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Planning, scheduling, and control typically constitute separate decision-making units within chemical companies. Traditionally, their integration is modelled sequentially, but recent efforts prioritize lower-level feasibility and optimality, leading to large-scale, potentially multi-level, hierarchical formulations. Data-driven techniques, like optimality surrogates or derivative-free optimization, become essential in addressing ensuing tractability challenges. We demonstrate a step-by-step workflow to find a tractable solution to a tri-level formulation of a multi-site, multi-product planning-scheduling-control case study. We discuss solution tractability-accuracy trade-offs and scaling properties for both methods. Despite individual improvements over conventional heuristics, both approaches present drawbacks. Consequently, we synthesize our findings into a methodology combining their strengths. Our approach remains agnostic to the level-specific formulations when the linking variables are identified and retains the heuristic sequential solution as fallback option. We advance the field by leveraging parallelization, hyperparameter tuning, and a combination of off- and on-line computation, to find tractable solutions to more accurate multi-level formulations. • Tractable solution to multi-level integrated planning-scheduling-control formulations. • Surrogates and black-box optimization outperform heuristics in tri-level solutions. • Leverages derivative-free optimization and assesses benefits and drawbacks. • Combines workflows leveraging tractability and accuracy strengths of both. • Methodology is flexible to other formulations and preserves solution guarantees. [ABSTRACT FROM AUTHOR]

The scheduling of crude oil operations holds critical significance in the petrochemical industry due to its profound influence on downstream unit operations and, consequently, overall business profitability. This work presents a novel multi-operation sequencing formulation considering operations with restricted overlapping constraints. This operation-centric model also distinguishes itself by incorporating constraints posed by refinery practice such as downstream product management, multiparcel unloading, brine settling, and changeover detection. A new symmetry-breaking strategy is applied to remove symmetric solutions properly and expedite problem solving while ensuring solution quality. Case studies of various examples are conducted to validate the efficacy of the proposed model. Comparative analyses are performed with the unit-specific event-based formulation, which enables multiple time grids tailored to different units and is widely used in continuous-time modeling. Results further demonstrate the great potential of the presented formulation in generating tighter bounds and accelerating convergence. • A new operation-centric model to solve crude oil scheduling problem is proposed. • Operations with max overlaps and other real-world constraints are considered. • A new sequencing rule is developed to break symmetry and expedite problem solving. • Case studies demonstrate the great computational potential of the proposed model. [ABSTRACT FROM AUTHOR]

• First integrated optimization of crude oil procurement and blending. • Proposing a hybrid time-event representation to address different time horizons. • Considers the stability of blended crude oil properties in the optimization process. • Verification of the authenticity and validity of the model on the basis of real cases. • Optimization results in effective reduction of crude oil procurement costs. Crude oil procurement and blending are key processes in refinery production. When solving the integrated optimization problem of simple oil procurement and blending, the following issues are mainly considered: how to establish an integrated optimization model of crude oil procurement and blending process under different time scales to minimize the cost of procurement under the premise of ensuring the stability of the properties of blended crude oil. The paper proposes an integrated optimization model, takes cost minimization as the model's objective function, and provides stability through the yield and property constraints of blended crude oil. Then, the paper describes the procurement process by an event-based representation and the blending process by a continuous event representation and proposes a hybrid event-time-based representation to describe the model. Finally, this paper verifies the model's effectiveness in solving real production problems through case simulations. [ABSTRACT FROM AUTHOR]

Plant-wide scheduling optimization of multi-grade PET production is of great significance for increasing the economic benefits and market competitiveness of PET plants. However, dealing with changeover operations between the production of products with different grades is challenging due to multiple timing limitations in the actual process. This study proposes a novel plant-wide scheduling optimization model for multi-grade PET production. The model focuses on three major categories of products, namely PET fibers, PET chips, and bottle-grade PET. Considering the impacts of nights and weekends on the production, a hybrid discrete/continuous-time representation method is developed to handle changeover operations with time window constraints. Afterward, a multi-objective optimization framework for multi-grade PET production is formulated to balance economic benefits and production stability. Case studies on a real-world PET plant are presented to verify the effectiveness and applicability of the proposed method. • A plant-wide scheduling optimization model of multi-grade PET production is proposed. • The impacts of nights and weekends on changeovers are considered. • A hybrid discrete/continuous-time representation method is developed. • The relationship between economic benefits and production stability is analyzed. [ABSTRACT FROM AUTHOR]

• State-of-the-art modeling and optimization of industrial-size refinery scheduling. • Integrated refinery scheduling network with advanced process-unit modeling. • Optimization decision-making with advanced re-optimization mechanisms. • Nonconvex mixed-integer nonlinear programming (MINLP) model for refinery scheduling. • Refinery scheduling optimization leads to higher profitability and more efficient operations. Modeling and optimization of large-scale refinery scheduling problems is challenging because of their complexity and size. Herein, we propose a mathematical model to represent such problems more accurately and realistically, and a state-of-the-art optimization framework for its solution. The framework leverages the use of mathematical optimization and algorithmic methods by combining modeling approaches (process design, model decompositions), solving strategies (rescheduling, heuristics), and machine learning regression (surrogate models). An industrial-size refinery scheduling problem (2 blenders, 4 feed tanks, distillation network with 5 towers, processing network with FCC, hydrotreaters, debutanizers, superfractionator, catalytic reformer) is formulated as a hierarchical nonconvex mixed-integer nonlinear programming (MINLP) model and is successfully optimized, providing higher profitability and more efficient scheduling operations considering 12 feedstocks, 10 products and multiple scenarios for time horizon and step. Results highlight the importance of tuning scheduling parameters and employing an enhanced computer-aided framework to enable the solution of industrial refinery scheduling operations. [ABSTRACT FROM AUTHOR]

Machine scheduling is one of the most studied problems due to its technical challenges and prevalence in real life. In the literature, continuous- and discrete-time formulations are the two most known formulations for scheduling problems. However, continuous-time formulations often suffer from weak linear relaxations, while discrete-time formulations struggle with large numbers of variables. In contrast, the bucket-indexed formulation is an alternative that mitigates both issues by working with partial time discretization. We propose a mixed-integer linear programming model based on a bucket-indexed formulation to solve a nonpreemptive scheduling problem of identical parallel machines considering release dates, deadlines, precedence, eligibility, and machine availability constraints. We evaluate the proposed formulation against real-world instances comprising more than 400 jobs and 100 machines, comparing its performance against equivalent continuous- and discrete-time formulations. Remarkably, our formulation can be solved to optimality for all instances, outperforming both continuous- and discrete-time formulations. • Proposes a new bucket-indexed formulation for parallel machine scheduling. • Deals with large-scale instances based on real-world rig scheduling problems. • The proposed formulation outperforms other formulations in the literature. [ABSTRACT FROM AUTHOR]

• Cyclic scheduling optimization for the whole ethylene plant (CSO-EP). • A backup furnace mode in parallel and semi-continuous process is considered. • Separation capacity constraints are introduced to qualify products. • A disaggregation-based optimization framework is formulated for the CSO-EP. • An industrial case study is carried out to verify the effectiveness. Ethylene plants (EPs) are a critical output source of ethylene. The cyclic scheduling optimization is crucial to increase the profitability of an EP. The EP comprises the ethylene cracking furnace system (ECFS), quenching, compression, separation sections, etc., which culminates in a large-scale optimization problem. In addition, the performance-decaying and semi-continuous characteristics of the ECFS inevitably lead to fluctuations in product throughput, resulting in an unstable production process and product quality decline. To address this issue, we propose a mixed-integer quadratic programming (MIQP) model for the cyclic scheduling of the EP in backup furnace mode with separation capacity constraints. This novel model can reduce fluctuations in product throughput by running a backup furnace when one furnace is shut down for decoking. Besides, the separation capacity constraints ensure that high-quality products can be separated from the cracked gas downstream. Moreover, the reformulated normalized multiparametric disaggregation technique (RNMDT), which relies on convex envelopes, is employed to relax the proposed MIQP model into a mixed-integer linear programming (MILP) model by partitioning the domain of the variables in the quadratic terms. Subsequently, an optimization framework based on the RNMDT is established to enhance the solution efficiency of the original problem. Finally, a case study from the real world reveals the effectiveness of the proposed method, which can provide instructive optimal cyclic scheduling for the EP. [ABSTRACT FROM AUTHOR]

The batch process plays an important role in industrial production. Among them, production processes that have specific requirements for operational continuity in each processing stage should consider the no-wait constraint to meet the production reality. The batch process with a no-wait constraint is a typical NP-hard problem. In this work, we propose a framework for the integration of planning, scheduling, and control. We also propose a decomposition method with an improved genetic algorithm to solve the integration problem of scheduling and control for the no-wait batch process. The integrated formulation represents a typical mixed-logic dynamic optimization (MLDO) problem, which involves logical disjunctions and operational dynamics. Then, we address the integrated problem as a grey-box optimization problem, using data-driven feasibility analysis and surrogate models to approximate the unknown black-box constraints. Finally, we test specific production instances to demonstrate the feasibility and superiority of the proposed integration model of the no-wait batch process and optimization algorithm. • Planning, scheduling, and control problems are considered individually. • No-wait constraints are common in the batch plant and complicate the model. • The detailed lower-level problems are incorporated as constraints in the upper level. • The integration problem is formulated as a grey-box optimization problem. [Display omitted] [ABSTRACT FROM AUTHOR]

Rigorous scheduling that uses hard heuristics and allows forceful shutdown of process units, whether intentionally or unintentionally, in the copper smelting process always harms the process operation. This way of process scheduling often results in sub-optimal process operation. Although a flexible scheduling framework that empowers process units to make independent operational decisions is desirable, the inter-dependencies among these units continue to pose a challenge in its design. This study presents a hierarchical scheduling framework for the copper smelting process, which uses price-based heuristics to resolve process inter-dependencies among the process units. These inter-dependencies arise due to the bottlenecks present in the process. Taking advantage of market theory, the coordinator uses PI controllers to find the appropriate prices to address the inter-dependencies. Two case studies are presented to demonstrate that the proposed framework effectively resolves all the process inter-dependencies, indicating its potential for application in other large-scale scheduling applications. • Hierarchical Scheduling Framework for Copper Smelting Process. • Optimal scheduling of Copper Smelting Process. • Heuristics based Coordination. • Price based Coordination in Plant-Wide Optimization. • Optimal operation of Flash Smelting process and Peirce-Smith Converter. [ABSTRACT FROM AUTHOR]

The reception, mixture, delivery, and processing of crude oil at a refinery are modeled and validated. We employ a continuous-time model based on priority-slots and a multi-operation sequencing approach. The refinery's desired qualities are defined as equivalent to the terminal mixtures, thus streamlining the formulation and eliminating any bilinear terms in the equations related to pipeline delivery. The goal is to find an optimized schedule that satisfies all constraints, for which an MINLP model is proposed and solved. However, by ruling out mixtures in tanks, the formulation is reduced to a manageable MILP model. Also, the Relax & Fix strategy can be used to determine an optimized schedule of operations over a time horizon in a timely and cost-effective manner. This work presents an innovative solution to the complex challenge of crude oil reception, mixture, pipeline delivery, and refinery processing. • Continuous time model, a priority-slot and multi-operation sequencing (MOS) approach. • Bilinear terms are not required in the equations related to pipeline delivery. • Symmetry breaking equations are formulated and allow feasibility for certain operations. • MINLP model. If mixtures are not permitted in tanks, it is reduced to a MILP model. • The Relax & Fix strategy can be considered to determine the optimal schedule. [ABSTRACT FROM AUTHOR]

• Multi-objective planning under uncertainty using a continuous-time heuristic model. • Monte Carlo simulation is integrated with a variable-length multi-objective GA. • Monte Carlo simulation is accelerated with a Graphics Processing Unit (GPU). • The proposed approach is validated on an industrially-relevant case study. • The benefits of the approach are demonstrated by comparison with a deterministic GA. This paper presents a flexible genetic algorithm optimisation approach for multi-objective biopharmaceutical planning problems under uncertainty. The optimisation approach combines a continuous-time heuristic model of a biopharmaceutical manufacturing process, a variable-length multi-objective genetic algorithm, and Graphics Processing Unit (GPU)-accelerated Monte Carlo simulation. The proposed approach accounts for constraints and features such as rolling product sequence-dependent changeovers, multiple intermediate demand due dates, product QC/QA release times, and pressure to meet uncertain product demand on time. An industrially-relevant case study is used to illustrate the functionality of the approach. The case study focused on optimisation of conflicting objectives, production throughput, and product inventory levels, for a multi-product biopharmaceutical facility over a 3-year period with uncertain product demand. The advantages of the multi-objective GA with the embedded Monte Carlo simulation were demonstrated by comparison with a deterministic GA tested with Monte Carlo simulation post-optimisation. [ABSTRACT FROM AUTHOR]

Countries in the Middle East are requiring larger and more complex shipping operations for the growing downstream sectors of the hydrocarbon industry, such as refining and petrochemistry. These shipping operations generally entail a closed-loop system, in which the vessels travel back and forth from a manufacturing plant to various international ports for exporting the hydrocarbon products. The current shipping systems only focus on feasible, smooth, and repeatable operations with a first-available-first-use (FAFU) policy, owing to the lack of a rigorous and systematic optimal scheduling method for maritime transportation systems. This study presents an integrated short-term scheduling model formulated as a mixed integer linear programming (MILP) model, for dispatching vessels from a petrochemical plant to international ports and economically operating a plant-side port in the closed-loop shipping system. Further, the MILP model considers varying vessel capacities and other related complex restrictions. A constructive heuristic algorithm combined with an optimization solver is adopted to solve the MILP model with sufficient speed for practical use. Numerical studies using a real data set demonstrate the effectiveness of the developed model compared to the current scheduling policy, FAFU. Moreover, we analyze the economic and computational performances of the developed solution method. Our method solves the test scenarios effectively, presenting a cost saving opportunity of 11.3% on average, which is equivalent to 439,829 USD per year for the studied operation. [ABSTRACT FROM AUTHOR]

• An evolutionary framework for scheduling of multipurpose batch plants • A method that does not rely on time or event points • No need for binary variables • The method does not suffer scalability issues of mathematical programming methods • Solution times reduced by almost 98 In a recent publication by Woolway and Majozi (2018), a novel framework for the application of metaheuristics to the scheduling of multipurpose batch plants was proposed. The initial framework was only developed for continuous-time approaches. This work extends this framework to the discrete-time approach. Additionally, a suite of metaheuristics is applied to two well-known literature examples in both of these frameworks with serial and parallel implementations. Results show these metaheuristics capable of achieving global solutions in the discrete-time approaches and close-to-optimal solutions in continuous-time approaches. These solutions can be found in reduced computational times of up to six orders of magnitude when compared to modern mathematical programming approaches. [ABSTRACT FROM AUTHOR]

Fouling is a major source of energy inefficiencies that decreases the performance of process units. Fouling mitigation alternatives are required to ensure a sustainable, profitable, and safe operation. In heat exchanger networks, two mitigation alternatives are: flow distribution control, and periodical cleanings. This paper addresses the optimal control and optimal cleaning scheduling, individually and simultaneously, for heat exchangers in refining operations. The problem is formulated as a MINLP, which uses an accurate model of the process, logic disjunctions, and a continuous time representation. To solve it efficiently, it is reformulated as a mathematical program with complementarity constraints (MPCC). The modelling and solution strategies are demonstrated in several case studies, from small to moderately large networks for realistic applications. The formulation is versatile, and large network problems are solved in a reasonable computational time. The integration of optimal scheduling and control decreases the operational cost substantially relative to independent mitigation alternatives. [ABSTRACT FROM AUTHOR]

• A new MIQCP model for scheduling of olefin plant furnace operations. • Simultaneously optimize furnace system manufacturing and decoking schedules. • Grouping decoking operations together to reduce product throughput upsets. • Well balancing chemical plant profitability and operability. Olefin plants employ multi-type cracking furnaces in parallel to convert various hydrocarbon feeds into products such as ethylene and propylene. The cracking process of each furnace is a performance-decaying batch operation, which needs periodic shutdowns for decoking and thus involves inherent and frequent upsets to the downstream process. Thus, the furnace feed allocation, batch processing time, and decoking sequence of the entire furnace system must be optimally scheduled to maximize the plant profitability as well as minimize the process upset induced by furnace decoking for the sake of the plant operability. In this paper, a novel MIQCP (mixed-integer quadratically constrained programming) model has been developed for the optimal scheduling of such parallel and performance-decaying unit system with consideration of inherent upset reduction. The idea is to group decoking operations of different furnaces together, so that the downstream has less frequency to suffer the product throughput upsets from the furnace system. The MIQCP model also addresses major scheduling issues of furnace systems, such as semi-continuous operation, non-simultaneous shutdowns, and secondary ethane cracking. The MIQCP model can be further converted to the MILP model by piece-wise approximation to speed the solving time. Case studies have demonstrated the efficacy of the developed methodology with significant economic potential and operational benefits. [ABSTRACT FROM AUTHOR]

The paper deals with the integration of shared resources in the formulation of process industry scheduling problems, with reference to the optimal operation of those processes that are composed by continuous and batch units tightly integrated by means of mass or energy flows. It uses as a reference a benchmark developed in the EU project HYCON2: a simplified crystallization section of a sugar factory. The aim is to present a novel formulation that allows the coordination of the continuous and discrete processes with shared resources generating feasible schedules that can be easily integrated in a wider optimization scheme. The approach uses formal scheduling methods, mixing three different time frames: one in continuous time for scheduling, another to describe the time evolution of the shared resources and a discrete one for synchronization of the shared resources and the integration with the continuous dynamics. [ABSTRACT FROM AUTHOR]

• A dynamic scheduling framework for perfusion processes in a facility is presented. • Scheduling policies are adapted and proposed to react to failure and varying demand. • Policy parameters and process run times are tuned using evolutionary algorithms. • Tuned policies perform better than service level- or fixed cycle-based policies. • Novel policy with look-ahead heuristic is best especially with run times optimised. The biopharmaceutical industry is increasingly interested in moving from batch to semi-continuous manufacturing processes. These continuous bioprocesses are more failure-prone and process failure is more consequential. In addition, the probability of failure is dependent on process run time which generally is determined independent of scheduling considerations. This work presents a discrete-event simulation of continuous bioprocesses in a scheduling environment. Dynamic scheduling policies are investigated to make operational decisions in a multi-product manufacturing facility and react to process failure events and uncertain demand. First, different scheduling policies are adapted from the stochastic lot sizing literature and a novel look-ahead scheduling policy is proposed. Then, policy parameters (including process run time) are tuned using evolutionary algorithms. Our results demonstrate that the tuned policies perform much better than a policy that estimates policy parameters based on service level considerations and a policy based on a fixed cyclical sequence. [ABSTRACT FROM AUTHOR]

• Uncertainties in by-product gas scheduling are considered. • The proposed rolling-horizon algorithm maximizes energy efficiency. • BFG, COG and LDG gases are forecasted in real time using time series models. • Short-term decisions are calculated iteratively by solving a MILP problem. • Forecasting error effect in the algorithm performance is analyzed. This paper addresses the real-time by-product gas scheduling in an integrated iron- and steel-making industry with uncertainty in by-product gas flows from a rolling horizon algorithm. Adaptive time-series models determined from real data performs forecast for each producer and consumer of by-product gases in main units of the steel-making plant. The individual consumptions of the blast furnace and coke oven gases are modelled using the seasonal Holt-Winters method with smoothing constants estimated via genetic algorithm, whereas the individual productions of the blast furnace and coke oven are identified from autoregressive and integrated moving-average. LDG gas production is forecasted using a heuristic method that leverages the operational information. The model's parameters are updated periodically due to the nonlinearities present in the time series. After the forecasting phase, the algorithm performs short-term decisions using a MILP optimization model, that minimizes the imbalance between the random dynamics of by-product fuel generation and consumption and maximizes the energy efficiency. Through computational simulations, we show that the operational stability of gas holders and the electrical energy production increase, whereas the waste of gas in flare stack decreases, when the control horizon of the rolling horizon algorithm is reduced. [ABSTRACT FROM AUTHOR]

Highlights • Fast GA approaches for capacity planning and scheduling of multi-product, multi-site biomanufacture are presented. • The key features include the chromosome encoding strategy, algorithms capturing the capacity planning objectives, and a meta-optimisation strategy to tune the GA. • The proposed approaches are validated on two literature examples. • The proposed GA approaches are shown to achieve near-exact solutions and are demonstrated as a valid alternative to MILP models. Abstract The previous research work in the literature for capacity planning and scheduling of biopharmaceutical manufacture focused mostly on the use of mixed integer linear programming (MILP). This paper presents fast genetic algorithm (GA) approaches for solving discrete-time MILP problems of capacity planning and scheduling in the biopharmaceutical industry. The proposed approach is validated on two case studies from the literature and compared with MILP models. In case study 1, a medium-term capacity planning problem of a single-site, multi-suite, multi-product biopharmaceutical manufacture is presented. The GA is shown to achieve the global optimum on average 3.6 times faster than a MILP model. In case study 2, a larger long-term planning problem of multi-site, multi-product bio-manufacture is solved. Using the rolling horizon strategy, the GA is demonstrated to achieve near-optimal solutions (1% away from the global optimum) as fast as a MILP model. [ABSTRACT FROM AUTHOR]

Highlights • Mathematical programming formulation and solution of an industrial scheduling problem. • Novel modeling of semi-continuous operation of nickel smelting flash furnaces. • Multi-tiered optimization methodology devised to improve industrial operability. • Representation of environmental emission limits via event timing constraints. • Sequencing, symmetry-breaking and constraint tightening schemes to reduce solution times. Abstract The scheduling of converter aisle operation in a nickel smelting plant is a complex task with significant ramifications to plant profitability and production. An optimization-based scheduling formulation is developed using a continuous-time paradigm to accurately represent event timings. The formulation accounts for environmental restrictions on sulfur dioxide emissions, using event timing constraints. Flash furnaces are characterized by a continuous inlet flow and intermittent, discrete material removal, which is captured via novel semi-continuous modeling. An innovative sequencing and symmetry-breaking scheme is introduced to exploit identical units operating in parallel. A rolling horizon feature is included to accommodate real-time optimization. Tightening constraints are developed to improve the computational performance. A unique, multi-tiered procedure enhances the practicality of the solution and supports additional operability objectives, without compromising the optimality of the primary objective. The success of the approach is demonstrated via case studies arising from industrial production scenarios. [ABSTRACT FROM AUTHOR]

Highlights • Formulated optimal operation of water distribution networks with storage facilities. • Proposed efficient decomposition solution for solving resulting MINLP. • Demonstrated energy savings through optimal scheduling of valve and pump operations. Abstract The nexus between water and energy reveals that transporting water for end use is a highly energy intensive operation. In this work we consider the optimal operation of a water distribution network consisting of pumps delivering water to different reservoirs, with each reservoir catering to a time varying demand. Pumps and ON/OFF valves are used as manipulated variables to minimize energy consumption while meeting the demand. Due to the nonlinear nature of the pump operating curve and the hydraulics, this results in a Mixed Integer Nonlinear Program (MINLP). We propose a three step decomposition approach to solve this problem efficiently. The applicability of this technique is demonstrated on a water network proposed for a municipality in India and the potential advantages are reported. We also compare the solution times required for the proposed technique and a standard solver and demonstrate the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

We propose a new time-bucket MILP model for lot-sizing and scheduling problems arising in chemical batch plants. The main idea behind time-bucket models is to partition time into fixed-length macroperiods and flexible length microperiods, that lie within the macroperiods. We show that the time-bucket model benefits from advantages of both continuous and discrete time representations. It allows to include important real-world constraints, can be solved with moderate computational effort, and thus promotes MILP for large-scale, industrial problems. We investigate the scalability of the model and apply it to a formulation and filling process from an industrial agrochemical production with 7 formulation lines, intermediate buffer tanks, and 7 filling lines. We optimize a one month period with 50 intermediates, and 83 finished products. A comparison of the MILP solution to a discrete event simulation solution shows that 17% of production capacity can be freed up and significant improvement in on-time delivery. • Time-bucket MILP model for multistage lot-sizing and scheduling problems. • In-depth investigation of model scalability and model parameters. • Application to a real-world formulation and filling process for agrochemicals. [ABSTRACT FROM AUTHOR]

This paper addresses how to combine the two main engineering design tools, optimization and feedback, to obtain high performance process control or process operation systems. We discuss the historical development of process control, where feedback dominated the early practical designs, and optimization was then incorporated much later through technologies like model predictive control. In chemical production scheduling, on the other hand, optimization had a strong early influence on the problem formulation, and feedback has only recently made an appearance. The recent developments in both process control and scheduling are illustrated with specific examples emerging from this series of FOCAPO/CPC meetings. The paper next presents recent theoretical developments in nominal and stochastic model predictive control. The closed-loop properties that arise from these different open-loop optimal control problems are then compared. The paper closes with some discussion of when the improvements of the closed-loop properties are worth the added complexity of the stochastic optimal control problem. • Paper addresses how to combine optimization and feedback to obtain high performance process control systems. • Illustrates recent developments with examples from this series of FOCAPO/CPC meetings. • Presents recent theoretical developments in nominal and stochastic model predictive control. • Discusses when improvements in closed-loop properties are worth the complexity of a stochastic model. [ABSTRACT FROM AUTHOR]

• The issue of calculating the minimum cycle time in periodic scheduling for batch processes is addressed. • Process tasks are assumed to share common resources. • An exact algorithm is developed first for the case of a single shared resource and, subsequently, for multiple shared resources. • The algorithm computes the minimum cycle time and all feasible cycle time ranges. • Illustrative and real-world examples are used to demonstrate the implementation of the algorithm. Cyclic execution of processing activities is a mode of operation frequently employed by batch manufacturers. Periodic scheduling of these cyclic activities is characterized by the cycle time, a variable that represents the time interval between the start of consecutive cycles. The cycle time determines the number of production batches that can be executed in a given time horizon and, consequently, defines the plant throughput. In this paper, an exact, exhaustive algorithm is developed for the calculation of the minimum cycle time and all feasible cycle time ranges in the context of periodic scheduling with shared resources among tasks. The algorithm is first developed for the case where multiple production tasks share a single resource and then extended for the multiple shared resources case. The implementation and efficiency of these algorithms is demonstrated with the use of illustrative and real-world industrial examples. [ABSTRACT FROM AUTHOR]

This “white paper” is a concise perspective based on a session during FIPSE 3, held in Rhodes, Greece, June 20–23, 2016. This was the third conference in the series “Future Innovation in Process Systems Engineering” (http://fi-in-pse.org), which takes place every other year in Greece, with a limited number of participants and just three topics/sessions whose objective is to pose and discuss open research challenges in Process Systems Engineering. This specific session comprised invited talks by Sigurd Skogestad and Iiro Harjunkoski, followed by short presentations by the participants and extensive discussions. The paper does not intend to provide a comprehensive review on the subject, or a detailed exposition of the concepts and problems. Its aim is to highlight open problems and directions for future research. [ABSTRACT FROM AUTHOR]

Integrated scheduling and control (SC) seeks to unify the objectives of the various layers of optimization in manufacturing. This work investigates combining scheduling and control using a nonlinear discrete-time formulation, utilizing the full nonlinear process model throughout the entire horizon. This discrete-time form lends itself to optimization with time-dependent constraints and costs. An approach to combined SC is presented, along with sample pseudo-binary variable functions to ease the computational burden of this approach. An initialization strategy using feedback linearization, nonlinear model predictive control, and continuous-time scheduling optimization is presented. The formulation is applied with a generic continuous stirred tank reactor (CSTR) system in open-loop simulations over a 48-h horizon and a sample closed-loop implementation. The value of time-based parameters is demonstrated by applying cooling constraints and dynamic energy costs of a sample diurnal cycle, enabling demand response via combined scheduling and control. [ABSTRACT FROM AUTHOR]

With the potential to decrease operating costs and improve energy efficiency, model predictive control (MPC) has been proposed as a replacement for traditional heuristic, PID, and other conventional control strategies for heating, ventilation, and air conditioning (HVAC) systems in commercial buildings. Due to the size of large commercial HVAC systems, implementing MPC as a single monolithic optimization problem is not practical nor desirable given real-time operating requirements. In this paper, we present a hierarchical decomposition for economic MPC in large-scale commercial HVAC systems using a two-layer approach. We show a sample optimization for a campus of 25 buildings with 500 total zones and a central plant consisting of eight chillers. Then, we discuss an application of the ideas presented here in the recently completed $485-million replacement of the Stanford campus heating and cooling systems and conclude with some of the control theory challenges presented by this new class of applications. [ABSTRACT FROM AUTHOR]

The notion of Internet of Things (IoT), as well as related topics such as Cyber-Physical Systems, Industrie 4.0 and Smart Manufacturing are currently attracting a lot of attention within the process and manufacturing industries. Clearly, IoT offers many potential applications for automation, ranging from engineering installation of new plants to production management and more intelligent maintenance schemes including novel sensor technologies. The focus of this paper is, however, on the control and operations. Most likely IoT leads to new system architectures where open standards play a significant role. Through better connectivity, information will be much more easily available, which could result in that previously isolated functions will become more closely integrated. Here modeling at the right level of fidelity will be absolutely key. It can be expected that the importance of optimization will increase and this paper discusses some aspects related to the opportunities, challenges and changes triggered by IoT. [ABSTRACT FROM AUTHOR]

In this paper, we present a brief overview of enterprise-wide optimization and challenges in multiscale temporal modeling and integration of different models for the levels of planning, scheduling and control. Next, we review Generalized Disjunctive Programming (GDP), as a new modeling paradigm for scheduling problems that are illustrated with the STN and RTN models. We then address scheduling problems that expand the scope of the area: simultaneous scheduling and heat integration, pipeline scheduling, crude oil and refined products blending, and demand side management. We illustrate the advantage of the GDP modeling framework, describe effective strategies for global optimization, and describe multistage affinely adjustable robust optimization for uncertain interruptible load. We address integration of planning and scheduling, for which several approaches are reviewed, including use of traveling salesman constraints for multiperiod refinery planning, and multisite planning and scheduling of multiproduct batch plants. We report computational results to highlight the challenges. [ABSTRACT FROM AUTHOR]

An approach for optimising the cleaning schedule in heat exchanger networks (HENs) subject to fouling is presented. This work focuses on HEN applications in crude oil preheat trains located in refineries. Previous approaches have focused on using mixed-integer nonlinear programming (MINLP) methods involving binary decision variables describing when and which unit to clean in a multi-period formulation. This work is based on the discovery that the HEN cleaning scheduling problem is in actuality a multistage optimal control problem (OCP), and further that cleaning actions are the controls which appear linearly in the system equations. The key feature is that these problems exhibit bang-bang behaviour, obviating the need for combinatorial optimisation methods. Several case studies are considered; ranging from a single unit up to 25 units. Results show that the feasible path approach adopted is stable and efficient in comparison to classical methods which sometimes suffer from failure in convergence. [ABSTRACT FROM AUTHOR]

In this study, a two-level control methodology consisting of an upper-level scheduler and a lower-level supervisory controller is proposed for an advanced load-following energy plant with CO 2 capture. With the use of an economic objective function that considers fluctuation in electricity demand and price at the upper level, optimal scheduling of energy plant electricity production and carbon capture with respect to several carbon tax scenarios is implemented. The optimal operational profiles are then passed down to corresponding lower-level supervisory controllers designed using a methodological approach that balances control complexity with performance. Finally, it is shown how optimal carbon capture and electricity production rate profiles for an energy plant such as the integrated gasification combined cycle (IGCC) plant are affected by electricity demand and price fluctuations under different carbon tax scenarios. The paper also presents a Lyapunov stability analysis of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper presents a generic heuristic-based scheduling solution. It highlights the flexibility that a simple heuristic method can offer and shows that using the ISA-95 standard it is possible to express the most relevant problem requirements. In order to illustrate the possible benefits, the paper also compares the solution quality of a smaller scale example scheduling problem to a rigorous mixed-integer linear programming (MILP) approach and shows how a heuristic approach scales towards large-size industrial problems. The paper concludes with a discussion of the advantages and disadvantages of both approaches, showing that for certain types of problems, the heuristic approach is fully sufficient, even if it cannot be expected to result in optimal solutions. [ABSTRACT FROM AUTHOR]

We propose two novel discrete-time mixed-integer programming models for simultaneous batching and scheduling in multipurpose batch plants with storage constraints. The proposed models adopt two different modeling approaches. The first is based on explicit labeling of batches, while the second is based on identifying possible batch size intervals for each order and the corresponding unit routings. We also present extensions that allow us to consider limited shared utilities (with both fixed and time-varying availability and cost), storage with capacity limits and stage-dependent batch sizes. Finally, we study how instance characteristics (e.g. expected number of batches per order, uniformity in unit capacities) impact the effectiveness of the proposed models. We show that by carefully selecting the model allows us to effectively solve large-scale instances. [ABSTRACT FROM AUTHOR]

In the steelmaking continuous-casting (SCC) process, scheduling problem is a key issue for the iron and steel production. To improve the productivity and reduce material consumption, optimal models and approaches are the most useful tools for production scheduling problems. In this paper, we firstly develop a mixed integer nonlinear mathematical model for the SCC scheduling problem. Due to its combinatorial nature and complex practical constraints, it is extremely difficult to cope with this problem. In order to obtain a near-optimal schedule in a reasonable computational time, Lagrangian relaxation approach is developed to solve this SCC scheduling problem by relaxing some complicated constraints. Owing to the existence of the nonseparability coming from the product of two binary variables, it is still hard to deal with this relaxed problem. By making use of their characteristics, the subproblems of the relaxed problem can be converted into different difference of convex (DC) programming problems, which can be solved effectively by using the concave–convex procedure. Under some reasonable assumptions, the convergence of the concave–convex procedure can be established. Furthermore, we introduce an improved conditional surrogate subgradient algorithm to solve the Lagrangian dual (LD) problem and analyze its convergence under some appropriate assumptions. In addition, we present a simple heuristic algorithm to construct a feasible schedule by adjusting the solutions of the relaxed problem. Lastly, some numerical results are reported to illustrate the efficiency and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

A novel dynamic optimization framework is presented for integration of design, control, and scheduling for multi-product processes in the presence of disturbances and parameter uncertainty. This framework proposes an iterative algorithm that decomposes the overall problem into flexibility and feasibility analyses. The flexibility problem is solved under a critical (worst-case) set of disturbance and uncertainty realizations, whereas the feasibility problem evaluates the dynamic feasibility of each realization, and updates the critical set accordingly. The algorithm terminates when a robust solution is found, which is feasible under all identified scenarios. To account for the importance of grade transitions in multiproduct processes, the proposed framework integrates scheduling into the dynamic model by the use of flexible finite elements. This framework is applied to a multi-product continuous stirred-tank reactor (CSTR) system subject to disturbance and parameter uncertainty. The proposed method is shown to return robust solutions that are of higher quality than the traditional sequential method. The results indicate that scheduling decisions are affected by design and control decisions, thus motivating the need for integration of these three aspects. [ABSTRACT FROM AUTHOR]

• A novel methodology for scheduling of energy intensive industries under the uncertainty of spot electricity market. • Development of a scenario generator tool using ARIMA for electricity price forecasting. • Integration of deterministic optimization with multi scenario approach. • Risk metric analysis to facilitate decision making in choosing the best suited scenario. • Implementation of the methodology in a real-life cryogenic air separation plant. The planning of energy-intensive processes is intrinsically uncertain due to their dependence on the volatile energy market, with scheduling having a vast impact on the final production cost of these plants. Traditional stochastic methods are mathematically very complex, which translates into a significant computational effort that might prevent a timely response to varying electricity prices. To encounter this uncertainty, we develop a reliable hybrid simulation-optimization approach for optimizing the production plant scheduling, combining scenario analysis with risk analysis. The proposed methodology is demonstrated with real data from a cryogenic air separation plant in Tarragona (Spain). This approach also informs decision-makers about risk or expected shortfall associated with the implied scenario. The generic methodology used here can be easily adapted to schedule facilities in other energy-intensive sectors such as cement, metallurgy or pulp and paper. [Display omitted] [ABSTRACT FROM AUTHOR]

Optimal scheduling of the copper smelting process is of great concern in the process industry due to the contradictory objectives of the process units and the presence of inter-dependencies between them. This in combination with commercial interests such as maximizing input concentrates to the Flash Smelting Furnace (FSF), continuous operation of the FSF, and production of the blister copper batches with a shorter batch time hinders the development of a scheduling algorithm based on linear optimization techniques. In this study, a hierarchical scheduling framework is developed that finds feasible schedules for the copper smelting process by solving process inter-dependencies using heuristics. For addressing the FSF inter-dependencies, this framework sees the FSF matte as a scarce resource, and the coordinator uses price-based heuristics for the optimal allocation of the matte to various Peirce-Smith converters. Two case studies are presented to demonstrate the effectiveness of the framework. • Hierarchical Scheduling Framework for Copper Smelting Process. • Optimal scheduling of Copper Smelting Process. • Heuristics based Coordination. • Price based Coordination in Plant-Wide Optimization. • Optimal operation of Flash Smelting process and Peirce-Smith Converter. [ABSTRACT FROM AUTHOR]

Linear model predictive control is extended to both control and optimize a product grade schedule. The proposed methods are time-scaling of the linear dynamics based on throughput rates and grade-based objectives for product scheduling based on a mathematical program with complementarity constraints. The linear model is adjusted with a residence time approximation to time-scale the dynamics based on throughput. Although nonlinear models directly account for changing dynamics, the model form is restricted to linear differential equations to enable fast online cycle times for large-scale and real-time systems. This method of extending a linear time-invariant model for scheduling is designed for many advanced control applications that currently use linear models. Simultaneous product switching and grade target management is demonstrated on a reactor benchmark application. The objective is a continuous form of discrete ranges for product targets and economic terms that maximize overall profitability. [ABSTRACT FROM AUTHOR]

In recent years there has been increased concern on energy efficiency of industries. Since the scheduling problems in the shop floors are directly related to the energy consumption, an appropriate way to improve energy efficiency in industrial plants is to develop effective scheduling strategies. Hence, the aim of this paper is to design an energy-efficient scheduling in a shop floor industrial environment, i.e., flexible job-shop scheduling problem (FJSP). To this end, a multi-objective optimization model is developed with three objective functions: (i) minimizing total completion time, (ii) maximizing the total availability of the system, and (iii) minimizing total energy cost of both production and maintenance operations in the FJSP. To cope with this multi-objective optimization problem, an enhanced evolutionary algorithm incorporated with the global criterion, as a multi-objective handling technique, is proposed and then performance evaluation is performed based on an extensive numerical analysis. [ABSTRACT FROM AUTHOR]

The introduced work aims to systematic optimize detailed short-term scheduling for industrial waste incineration to support daily decision-making processes. The overall objective is to reduce the utilization of auxiliary fuel used to overcome waste related energy in the incineration process. The reduction is achieved through adequate mixing and scheduling of waste streams with different energy content and improved logistic strategies. With it, regulatory and technical constraints are fulfilled and holdups in production processes derived from bottlenecks in the waste treatment are avoided. The considered system consists of storage tanks, a piping network, tank wagons for waste transportation, unloading pumps and incineration lances. The optimization model is formulated as a mixed-integer linear programming (MILP) problem with a discrete time representation based on a single uniform grid. It consists of two blocks: i) waste transfer and mixing, and ii) the incineration process itself including energy calculations and constraints. The industrial case study of this work shows a saving potential of auxiliary fuel of up to 90%, leading to a reduction of CO 2 emissions of up to 13%. Hence, the systematic scheduling of industrial waste incineration leads to an important reduction of auxiliary fuel consumption, resulting in economic and environmental benefits. [ABSTRACT FROM AUTHOR]

Continuous-time scheduling models for multiproduct pipelines typically view the contents of a pipeline as a set of batches. It facilitates tracking batch coordinates but prevents rigorously enforcing forbidden product sequences when dealing with intermediate dual-purpose nodes. Such models require the initial characterization of the pipeline and total number of batches as inputs, decisions that can be non-trivial. To overcome these limitations, this paper presents a new mixed-integer linear programming (MILP) formulation for straight pipelines with a single tuning parameter, the number of event points in the grid. It is derived from Generalized Disjunctive Programming (GDP) followed by a convex hull reformulation. Compared to a product-centric formulation based on the Resource-Task Network (RTN), it is much simpler, smaller in size and can be up to two orders of magnitude faster. Comparison to its batch-centric counterpart is not as favorable, the highlight being an 8% improvement in makespan for a benchmark problem. [ABSTRACT FROM AUTHOR]

Scheduling of production and maintenance plays a fundamental role in the effective operation of process plants. Frequently the two decision processes are independently addressed, overlooking the tight relation existing between the way the plant is operated to produce the required goods and the appearance of maintenance requirements. The presence of degradation phenomena affecting the performance of plant units and limiting the operational choices makes the integration of the two decision processes even more important. In this paper an industrial framework for the integration of maintenance and production scheduling of process plants is presented as well as some considerations on how the presence of plant unit degradation impacts on the scheduling problem. The proposed approach ties industrial key-components such as asset management and production scheduling closer together and represents therefore a contribution to the smart manufacturing revolution. The integrated maintenance and production scheduling problem is formulated as a mixed integer linear program (MILP) and tested on a generic process plant described as a State Task Network (STN). [ABSTRACT FROM AUTHOR]

The refined oil transportation problem investigated in this paper lies on the intersection of the scheduling and routing of tramp shipping and the petroleum supply chain, with unprecedented large-scale and complex rules. Two mixed-integer linear programming formulations are developed for the assignment between tasks, vessels, and timing issues. The first model uses a time-slot concept under a continuous-time representation, where the constraints that deal with vessel assignment, capacity, timing, demand, and slack stock control are considered. The second model uses a discrete-time representation with time assignment, portal counting, and strict stock control constraints. By virtue of the data collected from an oil company, this modeling approach is validated and used to generate feasible scheduling solutions with lower costs than are currently achieved in the real situation. Finally, the impact of the model parameters is analyzed under different optimization scenarios. [ABSTRACT FROM AUTHOR]

Short-term scheduling in multipurpose batch plants has received significant attention in the past two decades. Both discrete-time and continuous time formulations have been proposed to model the problem; however, multipurpose plants that have machines with the ability to process multiple tasks at the same time, i.e. multitasking, have been overlooked by the available continuous time formulations in the literature. This paper presents a novel MILP formulation that is capable of accommodating the multitasking feature in the machines of a facility. The performance of the presented formulation is studied in comparison with a single-tasking formulation. The results show that, while the multitasking formulation is not more costly in terms of solution time, it is capable of producing significantly better solutions. The presented formulation takes into account several other operational constraints of multipurpose facilities and can be readily applied to facilities that have machines capable of multitasking, including plants in the analytical services sector. [ABSTRACT FROM AUTHOR]

The minimization of water in batch plants through process integration has been well established in the literature. While many existing methods have relied on a fixed batch schedule, a few have employed variable production schedules. Nevertheless, methods employing variable schedules in fixed mass load problems have assumed that water-using operations (washing) are sequence independent. This paper presents a mathematical formulation for the simultaneous optimization of batch production and minimization of wastewater in fixed mass load problems. Wastewater minimization is achieved by exploring the sequence of tasks in a unit. The effectiveness of the formulation was demonstrated using three case studies. The results show that even without process integration, water usage can be minimized through the appropriate selection of task sequences in a unit. Reductions in water usage of 33% and 48.8% were observed in case study I and case study II respectively. [ABSTRACT FROM AUTHOR]

• A new crude oil scheduling optimization model with a distributionally robust joint chance constraint is proposed to handle multiple uncertainties. • A data-driven ambiguity set based on the Wasserstein distance is formulated to characterize uncertainties. • The DRJCC model is transformed into an MINLP problem by introducing the CVaR, a big-M coefficient, and additional binary variables. • The DRJCC model is compared with traditional optimization models in case studies. Crude oil scheduling optimization is crucial for decreasing the production cost of refineries. However, the feasibility of the optimized schemes is challenged by uncertainties such as possible ship arrival delays and fluctuating crude demands. This study develops a novel data-driven continuous-time optimization model with a distributionally robust joint chance constraint to ensure the overall feasibility probability of the crude oil processing plan under multiple uncertainties. Industrial data are collected to build an ambiguity set using Wasserstein distance to include the potential joint probability distribution of uncertainties. The radius of the ambiguity set is chosen by cross-validation. The model is constructed considering the worst case in the ambiguity set. First, it is formulated as a conditional value-at-risk constrained optimization model. A big-M coefficient and additional binary variables are then utilized to convert the proposed model into a resolvable problem. The efficacy and reliability of the method are explored through case studies. [ABSTRACT FROM AUTHOR]

In the light of the increasing share of power generation from renewable energy sources, there is a growing interest in flexible operation of power-intensive processes for demand-side management/demand response. In this article, we investigate the potential application of a large-scale power-to-ammonia process in demand response programs. The process system under consideration consists of a polymer exchange membrane electrolysis that is optimally scheduled in accordance with day-ahead prices and a large-scale Haber–Bosch process that serves as a downstream energy storage. We apply a demand-side management framework with a sequential approach to identify the indirect demand response potential of the considered process system. Our results show that the power-to-ammonia process provides significant leverage for demand-side management. Moreover, we find that increasing process flexibility by optimizing operational parameters improves the demand response potential and that price profile dispersion can be used as an indicator to predict the economic performance of demand response scheduling. [Display omitted] • Evaluation of the demand response potential of a large-scale power-to-ammonia process. • Dynamic optimization to assess demand response scheduling economics. • Prediction of cost savings by means of price profile characteristics. • Parameter optimization to enhance profitability of demand response scheduling. [ABSTRACT FROM AUTHOR]

• Establishing the mathematical models for the optimization problem of the CBM well maintenance tasks scheduling. • The Q-learning based algorithm for the CBM well maintenance tasks scheduling is proposed. • The proposed Q-learning based algorithm can solve the optimization problem with relatively large number of maintenance tasks. • The proposed Q-learning based algorithm can meet the real time requirements for the CBM well maintenance tasks scheduling. The Coalbed Methane (CBM) well maintenance tasks scheduling optimization is of importance for improving the CBM production efficiency. Traditionally, this problem is addressed using mathematical model based classical optimization method or some meta-heuristic algorithms. However, due to the large-scale nature of this problem, these trials often fail in practical use. Therefore, the Q-learning algorithm based solving method is proposed in this paper. An interactive environment for reinforcement learning is constructed. To validate the effectiveness of proposed method, scenarios with different scales are provided. For the cases with 10, 14, 20, 30, 47, 60, 80 and 100 maintenance tasks respectively, the required solution time is 3.66 s, 4.94 s, 7.66 s, 12.48 s, 21.82 s, 30.82 s, 48.33 s, 73.17 s respectively. The proposed Q-learning algorithm is insensitive with the problem scale, which is promising. Moreover, the Q-learning based algorithm is more efficient than the traditional algorithm along with the increase of the number of tasks. [ABSTRACT FROM AUTHOR]

• Discrete-time modeling for operational scheduling of crane-assisted pipeless process plants. • Precedence-based continuous-time modeling for operational scheduling of crane-assisted pipeless process plants. • Comparison between discrete-time and continuous-time scheduling approaches. • Application of models on different crane-assisted pipeless process environments. In pipeless process plants that employ cranes to transfer material-containing-vessels between equipment, scheduling of cranes along with the equipment-operations on vessels is crucial from a productivity perspective. The workings of such crane-assisted pipeless process plants can differ from each other depending on the nature of their set-ups and product(s) produced. For the scheduling of such plants which currently lack substantive research in the literature, it is important to explore and develop general methods, and the current work is an endeavor in this direction. Mixed integer linear programming (MILP) based models are developed in this work using the discrete-time and precedence-based continuous-time approaches. While the modeling using the discrete-time approach is developed from scratch, that based on the continuous-time approach is a continuation from our prior work (Aravind et al., 2021). We compare the two approaches and draw generic model-agnostic insights about the aptness of the approaches to suit the practical requirements of implementation, through computational studies. Modeling based on the continuous-time approach is found to be favored from a computational perspective despite its inherent complexity in construction. [ABSTRACT FROM AUTHOR]

• Steel scheduling with self-generation under real-time and demand charge tariffs. • A model based on event expression and generalized disjunctive programming. • A new encoding and decoding to create the initial population and scheduling scheme. • A conflict resolution strategy to amend infeasible solution. It is difficult for energy-intensive enterprises equipped with self-generation to incentivize consumers to shift load to low-demand periods through time-based pricing. This paper addresses a scheduling problem of steel plant equipped with self-generation under real-time electricity prices. Considering the possibility of centralized load shifting resulting in excessive loads for some periods, we also consider the demand charge pricing. A continuous-time mixed-integer linear programming model based on event expression and generalized disjunctive programming is proposed. As industrial scale problems cannot be solved by some commercial solvers in an acceptable time, a SPEA2 algorithm is tailored. Effective encoding based on decomposition-and-offsetting mechanism and decoding based on backward-and-rules are used to generate the initial population and scheduling scheme, respectively. Meanwhile, crossover and mutation operators incorporating conflict resolution strategies can strike a balance between exploring and exploiting to produce high-quality solutions. Numerical experiments indicate that the proposed approach has superiority in performance and efficiency. [ABSTRACT FROM AUTHOR]