=Paper=
{{Paper
|id=Vol-1623/paperme9
|storemode=property
|title=Public-Private Partnership Models for the Russian Mineral Resource Complex
|pdfUrl=https://ceur-ws.org/Vol-1623/paperme9.pdf
|volume=Vol-1623
|authors=Sergey Lavlinskii
|dblpUrl=https://dblp.org/rec/conf/door/Lavlinskii16
}}
==Public-Private Partnership Models for the Russian Mineral Resource Complex==
https://ceur-ws.org/Vol-1623/paperme9.pdf
Public-Private Partnership Models for the Russian
Mineral Resource Complex
Sergey Lavlinskii
Sobolev Institute of Mathematics
4 Acad. Koptyug avenue, 630090 Novosibirsk Russia
lavlin@math.nsc.ru
Abstract. We propose a new approach to the development program for a raw-
material base based on public-private partnership (PPP) mechanisms. This
scheme is applied in production infrastructure development projects financed
by the Investment Fund of Russia. This is a Russia-specific mechanism; thus,
a special toolkit is designed for its assessment and formation. Our approach is
based on synthesis of a simulation forecasting model and a planning model for-
mulated as a bilevel Boolean programming problem. The technique applied in
the proposed approach is presented using the examples of the PPP mechanisms
practiced in Transbaikal.
Keywords: Production infrastructure development project, Raw-material base
development program, Simulation forecasting model, Bilevel Boolean program-
ming problem
Introduction
Public-private partnerships (PPPs) are widely used throughout the world and are an
effective way to achieve a compromise of interests in various spheres of economy. World
experience shows that PPPs can be a successful means, primarily, of creating new and
maintaining the existing public sector infrastructure. In the mineral complex, PPPs
help to considerably expand project financing and encourage subsoil users to develop
new fields in remote areas.
How broadly is the PPP institution implemented in the mineral resources complex
of Russia? It is quite often that the investor cannot implement an investment project
due to a lack of the necessary infrastructure, and the state officials are unwilling to
invest in infrastructure until they are sure it is used efficiently. What steps are taken
to break this vicious circle? What economic and mathematical tools for designing an
efficient PPP model can be used in the Russian context?
These questions are the focus of this paper. The author proposes the original ap-
proach based on synthesis of a simulation forecasting model and a planning model
formulated as a bilevel Boolean programming problem. The corresponding decision
support system, which has been tested in real-life conditions, would help to create an
Copyright ⃝
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In: A. Kononov et al. (eds.): DOOR 2016, Vladivostok, Russia, published at http://ceur-ws.org
Public-Private Partnership Models 625
effective PPP arrangement and ensure long-term efficiency for the state as well as the
private investor.
Section 2 gives an analysis for the current development level of the PPP institution
around the world and in the mineral resource complex of Russia. Section 3 defines a
technique of PPP mechanism assesment using simulation forecasting model. Section
4 gives the informal problem setting, introduces the main notation, and proceeds to
a mathematical formulation of the planning model designed as a bilevel Boolean pro-
gramming problem. In section 5 the received results are discussed and an area for
further development of the prorposed tools is outlined.
1 Decision-Making Mechanisms
The original form of the PPP mechanism is traditionally termed BOT (Built, Own,
Transfer) and is known worldwide as concession. This PPP mechanism was broadly
used in Europe since the 19th century in the development of transport infrastructure
[1].
The next step in the development of PPPs — the BOOT mechanism (Built, Own,
Operate, Transfer) — was taken in Australia [2]. In this scheme, the private investor
builds, finances, manages, and operates an infrastructure object. In this case, the own-
ership of the created object belongs to a private partner until the end of the contract,
after which it passes to the state [3].
The next stage in the development of PPPs is associated with the DBFO (Design,
Built, Finance, Operate) mechanism [4] and the adoption of a new strategy for gov-
ernment projects in the UK, i.e., the Private Finance Initiative [5]. In this scheme, the
private investor sets up a management company for a long term (30–60 years) to build,
finance, and manage the object and provide the services specified in the government
contract [6].
This is a general outline of the two-centuries long evolution of the PPP institution in
the world. The history of the PPP institution in Russia is much less eventful. There were
attempts at using PPPs in Russia, but those were isolated instances of an experimental
nature.
The situation has changed only in the last decades. Private capital began to flow
to the infrastructure sector, but on a lower scale compared with developed nations.
A particularly complex situation is observed in the mineral resource sector, which
has traditionally been in focus of the state. Here the state is most interested in the
development of PPP tools capable of attracting the resources of the various financial
and credit institutions to the implementation of major investment programs.
PPP projects financed by the Investment Fund of Russia have been most widely
used in the Russian mineral resources complex. This mechanism is based on interna-
tional experience, but its original form has undergone serious change in the process of
adaptation to the Russian conditions.
The production infrastructure projects financed by the Investment Fund use a non-
classical PPP mechanism evolved due to the specific features of the Russian economy.
What the Russian government calls a PPP is not considered PPP in Western literature.
626 Sergey Lavlinskii
Methodologically, investment projects become PPP projects only when a private com-
pany finances the construction and (or) operation of state-owned objects [7]. Within
Russian projects, production infrastructure is built under the principle that each par-
ticipant finances their own objects only.
The major infrastructure projects supported by the Investment Fund are imple-
mented according to the above scheme. The federal investment project on the inte-
grated development of the Lower Angara region includes infrastructure projects and
the construction of the Boguchansk hydroelectric power plant (HPP), an aluminum
smelter, and a pulp and paper plant. The support of the Investment Fund is to come
in the form of co-financing of the investment project on negotiated terms through con-
struction of the HPP and infrastructure facilities that will become the property of the
Russian Federation.
Another such project is the one to create the transport infrastructure for the de-
velopment of mineral resources in the southeast of the Chita oblast. In this project,
the government builds the Naryn-Lugokan railway line to provide access to a cluster
of prospective fields to be developed by a private investor.
It is possible to say that the first experience of Russian PPPs in the production
infrastructure sector with the support of the Investment Fund was not very successful
already today. This result is due not only to the transition nature of the economy and
the lack of the necessary market institutions. An important role was played by the
absence of a comprehensive assessment procedure for the implementation of the PPP
project and by the financing scheme that was used at the time of making the decision.
How to create an effective PPP arrangement?
An analysis of the feasibility studies submitted to the Investment Fund for the
PPP projects in the Lower Angara region and Transbaikal reveals insufficient project
preparation [8–10]. In these materials the main focus is on the subprojects implemented
by private investors. There are independent economic assessments for these subprojects,
but no comprehensive assessment for the entire project, which would take into account
the contribution of the Investment Fund to the infrastructure development.
The available experience shows that designing an efficient PPP mechanism for the
Russian mineral resource sector would require specialized economic and mathematical
tools for the development, assessment, and support of PPP projects. It is only these
tools that can provide a comprehensive socioeconomic and environmental assessment
of a PPP project and its funding scheme.
The subsequent sections of this paper are devoted mainly to the description of
one of the possible approaches to this problem. This approach, which has been tested
in real-life conditions, may be useful for natural resource-based regions that consider
the use of PPP mechanisms in designing a program for the development of their raw
material base.
2 PPP Mechanism Assessment: Simulation Forecasting Model
Necessary tools are essentially a forecasting model used to assess the consequences of
a regional development program based on a particular PPP model. The procedure for
an assessment of a PPP model is as follows.
Public-Private Partnership Models 627
Considering a mineral resource base development program as a set of long-term
investment projects, the state seeks to achieve a compromise between the interests of
all the stakeholders.
The assessment of a field in terms of economic rent plays an important role in the
selection of projects by the investor. It characterizes the project profitability and is
based on the net present value N P V of the project:
∑
T
Dt − R t
NPV = , (1)
t=1
(1 + E)t
where Dt and Rt are the sales revenues and the technological costs of the project
(capital investment, operational costs, and labor remuneration) in comparable prices
in year t; E is the discount rate; and T is the field development period. An internal
rate of return IRR is the discount rate, turning N P V into zero.
The investor’s tax payments are not included into the technological costs Rt , since
they are considered as part of the project’s positive cash flow. N P V reflects the general
efficiency of the project and corresponds to the discounted cash flow of the state and
the investor taken together whereby the state plays a passive role of resource owner
and recipient of fiscal revenues according to a particular tax system.
A proactive position of the state, which is associated with the use of PPPs, has
a profound effect on the situation. Being part of a PPP, the state is involved in the
financing of capital investment by building a part of the infrastructure needed for the
technological project and implementing a range of environmental activities.
In this case, a relationship similar to (1) may also be constructed for the state
(N P Vst ). It uses a longer time horizon T S and a discount rate Est that is considerably
smaller than that of the investor:
∑
TS
IBRt − Rst + taxt
t
N P Vst = . (2)
t=1
(1 + Est )t
Here the costs of the state Rtst are the capital investments in the infrastructure
and environmental activities; the state revenues include not only the tax payments
taxt arising from the project but also the non-project revenues IBRt generated by the
development of local infrastructure.
The key efficiency indicator for the investor is N P Vinv , an analog of (1), which is
characterized by reduced capital costs due to the state participation and by additional
costs, i.e., tax payments:
∑
T
Dt − Rt + Rst − taxtt
N P Vinv = . (3)
t=1
(1 + Einv )t
The investor is interested in a project if N P Vinv ≥ 0.
The state implements the raw-material base development program as an integrated
project consisting of a set of investment subprojects within a PPP mechanism. Within
this project, the state builds infrastructure facilities and finances environmental ac-
tivities. It receives tax revenues from all the investment subprojects and non-project
628 Sergey Lavlinskii
revenues as a result of the development of local infrastructure. For such an integrated
project, we can derive the state’s integral N P Vstint , which is defined by the selected
PPP mechanism (cost-sharing arrangement) and is similar to (2). A compromise be-
tween the interests of all the stakeholders (the state and investors) is achieved if
{for each investor N P Vinv ≥ 0} and {N P Vstint ≥ 0}. (4)
The above procedure for an assessment is according to the requirements of the
Guidelines for the assessment of projects with state participation, which are officially
accepted in Russia. However, the official methodology becomes absolutely useless if it
isn’t supported with the field development models adapted to the Russian conditions
[12].
The key role in designing the tools to assess a raw-material base development pro-
gram using a specific PPP mechanism is played by a model describing the implementa-
tion of an investment project. This model makes it possible to assess the profitability
of a project and its implications for the region within a given scenario of external con-
ditions, a part of which are determined by the chosen PPP mechanism and project
financing scheme. The core idea is to use a computer model describing the operation
of an enterprise created by the investor to implement the project. The model helps
generate a forecast for the trajectory of the key economic indicators depending on a
variety of factors. The formal scheme of the model is given by a system of recurrence
equations:
Xt = F (Xt−1 , P, Et , P P P M ), t = 1, ..., T, (5)
where P is the original technological project; Et is the forecast for the external opera-
tional conditions; and Xt is the vector describing the state of the enterprise at the end
of year t. The components of Xt determine the production capacity and output, the
mining of ore, oil, and gas, the results of their processing, the loans and interest paid
under the chosen project financing scheme, tax payments by category, and financial
and economic indicators showing the performance of the enterprise in year t.
The applied PPP mechanism P P P M directly affects the project configuration be-
cause a part of the production infrastructure and necessary environmental projects are
implemented by the state. The system’s operator F is formalized as a set of simulation
algorithms describing the functioning of individual units within the investor’s enter-
prise. The model describes the interactions between the units and the decision-making
routines to generate a forecast for the dynamics of the resulting material and financial
flows of all kinds. An example showing the interactions for a typical mineral resource
project such as the development of a polymetallic ore field can be found in [12].
Once a PPP mechanism P P P M is chosen (exogenously) by an expert and the
initial state of the investor’s enterprise X0 is described, the recurrence equations in
model (5) are used to derive the enterprise development trajectory {Xt , t = 0, ..., T }
for each scenario {Et , t = 1, ..., T }.
For field development projects that are most typical of the natural resource sector,
model (5) allows the construction of annual charts of revenues and expenses for the
state and the investor and the assessment of the economic rent from the field N P V
and the corresponding N P Vinv and N P Vst . The rent sharing proportions between the
Public-Private Partnership Models 629
participants are analyzed to determine the degree of compromise between their interests
and evaluate of the chosen PPP mechanism.
The basic element of the assessment procedure is the investment project model (5)
within a given PPP mechanism. For field development projects, one can use the original
models for an oil-and-gas complex and a mining factory [11, 12].
The road, power line, HPP, etc. construction projects are standard infrastructure
projects. An HPP is the most complex object in the group; it requires a special model
with a dedicated environmental block describing the preparation, construction, and
operation processes. In the general case [8], the environmental block contains a set of
environmental project models to implement a range of compensatory actions such as
resettlement from the flooding zone, protection from flash flooding, protective measures
against ice weakening, etc. The road and power line models describe the construction
and operation (maintenance and service) processes. They use the general investment
project model (5) supplemented by a detailed project financing scheme.
The output of the assesment procedure is a forecast of the revenues and expenses
of the private investor and the state during the implementation of the entire set of
projects within the assessed cost-sharing arrangement. These data allow one to assess
the efficiency of the selected PPP mechanism and the degree of compromise of interests
provided by positive N P V and N P Vinv .
Thus, the core of the proposed PPP assessment technology is a forecasting model
allowing the expert to evaluate the PPP mechanism and uncover its internal imbalances
(negative N P V of some of the participants). A “manual” adjustment of the cost-sharing
arrangement and repeated application of the model procedure make it possible to find
a partnership mechanism ensuring a compromise of interests.
Fig. 1. State’s internal rate of return for the PPP project
630 Sergey Lavlinskii
Fig. 2. Investor’s internal rate of return for the Bystrinskoe and Bugdainskoe fields
The possibilities of the proposed approach are illustrated using the above described
infrastructure projects implemented with the participation of the Investment Fund of
Russia. Here, construction works are being completed on the Naryn-Lugokan railway
line (up to the Gazimurovsky Zavod station) for a total cost of about 20 billion rubles;
the project is financed by the Investment Fund of Russia. This opens up prospects
for launching the first phase of the project to create the transport infrastructure for
the development of mineral resources in the southeast of the Chita oblast and develop
the Bystrinskoe and Bugdainskoe fields. The chosen PPP model allowed OAO Norilsk
Nickel to build the key transport infrastructure element through the federal budget and
create an economic background to launch the field development projects. How good
was the choice of a PPP model for the Bugdainskoe and Bystrinskoe fields?
This question can be answered by applying the procedure for an assessment of a
PPP model, which allows one to assess the two projects from the point of view of the
investor as well as the regional and federal budgets under different PPP arrangements.
In the model experiments, the state’s participates in the infrastructure project
by sharing with the investor the construction costs of the railway line. The state’s
participation in these costs can range from 0 to 100%. The zero level corresponds to a
situation whereby the investor independently finances the infrastructure project (the
target object of the PPP). The 100% level means that the construction is financed from
the federal budget. In the subsequent numerical experiments, we consider 11 levels of
state participation with a step of 10%.
We consider three product price scenarios: optimistic (market 1), inertial (market
2), and pessimistic (market 3). The scenarios are based on a retrospective analysis and
retain the general upward trends in the raw materials sector, which have been observed
for the last decade. Our calculations show that the minimum number of process stages
in the field development projects predetermines the maximum level of sensitivity of
performance indicators to a change in the market conditions.
Public-Private Partnership Models 631
An analysis of Fig. 1 suggests that the internal rate of return for the federal budget
financing of the railway construction falls sharply with the increase in the main PPP
parameter, i.e., the state’s share in the capital investments for this infrastructure.
The state is in general much less sensitive; nevertheless, its internal rate of return
becomes less than the modeled 5% discount for adverse market conditions if the state
participation is more than 75%.
The calculations show that even under the most favorable price conditions, at least
80% state participation is required for an investor with a discount of 15 % to invest in
the Bystrinskoe and Bugdainskoe fields. Any other market situation pushes the investor
into the domain of smaller IRR and negative N P V (Fig. 2).
Thus, the evaluated fragment of the Transbaikal mineral resource base development
program using a PPP whereby the state builds the Naryn-Gazimurovsky Zavod railway
line ensures a positive return for the state in a wide range of market conditions. Within
the initial technological projects for the development of the Bystrinskoe and Bugdain-
skoe fields, the chosen PPP gives a sufficient return for the investor under favorable
market conditions only. To achieve greater price stability for the field development
projects, they should plan a greater number of technological process stages.
3 PPP Mechanism Formation: Bilevel Boolean Programming
Problem
In the above example, a special forecasting tool allowed the expert to reasonably split
the infrastructure projects between the investor and the state. Such a cost-sharing
arrangement for a small fragment of the raw-material base development program helps
design a specific PPP mechanism to achieve a compromise between the interests of the
investor and the state. In real life, a similar problem would comprise hundreds of fields
and require a special planning model. This model complements the forecasting model
and allows one to optimize the designing of a PPP mechanism within a development
program for a natural resource-based region.
The planning model is formulated as a bilevel Boolean programming problem where
the state’s objective function is maximized at the upper level and the investor’s N P V
is maximized at the lower level.
We introduce the following notations:
N P ,N I,N E — number of investment, infrastructural and ecological projects, T —
planning horizon, i = 1, ..., N P, j = 1, ..., N I, k = 1, ..., N E, t = 1, ..., T :
• CFit is the cash flow of the production project i in year t.
• ELit is the cost estimate for the environmental losses in project i.
• BRit is the budget revenues from project i in year t.
• W Pit is the wages paid during the implementation of project i.
• CIjt is the cost schedule for the infrastructure project j in year t.
• ELIjt is the cost estimate for the environmental losses in project j.
• IBRjt is the non-project (indirect) budget revenues from the implementation of
project j, which are associated with the overall economic development of the region.
• W Ijt is the wages paid during the implementation of project j in year t.
632 Sergey Lavlinskii
• CEkt is the cost schedule for the environmental project k in year t.
• ERkt is the cost estimate for the environmental revenue from project k.
• W Ekt is the wages paid during the implementation of project k in year t.
• µij is a coherence indicator for the production and infrastructure projects: we
assume that µij = 1 if the production project i cannot be implemented unless the
infrastructure project j is implemented, and µij = 0 otherwise.
• νik is a coherence indicator for the production and environmental projects: we
assume that νik = 1 if the production project i cannot be implemented unless the
environmental project k is implemented, νik = 0 otherwise.
• Θ and θ are the discounts of the state and investor, respectively, Bt and bt are the
budget constraints of the state and investor, respectively.
The Booleans variables:
• zi = 1 if the investor runs the production project i; and zi = 0 otherwise.
• xj = 1 if the state runs the infrastructure project j; and xj = 0 otherwise.
• yk = 1 if the state runs the environmental project k; and yk = 0 otherwise.
• uk = 1 if the investor runs the environmental project k; and uk = 0 otherwise.
• y k = 1 if the state declares readiness to undertake the environmental project k;
and y k = 0 otherwise.
State’s Problem
The state’s goal is to maximize the discounted cash flow of the region:
T (∑
∑ NP ∑
NI
(BRit + W Pit − ELit )zi + (IBRjt + W Ijt − ELIjt − CIjt )xj +
t=1 i=1 j=1
∑
NE ∑
NE )
+ (ERkt + W Ekt − CEkt )yk + (ERkt + W Ekt )uk /(1 + Θ)t → max (6)
x,y,y,z,u
k=1 k=1
subject to
∑
NI ∑
NE
CIjt xj + CEkt y k ≤ Bt ; t = 1, ..., T ; (7)
j=1 k=1
(y, z, u) ∈ F ∗ (x, y); (8)
xj , y k ∈ {0, 1}; j = 1, ..., N I, k = 1, ..., N E. (9)
where F ∗ (x, y) is the set of the optimal solutions of the investor’s problem:
Investor’s Problem
The investor maximizes its total net present value:
T (∑
∑ NP ∑
NE )
CFit zi − CEkt uk /(1 + θ)t → max (10)
z,u
t=1 i=1 k=1
subject to
Public-Private Partnership Models 633
xj ≥ µij zi ; i = 1, ..., N P, j = 1, ..., N I; (11)
yk + uk ≤ 1; k = 1, ..., N E; (12)
yk + uk ≥ νik zi ; i = 1, ..., N P, k = 1, ..., N E; (13)
zi ≥ νik (yk + uk ); i = 1, ..., N P, k = 1, ..., N E; (14)
yk ≤ y k ; k = 1, ..., N E; (15)
∑
NE ∑
NP
CEkt uk − CFit zi ≤ bt ; t = 1, ..., T ; (16)
k=1 i=1
T (∑
∑ NP ∑
NI
(W Pit − ELit )zi + (W Ijt − ELIjt )xj +
t=1 i=1 j=1
∑
NE )
+ (ERkt + W Ekt )(yk + uk ) /(1 + Θ)t ≥ 0; (17)
k=1
yk , zi , uk ∈ {0, 1}; i = 1, ..., N P, k = 1, ..., N E. (18)
In the upper-level problem, the state maximizes an analogue of N P Vstint (6) of the
entire development program. The objective function is constructed so as to take into
account the interests of the population and includes the economic benefits of new jobs
and the accompanying environmental losses. The budget constraint (7) determines the
limit for the state spending on environmental projects and infrastructure development.
In the lower-level problem, the investor maximizes its N P V (10), which takes into
account the costs of the investor’s environmental projects. Constraints (11)–(15) show
the relationship of the production, environmental, and infrastructure projects. The
form of objective function and the budget constraints (16) guarantee that the cost-
sharing arrangement for the infrastructure and environmental projects between the
state and the investor ensures a normal profit for the investor. Constraint (17) shows
a long-term positive balance between the costs and benefits of the population from the
entire array of the projects. This is a way to protect the rights of the local people, who
are the first to feel the consequences of environmental pollution and who are interested
in new jobs and green technologies.
The input of the planning model (6)–(18) is the full range of projects planned by
the state and the private investor. The state forms a list of infrastructure projects on
the basis of the efficiency estimates considering the long-term regional development
prospects. The investor’s choice defines a necessary set of environmental projects and
depends on what the state offers in terms of infrastructure construction.
The output of the model is a set of vectors {zi ; xj ; yk ; uk }, which determines the
raw-material base development program and the cost-sharing arrangement underlying
the PPP mechanism.
It is fundamentally important that the input data of the planning model be formed
using the forecasting model database and individual assessment procedure. Although
model (6)–(18) is formulated in comparable prices, some of its input parameters cannot
634 Sergey Lavlinskii
Fig. 3. Objective function of the investor
be obtained by expert assessment. Thus, the cash flow of the production projects and
the budget revenues depend on the starting time of the projects and market conditions.
This circumstance defines the source of these data for the planning model — they are
generated in the field model by varying the project start year.
Thus, the planning model is a bilevel integer programming problem, the solving of
which is, generally speaking, a serious challenge [13–18]. In [19], we have shown that
the problem is NPO-hard, and the investor’s problem is NPO-complete. A local search
algorithm with alternating heuristics is proposed for solving this problem [19]. The
algorithm gives good results for the real-life cases (T = 20, N P = N E = 100, N I = 20).
Figs. 3–4 show some of the impirical results for the mineral resources base development
program of the Zabaikalsky krai (51 fields of polymetallic ores).
The figures show change in the PPP performance depending on a ratio of ecological
costs and losses. For the investor used “green” technologies with small ecological losses,
value of objective function decreases monotonously when ecological costs increase. A
linear nature of this dependence is broken when ecological losses increase. Then the
state begins to help an investor for implementation of ecological projects. However, the
state closes up an infrastructure program and stops the help an investor if pollution
reaches some critical level. It leads to strong decrease of investor’s N P V .
The planning model (6)–(18) is fine-tuned to the Russian PPP production infras-
tructure projects whereby private companies build private objects and the state builds
state-owned ones. Together with the forecasting model, the planning model provides
Public-Private Partnership Models 635
Fig. 4. Share of the state in ecological costs
a special modeling toolkit for decision-making in the development, assessment, and
support of this type of PPP projects.
4 Conclusions
From the retrospective analysis of the development of the PPP institution in modern
Russia we conclude that it is far from the western analogs. Although the government
pays much attention to the development of the mineral resources complex, its attempts
to stimulate the use of the various PPP models are not reinforced by economically sound
administrative decisions. The political losses due to the failure of the PPP projects
financed by the Investment Fund of Russia are big enough for the government to
become seriously concerned about decision-making in this sphere.
The proposed approach to the development of economic and mathematical tools to
design and evaluate PPP models may address a substantial part of these issues. The
forecasting model takes into account all the features of the mineral resources complex
and project financing details when evaluating a particular PPP arrangement. Having
been tested in real-life contexts, the model can be used already at the decision-making
stage to predict situations involving the risk of partnership termination and project
suspension.
The planning model (6)–(18) is configured to address the issues faced by natural
resource-based regions and to design an effective raw-material base development pro-
gram. Solving (6)–(18) generates both the program and a cost-sharing arrangement
between the state and the private investor, which fits into the current model of the
636 Sergey Lavlinskii
majority of Russian PPPs. However, the development of effective methods to solve
(6)–(18) for real-life cases with hundreds of projects is still a challenge. This is an area
for further development of the proposed tools. Here, it might be useful to apply the
approaches to solving bilevel integer programming problems [16, 17, 19].
Acknowledgements. This work was partially supported by the Russian Founda-
tion for Basic Research (project No 16-06-00046), the Russian Foundation for Human-
ities (project No 16-02-00049) and Ministry of Education and Science of the Russian
Federation (Government assignment No 2598).
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