Modeling of storage in batching and scheduling of multistage processes

The goal of this paper is the development of a mixed-integer programming formulation for the simultaneous batching and scheduling in multiproduct multistage processes with storage constraints. Storage vessels are modeled as additional processing units for which assignment and sequencing constraints are expressed. Our formulation involves selection (batching), assignment and precedence (scheduling) binary variables as well as batch-size and timing continuous variables. We also discuss a general classification of storage policies in multistage processes and show how the proposed formulation can be readily modified to address all classes of problems. Finally, we extend our approach to address problems with sequence-dependent changeovers and stand-alone scheduling problems, and we present a set of tightening constraints that enhance me solution of the proposed models.