Model-based design has received considerable attention in biological and chemical industries over the last two decades. However, the parameter uncertainties of first-principle models are critical in model-based design and have led to the development of robustification concepts. Various strategies were introduced to solve the robust optimization problem. Most approaches suffer from either unreasonable computational expense or low approximation accuracy. Moreover, they are not rigorous and do not consider robust optimization problems where parameter correlation and equality constraints exist. In this work, we propose a highly efficient framework for solving robust optimization problems with the so-called point estimation method (PEM). The PEM has a fair trade-off between computation expense and approximation accuracy and can be easily extended to problems of parameter correlations. From a statistical point of view, moment-based methods are used to approximate robust inequality and equality constraints. We also suggest employing the information from global sensitivity analysis to further simplify robust optimization problems with a large number of uncertain parameters. We demonstrate the performance of the proposed framework with two case studies where one is to design a heating/cooling profile for the essential part of a continuous production process and the other is to optimize the feeding profile for a fed-batch reactor of the penicillin fermentation process. The results reveal that the proposed approach can be used successfully for complex (bio)chemical problems in model-based design.