A Rolling Horizon Approach for Stochastic Mixed Complementarity Problems with Endogenous Learning: Application to Natural Gas Markets

In this paper we present a new approach for solving energy market equilibria that is an extension of the classical Nash-Cournot approach. Specifically, besides allowing the market participants to decide on their own decision variables such as production, flows or the like, we allow them to compete in terms of adjusting the data in the problem such as scenario probabilities and costs, consistent with a dynamic, more realistic approach to these markets. Such a problem in its original form is very hard to solve given the product of terms involving decision-dependent data and the variables themselves. Moreover, in its more general form, the players can affect not only each others׳ objective functions but also the constraint sets of opponents making such a formulation a more complicated instance of generalized Nash problems. This new approach involves solving a sequence of stochastic mixed complementarity (MCP) problems where only partial foresight is used, i.e., a rolling horizon. Each stochastic MCP or roll, involves a look-ahead for a fixed number of time periods with learning on the part of the players to approximate the extended Nash paradigm. Such partial foresight stochastic MCPs also offer a realism advantage over more traditional perfect foresight formulations. Additionally, the rolling-horizon approach offers a computational advantage over scenario-reduction methods as is demonstrated with numerical tests on a natural gas market stochastic MCP. Lastly, we introduce a new concept, the Value of the Rolling Horizon (VoRH) to measure the closeness of different rolling horizon schemes to a perfect foresight benchmark and provide some numerical tests on it using a stylized natural gas market.