## 2 Materials and Methods  
The aims of this research were as follows:  
1. To demonstrate the need to combine decision-making problems concerning the choice between the Pull and Push strategy in the field of goods distribution with the degree of centralization of the distribution network;
2. To present the conditions under which given strategies are most effective.  
These goals were achieved through simulations conducted with the use of a simulation model developed by the author of the article. The purpose of developing this model and running simulations using it was to see how the size of a distribution network, combined with a given replenishment system (Pull or Push) in that network, affects the efficiency of production and logistics processes. The model can be used to calculate process parameters alone--the level of the inventories, the availability of products (stocked in warehouses) for customers, and the amount of production capacity required. Once the cost elements are taken into account, it can be used to calculate the costs of a given strategy. If this model is expanded to include the costs of logistics processes, it will allow us to calculate the economic efficiency of different strategies or combinations of different strategies. The model can be further expanded by adding production and material procurement costs.  
The model uses one measure of the level of logistics service, namely the availability of inventory in a distribution warehouse, which affects the \"opportunity cost of sales\". The model calculates how many products could not be sold if the inventory level was insufficient. Thus, it measures the percentage of actual sales versus projected sales.  
The tool used to build this model is an Excel spreadsheet with formulae to generate daily demand based on an assumed average daily demand and standard deviation. Simulations are conducted for two types of the demand distribution: Gaussian and Gamma distribution with Excel's function \"IF\", in which the \"GAUSS.DIST\" or \"GAMMA.DIST\" function appears, respectively. This is because the model replicates (simulates) the operation of the system throughout the year. The idea is not to use average yearly data, but to reproduce the functioning of a real system as precisely as possible. The demand on each day is generated by a computer \"day by day\".  
The inventory level on a given day is derived from the inventory level on the previous day, the volume of deliveries on that day, and the sales on that day.  
With regard to production, the model works as follows: in the case of the Pull strategy, production volume is adjusted to the current orders of the distribution centers, and in the case of the Push strategy, it is based on the forecasted needs of these centers. In other words, the model adjusts production capacity so that the orders of the warehouses can be 100% fulfilled. This means that in the \"Push\" system, production should be stable because deliveries to distribution warehouses are made at a constant level. The demand for production capacity should also be lower. In the \"Pull\" system, in which distribution centers decide when deliveries are to be made, the production system must adapt to current needs. This means that if demand fluctuates, production capacity must be higher and there will be idle production capacity at certain times. This problem will occur especially with seasonal demand. However, to assess whether this will really be the case, calculations must be carried out.