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     

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     

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 novel approach to scheduling multipurpose batch plants using unit‐slots

Several models for scheduling multipurpose batch plants exist in the literature. The models using unit‐specific event points have shown better solution efficiency on various literature examples. This article presents a novel approach to scheduling multipurpose batch plants, which uses unit‐slots instead of process‐slots to manage shared resources such as material storage. We develop two slightly different models that are even more compact and simpler than that of Sundaramoorthy and Karimi, Chem Eng Sci. 2005;60:2679–2702. Although we focus on material as a shared resource, our multi‐grid approach rationalizes, generalizes, and improves the current multi‐grid approaches for scheduling with shared resources. Our models allow nonsimultaneous transfers of materials into and out of a batch. We show by an example that this flexibility can give better schedules than those from existing models in some cases. Furthermore, our approach uses fewer slots (event‐points) on some examples than even those required by the most recent unit‐specific event‐based model. Numerical evaluation using literature examples shows significant gains in solution efficiency from the use of unit‐slots except where the number of unit‐slots required for the optimal solution equals that of process slots. We also highlight the importance of constraint sequencing in GAMS implementation for evaluating mixed‐integer linear programming based scheduling models fairly. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Efficient scheduling method of complex batch processes with general network structure via agent‐based modeling

A novel efficient agent‐based method for scheduling network batch processes in the process industry is proposed. The agent‐based model is based on the resource‐task network. To overcome the drawback of localized solutions found in conventional agent‐based methods, a new scheduling algorithm is proposed. The algorithm predicts the objective function value by simulating another cloned agent‐based model. Global information is obtained, and the solution quality is improved. The solution quality of this approach is validated by detailed comparisons with the mixed‐integer programming (MIP) methods. A solution close to the optimal one can be found by the agent‐based method with a much shorter computational time than the MIP methods. As a scheduling problem becomes increasingly complicated with increased scale, more specifications, and uncertainties, the advantages of the agent‐based method become more evident. The proposed method is applied to simulated industrial problems where the MIP methods require excessive computational resources. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2884–2906, 2013     

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     

Multiobjective evolutionary optimization of batch process scheduling under environmental and economic concerns

The simultaneous consideration of economic and environmental objectives in batch production scheduling is today a subject of major concern. However, it constitutes a complex problem whose solution necessarily entails production trade‐offs. Unfortunately, a rigorous multiobjective optimization approach to solve this kind of problem often implies high computational effort and time, which seriously undermine its applicability to day‐to‐day operation in industrial practice. Hence, this work presents a hybrid optimization strategy based on rigorous local search and genetic algorithm to efficiently deal with industrial scale batch scheduling problems. Thus, a deeper insight into the combined environmental and economic issues when considering the trade‐offs of adopting a particular schedule is provided. The proposed methodology is applied to a case study concerning a multiproduct acrylic fiber production plant, where product changeovers influence the problem results. The proposed strategy stands for a marked improvement in effectively incorporating multiobjective optimization in short‐term plant operation. © 2012 American Institute of Chemical Engineers AIChE J, 59: 429–444, 2013     

Integrating data‐based modeling and nonlinear control tools for batch process control

A data‐based multimodel approach is developed in this work for modeling batch systems in which multiple local linear models are identified using latent variable regression and combined using an appropriate weighting function that arises from fuzzy c‐means clustering. The resulting model is used to generate empirical reverse‐time reachability regions (RTRRs) (defined as the set of states from where the data‐based model can be driven inside a desired end‐point neighborhood of the system), which are subsequently incorporated in a predictive control design. Simulation results of a fed‐batch reactor system under proportional‐integral (PI) control and the proposed RTRR‐based design demonstrate the superior performance of the RTRR‐based design in both a fault‐free and faulty environment. The data‐based modeling methodology is then applied on a nylon‐6,6 batch polymerization process to design a trajectory tracking predictive controller. Closed‐loop simulation results illustrate the superior tracking performance of the proposed predictive controller over PI control. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

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     

Greedy algorithm for scheduling batch plants with sequence‐dependent changeovers

This article presents a new algorithm for scheduling multistage batch plants with a large number of orders and sequence‐dependent changeovers. Such problems are either intractable when solved with full‐space approaches or poor solutions result. We use decomposition on the entire set of orders and derive the complete schedule in several iterations, by inserting a couple of orders at a time. The key idea is to allow for partial rescheduling without altering the main decisions in terms of unit assignments and sequencing (linked to the binary variables) so that the combinatorial complexity is kept at a manageable level. The algorithm has been implemented for three alternative continuous‐time mixed integer linear programing models and tested through the solution of 10 example problems for different decomposition settings. The results show that an industrial‐size scheduling problem with 50 orders, 17 units distributed over six stages can effectively be solved in roughly 6 min of computational time. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

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     

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     

A pattern matching method for large‐scale multipurpose process scheduling

This article proposes a novel pattern matching method for the large‐scale multipurpose process scheduling with variable or constant processing times. For the commonly used mathematical programming models, large‐scale scheduling with long‐time horizons implies a large number of binary variables and time sequence constraints, which makes the models intractable. Hence, decomposition and cyclic scheduling are often applied to such scheduling. In this work, a long‐time horizon of scheduling is divided into two phases. Phase one is duplicated from a pattern schedule constructed according to the principle that crucial units work continuously, in parallel and/or with full load as possible, exclusive of time‐consuming optimization. Phase two involves a small‐size subproblem that can be optimized easily by a heuristic method. The computational effort of the proposed method does not increase with the problem size. The pattern schedule can be not only used for production/profit maximization but also for makespan estimation and minimization. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Dynamic models and fault diagnosis‐based triggers for closed‐loop scheduling

Establishing an explicit feedback connection between production management and process control decisions is a key requirement for more nimble and cost effective process operations in today's variable market conditions. Past research efforts focused on embedding dynamic process information in the production scheduling problem. In this article, we propose a novel framework for closing the scheduling loop, based on considering the process‐level events and disturbances that impact the implementation of scheduling decisions. We emphasize the role of a comprehensive fault detection, isolation and reconstruction mechanism as a trigger for rescheduling decisions and for reflecting the process capabilities altered by these events in the rescheduling problem formulation. Our framework is agnostic to the process type, and we present two (continuous process, sequential batch process) case studies to demonstrate its applicability. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1959–1973, 2017     

Robust batch‐to‐batch optimization in the presence of model‐plant mismatch and input uncertainty

In model‐based optimization in the presence of model‐plant mismatch, the set of model parameter estimates which satisfy an identification objective may not result in an accurate prediction of the gradients of the cost‐function and constraints. To ensure convergence to the optimum, the predicted gradients can be forced to match the measured gradients by adapting the model parameters. Since updating all available parameters is impractical due to estimability problems and overfitting, there is a motivation for adapting a subset of parameters for updating the predicted outputs and gradients. This article presents an approach to select a subset of parameters based on the sensitivities of the model outputs and of the cost function and constraint gradients. Furthermore, robustness to uncertainties in initial batch conditions is introduced using a robust formulation based on polynomial chaos expansions. The improvements in convergence to the process optimum and robustness are illustrated using a fed‐batch bioprocess. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2660–2670, 2017     

Multiway discrete hidden Markov model‐based approach for dynamic batch process monitoring and fault classification

A new multiway discrete hidden Markov model (MDHMM)‐based approach is proposed in this article for fault detection and classification in complex batch or semibatch process with inherent dynamics and system uncertainty. The probabilistic inference along the state transitions in MDHMM can effectively extract the dynamic and stochastic patterns in the process operation. Furthermore, the used multiway analysis is able to transform the three‐dimensional (3‐D) data matrices into 2‐D measurement‐state data sets for hidden Markov model estimation and state path optimization. The proposed MDHMM approach is applied to fed‐batch penicillin fermentation process and compared to the conventional multiway principal component analysis (MPCA) and multiway dynamic principal component analysis (MDPCA) methods in three faulty scenarios. The monitoring results demonstrate that the MDHMM approach is superior to both the MPCA and MDPCA methods in terms of fault detection and false alarm rates. In addition, the supervised MDHMM approach is able to classify different types of process faults with high fidelity. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Continuous‐time modeling and global optimization approach for scheduling of crude oil operations

Scheduling of crude oil operations is a critical and complicated component of overall refinery operations, because crude oil costs account for about 80% of the refinery turnover. Moreover, blending with less expensive crudes can significantly increase profit margins. The mathematical modeling of blending different crudes in storage tanks results in many bilinear terms, which transforms the problem into a challenging, nonconvex, and mixed‐integer nonlinear programming (MINLP) optimization model. Two primary contributions have been made. First, the authors developed a novel unit‐specific event‐based continuous‐time MINLP formulation for this problem. Then they incorporated realistic operational features such as single buoy mooring (SBM), multiple jetties, multiparcel vessels, single‐parcel vessels, crude blending, brine settling, crude segregation, and multiple tanks feeding one crude distillation unit at one time and vice versa. In addition, 15 important volume‐based or weight‐based crude property indices are also considered. Second, they exploited recent advances in piecewise‐linear underestimation of bilinear terms within a branch‐and‐bound algorithm to globally optimize the MINLP problem. It is shown that the continuous‐time model results in substantially fewer bilinear terms. Several examples taken from the work of Li et al. are used to illustrate that (1) better solutions are obtained and (2) ε‐global optimality can be attained using the proposed branch‐and‐bound global optimization algorithm with piecewise‐linear underestimations of the bilinear terms. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Real‐time dynamic hoist scheduling for multistage material handling process under uncertainties

Multistage material handling processes are broadly used for manufacturing various products/jobs, where hoists are commonly used to transport inline products according to their processing recipes. When multiple types of jobs with different recipes are simultaneously and continuously handled in a production line, the hoist movement scheduling should be thoroughly investigated to ensure the operational feasibility of every job inline and in the meantime to maximize the productivity if possible. The hoist scheduling will be more complicated, if uncertainties of new coming jobs are considered, that is, the arrival time, type, recipe, and number of new jobs are totally unknown and unpredictable before they join the production line. To process the multiple jobs already inline and the newly added jobs, the hoist movements must be swiftly rescheduled and precisely implemented whenever new job(s) come. Because a reschedule has to be obtained online without violating processing time constraints for each job, the solution identification time for rescheduling must be taken into account by the new schedule itself. All these stringent requisites motivate the development of real‐time dynamic hoist scheduling (RDHS) targeting online generation of reschedules for productivity maximization under uncertainties. Hitherto, no systematic and rigorous methodologies have been reported for this study. In this article, a novel RDHS methodology has been developed, which takes into account uncertainties of new coming jobs and targets real‐time scheduling optimality and applicability. It generally includes a reinitialization algorithm to accomplish the seamless connection between the previous scheduling and rescheduling operations, and a mixed‐integer linear programming model to obtain the optimal hoist reschedule. The RDHS methodology addresses all the major scheduling issues of multistage material handling processes, such as multiple recipes, multiple jobs, multicapacity processing units, diverse processing time requirements, and even optimal processing queue for new coming jobs. The efficacy of the developed methodology is demonstrated through various case studies. © 2012 American Institute of Chemical Engineers AIChE J, 59: 465–482, 2013     

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.     

An iterative two‐step sequential phase partition (ITSPP) method for batch process modeling and online monitoring

Operating at different manufacturing steps, multiphase modeling and analysis of the batch process are advantageous to improving monitoring performance and understanding manufacturing processes. Although many phase partition algorithms have been proposed, they have some disadvantages and cause problems: (1) time sequence disorder, which requires elaborate post‐treatments; (2) a lack of quantitative index to indicate transition patterns; and (3) tunable parameters that cannot be quantitatively determined. To effectively overcome these problems, an iterative two‐step sequential phase partition algorithm is proposed in the present work. In the first step, initial phase partition results are obtained by checking changes of the control limit of squared prediction error. Sequentially, the fast search and find of density peaks clustering algorithm is employed to adjust the degradation degree and update the phase partition results. These two steps are iteratively executed until a proper degradation degree is found for the first phase. Then, the remaining phases are processed one by one using the same procedure. Moreover, a statistical index is quantitatively defined based on density and distance analysis to judge whether a process has transitions, and when the transition regions begin and end. In this way, the phases and transition patterns are quantitatively determined without ambiguity from the perspective of monitoring performance. The effectiveness of the proposed method is illustrated by a numerical example and a typical industrial case. Several typical phase partition algorithms are also employed for comprehensive comparisons with the proposed method. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2358–2373, 2016