Marianthi G. Ierapetritou

Process scheduling under uncertainty : Review and challenges

Uncertainty is a very important concern in production scheduling since it can cause infeasibilities and production disturbances. Thus scheduling under uncertainty has received a lot of attention in the open literature in recent years from chemical engineering and operations research communities. The purpose of this paper is to review the main methodologies that have been developed to address the problem of uncertainty in production scheduling as well as to identify the main challenges in this area. The uncertainties in process scheduling are first analyzed, and the different mathematical approaches that exist to describe process uncertainties are classified. Based on the different descriptions for the uncertainties, alternative scheduling approaches and relevant optimization models are reviewed and discussed. Further research challenges in the field of process scheduling under uncertainty are identified and some new ideas are discussed.

Novel approach for optimal process design under uncertainty

Abstract This paper presents the theoretical developments of a novel approach for the optimization of design models involving stochastic parameters. Based on the postulation of general probability distribution functions describing process uncertainty and variations, the problem is formulated as a two-stage stochastic programming problem where the objective is to determine the design that maximizes an expected revenue or profit while simultaneously measuring design feasibility. In contrast to previous approaches, design feasibility and economic optimality are simultaneously obtained without requiring an a priori discretization of the uncertainty. The decomposition based approach is general to deal with linear and convex nonlinear models involving uncertainty described by arbitrary probability distribution functions. A very attractive feature of this approach is that since most optimization tasks can be performed independently the algorithm has a highly parallel structure that can be further exploited. The steps of the proposed algorithmic procedure are illustrated in detail through four example problems.

Efficient short-term scheduling of refinery operations based on a continuous time formulation

The problem addressed in this work is to develop a comprehensive mathematical programming model for the efficient scheduling of oil-refinery operations. Our approach is first to decompose the overall problem spatially into three domains: the crude-oil unloading and blending, the production unit operations and the product blending and delivery. In particular, the first problem involves the crude-oil unloading from vessels, its transfer to storage tanks and the charging schedule for each crude-oil mixture to the distillation units. The second problem consists of the production unit scheduling which includes both fractionation and reaction processes and the third problem describes the finished product blending and shipping end of the refinery. Each of those sub-problems is modeled and solved in a most efficient way using continuous time representation to take advantage of the relatively smaller number of variables and constraints compared to discrete time formulation. The proposed methodology is applied to realistic case studies and significant computational savings can be achieved compared with existing approaches.

An integrated approach for dynamic flowsheet modeling and sensitivity analysis of a continuous tablet manufacturing process

Abstract Manufacturing of powder-based products is a focus of increasing research in the recent years. The main reason is the lack of predictive process models connecting process parameters and material properties to product quality attributes. Moreover, the trend towards continuous manufacturing for the production of multiple pharmaceutical products increases the need for model-based process and product design. This work aims to identify the challenges in flowsheet model development and simulation for solid-based pharmaceutical processes and show its application and advantages for the integrated simulation and sensitivity analysis of two tablet manufacturing case studies: direct compaction and dry granulation. The developed flowsheet system involves a combination of hybrid, population balance and data-based models. Results show that feeder refill fluctuations propagate downstream and cause fluctuations in the mixing uniformity of the blend as well as the tablet composition. However, this effect can be mitigated through recycling. Dynamic sensitivity analysis performed on the developed flowsheet, classifies the most significant sources of variability, which are material properties such as mean particle size and bulk density of powders.

An engineering study on the enhanced control and operation of continuous manufacturing of pharmaceutical tablets via roller compaction.

A novel manufacturing strategy based on continuous processing integrated with online monitoring tools coupled with efficient automatic feedback control system is highly desired for efficient Quality by Design (QbD) based manufacturing of the next generation of pharmaceutical products with optimal consumption of time, space and resources. In this manuscript, an efficient plant-wide control strategy for an integrated continuous pharmaceutical tablet manufacturing process via roller compaction has been designed in silico. The designed control system consists of five cascade control loops and three single control loops resulting in 42 controller tuning parameters. An effective controller parameter tuning strategy involving an ITAE method coupled with an optimization strategy has been proposed and the designed control system has been implemented in a first principle model-based flowsheet that was simulated in gPROMS (Process System Enterprise). The advanced techniques (e.g. anti-windup) have been employed to improve the performance of the control system. The ability of the control system to reject the unknown disturbances as well as to track the set point has been analyzed. Results demonstrated enhanced performance of critical quality attributes (CQAs) under closed-loop control compared to open-loop operation thus illustrating the potential of closed-loop feedback control in improving pharmaceutical manufacturing operations.

An optimization approach for process engineering problems under uncertainty

The problem of selecting an optimal design/plan for process models involving stochastic parameters is addressed in this paper. A classification of uncertainty is introduced depending on its sources and mathematical model structure. A combined multiperiod/stochastic optimization formulation is then proposed along with a decomposition-based algorithmic procedure for its solution. The approach is illustrated with a process synthesis/planning example problem.

Accelerating Benders method using covering cut bundle generation

Over the years, various techniques have been proposed to speed up the classical Benders decomposition algorithm. The work presented in the literature has focused mainly on either reducing the number of iterations of the algorithm or on restricting the solution space of the decomposed problems. In this article, a new strategy for Benders algorithm is proposed and applied to two case studies in order to evaluate its efficiency. This strategy, referred to as covering cut bundle (CCB) generation, is shown to implement in a novel way the multiple constraints generation idea. The CCB generation is applied to mixed integer problems arising from two types of applications: the scheduling of crude oil and the scheduling problem for multi-product, multi-purpose batch plants. In both cases, CCB significantly decreases the number of iterations of the Benders method, leading to improved resolution times.

Resolution method for mixed integer bi-level linear problems based on decomposition technique

In this article, we propose a new algorithm for the resolution of mixed integer bi-level linear problem (MIBLP). The algorithm is based on the decomposition of the initial problem into the restricted master problem (RMP) and a series of problems named slave problems (SP). The proposed approach is based on Benders decomposition method where in each iteration a set of variables are fixed which are controlled by the upper level optimization problem. The RMP is a relaxation of the MIBLP and the SP represents a restriction of the MIBLP. The RMP interacts in each iteration with the current SP by the addition of cuts produced using Lagrangian information from the current SP. The lower and upper bound provided from the RMP and SP are updated in each iteration. The algorithm converges when the difference between the upper and lower bound is within a small difference ε. In the case of MIBLP Karush–Kuhn–Tucker (KKT) optimality conditions could not be used directly to the inner problem in order to transform the bi-level problem into a single level problem. The proposed decomposition technique, however, allows the use of KKT conditions and transforms the MIBLP into two single level problems. The algorithm, which is a new method for the resolution of MIBLP, is illustrated through a modified numerical example from the literature. Additional examples from the literature are presented to highlight the algorithm convergence properties.

Optimal design of sustainable chemical processes and supply chains: A review

Abstract The importance of balancing social, environmental and economic objectives in companies’ development has cultivated a growing awareness on the sustainable optimal design and planning of supply chains. In the past years, significant research effort has been devoted to extend current approaches to capture these objectives in order to guarantee long term sustainability. Among the various approaches developed, inventory management, product design, production planning and control for remanufacturing, product recovery, reverse logistics and closed-loop supply chains have gained more attention in the literature. In this paper, we review some of the relevant research on sustainable chemical processes and supply chain design focusing on three main areas: (i) sustainable supply chains with respect to energy efficiency and waste management, (ii) environmentally sustainable supply chains and (iii) sustainable water management. The emerging challenges in this area are summarized, and future opportunities are highlighted.

Uncertainty reduction and characterization for complex environmental fate and transport models: An empirical Bayesian framework incorporating the stochastic response surface method

In this work, a computationally efficient Bayesian framework for the reduction and characterization of parametric uncertainty in computationally demanding environmental 3-D numerical models has been developed. The framework is based on the combined application of the Stochastic Response Surface Method (SRSM, which generates accurate and computationally efficient statistically equivalent reduced models) and the Markov Chain Monte Carlo method. The application selected to demonstrate this framework involves steady state groundwater flow at the U.S. Department of Energy Savannah River Site General Separations Area, modeled using the Subsurface Flow And Contaminant Transport (FACT) code. Input parameter uncertainty, based initially on expert opinion, was found to decrease in all variables of the posterior distribution. The joint posterior distribution obtained was then further used for the final uncertainty analysis of the stream baseflows and well location hydraulic head values.