A Nonlinear Optimal Control Approach to Process Scheduling

Abstract

Scheduling problems in the process industry feature combinatorial and nonlinear aspects arising from task sequencing and product blending. In this chapter, we present an optimal control approach, recognizing that process scheduling problems can be modeled as dynamic systems, where flows are control variables and volumes and composition are state variables. This approach yields a nonlinear optimal control model with continuous state and control variables, bounded by lower and upper limits, avoiding the use of discrete variables. In this optimal control model, mixed-integer constraints are replaced by complementarity constraints. Moreover, we present a hybrid procedure which combines mixed-integer and nonlinear models. Numerical test instances are presented and solved by well-known optimization solvers.