## 2 Literature Review
### Theoretical Substantiation of the Required Number of Asphalt Mixing Plants
The developing economies make smaller investments in road maintenance and development than is required to preserve appropriate road pavement conditions and build new roads. An insufficient amount of the asphalt mixture manufactured can also be determined by the lack of AMPs operating in the country and their low MC when the outdated technological equipment is not replaced with modern AMPs for economic reasons. The MC of many AMPs allows for the manufacture of much more asphalt mixture than is produced and consumed each year in most countries. Therefore, some AMPs are inefficiently used because of the extended downtime that is not always due to adverse weather conditions. In certain months of the year, an uneven demand for the asphalt mixture makes it necessary to increase the number of AMPs so that their production capacities could be sufficient to meet demand in the case of a sudden increase in the scope of asphalt paving (work volume). The colder the climate of a country, the greater the difference between the amounts of the asphalt mixture produced over the months and during different seasons. Statistical Analysis of the Amount of Asphal Mixture Produced and the number of Asphal Mixing Plants  
According to the overview _Asphalt in Figures 2005 to 2016_, publicly provided by the EAPA every year [73], the correlation between the amount of asphalt mixture produced in different European countries and the number of AMPs operating across Europe has been determined. The collected data refer to asphalt production, application, binders and the number of production sites. Initially, the total production of HMA and WMA mixtures in metric tonnes for each of the 30 European countries included for one calendar year for the period from 2005 to 2016 has been calculated:  
\[\overline{P}_{c}=\frac{\sum_{y=1}^{Y}P_{yc}}{Y}, \tag{1}\]  
where \(P_{yc}\) represents the total annual production of the HMA and WMA asphalt mixture in the \(c\)-th country (millions of tonnes); \(c=1,2,\ldots\)\(C\), for the number of countries included in the study, with \(C=30\); and \(Y\) is the number of years (\(y=1,2,\ldots\)\(Y\), with \(Y=12\)). Figure 2: The model of the dependence between the number of AMPs in a country and expenses. In addition, the average number of production sites, i.e., the number of AMPs operating in every \(c\)-th country, has been calculated:  
\[\overline{N}_{c}=\frac{\sum_{y=1}^{Y}N_{yc}}{Y}, \tag{2}\]  
where \(N_{yc}\) is the number of AMPs in the units that had annually been operating in the \(c\)-th country for 12 years, and \(Y\) is the number of years (\(y=1\), 2,..., \(Y\), with \(Y=12\)). The calculated values of \(\overline{P}_{c}\) and \(\overline{N}_{c}\) for each European country are provided in Figure 3. The length of the column indicates the average annually produced mass of HMA and WMA mixtures in millions of tonnes for 12 years in each country. The additional horizontal lines in each of the columns also present the minimum (min) and maximum (max) recorded annual amounts of the mixture produced in different countries. Respectively, from the data presented in Figure 3, it can be seen that the range between the minimum and maximum recorded annual amounts of the produced mixture in different countries is very high. Figure 3: The average, maximum and minimum values of the produced quality HMA and WMA mixture in the European countries for the period of 12 years (2005 to 2016) and the average annual number of the operating AMPs. The number of AMPs (\(\overline{N}_{c}\)) given along each column (Figure 3) was used for identifying the correlation (\(\overline{P}_{c}\)). None of the outliers were excluded during the identification of the correlation, and, as no specific non-linear correlation tendencies were noticed, a linear correlation for further analysis was selected. The positive linear correlation between \(\overline{P}_{c}\) and \(\overline{N}_{c}\) (Figure 4) shows that the higher the number of the operating AMPs in a country, the more HMA and WMA (coefficient of determination \(R^{2}\) = 0.9122) is produced.