7.9 Model for assessing the provision of public infrastructure
7.9.1 Purpose of the model
The purpose of the model is to assess the provision of socio-economic objects (SEO) in cities, identify power and quantity shortages (deficits) of SEO that form the potential for improving the quality of life in the city and direction of investments in urban infrastructure.
SEO provision indicators are used in the calculation of an integrated (system-dynamic) forecast of demographic and economic indicators of SED, assessing the impact of investments in SEO construction on the city’s SED and achieving target values of national goal indicators.
Calculations are carried out based on actual values for the reporting period and for forecast time periods (taking into account changes in the size and age structure of the population).
7.9.2 Terms and definitions
• SEO – socio-economic objects • Types of SEO objects – cultural objects (cinemas, theaters, libraries), healthcare objects (clinics, hospitals), education objects (preschool and secondary educational institutions), trade objects, sports objects (sports halls, swimming pools, flat structures) • RNGP (MNGP) — regional (local) standards of urban planning • Provision of SEO by types of socio-economic objects - a coefficient reflecting the percentage of satisfaction of the population’s need for SEO objects through the ratio of the actual power of the SEO, taking into account territorial accessibility, to that required according to the RNGP (MNGP)
7.9.3 Basic view of the model
The basic view of the SEO provision model is presented in the following form:
\[ O_{i}=\frac{Q_{i}^{*}}{N_{i} * Q_{\mathrm{H} i}} * 100 \ \ (1) \] where, i - type of SEO, \(\mathrm{Q}_{\text {ні }}\) - power of the i-th type of socio-economic object according to RNGP (MNGP) based on 1 person of the corresponding age group, \(\mathrm{Q}_{\mathrm{i}}^{*}\) - actual power of the i-th type of SEO, \(\mathrm{N}_{\mathrm{i}}\) - size of the population of the age group corresponding to the i-th type of SEO.
In the absence of data on the actual power of objects, the following formula for converting area characteristics into power characteristics is used:
\[ \mathrm{Q}_{\mathrm{i}}^{*}=K_{i} * S \ \ (2) \] where \(K_{i}\) - conversion, calibrated coefficient, \(S\) - total area of SEO objects.
To be able to compare provision indicators for different types of SEO with each other, normalization is performed using the formula:
\[ P_{\mathrm{OC} \ni \mathrm{H}}^{n o r m}=\frac{d}{1+\exp \left(-P_{\mathrm{OC} \ni \mathrm{H}}\right)} \ \ (3) \]
where \(d\) - normalization parameter, which takes a value from 1 to 2. For example: A parameter d equal to 1.2 means that all provision indicators for various types of SEO will not exceed 120% of the norms recommended by the RNGP.
Calculation of the integral provision index of SEO of the city as a whole:
\[ P_{\mathrm{OC} \ni \mathrm{H}}^{\text {integral }}=\operatorname{mean}\left(P_{\mathrm{OC \ni H}}^{\text {norm }}\right) \ \ (4) \]
7.9.4 Description of Model Input Variables
7.9.4.1 Description of data sources
The model uses several sets of data from various sources: - 2GIS - area characteristics of SEO, - approved urban planning standards MNGP/RNGP, - municipal statistics of Rosstat.
7.9.4.2 Description of indicators
Municipal statistics indicators:
| № | Symbol | Code | Name | Unit of measure |
|---|---|---|---|---|
| 1 | \(N_{i}\) | C013 | City population size | person |
| 2 | C014 | Population aged 0-2 years | person | |
| 3 | C015 | Population aged 3-5 years | person | |
| 4 | C016 | Population aged 6 years | person | |
| 5 | C017 | Population aged 7 years | person | |
| 6 | C018 | Population aged 8-13 years | person | |
| 7 | C019 | Population aged 14-15 years | person | |
| 8 | CO20 | Population aged 16-17 years | person | |
| 9 | \(Q^{*}\) | C115 | Number of places in preschool educational organizations | place |
| 10 | C165 | Number of hospital beds | place | |
| 11 | C166 | Capacity of outpatient clinics | visits per shift | |
| 12 | C181 | Number of public (general access) libraries | units | |
| 13 | C183 | Number of professional theaters | units |
Indicators in 2GIS and RNGP norms:
| № | Type of SEO | Units of measurement of SEO power | |
|---|---|---|---|
| 2GIS, \(Q^{*}\) | RNGP/MNGP - \(Q_{H}\) | ||
| 1 | Kindergartens | \(sq. m\) | places per 1000 people |
| 2 | Schools | \(sq. m\) | places per 1000 people |
| 3 | Hospitals | \(sq. m\) | beds per 1000 people |
| 4 | Clinics | \(sq. m\) | visits per shift per 1000 people |
| 5 | Retail space | \(sq. m\) | \(sq. m\) per 1000 people |
| 6 | Libraries | \(sq. m\) | units per 1000 people |
| 7 | Cinemas | \(sq. m\) | places per 1000 people |
| 8 | Theaters | \(sq. m\) | units per 1000 people |
| 9 | Parks | \(sq. m\) | \(sq. m\) per 1000 people |
| 10 | Sports halls | \(sq. m\) | \(sq. m\) per 1000 people |
| 11 | Sports grounds | \(sq. m\) | \(sq. m\) per 1000 people |
| 12 | Swimming pools | \(sq. m\) | \(sq. m\) of water surface per 1000 people |
7.9.5 Description of the model result
List of final calculation indicators obtained from the Model:
| № | Indicator | Unit of measure |
|---|---|---|
| 1 | Clinic capacity | visits per shift |
| 2 | Number of beds in hospitals | beds |
| 3 | Preschool children | person |
| 4 | Places in kindergartens | places |
| 5 | Number of libraries | units |
| 6 | Number of theaters | units |
| 7 | School-age children | person |
| 8 | Places in schools | places |
| 9 | Retail space | \(sq. m\) |
| 10 | Places in cinema halls | places |
| 11 | Area of parks | \(sq. m\) |
| 12 | Area of sports halls | \(sq. m\) |
| 13 | Area of sports grounds | \(sq. m\) |
| 14 | Area of swimming pools | \(sq. m\) |
| 15 | Places in kindergartens RNGP | places per 1000 people |
| 16 | Places in schools RNGP | places per 1000 people |
| 17 | Beds in hospitals RNGP | beds per 1000 people |
| 18 | Clinic capacity RNGP | visits per shift per 1000 people |
| 19 | Retail space RNGP | \(sq. m\) per 1000 people |
| 20 | Number of libraries RNGP | units per 1000 people |
| 21 | Places in cinema halls RNGP | places per 1000 people |
| 22 | Number of theaters RNGP | units per 1000 people |
| 23 | Area of parks RNGP | \(sq. m\) per 1000 people |
| 24 | Area of sports halls RNGP | \(sq. m\) per 1000 people |
| 25 | Area of sports grounds RNGP | \(sq. m\) per 1000 people |
| 26 | Area of swimming pools RNGP | \(sq. m\) of water surface per 1000 people |
| 27 | Provision of cinemas | \(\%\) |
| 28 | Provision of theaters | \(\%\) |
| 29 | Provision of libraries | \(\%\) |
| 30 | Provision of parks | \(\%\) |
| 31 | Provision of clinics | \(\%\) |
| 32 | Provision of hospitals | \(\%\) |
| 33 | Provision of kindergartens | \(\%\) |
| 34 | Provision of schools | \(\%\) |
| 35 | Provision of retail space | \(\%\) |
| 36 | Provision of sports halls | \(\%\) |
| 37 | Provision of sports grounds | \(\%\) |
| 38 | Provision of swimming pools | \(\%\) |
| 39 | Urban environment (provision) index | index |
7.9.6 Calibration of the model
The calibrated coefficient for the Model is the coefficient for converting area characteristics into power characteristics - \(К_{і}\).
Calibration of the coefficient for converting area characteristics into power characteristics is carried out by determining the median value of the ratio of actual area characteristics of SEO to actual power of SEO objects, obtained for individual cities for which statistical observations are carried out. \[ K_{i}=\operatorname{median}\left(\frac{\sum s_{i}}{\sum Q_{i}^{*}}\right) \ \ (5) \]
7.9.7 Result of model application
During trial operation, the model confirmed its efficiency.
The accuracy assessment for the Model corresponds to the product of the accuracy of calculating the size of the population for individual age groups performed in the system-dynamic model and the accuracy of determining the coefficient for converting area characteristics into power characteristics.
7.9.8 Requirements for model support and regularity of recalibration
It is advisable to carry out model calibration no more than once every 5 years, due to the fact that changes in regulatory requirements regarding SEO capacity occur rather slowly, which is consistent with changes in urban planning policy and depends on the speed of natural renewal of SEO infrastructure (the cycle is approximately 30-50 years).
7.9.9 Assumptions necessary for carrying out calculations
The conversion of SEO area characteristics into power characteristics was carried out on the basis of a regulatory table obtained from information from open public sources.
7.9.10 Description of the calculation algorithm
The calculation algorithm consists of three sequential stages:
- collection of information on the total areas of SEO in the city, which, in accordance with the coefficients, are converted into an estimated value of actual power.
- calculation of SEO provision indicators according to MNGP/RNGP standards and population size of the corresponding age groups.
- calculation of predicted values of SEO provision indicators.
7.9.11 Scope (boundaries) of permissible application of the mathematical model
The SEO provision assessment model for the city as a whole is applicable for carrying out a macroeconomic assessment of the quality of life of the population in the city, ranking cities by quality of life, assessing the degree of influence of the provision indicator on other indicators of socio-economic development.
SEO provision assessment can be used to calculate the required volumes of capital investments to bring the provision indicator to the median values in the country and/or before meeting the standards of urban planning adopted at the regional and municipal level.