Scheduling of multistage batch processes under utility constraints

We present a novel discrete-time mixed-integer programming (MIP) formulation for the simultaneous batching and scheduling in multiproduct multistage processes under utility constraints. In addition to processing units and storage vessels, we consider utilities such as cooling water, steam, and electricity that are available in limited quantities. Since different tasks often share the limited utilities at the same time, we use a common time-grid approach. Further, the proposed method handles the batching decisions (the number and sizes of batches) seamlessly without the usage of explicit batch-selection variables. To preserve batch identity in storage vessels, we introduce a new class of inventory variables and constraints. Our approach is the first to address limited utilities for simultaneous batching and scheduling in multistage processes.