  The problem of real-time control and optimization of components' routing in
discrete manufacturing plants, where distinct items must undergo a sequence of
jobs, is considered. This problem features a large number of discrete control
inputs and the presence of temporal-logic constraints. A new approach is
proposed, adopting a shift of perspective with respect to previous
contributions, from a Eulerian system model that tracks the state of plant
nodes, to a Lagrangian model that tracks the state of each part being
processed. The approach features a hierarchical structure. At a higher level, a
predictive receding horizon strategy allocates a path across the plant to each
part in order to minimize a chosen cost criterion. At a lower level, a path
following logic computes the control inputs in order to follow the assigned
path, while satisfying all constraints. The approach is tested here in
simulations, reporting extremely good performance as measured by closed-loop
cost function values and computational efficiency, also with very large
prediction horizon values. These features pave the way to a number of
subsequent research steps, which will culminate with the experimental testing
on a pilot plant.
