## 3 Results--Effectiveness of Pull and Push Strategies in Production and Distribution
### Impact on Logistics-Production Potential
To ensure comparability, calculations were also made for a situation when the level of service in all variants was 100%, which is presented in Table 3 and Figures 9 and 10. In all variants, there were large increases in stocks, even in the first variant--\"Pull daily\"/one DC/5% standard deviation. This confirms the relationship between service level, sales, and costs that is known in the logistics literature, and that when the service level is already very high, increasing it even by a small percentage requires a large increase in costs. Figure 8: Level of stocks in warehouses—30% standard deviation of average sales (Gaussian distribution [1000 pcs.]). Different strategies for distribution. Figure 7: Level of stocks in warehouses—5% standard deviation of average sales (Gaussian distribution [1000 pcs.]). Different strategies for distribution. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Strategy**} & \multicolumn{2}{c}{**Stand. Dev. of**} & \multicolumn{3}{c}{**No of DCs**} & \multirow{2}{*}{**5**} & \multirow{2}{*}{**6**} \\  & **Average Sales** & & & & & **3** \\ \hline Pull daily & 5\% & 831 & 1106 & 1161 & 1216 & 1271 & 1437 \\ Push daily & 5\% & 944 & 1164 & 1438 & 1713 & 1987 & 2262 \\ Push weekly & 5\% & 2390 & 2923 & 3472 & 3746 & 4569 & 4843 \\ Pull daily & 30\% & 1390 & 1667 & 1944 & 2221 & 2498 & 3330 \\ Push daily & 30\% & 2853 & 3128 & 3404 & 3679 & 4505 & 5055 \\ Push weekly & 30\% & 4393 & 4913 & 6129 & 6688 & 7932 & 9286 \\ \hline \end{tabular} Source: own calculations.  
\end{table} 
Table 3: Impact of distribution strategies on the level of inventories [1000 pcs.] (100% AoS and Gaussian distribution). Yearly sales [items/year] = 40,000. The differences were larger in the case of \"Pull daily\" but smaller in the case of \"Push weekly\", which can be explained by the fact that deliveries in larger quantities already resulted in high inventory levels. The differences increased as the number of warehouses increased, once again showing the benefits of centralizing warehousing and confirming the need to combine these two decision problems. In all variants, increasing the number of warehouses resulted in a very high increase in inventory levels. This increase was even greater if sales fluctuations are greater. The purpose of the next simulation was to examine how these strategies affected the amount of production capacity required in the case in which customer demand was to be 100% satisfied. The impact here was weaker than in the case of inventory (Table 4). However, given that the cost of maintaining production potential may have been greater than maintaining inventory, there was a need to take this relationship into account as well. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{**Strategy**} & \multicolumn{5}{c}{**Stand. Dev. of**} & \multicolumn{5}{c}{**No of DCs**} & \\  & **Average Sales** & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline Pull daily & 5\% & 585 & 585 & 585 & 585 & 585 & 585 \\ Push daily & 5\% & 549 & 549 & 549 & 549 & 549 & 549 \\ Push weekly & 5\% & 549 & 549 & 549 & 549 & 549 & 549 \\ Pull daily & 30\% & 712 & 712 & 712 & 712 & 712 & 712 \\ Push daily & 30\% & 554 & 554 & 554 & 554 & 554 & 554 \\ Push weekly & 30\% & 551 & 551 & 551 & 551 & 551 & 551 \\ \hline \end{tabular} Source: own calculations.  
\end{table} 
Table 4: Impact of distribution strategies on the production level and capacity. Yearly sales [items/year] = 40,000. Figure 10: Level of stocks in warehouses—30% standard deviation of average sales. (Gaussian distribution [1000 pcs.]. Different strategies for distribution (100% AoS). Figure 9: Level of stocks in warehouses—5% standard deviation of average sales. (Gaussian distribution [1000 pcs.]). Different strategies for distribution (100% AoS). One can see a regularity--the highest required production potential occurred in the \"Pull daily\" strategy, and the lowest when the products were \"Pushed out\" in weekly volumes.