In this paper, in a Model Predictive Control problem, we tackle the integration of uncertain constraints that belong to a discrete set. We propose a controller that offers a solution to reformulate the discrete stochastic constraints to avoid the exponential growth of scenario tree experienced by existing controllers. The proposed controller's efficiency is shown by benchmarking and comparing it with the Multistage Stochastic Programming algorithm in a context of Home Energy Management System. The comparison is made based on simulations using real-life data to manage the energy flow within a building connected to the electricity feeder, which random character involves its availability and nonavailability.