs) terms. The results of simulations indicate that while the effects of a particular strategy may vary, in many cases the influence on both the efficiency of the logistics processes and the external costs of transportation can be significant.  
This paper presents the results of simulations that are an extension of this model. The authors conducted tests for more variants and for two types of demand deviations: the Gaussian and Gamma distributions.