  Scheduling problems requires to explicitly account for control considerations
in their optimisation. The literature proposes two traditional ways to solve
this integrated problem: hierarchical and monolithic. The monolithic approach
ignores the control level's objective and incorporates it as a constraint into
the upper level at the cost of suboptimality. The hierarchical approach
requires solving a mathematically complex bilevel problem with the scheduling
acting as the leader and control as the follower. The linking variables between
both levels belong to a small subset of scheduling and control decision
variables. For this subset of variables, data-driven surrogate models have been
used to learn follower responses to different leader decisions. In this work,
we propose to use ReLU neural networks for the control level. Consequently, the
bilevel problem is collapsed into a single-level MILP that is still able to
account for the control level's objective. This single-level MILP reformulation
is compared with the monolithic approach and benchmarked against embedding a
nonlinear expression of the neural networks into the optimisation. Moreover, a
neural network is used to predict control level feasibility. The case studies
involve batch reactor and sequential batch process scheduling problems. The
proposed methodology finds optimal solutions while largely outperforming both
approaches in terms of computational time. Additionally, due to well-developed
MILP solvers, adding ReLU neural networks in a MILP form marginally impacts the
computational time. The solution's error due to prediction accuracy is
correlated with the neural network training error. Overall, we expose how - by
using an existing big-M reformulation and being careful about integrating
machine learning and optimisation pipelines - we can more efficiently solve the
bilevel scheduling-control problem with high accuracy.
