There exist several inherent uncertainties in the energy optimization modeling of Oil Sands operations. In this work, the deterministic model proposed by Betancourt-Torcat et al. in 2011 has been extended to account for parameter uncertainty in the natural gas price and steam-to-oil ratio (SOR). The new extended steady-state model considers freshwater withdrawal constraints and a new methodology to account for greenhouse gas (GHG) emissions. The problem was formulated as a single-period stochastic (MINLP). The application of the stochastic energy optimization model includes results reflecting all uncertain outcomes simultaneously and enabling optimal arrangement of the energy supply and oil producer infrastructures. The model’s capabilities have been shown in the present work through two new case studies accounting for uncertainty while the deterministic case is presented as a reference. The case studies under uncertainty consider the forecasted oil production scenario for the year 2035 in an uncertain environment where the price of natural gas is volatile and the SOR unknown. The results of the stochastic model were compared with those of the deterministic model by studying the expected values of the stochastic approach and those of the deterministic solution. The results presented in this study were discussed regarding the characteristics of uncertainty of the varied fuel price and SOR parameter. The key findings of this study are that oil producers considering hydrocracking are favored over thermocracking-based schemes, and the GHG emission constraint cannot be met for SOR values higher than 2.48.