16. Combining Mathematical Programming and Monte Carlo Simulation to Deal with Uncertainty in Energy Project Portfolio Selection

Mathematical programming (MP) is the most common methodology for modeling and optimization of energy systems. Energy systems’ planning and optimization assume the knowledge of future situation, which is usually known with limited certainty. Therefore, the parameters of the model (data which assumed to be known during the modeling process) have usually a degree of uncertainty. Various methods have been proposed for dealing with this uncertainty, the most common ones being fuzzy programming, chance constrained programming, robust programming, and stochastic programming. In this work, we consider the implied uncertainty in the parameters as being of stochastic nature. Each uncertain parameter is characterized by a probability distribution. Subsequently, a Monte Carlo simulation samples the values from these distributions, and the MP models with the sampled values are solved. This process is repeated many times (1,000) in order to have an adequate sample for drawing robust conclusions. Relationships between the values of these parameters (i.e., interdependent parameters) can also be incorporated in the Monte Carlo process. The specific work is focused on the energy project portfolio selection problem where the output of each project as well as other parameters may be uncertain. In the current work, we introduce the iterative trichotomic approach (ITA) that gradually separates projects into green (selected under all circumstances), red (rejected under all circumstances), and gray sets (need further elaboration), combining Monte Carlo simulation and MP. The process output is not only the final portfolio, but also information about the certainty of participation or exclusion of every project in the final portfolio. A case study with real data from clean development mechanism (CDM) projects’ database is elaborated in order to illustrate the method.