Process optimization under uncertainty
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Date
2023
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Abstract
The ability of a production plant to be flexible by adjusting the operating conditions
to changing demands, prices of the products and the raw materials is crucial to
maintain a profitable operation. In this respect, the application of mathematical
optimization techniques is unanimously recognized to be successful to improve the
decision-making process. Typical examples are production planning, scheduling,
real-time optimization and advanced process control. The more information are available
to the optimization approach, the more "optimal" are the resulting decisions: the
"optimal" production strategy cannot reduce the inventory costs if no supply-chain
model is integrated into the production planning optimization. This thesis lies in the
context of Enterprise-wide optimization with the goal of integrating decision layers
and functions while accounting for uncertain information. A stochastic programming
approach is adopted to integrate production scheduling with energy management
and production planning with predictive maintenance. The approaches are analysed
from a formulation perspective and from a computational point of view, which is
necessary to deal with one of the challenges of the presented methods consisting in
the size of the resulting optimization problems.
To reduce the electricity cost that is generated by the uncertain peaks of the dayahead
price, a two-stage risk-averse optimization is proposed to simultaneously
define the optimal bidding curves for the day-ahead market and the optimal production
schedule. The large-scale MILP problem is solved with a scenario-based
decomposition technique, the progressive hedging algorithm. Heuristic procedures
are applied to speed up the solution phase and to avoid the oscillatory behaviour due
to the integer variables. Since large electricity consumers rely on Time-Of-Use power
contracts to handle the volatility of the day-ahead price, the two-stage formulation
is expanded into a multi-stage optimization to optimally purchase electricity from
different sources and to generate electric power with a power plant. The unpractical
size of the resulting problem is handled by approximating the multi-stage tree with a
series of two-stage scenario-trees within a rolling horizon procedure. A mixed time
grid handles the multi-scale nature of the problem by making short-term decisions
with a detailed model and catching their effect on the long-term future with an aggregated
model.
While the electricity prices introduce exogenous uncertain information into the optimization
problem, the predictive maintenance optimization carries endogenous
uncertain sources into the production planning problem. Endogenous uncertainties,
contrary to the exogenous ones, are uncertain information that can be modified (in the
probability or in the timing of the realization) by the decision maker. The prognosis
technique of the Cox model is embedded into a multi-stage stochastic program to
consider an uncertain Remaining Useful Life of the equipment when the optimal
operating conditions of the plant are defined. Two modelling approaches (based on
superstructure-scenario trees and on conditional non-anticipativity constraints) are
proposed to formulate the optimization problem with endogenous uncertainties. Two
Benders-like decomposition techniques and several branching priority schemes are
applied to handle the high complexity of the resulting optimization problems.
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Keywords
Process optimization, Stochastic programming