## 3 Results--Effectiveness of Pull and Push Strategies in Production and Distribution
### Impact on Logistics-Production Potential
This also seems easy to interpret--\"Pull\" requires either a flexible production system or a high potential for the system to adapt to changing needs. Scheduled deliveries, on the other hand, promote production stability. If demand has a Gamma distribution, service levels are slightly lower than in the case of Gaussian distribution (Table 5 and Figures 11 and 12). The difference, however, is which strategy is more efficient. In the case of Gamma, in almost all cases the level of service was better with daily deliveries than with weekly deliveries. In the strategy \"Push weekly\", the level of service was slightly better with a single warehouse. However, it decreased to a large extent with more warehouses. Thus, with weekly deliveries to one warehouse and a standard deviation of 3%, the inventory availability level was 99.0%. When deliveries were made to six DCs, the service level dropped to 97.8%. The situation was similar when the standard deviation was 6%. Service levels for both Pull and Push daily deliveries also decrease as the number of warehouses increases, but to a much lesser extent than for weekly deliveries. However, despite not much difference in service levels, the impact of these strategies on stocks is greater. In all cases, stock levels are significantly higher for Gamma than Gaussian distributions (Table 6), and in most cases, these differences increase with the number of warehouses. For example, with small standard deviations of demand and one warehouse, the inventory level is 126.85% higher in the case of a Gamma distribution than in the case of a Gaussian distribution. If the goods are distributed over a network  
Figure 11: Availability of stocks in warehouses—5% standard deviation of average sales. Different strategies for distribution (Gamma distribution). \begin{table} \begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Strategy**} & \multicolumn{2}{c}{**Stand. Dev. of**} & \multicolumn{5}{c}{**No of DCs**} & \multirow{2}{*}{} \\  & **Average Sales** & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline Pull daily & 3\% & 98.8\% & 98.8\% & 98.7\% & 98.7\% & 98.6\% & 98.5\% \\ Push daily & 3\% & 99.0\% & 98.9\% & 98.8\% & 98.8\% & 98.7\% & 98.5\% \\ Push weekly & 3\% & 99.0\% & 98.8\% & 98.5\% & 98.3\% & 98.1\% & 97.8\% \\ Pull daily & 6\% & 98.7\% & 98.5\% & 98.2\% & 98.3\% & 98.2\% & 98.1\% \\ Push daily & 6\% & 98.8\% & 98.6\% & 98.3\% & 98.2\% & 98.1\% & 97.8\% \\ Push weekly & 6\% & 98.8\% & 98.5\% & 98.0\% & 97.8\% & 97.5\% & 97.1\% \\ \hline \hline \end{tabular}  Source: own calculations. \begin{tabular}{c c c c c c} AoS & & & & & \\
99.00\% & & & & & \\
98.80\% & & & & & \\
98.60\% & & & & & \\
98.40\% & & & & & \\
98.20\% & & & & & \\
98.00\% & & & & & \\
97.80\% & & & & & \\
97.60\% & & & & & \\
97.40\% & & & & & \\
97.20\% & &of six warehouses, this difference is even greater, at 155.27%. Stocks in the other variants are also significantly higher than under the Gamma distribution. Interestingly, however, these differences would also be very large if customer orders were fully (100%) satisfied. However, in the case of \"Pull daily\", inventory levels are very similar (Table 7). This leads to the conclusion that the quick response strategy allows for a high level of customer service without building up high inventory levels. The effect of the distribution strategy on the production potential for Gamma distribution was also analyzed. The results are similar--first, for each strategy, the amount of required potential is the same for each size of distribution network (number of DCs). Second, the largest production potential is required with the Pull strategy. Thirdly, it is larger with larger sales fluctuations (Table 8). However, in the case of Gamma distribution, it is more than 30% larger than in the case of Gaussian distribution. The simulation results prove that decisions on the choice of replenishment strategy and the size of the warehouse network should be considered together. However, this is