Multiobjective optimization of multiproduct batch plants scheduling under environmental and economic concerns

In batch process scheduling, production trade‐offs arise from the simultaneous consideration of different objectives. Economic goals are expressed in terms of plant profitability and productivity, whereas the environmental objectives are evaluated by means of metrics originated from the use of life cycle assessment methodology. This work illustrates a novel approach for decision making by using multiobjective optimization. In addition, different metrics are proposed to select a possible compromise based on the distance to a nonexistent utopian solution, whose objective function values are all optimal. Thus, this work provides a deeper insight into the influence of the metrics selection for both environmental and economic issues while considering the trade‐offs of adopting a particular schedule. The use of this approach is illustrated through its application to a case study related to a multiproduct acrylic fiber production plant, special attention is put to the influence of product changeovers. © 2010 American Institute of Chemical Engineers AIChE J, 57: 2766–2782, 2010     

Multiobjective optimization under uncertainty of the economic and life‐cycle environmental performance of industrial processes

The combined use of multiobjective optimization and life‐cycle assessment (LCA) has recently emerged as a useful tool for minimizing the environmental impact of industrial processes. The main limitation of this approach is that it requires large amounts of data that are typically affected by several uncertainty sources. We propose herein a systematic framework to handle these uncertainties that takes advantage of recent advances made in modeling of uncertain LCA data and in optimization under uncertainty. Our strategy is based on a stochastic, multiobjective, and multiscenario mixed‐integer nonlinear programming approach in which the uncertain parameters are described via scenarios. We investigate the use of two stochastic metrics: (1) the environmental impact in the worst case and (2) the environmental downside risk. We demonstrate the capabilities of our approach through its application to a generic complex industrial network in which we consider the uncertainty of some key life‐cycle inventory parameters. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2098–2121, 2014     

Integrated scheduling and dynamic optimization of batch processes using state equipment networks

A systematic framework for the integration of short‐term scheduling and dynamic optimization (DO) of batch processes is described. The state equipment network (SEN) is used to represent a process system, where it decomposes the process into two basic kinds of entities: process materials and process units. Mathematical modeling based on the SEN framework invokes both logical disjunctions and operational dynamics; thus the integrated formulation leads to a mixed‐logic dynamic optimization (MLDO) problem. The integrated approach seeks to benefit the overall process performance by incorporating process dynamics into scheduling considerations. The solution procedure of an MLDO problem is also addressed in this article, where MLDO problems are translated into mixed‐integer nonlinear programs using the Big M reformulation and the simultaneous collocation method. Finally, through two case studies, we show advantages of the integrated approach over the conventional recipe‐based scheduling method. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

A novel adaptive surrogate modeling‐based algorithm for simultaneous optimization of sequential batch process scheduling and dynamic operations

A novel adaptive surrogate modeling‐based algorithm is proposed to solve the integrated scheduling and dynamic optimization problem for sequential batch processes. The integrated optimization problem is formulated as a large scale mixed‐integer nonlinear programming (MINLP) problem. To overcome the computational challenge of solving the integrated MINLP problem, an efficient solution algorithm based on the bilevel structure of the integrated problem is proposed. Because processing times and costs of each batch are the only linking variables between the scheduling and dynamic optimization problems, surrogate models based on piece‐wise linear functions are built for the dynamic optimization problems of each batch. These surrogate models are then updated adaptively, either by adding a new sampling point based on the solution of the previous iteration, or by doubling the upper bound of total processing time for the current surrogate model. The performance of the proposed method is demonstrated through the optimization of a multiproduct sequential batch process with seven units and up to five tasks. The results show that the proposed algorithm leads to a 31% higher profit than the sequential method. The proposed method also outperforms the full space simultaneous method by reducing the computational time by more than four orders of magnitude and returning a 9.59% higher profit. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4191–4209, 2015     

Moving horizon approach of integrating scheduling and control for sequential batch processes

Online integration of scheduling and control is crucial to cope with process uncertainties. We propose a new online integrated method for sequential batch processes, where the integrated problem is solved to determine controller references rather than process inputs. Under a two‐level feedback loop structure, the integrated problem is solved in a frequency lower than that of the control loops. To achieve the goal of computational efficiency and rescheduling stability, a moving horizon approach is developed. A reduced integrated problem in a resolving horizon is formulated, which can be solved efficiently online. Solving the reduced problem only changes a small part of the initial solution, guaranteeing rescheduling stability. The integrated method is demonstrated in a simulated case study. Under uncertainties of the control system disruption and the processing unit breakdown, the integrated method prevents a large loss in the production profit compared with the simple shifted rescheduling solution. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1654–1671, 2014     

Proactive scheduling of batch processes by a combined robust optimization and multiparametric programming approach

We address short‐term batch process scheduling problems contaminated with uncertainty in the data. The mixed integer linear programming (MILP) scheduling model, based on the formulation of Ierapetritou and Floudas, Ind Eng Chem Res. 1998; 37(11):4341–4359, contains parameter dependencies at multiple locations, yielding a general multiparametric (mp) MILP problem. A proactive scheduling policy is obtained by solving the partially robust counterpart formulation. The counterpart model may remain a multiparametric problem, yet it is immunized against uncertainty in the entries of the constraint matrix and against all parameters whose values are not available at the time of decision making. We extend our previous work on the approximate solution of mp‐MILP problems by embedding different uncertainty sets (box, ellipsoidal and budget parameter regulated uncertainty), and by incorporating information about the availability of uncertain data in the construction of the partially robust scheduling model. For any parameter realization, the corresponding schedule is then obtained through function evaluation. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4184–4211, 2013     

Theoretical and computational comparison of continuous‐time process scheduling models for adjustable robust optimization

Coping with uncertainty in system parameters is a prominent hurdle when scheduling multi‐purpose batch plants. In this context, our previously introduced multi‐stage adjustable robust optimization (ARO) framework has been shown to obtain more profitable solutions, while maintaining the same level of immunity against risk, as compared to traditional robust optimization approaches. This paper investigates the amenability of existing deterministic continuous‐time scheduling models to serve as the basis of this ARO framework. A comprehensive computational study is conducted that compares the numerical tractability of various models across a suite of literature benchmark instances and a wide range of uncertainty sets. This study also provides, for the first time in the open literature, robust optimal solutions to process scheduling instances that involve uncertainty in production yields. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3055–3070, 2018     

Multiobjective optimization of biorefineries with economic and safety objectives

A new approach for the incorporation of safety criteria into the selection, location, and sizing of a biorefinery is introduced. In addition to the techno‐economic factors, risk metrics are used in the decision‐making process by considering the cumulative risk associated with key stages of the life cycle of a biorefinery that includes biomass storage and transportation, process conversion into biofuels or bioproducts, and product storage. The fixed cost of the process along with the operating costs for transportation and processing as well as the value of the product are included. An optimization formulation is developed based on a superstructure that embeds potential supply chains of interest. The optimization program establishes the tradeoffs between cost and safety issues in the form of Pareto curves. A case study on bio‐hydrogen production is solved to illustrate the merits of the proposed approach. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2427–2434, 2013     

Multiobjective optimization of the continuous casting process for poly (methyl methacrylate) using adapted genetic algorithm

The nondominated sorting genetic algorithm (NSGA) has been used to optimize the operation of the continuous casting of a film of poly (methyl methacrylate). This process involves two reactors, namely, an isothermal plug flow tubular reactor (PFTR) followed by a nonisothermal film reactor. Two objective functions have been used in this study: the cross‐section average value of the monomer conversion, x̄_mf , of the product is maximized, and the length, z_f , of the film reactor is minimized. Simultaneously, the cross‐section average value of the number‐average molecular weight of the product is forced to have a certain prescribed (desired) value. It is also ensured that the temperature at any location in the film being produced lies below a certain value, to avoid degradation reactions. Seven decision variables are used in this study: the temperature of the isothermal PFTR, the flow rate of the initiator in the feed to the PFTR (for a specified feed flow rate of the monomer), the film thickness, the monomer conversion at the output of the PFTR, and three coefficients describing the wall temperature to be used in the film reactor. Sets of nondominating (equally good) optimal solutions (Pareto sets) have been obtained due to the conflicting requirements for the several conditions studied. It is interesting to observe that under optimal conditions, the exothermicity of the reactions drives them to completion near the center of the film, while heat conduction and higher wall temperature help to achieve this in the outer regions. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 78: 1439–1458, 2000     

Continuous-time approaches for short-term scheduling of network batch processes: Small-scale and medium-scale problems

Two time representation approaches, discrete-time and continuous-time approaches, have been developed for short-term scheduling of batch process in small-scale and medium-scale during the last two decades. As usually establishing advantages over discrete-time approaches in the scheduling problems, continuous-time approaches have gained increasing attention in the last 10 years. The reported continuous-time approaches can be divided into four categories: global event-based, unit-specific event-based, slot-based and precedence-based models. In this paper, more complex processes, network batch processes in small and medium scales, are considered. Six models based on different continuous-time representations are compared in several benchmark examples from the literature. The compared items include problem size, computational times and model convergence. Moreover, two intermediate storage policies (limited and unlimited intermediate storage) and two objective functions (maximization of profit and minimization of makespan) are addressed.     

A computational framework and solution algorithms for two‐stage adaptive robust scheduling of batch manufacturing processes under uncertainty

A novel two‐stage adaptive robust optimization (ARO) approach to production scheduling of batch processes under uncertainty is proposed. We first reformulate the deterministic mixed‐integer linear programming model of batch scheduling into a two‐stage optimization problem. Symmetric uncertainty sets are then introduced to confine the uncertain parameters, and budgets of uncertainty are used to adjust the degree of conservatism. We then apply both the Benders decomposition algorithm and the column‐and‐constraint generation (C&CG) algorithm to efficiently solve the resulting two‐stage ARO problem, which cannot be tackled directly by any existing optimization solvers. Two case studies are considered to demonstrate the applicability of the proposed modeling framework and solution algorithms. The results show that the C&CG algorithm is more computationally efficient than the Benders decomposition algorithm, and the proposed two‐stage ARO approach returns 9% higher profits than the conventional robust optimization approach for batch scheduling. © 2015 American Institute of Chemical Engineers AIChE J, 62: 687–703, 2016     

A data‐driven multistage adaptive robust optimization framework for planning and scheduling under uncertainty

A novel data‐driven approach for optimization under uncertainty based on multistage adaptive robust optimization (ARO) and nonparametric kernel density M‐estimation is proposed. Different from conventional robust optimization methods, the proposed framework incorporates distributional information to avoid over‐conservatism. Robust kernel density estimation with Hampel loss function is employed to extract probability distributions from uncertainty data via a kernelized iteratively reweighted least squares algorithm. A data‐driven uncertainty set is proposed, where bounds of uncertain parameters are defined by quantile functions, to organically integrate the multistage ARO framework with uncertainty data. Based on this uncertainty set, we further develop an exact robust counterpart in its general form for solving the resulting data‐driven multistage ARO problem. To illustrate the applicability of the proposed framework, two typical applications in process operations are presented: The first one is on strategic planning of process networks, and the other one on short‐term scheduling of multipurpose batch processes. The proposed approach returns 23.9% higher net present value and 31.5% more profits than the conventional robust optimization method in planning and scheduling applications, respectively. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4343–4369, 2017     

Integration of scheduling and control for batch processes using multi‐parametric model predictive control

Integration of scheduling and control results in Mixed Integer Nonlinear Programming (MINLP) which is computationally expensive. The online implementation of integrated scheduling and control requires repetitively solving the resulting MINLP at each time interval. (Zhuge and Ierapetritou, Ind Eng Chem Res. 2012;51:8550–8565) To address the online computation burden, we incorporare multi‐parametric Model Predictive Control (mp‐MPC) in the integration of scheduling and control. The proposed methodology involves the development of an integrated model using continuous‐time event‐point formulation for the scheduling level and the derived constraints from explicit MPC for the control level. Results of case studies of batch processes prove that the proposed approach guarantees efficient computation and thus facilitates the online implementation. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3169–3183, 2014     

Sequential methodology for integrated optimization of energy and water use during batch process scheduling

Though commonly encountered in practice, energy and water minimization simultaneously during batch process scheduling has been largely neglected in literature. In this paper, we present a novel framework for incorporating simultaneous energy and water minimization in batch process scheduling. The overall problem is decomposed into three parts - scheduling, heat integration, and water reuse optimization - and solved sequentially. Our approach is based on the precept that in any production plant, utilities (energy and water) consumption is subordinate to the production target. Hence, batch scheduling is solved first to meet an economic objective function. Next, alternate schedules are generated through a stochastic search-based integer cut procedure. For each resulting schedule, minimum energy and water reuse targets are established and networks identified. As illustrated using two well-known case studies, a key feature of this approach is its ability to handle problems that are too complex to be solved using simultaneous methods.     

A property‐based approach to the synthesis of material conservation networks with economic and environmental objectives

This article presents a multiobjective optimization model for the recycle and reuse networks based on properties while accounting for the environmental implications of the discharged wastes using life‐cycle assessment. The economic objective function considers fresh sources and treatment costs, whereas the environmental objective function is measured through the eco‐indicator 99. The model considers constraints in the process sinks as well as in the environment based on stream properties such as pH, chemical oxygen demand, toxicity, density, and color, in addition to the composition of the waste streams. A global optimization procedure is developed by indirectly tackling properties through property operators and by segregating the process streams before treatment. Three examples are included, and the results show that it is possible to consider simultaneously the trade‐offs between the total annual costs and the overall environmental impact using the proposed methodology. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Energy optimization of water supply system scheduling: Novel MINLP model and efficient global optimization algorithm

This article is concerned with global optimization of water supply system scheduling with pump operations to minimize total energy cost. The scheduling problem is first formulated as a non‐convex mixed‐integer nonlinear programming (MINLP) problem, accounting for flow rates in pipes, operation profiles of pumps, water levels of tanks, and customer demand. Binary variables denote on–off switch operations for pumps and flow directions in pipes, and nonlinear terms originate from characteristic functions for pumps and hydraulic functions for pipes. The proposed MINLP model is verified with EPANET, which is a leading software package for water distribution system modeling. We further develop a novel global optimization algorithm for solving the non‐convex MINLP problem. To demonstrate the applicability of the proposed model and the efficiency of the tailored global optimization algorithm, we present results of two case studies with up to 4 tanks, 5 pumps, 5 check valves, and 21 pipes. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4277–4296, 2016     

Multiobjective optimization of product and process networks: General modeling framework,efficient global optimization algorithm,and case studies on bioconversion

A comprehensive optimization model that can determine the most cost‐effective and environmentally sustainable production pathways in an integrated processing network is needed, especially in the bioconversion space. We develop the most comprehensive bioconversion network to date with 193 technologies and 129 materials/compounds for fuels production. We consider the tradeoff between scaling capital and operating expenditures (CAPEX and OPEX) as well as life cycle environmental impacts. Additionally, we develop a general network‐based modeling framework with nonconvex terms for CAPEX. To globally optimize the nonlinear program with high computational efficiency, we develop a specialized branch‐and‐refine algorithm based on successive piecewise linear approximations. Two case studies are considered. The optimal pathways have profits from ?$12.9 to $99.2M/yr, and emit 791 ton CO₂‐eq/yr to 31,571 ton CO₂‐eq/yr. Utilized technologies vary from corn‐based fermentation to pyrolysis. The proposed algorithm reduces computational time by up to three orders of magnitude compared to general‐purpose global optimizers. © 2014 American Institute of Chemical Engineers AIChE J, 61: 530–554, 2015     

Optimal planning for the reuse of municipal solid waste considering economic,environmental, and safety objectives

A mathematical programming model is presente for the optimal planning of the reuse of municipal solid waste (MSW) to maximize the economic benefit while simultaneously considering sustainability and safety criteria. The proposed methodology considers several phases of the supply chain including waste separation, distribution to processing facilities, processing to obtain useful products, and distribution of products to consumers. Additionally, the safety criteria are based on the potential fatalities associated with waste management. The proposed optimization model is formulated as a multiobjective optimization problem, which considers three different objectives including the maximization of the net annual profit, the maximization of the amount of reused MSW, and the minimization of the social risk associated with the supply chain. The proposed model is applied to a case study in the central‐west region of Mexico. The results show the tradeoff between the social risk and the economic and environmental criteria. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1881–1899, 2015     

Optimal design of sustainable cellulosic biofuel supply chains: Multiobjective optimization coupled with life cycle assessment and input–output analysis

This article addresses the optimal design and planning of cellulosic ethanol supply chains under economic, environmental, and social objectives. The economic objective is measured by the total annualized cost, the environmental objective is measured by the life cycle greenhouse gas emissions, and the social objective is measured by the number of accrued local jobs. A multiobjective mixed‐integer linear programming (mo‐MILP) model is developed that accounts for major characteristics of cellulosic ethanol supply chains, including supply seasonality and geographical diversity, biomass degradation, feedstock density, diverse conversion pathways and byproducts, infrastructure compatibility, demand distribution, regional economy, and government incentives. Aspen Plus models for biorefineries with different feedstocks and conversion pathways are built to provide detailed techno‐economic and emission analysis results for the mo‐MILP model, which simultaneously predicts the optimal network design, facility location, technology selection, capital investment, production planning, inventory control, and logistics management decisions. The mo‐MILP problem is solved with an ε‐constraint method; and the resulting Pareto‐optimal curves reveal the tradeoff between the economic, environmental, and social dimensions of the sustainable biofuel supply chains. The proposed approach is illustrated through two case studies for the state of Illinois. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Design under uncertainty of hydrocarbon biorefinery supply chains: Multiobjective stochastic programming models,decomposition algorithm,and a Comparison between CVaR and downside risk

A bicriterion, multiperiod, stochastic mixed‐integer linear programming model to address the optimal design of hydrocarbon biorefinery supply chains under supply and demand uncertainties is presented. The model accounts for multiple conversion technologies, feedstock seasonality and fluctuation, geographical diversity, biomass degradation, demand variation, government incentives, and risk management. The objective is simultaneous minimization of the expected annualized cost and the financial risk. The latter criterion is measured by conditional value‐at‐risk and downside risk. The model simultaneously determines the optimal network design, technology selection, capital investment, production planning, and logistics management decisions. Multicut L‐shaped method is implemented to circumvent the computational burden of solving large scale problems. The proposed modeling framework and algorithm are illustrated through four case studies of hydrocarbon biorefinery supply chain for the State of Illinois. Comparisons between the deterministic and stochastic solutions, the different risk metrics, and two decomposition methods are discussed. The computational results show the effectiveness of the proposed strategy for optimal design of hydrocarbon biorefinery supply chain under the presence of uncertainties. © 2012 American Institute of Chemical Engineers AIChE J, 2012