A novel network-based continuous-time representation for process scheduling: Part I. Main concepts and mathematical formulation

A novel network-based framework for the short-term scheduling of multi-purpose batch processes is presented. The novelty of the proposed approach lies in five key concepts. First, it is based on a new continuous-time representation that does not require tasks to start (end) exactly at a time point; thus reducing the number of time points needed to represent a solution. Second, processing units are modeled as being in different activity states to allow storage of input/output materials. Third, time variables for "idle" and "storage" periods of a unit are introduced to enable the matching between tasks and time points without big-M constraints. Fourth, material transfer variables are introduced to explicitly account for unit connectivity. Fifth, inventory variables for storage in processing units are incorporated to model non-simultaneous and partial material transfers. The proposed representation leads to MILP formulations which address limitations of existing scheduling methods.