Pathwise Optimization for Merchant Energy Production

Abstract

We study merchant energy production modeled as a compound switching and timing option. The resulting Markov decision process is intractable. State-of-the-art approximate dynamic programming methods applied to realistic instances of this model yield policies with large optimality gaps that are attributed to a weak upper (dual) bound on the optimal policy value. We extend path-wise optimization from stopping models to merchant energy production to investigate this issue. We apply principal component analysis and block coordinate descent in novel ways to respectively precondition and solve the ensuing ill conditioned and large scale linear program, which even a cutting-edge commercial solver is unable to handle directly. Compared to standard methods, our approach leads to substantially tighter dual bounds and smaller optimality gaps at the expense of considerably larger computational effort. Specifically, we provide numerical evidence for the near optimality of the operating policies based on least squares Monte Carlo and compute slightly better ones using our approach on a set of existing benchmark ethanol production instances. These findings suggest that both these policies are effective for the class of models we investigate. Our research has potential relevance for other commodity merchant operations settings.

Keywords: approximate dynamic programming, block coordinate descent, information relaxation and duality, merchant energy operations, pathwise optimization, principal component analysis, real options

JEL Classification: C02, C61, D24, G11, L6, L7