# Decision-Making Techniques of the Consumer Behaviour Optimisation of the Product Own Price
## 3 Methodology  
The proposed methodology (Figure 1) is based on the customer orders and the stock fluctuation in the warehouse regarding the real demand of the consumer. Figure 1 shows that the detection of a stock level change can be a result of changes in production or fluctuations in customer demand. A correction in production must be made to bring the stock level to an appropriate level. By obtaining data on consumer behaviour that will be useful in monitoring the lean production process, a mathematical model or a probability density function of the demand for a product needs to be created. The mathematical model will allow us to plan the production process in such a way as to avoid overproduction, which--according to [PERSON]--is the main waste, as it causes a majority of other waste. This is achieved by including a sales department that can provide us with sales data from past periods and projections of future sales trends. It is desirable that the probability density function of the product demand \(f_{X}(x)\) be as close as possible to the actual consumer purchasing behaviour. For our case, we selected the probability density function of the product demand \(f_{X}(x)=a^{2}x\cdot e^{-ax}\). \(X\) is the variable that indicates the level of demand. This function is considered to be a good approximation of the tendency of consumer demand in practice (Figure 2). The function can be different for some companies, such that the company  
Figure 1: Proposed model for the impact of consumer behaviour on the product’s own price. concerned needs to choose a curve that suits them and use the proposed model through the steps shown. However, in most cases, this proposed curve suits the product demand. Consumer purchasing behaviour is a random variable denoted by \(X\). The fluctuation of stock in the warehouse of finished products is also a random variable, and is denoted by \(Z\). \(Y\) is used to denote the production process as a random variable, but the production process will be defined in the following. This is because it is practically impossible to change the production capacity quickly in the short term. The fluctuation of stock in the warehouse is shown and marked in Figure 3, wherein \(z_{0}\) represents the initial stock level of finished products, and \(\Delta Z\) represents the fluctuation of the stock level in the warehouse; it can be defined as the difference between the quantity of products entering and the quantity of products leaving the warehouse. \[\Delta Z=Y-X \tag{1}\]  
\(\Delta Z\), \(Y\) and \(X\) are random variables; thus, it can be indicated that the mathematical expectation is  
\[E[\Delta Z]=E[Y]-E[X] \tag{2}\]  
The average value of the stock level change is \(E[\Delta Z]\), or the value of mathematical expectation equals zero \(E[\Delta Z]=0\). If \(E[\Delta Z]=0\), then  
\[0=E[Y]-E[X] \tag{3}\]  
The average quantity of products entering the warehouse, \(Q_{IN}\), equals the average quantity of products leaving the warehouse, \(Q_{OUT}\). The average quantity of product demand, \(E[X]\), cannot be influenced, as this is an external factor; however, we can influence the production process by adjusting the average quantity of manufactured products \(E[Y]\) that represent the internal organisation of production capacities. Let us assume that the production flow is constant and corresponds to the average quantity of product demand \([X]\); it is denoted by \(y_{0}\). In the ideal case, the product and production demand are constant and equal to \(y_{0}\). \[E[Y]=y_{0} \tag{4}\]  
Figure 3: Stock fluctuation in a warehouse of products. Figure 2: The figure shows the probability density of the demand \(f_{X}(x)=a^{2}x\cdot e^{-\alpha x}\). \[y_{0}=E[X] \tag{5}\]  
In order to immediately respond to a demand, a certain number of products should always be in stock \(z_{0}\); this is the initial level of stock.