Linear model predictive control is extended to both control and optimize a product grade schedule. The proposed methods are time-scaling of the linear dynamics based on throughput rates and grade-based objectives for product scheduling based on a mathematical program with complementarity constraints. The linear model is adjusted with a residence time approximation to time-scale the dynamics based on throughput. Although nonlinear models directly account for changing dynamics, the model form is restricted to linear differential equations to enable fast online cycle times for large-scale and real-time systems. This method of extending a linear time-invariant model for scheduling is designed for many advanced control applications that currently use linear models. Simultaneous product switching and grade target management is demonstrated on a reactor benchmark application. The objective is a continuous form of discrete ranges for product targets and economic terms that maximize overall profitability. (C) 2017 Elsevier Ltd. All rights reserved.