## 3 Results--Effectiveness of Pull and Push Strategies in Production and Distribution
### Impact of Delivery Times to Warehouses on Economic Efficiency  
The model can also be used to simulate the impact of delivery times to warehouses on economic efficiency. The model was modified to include delays after the order was placed by distribution warehouses to the production plant. It was assumed that this delay would be 2 days in all variants, i.e., that warehouses would receive products 3 days after placing an order (in the previous variant, this was after 1 day--Section 3.2. and Section 3.3). The effect of this factor was significant. As expected, the availability level of stocks was lower and the level of stocks in warehouses increased. Tables 13-17 summarize the results of the simulations--the level of customer service and the total costs (inventory and storage costs, transportation, lost sales) for three product groups. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Strategy**} & \multicolumn{3}{c}{**Stand. Dev. of**} & \multicolumn{6}{c}{**No of DCs**} \\  & **Average Sales** & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline Pull daily & 5\% & 98.34\% & 98.15\% & 98.19\% & 98.16\% & 98.24\% & 98.12\% \\ Push daily & 5\% & 98.86\% & 98.91\% & 98.87\% & 98.85\% & 98.74\% & 98.82\% \\ Push weekly & 5\% & 99.02\% & 98.84\% & 98.63\% & 98.48\% & 98.16\% & 98.03\% \\ Pull daily & 30\% & 98.94\% & 98.91\% & 98.52\% & 98.29\% & 98.14\% & 97.29\% \\ Push daily & 30\% & 97.93\% & 97.83\% & 97.71\% & 96.90\% & 96.58\% & 96.44\% \\ Push weekly & 30\% & 97.69\% & 98.27\% & 96.62\% & 97.05\% & 96.74\% & 96.97\% \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Impact of distribution strategies on the availability of stocks in DCs (Gaussian distribution). Three days of delivery to warehouses. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Strategy**} & \multicolumn{3}{c}{**Stand. Dev. of**} & \multicolumn{6}{c}{**No of DCs**} \\  & **Average Sales** & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline Pull daily & 5\% & 752 & 705 & 845 & 777 & 785 & 885 \\ Push daily & 5\% & 1734 & 642 & 689 & 640 & 703 & 705 \\ Push weekly & 5\% & 2301 & 2333 & 2453 & 2392 & 2351 & 2457 \\ Pull daily & 30\% & 912 & 1428 & 1839 & 1578 & 1837 & 1918 \\ Push daily & 30\% & 1567 & 1964 & 2877 & 1744 & 1857 & 2326 \\ Push weekly & 30\% & 2266 & 4494 & 2339 & 2443 & 2713 & 3709 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Impact of distribution strategies on the level of inventories [1000 pcs.] (Gaussian distribution). Three days of delivery to warehouses. The stock availability reached 99% when the demand had a Gaussian distribution in only one case: \"Push 1 warehouse\" (Table 13). In other cases, it was lower, and in the case of weekly deliveries, \"Push weekly\", it was 96-97%. Stock levels were also higher (Table 14). The distribution of demand was also important here. If the demand had a Gamma distribution, customer service was even lower: in the case of weekly deliveries to six warehouses, the availability was 93.7% (Table 15). The inventory level was also higher (Table 16). Tables 17-19 show a comparison of the simulation results for all variants (distribution of the change in demand and delivery time to warehouses). They show the supply strategies (combinations of these strategies) with the lowest costs. Extending the lead time of warehouse orders causes a significant increase in costs in every product group.