A Stochastic Approach to Solving Bilevel Natural Gas Cash-Out Problems

Abstract

We study a special bilevel programming problem that arises in transactions between a Natural Gas Shipping Company and a Pipeline Operator. Because of the business relationships between these two actors, the timing, and objectives of their decision-making process are different. In order to model that, bilevel programming was traditionally used. Apart from the theoretical studies of the problem to facilitate its solution a linear reformulation is required, as well as heuristic approaches, and branch-and-bound techniques may be applied. We present a linear programming reformulation of the latest version of the model, which is easier and faster to solve numerically. This reformulation makes it easier to theoretically analyze the problem, allowing us to draw some conclusions about the nature of the solution.Since elements of uncertainty are definitely present in the bilevel natural gas cash-out problem, its stochastic formulation is developed in the form of a bilevel multi-stage stochastic programming model with recourse. After reducing the original formulation to a bilevel linear problem, a stochastic scenario tree is defined by its node events, and time series forecasting is used to produce stochastic values for data of natural gas price and demand. Numerical experiments were run to compare the stochastic solution with the perfect information solution and the expected value solutions.