Billions of dollars are tied up in the inventories of manufacturing companies which cause large (interest) costs. A small decrease of the inventory and/or production costs without reduction of the service level can increase the profit substantially. Especially in the case of scarce capacity, efficient production schedules are fundamental for short delivery time and on-time delivery which are important competitive priorities. To support decision makers by improving their manufacturing resource planning system with appropriate methods is one of the most of production planning. interesting challenges The following chapters contain new models and new solution strategies which may be helpful for decision makers and for further research in the areas of production planning and operations research. The main subject is on lotsizing and scheduling. The objectives and further characteristics of such problems can be inferred from practical need. Thus, before an outline is given, we consider the general objectives of lotsizing and scheduling and classify the most important characteristics of such problems in the following sections.