## 2 Materials and Methods
### Methodology of Buffer Zones' Dimensioning
#### 2.2.3 Calculation of Optimal Inventory Control Parameters  
When calculating optimal inventory management parameters, we based our calculations on well-known order policies. These policies apply tensile inventory management principles. The DDMRP system represents a pressure-tensile steering system. Stocks in strategic DDMRP storage systems are replenished based on tensile signals, and stocks within one loop between two downstream disconnection points are controlled by pressure principles. * P systems (fixed-order period systems): These are replenishment systems operating with a fixed order cycle. Orders for new deliveries are executed at regular time intervals, and the size of the order is usually variable. The determination of the basic parameters of the P system involves the calculation of the order cycle length, premium,  
Figure 5: Statistical analysis of quantity variations—example of outputs. Figure 6: Probability distribution of quantity variations—example of outputs. and maximum (after-order) inventory level. The advantage of P systems is the lower difficulty of monitoring the development of inventory levels (inventory levels are evaluated periodically) and the possibility of ordering several items together (in the case of determining a common length of the order cycle). The disadvantage is the lower flexibility of the system for the real development of the inventory of items in stock and the need to hold a higher buffer stock. * Q systems (fixed-order quantity systems): These systems work with fixed order sizes and variable ordering dates. Ordering a new delivery is realised when the stock drops below the ROL (reorder level). The determination of the basic parameters of the Q system includes the calculation of the buffer stock, the signal inventory level (ROL), and the optimal order size. The advantage of Q systems is their ability to quickly react to changes in inventory levels and lower insurance stocks, while the disadvantage is the higher labour costs of inventory monitoring (continuous monitoring of inventory development). For the purpose of calculating basic inventory parameters, a combined ordering policy was used, which works with variable ordering dates and variable order sizes. This combination ensures the best inventory level flexibility for different types of variability and corresponds to the strategic storage management philosophy in the DDMRP concept. The basic parameters of inventories and the method of determining them are as follows:  
1. Safety stock: The buffer stock consists of three basic components:  
* insurance against the variability of consumption,
* insurance against the variability of the lead time,
* insurance against the variability of delivery sizes. The starting point for determining the optimal level of the buffer stock is the calculation of the optimal service level [41]:  
\[\text{SL}=\frac{\text{C}_{\text{s}}}{\text{C}_{\text{s}}+\text{C}_{\text{c}}} \times 100 \tag{10}\]  
where:  
SL--optimal service level (%),  
C\({}_{\text{s}}\)--stockout cost (EUR/(unit \(\times\) day)),  
C\({}_{\text{c}}\)--carrying cost (EUR/(unit \(\times\) day)). For a specified level of service, from the cumulative probability distribution functions (variations in consumption, variations in lead time, and variations in quantity), the required degree of coverage was assigned a corresponding insurance component (Figure 7). Figure 7: Example of safety stock determination based on the probability distribution function and required service level (95%). (**a**) Safety against the variability of demand. (**b**) Safety against the variability of lead time. The resulting buffer stock was determined as:  
\[\text{SS}=\text{Sd}+\text{ADU}\times\text{S}_{\text{I}}+\text{Sq}, \tag{11}\]  
where:  
SS--safety stock (units),  
Sd--safety against the variability of demand (units),  
S--safety against the variability of lead time (days),  
Sq--safety against the variability of delivered quantity (units),  
ADU--average daily usage. 2.