Simultaneous lotsizing and scheduling considering secondary resources: a general model, literature review and classification

Typical simultaneous lotsizing and scheduling models consider the limited capacity of the production system by respecting a maximum time the respective machines or production lines can be available. Further limitations of the production quantities can arise by the scarce availability of, e.g., setup tools, setup operators or raw materials which thus cannot be neglected in optimization models. In the literature on simultaneous lotsizing and scheduling, these production factors are called “secondary resources”. This paper provides a structured overview of the literature on simultaneous lotsizing and scheduling involving secondary resources. The proposed classification yields for the first time a unified view of scarce production factors. The insights about different types of secondary resources help to develop a new model formulation generalizing and extending the currently used approaches that are specific for some settings. Some illustrative examples demonstrate the functional principle and flexibility of this new formulation which can thus be used for a wide range of applications.