Process optimization under uncertainty

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

A holistic two-stage decision-making methodology for passive and active building design strategies under uncertainty

In the last decade, many studies focused on finding optimal design solutions considering trade-offs between different aspects of building design. Accordingly, multi-objective optimization (MOO) approaches have been increasingly applied in the building industry. However, certain aspects must be deepened to ensure a more effective decision-making process in the early planning phase. On the one hand, uncertainties should be considered before making decisions to ensure the robustness of the optimal solutions; on the other hand, decisions are made at different times in building planning, and the sequential order of making decisions should be modeled. This paper presents a holistic two-stage multi-objective stochastic optimization (MOSO)-II framework to minimize the environmental impact of global warming potential (GWP) and cost throughout the entire life cycle of a building (phases of A1-A3, B4, B6 and C3-C4), considering passive and active design strategies in two consecutive stages, under uncertainty. Herein, individual/use and political/market uncertainties are considered. As a proof of concept, the proposed framework is applied in a case study for a generic zone in a multi-family terraced residential building type with solid brick construction. The advantages of the proposed framework are validated by comparing it with alternative single-stage MOSO frameworks. Results show that the proposed two-stage MOSO-II framework can deliver a smaller range of solutions with a better performance in terms of lower GWP and cost. It indicates that the proposed framework can effectively assist planners in decision-making by reducing the effort in choosing the proper solution. Secondly, the results also emphasize the importance of passive design strategies in sustainable building planning. In addition, the energy mix structure and cost of energy sources should be carefully adjusted in the future to promote a more ecologically sustainable building design

Optimal management of bio-based energy supply chains under parametric uncertainty through a data-driven decision-support framework

This paper addresses the optimal management of a multi-objective bio-based energy supply chain network subjected to multiple sources of uncertainty. The complexity to obtain an optimal solution using traditional uncertainty management methods dramatically increases with the number of uncertain factors considered. Such a complexity produces that, if tractable, the problem is solved after a large computational effort. Therefore, in this work a data-driven decision-making framework is proposed to address this issue. Such a framework exploits machine learning techniques to efficiently approximate the optimal management decisions considering a set of uncertain parameters that continuously influence the process behavior as an input. A design of computer experiments technique is used in order to combine these parameters and produce a matrix of representative information. These data are used to optimize the deterministic multi-objective bio-based energy network problem through conventional optimization methods, leading to a detailed (but elementary) map of the optimal management decisions based on the uncertain parameters. Afterwards, the detailed data-driven relations are described/identified using an Ordinary Kriging meta-model. The result exhibits a very high accuracy of the parametric meta-models for predicting the optimal decision variables in comparison with the traditional stochastic approach. Besides, and more importantly, a dramatic reduction of the computational effort required to obtain these optimal values in response to the change of the uncertain parameters is achieved. Thus the use of the proposed data-driven decision tool promotes a time-effective optimal decision making, which represents a step forward to use data-driven strategy in large-scale/complex industrial problems.Peer ReviewedPostprint (published version

Multi-stage stochastic optimization framework for power generation system planning integrating hybrid uncertainty modelling

In this paper, a multi-stage stochastic optimization (MSO) method is proposed for determining the medium to long term power generation mix under uncertain energy demand, fuel prices (coal, natural gas and oil) and, capital cost of renewable energy technologies. The uncertainty of future demand and capital cost reduction is modelled by means of a scenario tree configuration, whereas the uncertainty of fuel prices is approached through Monte Carlo simulation. Global environmental concerns have rendered essential not only the satisfaction of the energy demand at the least cost but also the mitigation of the environmental impact of the power generation system. As such, renewable energy penetration, CO2,eq mitigation targets, and fuel diversity are imposed through a set of constraints to align the power generation mix in accordance to the sustainability targets. The model is, then, applied to the Indonesian power generation system context and results are derived for three cases: Least Cost option, Policy Compliance option and Green Energy Policy option. The resulting optimum power generation mixes, discounted total cost, carbon emissions and renewable share are discussed for the planning horizon between 2016 and 2030