The optimization of manufacturing systems is rarely a deterministic task in practice, as uncertainties of various origins often have significant impact on the feasibility or quality of a production plan. The decision making process is often a complex multi-stage mechanism that anticipates and reacts to numerous parameter changes, both internal and external. Such optimization problems and the corresponding approaches are often classified and categorized based on the features of the addressed uncertainties and the desired objective. The goal of this paper is twofold. First, a systematic approach is presented to enumerate the possible optimization problems for a given set of uncertainties and degree of freedom in the planning. This approach is illustrated via a scheduling example that is inspired by literature case studies and focuses on financial objectives with varying demands and prices in the market. Then, selected problem classes identified by the approach are discussed in detail, illustrating and examining the available techniques to tackle them, citing literature studies applying the same or similar approaches.