A stochastic optimization framework for integrated scheduling and control under demand uncertainty

Increased globalization and energy market deregulation are requiring process industries to respond more rapidly to fluctuations in demand levels, and utility and raw material prices, in order to remain competitive. In this study, a two-stage stochastic approach is proposed to account for demand uncertainty in a closed-loop dynamic real-time optimization (CL-DRTO) formulation that includes scheduling decisions. The CL-DRTO problem utilizes a prediction of the closed-loop response of the plant under the action of constrained MPC. The CL-DRTO system is executed in a rolling horizon fashion to compute economically optimal operation that is communicated to the plant through set-point trajectories assigned to the plant MPC. Nonlinear plant models are approximated using linear and piecewise affine (PWA) approximations, allowing the integrated CL-DRTO problem to be formulated as a mixed-integer linear program (MILP). Case studies demonstrate significantly higher expected profit using the proposed formulation than with a deterministic formulation utilizing the expected demand.