Abstract Time-sensitive electricity prices (as part of so-called demand-side management in the smart grid) offer economical incentives for large industrial customers. In part I of this paper, we propose an MILP formulation that integrates the operational and strategic decision-making for continuous power-intensive processes under time-sensitive electricity prices. We demonstrate the trade-off between capital and operating expenditures with an industrial case study for an air separation plant. Furthermore, we compare the insights obtained from a model that assumes deterministic demand with those obtained from a stochastic demand model. The value of the stochastic solution (VSS) is discussed, which can be significant in cases with an unclear setup, such as medium baseline product demand and growth rate, large variance or skewed demand distributions. While the resulting optimization models are large-scale, they can be solved within three days of computational time. A decomposition algorithm for speeding-up the solution time is described in part II.