This paper presents a scenario-based optimization framework applied to Daily Production Optimization (DPO) for an Electric Submersible Pump lifted oil field under parametric uncertainty. The study also develops a simplified combined well-reservoir model, which is used solely to assess the performance of the methods in a more realistic setting. The combined model consists of the steady-state model of wells combined with the reservoir model through bottom hole pressure and well flow. Moreover, it successfully represents the change in uncertain parameters based on reservoir dynamics rather than random variations. The superiority of scenario-based DPO and the importance of considering uncertainty are demonstrated through extensive comparisons between deterministic and robust methods. The comparisons show that the deterministic DPO fails to satisfy output constraints, leading to violations, particularly in wellhead pressure. Conversely, the scenario-based DPO exhibits significant potential for real oil field application, effectively respecting all input and output constraints. Nevertheless, this safety comes at the cost of sacrificing net profit to some extent. The research emphasizes the importance of considering uncertainty in DPO for oil field operations, providing valuable insights for achieving robustness and operational safety.