## 3 Results--Effectiveness of Pull and Push Strategies in Production and Distribution
### Impact of Delivery Times to Warehouses on Economic Efficiency
In a similar way, one can try to explain the smaller savings in the case when demand fluctuations are greater (6%--Gamma distribution). However, one should be careful in formulating such conclusions. It is surprising that the greatest savings are still seen in the case of medium-value \"Clothing\" (Table 19). With Gaussian distribution and a 5% demand fluctuation, the costs for this product group are 31% higher, and with a Gamma distribution and a 3% standard deviation, they are 36% higher. However, as with \"Food\" and \"Electronics\", the increases are relatively lower if the sales fluctuations are higher. Another interesting result of the simulations is that, compared to the \"1-day warehouse order fulfillment\" variant, if there are 2-day delivery delays, the optimal strategy in almost all cases is \"Pull daily\" and one central warehouse. Considering the share of these costs in the sales value, the question arises as to what impact the optimization of delivery processes has on the financial results of companies. This impact depends on the profitability level of companies. For example, the profitability of the largest Polish companies listed on the Warsaw Stock Exchange are as follows: \"Genevia\" (\"Electromechanical\")--13% in 2023, but only 3% in 2020. In \"Wielton\", from the same industry, it was only 2% and 3% in the same years. The profitability of the tycoons of the Polish Clothing industry in 2023 were as follows: \"LPP\" was only 9%, and \"Vistula Retail Group\" 8%. Companies from the food industry also achieved low profitability levels in 2024: \"Makarony Polskie\"--6%, \"Tarczynski\"--6%, and \"Zywice\"--3%. These profitability levels are therefore similar to the share of distribution costs in the sales value. They were used in individual product groups to simulate the impact of the distribution strategy on profits. The results are shown in Tables 17-19. Delivery delays to distribution centers result in a more than 20% reduction in profits in the \"Food\" sector, both in the case of the Gaussian and Gamma distributions for both low and high sales fluctuations, and in the \"Clothing\" sector, for the Gamma distribution and for both low and high sales fluctuations. The profit losses in \"Electronics\" are lower (3.6-5.3%). cheaper goods and smaller sales fluctuations, there is a tendency rather to \"Push\" in larger quantities to a larger distribution network. The simulation results, especially taking into account the extension of the delivery time (Section 3.4), further confirm the views found in scientific publications and case studies that the answer to uncertainty on both the sales and procurement sides is not to expand the distribution network, but on the contrary, to centralize it. The above calculations are only examples. They are based on the assumptions made regarding storage and transportation costs primarily. For example, it is assumed that the rates for transportation services by rail are 40% lower than by road. However, they may explain why the centralization of distribution systems is quite a common strategy but also why rail transportation has a small share in the transportation market. However, rail transportation requires a sufficient scale of operations to be profitable. This confirms the view that an important factor in choosing the Pull strategy is the level of production and sales [2]--in the case of low levels and small quantities of deliveries, MTO production and direct delivery to the customer seem to be the optimal solution. There are other assumptions as well. The model assumes that the company loses revenue in proportion to the availability of products in the warehouse. The impact, however, can be broader--the customer may abandon cooperation with the supplier entirely. Logistical customer service can also be measured by other parameters--the speed and timeliness of deliveries to customers. The effects of the deterioration of these parameters are even more difficult to estimate.