Unification of closed-loop scheduling and control: State-space formulations, terminal constraints, and nominal theoretical properties

Systematic generation of alternative production schedules

“…where M is a sufficiently large number (e.g., M = max j β max j ). Note that Equations (36)- (37) are trivially satisfied if the batch is a newly added batch (i.e., Y ij 0 t 0 = 1).…”

“…Earlier contributions include methods based on heuristics and repair algorithms . More recently, state‐space models have been proposed and generalized to account for various uncertainties . Finally, the quality of the implemented (closed‐loop) schedule and strategies to improve it have been investigated …”

“…[29][30][31][32][33] More recently, state-space models have been proposed and generalized to account for various uncertainties. [34][35][36][37] Finally, the quality of the implemented (closed-loop) schedule and strategies to improve it have been investigated. [38][39][40]…”

Bringing new technologies and approaches to the operation and control of chemical process systems

“…Each unit evolves dynamically while producing and/or consuming resources to give final products that can be sold for profit. From Risbeck et al 65 Answer: Anything you want it to mean so that you can write (2).…”

“…65 The overall plant is represented by a set of operating modes i 2 I, units j 2 J, and resources k 2 K. Operating modes are essentially predefined tasks for each unit, during which specific sets of resources are produced and consumed by the unit. Resources can additionally be purchased from the market and/or sold as products to meet demand γ kt .Unit production and consumption are determined based on the dynamic evolution of each unit.…”