About a regional development model that takes into account environmental problems with budgeting uncertainty

Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, Editorial Department, 630090 Novosibirsk, Russia

^* Corresponding author: artemka1387@bk.ru

Abstract

Raw-materials base (hereinafter RMB) is one of the largest industries for financial investments in Russia. There are various mathematical descriptions for the development of regions with resource-based economy. Earlier in [1] the researchers considered the model based on bilevel integer stochastic programming problems with Boolean variables. This paper proposes a new approach to public-private partnership modelling, including a bilevel linear stochastic programming problem. This model assumes that budget constraints of the state and the investor can vary in a random manner with a specific probability distribution. We put forward two methods to solve this problem: problem’s reduction to the deterministic bilevel one and formulation of deterministic problems sequence with help of Monte Carlo methods. In order to solve deterministic problems of integer programming, we suggest two approaches: direct enumeration and heuristic “Game” approach. The numerical experiments for proposed algorithms validation are conducted on the basis of actual data of Zabaykalsky Krai development. Multiple input parameters of the model vary in these experiments. Finally, we present a brief analysis of the obtained solutions to the stochastic linear programming problems with Boolean variables.