A time scale-bridging approach for integrating production scheduling and process control

In this paper, we propose a novel framework for integrating scheduling and nonlinear control of continuous processes. We introduce the time scale-bridging model (SBM) as an explicit, low-order representation of the closed-loop input–output dynamics of the process. The SBM then represents the process dynamics in a scheduling framework geared towards calculating the optimal time-varying setpoint vector for the process control system. The proposed framework accounts for process dynamics at the scheduling stage, while maintaining closed-loop stability and disturbance rejection properties via feedback control during the production cycle. Using two case studies, a CSTR and a polymerization reactor, we show that SBM-based scheduling has significant computational advantages compared to existing integrated scheduling and control formulations. Moreover, we show that the economic performance of our framework is comparable to that of existing approaches when a perfect process model is available, with the added benefit of superior robustness to plant-model mismatch.     

Multi-period scheduling of a multi-stage multi-product bio-pharmaceutical process

There have been several works in the literature for scheduling of multi-product continuous processes with significant attention laid on short-term scheduling. This work presents a continuous-time model for multi-period scheduling of a multi-stage multi-product process from bio-pharmaceutical industry. The overall model is a mixed-integer linear programming (MILP) formulation based on state-task-network (STN) representation of the process using unit-specific event-based continuous-time representation. The proposed model is an extension of model by Shaik and Floudas (2007, Industrial & Engineering Chemistry Research, 46, 1764) with several new constraints to deal with additional features such as unit and sequence dependent changeovers, multiple intermediate due dates, handling of shelf-life and waste disposal, and penalties on backlogs and late deliveries. Improved tightening and sequencing constraints have been presented. The validity of the proposed model has been illustrated through an example from the literature.     

一种改进的顺序型多目的间歇工厂生产调度的MILP模型

分析了顺序型多目的工厂间歇生产的特点,建立了一种新的混合整数线性规划（MILP）模型.该模型以操作活动序列作为建模的依据,将整个间歇生产过程分解成若干个子系统.在对各子系统建模的基础上,实现了顺序型多目的工厂间歇调度的全局性优化.并通过算例验证了该模型求解结果的正确性和可行性.然后将新模型运用到更大规模的调度问题上,均求解出了有效的调度方案.     

Scheduling of displacement batch digesters using discrete time formulation

This paper provides mathematical programming based optimization model and computational results for short-term scheduling of displacement batch digesters in a pulp industry. The scheduling problem involves development of an optimal solution that yields the best sequence of operations in each of the parallel batch digesters sharing common resources. The constraints are imposed on meeting the demand of pulp of different qualities within a specified time horizon. The problem comprises of both fixed-time and variable time durations of the tasks, different storage policies, zero-wait and finite wait times, and handling of shared resources. The scheduling problem is formulated using a state-task-network (STN) representation of production recipes, based on discrete time representation resulting in a mixed-integer linear programming (MILP) problem which is solved using GAMS software. The basic framework is adapted from the discrete-time model of Kondili et al. (Comput. Chem. Eng., 1993, 17, 211–227). Different case studies involving parallel digesters in multiple production lines are considered to demonstrate the effectiveness of the proposed formulation using two different objective functions.     

Three-scale integrated optimization model of furnace simulation,cyclic scheduling,and supply chain of ethylene plants

In order to explore the potential of profit margin improvement, a novel three-scale integrated optimization model of furnace simulation, cyclic scheduling, and supply chain of ethylene plants is proposed and evaluated. A decoupling strategy is proposed for the solution of the three-scale model, which uses our previously proposed reactor scale model for operation optimization and then transfers the obtained results as a parameter table in the joint MILP optimization of plant-supply chain scale for cyclic scheduling. This optimization framework simplifies the fundamental mixed-integer nonlinear programming (MINLP) into several sub-models, and improves the interpretability and extendibility. In the evaluation of an industrial case, a profit increase at a percentage of 3.25% is attained in optimization compared to the practical operations. Further sensitivity analysis is carried out for strategy evolving study when price policy, supply chain, and production requirement parameters are varied. These results could provide useful suggestions for petrochemical enterprises on thermal cracking production.     

A general framework and optimization models for the scheduling of continuous chemical processes

We present a framework for the formulation and solution of continuous process scheduling problems. We focus on modeling transient operations such as startups, shutdowns, and transitions between steady states. First, we show how the concept of processing tasks can be generalized to represent continuous processes, including their transient operations. Second, we discuss how to systematically calculate the parameters describing material consumption/production and utility consumption during transient operations. Finally, we present new mixed-integer linear programming formulations for the scheduling of continuous chemical production.     

聚氯乙烯生产过程全流程调度

研究了电石法制聚氯乙烯(PVC)全流程生产调度问题, 包括从电石生产、盐水电解到氯乙烯(VCM)聚合产品出厂各环节, 其中电石生产和VCM聚合是间歇过程, 其他生产环节是连续过程, 是一个混杂系统调度问题。本文针对过程特性对该问题进行了合理假设, 以包括电耗、库存、产品型号切换、交货延迟等的成本最小为目标, 建立了基于离散时间表示的混合整数线性规划(MILP)调度优化模型, 并针对一个案例进行了调度优化求解和分析, 验证了模型的可行性。     

A continuous-time formulation for refinery production scheduling problems involving operational transitions in mode switching

In the refinery scheduling, operational transitions in mode switching are of great significance to formulate dynamic nature of production and obtain efficient schedules. The discrete-time formulation meets two main challenges in modeling:discrete approximation of time and large size of mixed-integer linear problem (MILP). In this article, a continuous-time refinery scheduling model, which involves transitions of mode switching, is presented due to these challenges. To reduce the difficulty in solving large scale MILPs resulting from the sequencing constraints, the global event-based formulation is chosen. Both transition constraints and production transitions are introduced and the numbers of key variables and constraints in both of the discrete-time and continuous-time formulations are analyzed and compared. Three cases with different lengths of time horizons and different numbers of orders are studied to show the efficiency of the proposed model.     

Optimal planning and campaign scheduling of biopharmaceutical processes using a continuous-time formulation

This work addresses the optimal planning and campaign scheduling of biopharmaceutical manufacturing processes, considering multiple operational characteristics, such as the campaign schedule of batch and/or continuous process steps, multiple intermediate deliveries, sequence dependent changeovers operations, product storage restricted to shelf-life limitations, and the track-control of the production/campaign lots due to regulatory policies. A new mixed integer linear programing (MILP) model, based on a Resource Task Network (RTN) continuous time single-grid formulation, is developed to comprise the integration of all these features. The performance of the model features is discussed with the resolution of a set of industrial problems with different data sets and process layouts, demonstrating the wide application of the proposed formulation. It is also performed a comparison with a related literature model, showing the advantages of the continuous-time approach and the generality of our model for the optimal production management of biopharmaceutical processes.     

Simultaneous design and operation optimization of renewable combined cooling heating and power systems

Combined cooling, heating, and power (CCHP) systems are promising solutions for conserving energy and reducing emissions. This article proposes a new mixed-integer linear programming (MILP) model for simultaneous design and operation optimization of a renewable CCHP system, considering component nonlinear operating characteristics and performance degradation with time. A bi-objective MILP problem is solved to achieve a trade-off between total annual cost (TAC) and greenhouse gas emissions (GHGe). A case study of a commercial region is employed to demonstrate our proposed methodology. The results shows, in comparison with conventional cost minimization, our solution features a tardy increase of 12.8% in TAC and a sharp reduction of 75.5% in GHGe. Moreover, we find that ignoring performance degradation leads to an over-estimation of 2.3–13.7% in system economic performance. The proposed methodology provides an effective and flexible framework for optimal design and operational analysis of renewable CCHP systems.     

A discrete-time scheduling model for continuous power-intensive process networks with various power contracts

Increased volatility in electricity prices and new emerging demand side management opportunities call for efficient tools for the optimal operation of power-intensive processes. In this work, a general discrete-time model is proposed for the scheduling of power-intensive process networks with various power contracts. The proposed model consists of a network of processes represented by Convex Region Surrogate models that are incorporated in a mode-based scheduling formulation, for which a block contract model is considered that allows the modeling of a large variety of commonly used power contracts. The resulting mixed-integer linear programming model is applied to an illustrative example as well as to a real-world industrial test case. The results demonstrate the model's capability in representing the operational flexibility in a process network and different electricity pricing structures. Moreover, because of its computational efficiency, the model holds much promise for its use in a real industrial setting.     

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     

Design,synthesis and scheduling of multipurpose batch plants via an effective continuous-time formulation

Design, synthesis and scheduling issues are considered simultaneously for multipurpose batch plants. An earlier proposed continuous-time formulation for scheduling is extended to incorporate design and synthesis. Processing recipes are represented by the State-Task Network (STN). The superstructure of all possible plant designs is constructed according to the potential availability of all processing/storage units. The proposed model takes into account the trade-offs between capital costs, revenues and operational flexibility. Computational studies are presented to illustrate the effectiveness of the proposed formulation. Both linear and nonlinear models are included, resulting in MILP and mixed-integer nonlinear programming (MINLP) problems, respectively. The MILP problems are solved using a branch and bound method. Globally optimal solutions are obtained for the nonconvex MINLP problems based on a key property that arises due to the special structure of the resulting models. Comparisons with earlier approaches are also presented.     

Demand response potential of industrial processes considering uncertain short-term electricity prices

Time-varying electricity prices on the day-ahead and intraday market incentivize demand response of industrial processes. In prior work (Schäfer et al. AIChE J. 2020;66:1-14), we studied the demand response potential with a generalized process model, but neglected the intraday market. Extending our prior investigation, we account for uncertain intraday prices in a mixed-integer linear stochastic programming-based scheduling, that is, we minimize expected cost and conditional value-at-risk in a bi-objective optimization. We find that for very broad variations of the generalized process parameters, the conditional value-at-risk can be reduced significantly without drastically increasing the expected cost. Furthermore, simultaneously improving multiple process parameter leads to synergetic benefits. Moreover, the savings of three electrolysis processes can be more than doubled by marketing flexibility on the intraday market in addition to the day-ahead market. Overall, our model allows for a rapid early assessment of the demand response potential considering the two markets.     

An LSTM-based mixed-integer model predictive control for irrigation scheduling

The development of well-devised irrigation scheduling methods is desirable from the perspectives of plant quality and water conservation. Accordingly, in this article, a mixed-integer model predictive control system is proposed to address the daily irrigation scheduling problem. In this framework, a long short-term memory (LSTM) model of the soil–crop–atmosphere system is employed to evaluate the objective of ensuring optimal water uptake in crops while minimizing total water consumption and irrigation costs. To enhance the computational efficiency of the proposed method, a heuristic method involving the logistic sigmoid function is used to approximate the binary variable that arises in the mixed-integer formulation. Through computer simulations, the proposed scheduler is applied to homogeneous and spatially variable fields. The results of these simulation experiments reveal that the proposed method can prescribe optimal/near-optimal irrigation schedules that are typical of irrigation practice within practical computational budgets.     

Generalized capital investment planning of oil-refineries using MILP and sequence-dependent setups

Due to quantity times quality nonlinear terms inherent in the oil-refining industry, performing industrial-sized capital investment planning (CIP) in this field is traditionally done using linear (LP) or nonlinear (NLP) models whereby a gamut of scenarios are generated and manually searched to make expand and/or install decisions. Though mixed-integer nonlinear (MINLP) solvers have made significant advancements, they are often slow for large industrial applications in optimization; hence, we propose a more tractable approach to solve the CIP problem using a mixed-integer linear programming (MILP) model and input–output (Leontief) models, where the nonlinearities are approximated to linearized operations, activities, or modes in large-scaled flowsheet problems. To model the different types of CIP's known as revamping, retrofitting, and repairing, we unify the modeling by combining planning balances with scheduling concepts of sequence-dependent changeovers to represent the construction, commission, and correction stages explicitly in similar applications such as process design synthesis, asset allocation and utilization, and turnaround and inspection scheduling. Two motivating examples illustrate the modeling, and a retrofit example and an oil-refinery investment planning problem are also highlighted.     

多因素不确定条件下的间歇生产调度优化

不确定条件下的间歇生产调度优化是生产调度问题研究中具有挑战性的课题。提出了一种基于混合整数线性规划(MILP)的鲁棒优化模型,来优化不确定条件下的生产调度决策。考虑到生产过程中的操作成本和原料成本,建立了以净利润最大为调度目标的确定性数学模型。然后考虑需求、处理时间、市场价格三种不确定因素,建立可调整保守程度的鲁棒优化模型并转换成鲁棒对应模型。实例结果表明,鲁棒优化的间歇生产调度模型较确定性模型利润减少,但生产任务数量增加,设备空闲时间缩短,从而增强了调度方案的可靠性,实现了不确定条件下生产操作性和经济性的综合优化。     

Integrated process design,scheduling, and model predictive control of batch processes with closed-loop implementation

Simultaneous evaluation of multiple time scale decisions has been regarded as a promising avenue to increase the process efficiency and profitability through leveraging their synergistic interactions. Feasibility of such an integral approach is essential to establish a guarantee for operability of the derived decisions. In this study, we present a modeling methodology to integrate process design, scheduling, and advanced control decisions with a single mixed-integer dynamic optimization (MIDO) formulation while providing certificates of operability for the closed-loop implementation. We use multi-parametric programming to derive explicit expressions for the model predictive control strategy, which is embedded into the MIDO using the base-2 numeral system that enhances the computational tractability of the integrated problem by exponentially reducing the required number of binary variables. Moreover, we apply the State Equipment Network representation within the MIDO to systematically evaluate the scheduling decisions. The proposed framework is illustrated with two batch processes with different complexities.     

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     

考虑切料过程的乙烯裂解炉炉群调度建模与优化

乙烯裂解炉炉群通常由多台裂解炉并行运行,将烃类原料裂解成小分子烃类化合物。由于随着裂解炉连续运行不可避免地在炉管内壁产生结焦,结焦导致裂解炉运行效率下降,所以需要对裂解炉进行周期性的停炉清焦。对于不同价格参数的多种原料不同清焦费用的多台裂解炉来说,整个乙烯裂解炉炉群系统的循环调度应是求得最优解使得收益最大化。本文对此类裂解炉炉群循环调度问题提出了一个新的混合整数非线性（MINLP）模型,相比较以前的研究该模型能够得到更好的求解多原料多裂解炉的问题,同时解决了裂解过程中切料时机选择的问题。最后,以某乙烯厂为研究实例进行切料时机的优化,优化后裂解炉全周期的运行效益显著提高,为操作人员选择最佳切炉时机提供了理论依据,说明了此模型的有效性。