The flexible operation of continuous processes often requires the integration of scheduling and control. This can be achieved by top-down or bottom-up approaches. We compare the two paradigms in-silico using an air separation unit as a benchmark process. To demonstrate the top-down paradigm, we identify data-driven models of the closed-loop process dynamics based on a mechanistic model and use them in scheduling calculations that are performed offline. The resulting target trajectories are passed to a linear model predictive control (LMPC) system and implemented in the process. To demonstrate the bottom-up paradigm, we define an economic nonlinear model predictive control (eNMPC) scheme, which performs dynamic optimization using the full model in closed-loop to directly obtain the control variable profiles to be implemented in the process. We provide implementations of the process model equations as both a gPROMS and a Modelica model to encourage future comparison of approaches for flexible operation, process control, and/or handling disturbances. The performance, advantages, and disadvantages of the two strategies are analyzed using demand-response scenarios with varying levels of fluctuations in electricity prices, as well as considering the cases of known, instantaneous, and completely unknown load changes. The similarities and differences of the two approaches as relevant to flexible operation of continuous processes are discussed. Integrated scheduling and control leverages existing infrastructure and can be immediately applied to real operation tasks. Both operation strategies achieve successful process operation with remarkable economic improvements (up to 8%) compared to constant operation. eNMPC requires more computational resources, and is - at the moment - not implementable in real-time due to maximum optimization times exceeding the controller sampling time. However, eNMPC achieves up to 2.5 times higher operating cost savings compared to the top-down approach, owing in part to the more accurate modeling of key process dynamics. (C) 2020 Elsevier Ltd. All rights reserved.