Uncertainty is among the significant concerns in production scheduling. It has become increasingly important to take uncertainties into consideration for lot-sizing and scheduling. In this paper, we adopt the Hybrid Stochastic and Robust Optimization (HSRO) approach in lot-sizing and scheduling problems in which suppliers have the flexibility of satisfying a fraction of demand based on the market and their policies. Two types of uncertainties have been considered simultaneously: demand and overtime processing cost. Robust optimization is adopted for uncertain demand and Sample Average Approximation (SAA) technique is applied to solve the stochastic program for uncertain overtime processing cost. Numerical results based on a manufacturing company has been conducted to not only validate the proposed hybrid model but also quantitatively demonstrate the merit of our approach. Sample size stability test and sensitivity analyses on various parameters have also been conducted.