Bruno A. Calfa

Recent Advances in Mathematical Programming Techniques for the Optimization of Process Systems under Uncertainty

Abstract Optimization under uncertainty has been an active area of research for many years. However, its application in Process Synthesis has faced a number of important barriers that have prevented its effective application. Barriers include availability of information on the uncertainty of the data (ad-hoc or historical), determination of the nature of the uncertainties (exogenous vs. endogenous), selection of an appropriate strategy for hedging against uncertainty (robust optimization vs. stochastic programming), large computational expense (often orders of magnitude larger than deterministic models), and difficulty in the interpretation of the results by non-expert users. In this paper, we describe recent advances that have addressed some of these barriers.

Evolution of concepts and models for quantifying resiliency and flexibility of chemical processes

Abstract This paper provides a historical perspective and an overview of the pioneering work that Manfred Morari developed in the area of resiliency for chemical processes. Motivated by unique counter-intuitive examples, we present a review of the early mathematical formulations and solution methods developed by Grossmann and co-workers for quantifying Static Resiliency (Flexibility). We also give a brief overview of some of the seminal ideas by Manfred Morari and co-workers in the area of Dynamic Resiliency. Finally, we provide a review of some of the recent developments that have taken place since that early work.

Recent advances in mathematical programming techniques for the optimization of process systems under uncertainty

Abstract Optimization under uncertainty has been an active area of research for many years. However, its application in Process Systems Engineering has faced a number of important barriers that have prevented its effective application. Barriers include availability of information on the uncertainty of the data (ad-hoc or historical), determination of the nature of the uncertainties (exogenous vs. endogenous), selection of an appropriate strategy for hedging against uncertainty (robust/chance constrained optimization vs. stochastic programming), large computational expense (often orders of magnitude larger than deterministic models), and difficulty of interpretation of the results by non-expert users. In this paper, we describe recent advances that have addressed some of these barriers for mostly linear models.

Data-driven individual and joint chance-constrained optimization via kernel smoothing

Abstract We propose a data-driven, nonparametric approach to reformulate (conditional) individual and joint chance constraints with right-hand side uncertainty into algebraic constraints. The approach consists of using kernel smoothing to approximate unknown true continuous probability density/distribution functions. Given historical data for continuous univariate or multivariate random variables (uncertain parameters in an optimization model), the inverse cumulative distribution function (quantile function) and the joint cumulative distribution function are estimated for the univariate and multivariate cases, respectively. The approach relies on the construction of a confidence set that contains the unknown true distribution. The distance between the true distribution and its estimate is modeled via ϕ -divergences. We propose a new way of specifying the size of the confidence set (i.e., the ϕ -divergence tolerance) based on point-wise standard errors of the smoothing estimates. The approach is illustrated with a motivating and an industrial production planning problem with uncertain plant production rates.

Data-Driven Multi-Stage Scenario Tree Generation via Statistical Property and Distribution Matching

The objective of this paper is to bring systematic methods for scenario tree generation to the attention of the Process Systems Engineering community. In this paper, we focus on a general, data-driven optimization-based method for generating scenario trees, which does not require strict assumptions on the probability distributions of the uncertain parameters. This method is based on the Moment Matching Problem (MMP), originally proposed by Hoyland & Wallace (2001). In addition to matching moments, and in order to cope with potentially under-specified MMP, we propose matching (Empirical) Cumulative Distribution Function information of the uncertain parameters. The new method gives rise to a Distribution Matching Problem (DMP) that is aided by predictive analytics. We present two approaches for generating multi-stage scenario trees by considering time series modeling and forecasting. The aforementioned techniques are illustrated with a motivating production planning problem with uncertainty in production yield and correlated product demands.

Optimal Procurement Contract Selection with Price Optimization under Uncertainty for Process Networks

Abstract In this work, we propose extending the production planning decisions of a chemical process network to include optimal contract selection under uncertainty with suppliers and product selling price optimization. We use three quantity-based contract models: discount after a certain purchased amount, bulk discount, and fixed duration contracts. We propose the use of general regression models to describe the relationship between selling price, demand, and possibly other predictors, such as economic indicators. For illustration purposes, we consider three demand-response models (i.e., selling price as a function of demand) that are typically encountered in the literature: linear, constant-elasticity, and logit. We develop a mixed-integer nonlinear two-stage stochastic programming that accounts for uncertainty in both supply (e.g., raw material spot market price) and demand (random nature of the residuals of the regression models) for the planning of the process network. The proposed method is illustrated with two numerical examples of chemical process networks.

Mathematical Programming Techniques for Optimization under Uncertainty and Their Application in Process Systems Engineering

In this paper we give an overview of some of the advances that have taken place to address challenges in the area of optimization under uncertainty. We first describe the incorporation of recourse in robust optimization to reduce the conservative results obtained with this approach, and illustrate it with interruptible load in demand side management. Second, we describe computational strategies for effectively solving two stage programming problems, which is illustrated with supply chains under the risk of disruption. Third, we consider the use of historical data in stochastic programming to generate the probabilities and outcomes, and illustrate it with an application to process networks. Finally, we briefly describe multistage stochastic programming with both exogenous and endogenous uncertainties, which is applied to the design of oilfield infrastructures.