Process optimization under uncertainty

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.