Scheduling Of Multipurpose Batch Plants Research Articles

Novel Multiple Time-grid Continuous-time Mathematical Formulation for Short-term Scheduling of Multipurpose Batch Plants.

In this work, we have developed two novel unit-specific event-based mixed-integer linear programing models for scheduling multipurpose batch plants. The concept of indirect and direct material transfer is introduced to rigorously sequence and align tasks in different units. A batch after production is allowed to be partially transferred to storage and downstream processing units or held in processing units over multiple event points. The computational results demonstrate that the proposed models require a smaller number of event points in many cases to achieve optimality than existing unit-specific event-based models. It is interesting to find that no task is required to span over multiple event points to reach optimality for all addressed examples. The best variant developed is superior to existing unit-specific event-based models with the same or better objective values by a maximum improvement of 67%. The computational effort is significantly reduced by at least 1 order of magnitude in some cases.

Improved Multipopulation Discrete Differential Evolution Algorithm for the Scheduling of Multipurpose Batch Plants

The multipurpose batch plant scheduling problem (MSP) has been widely studied in the fields of theoretical research and practical industrial application environments in-depth for decades as it belo...

Heat integration and cyclic scheduling of multipurpose batch plants using three index unit-specific event based model

Process scheduling with a long time horizon always leads to large problem size, which is challenging to solve for global optimal solutions. The problem complexity further increases with the inclusion of additional tasks such as heat integration, water integration, material transfers and shared storage. Cyclic scheduling can be a potential option to handle the long time horizon scheduling problems. In this work, a novel unified three index unit-specific event-based mathematical formulation is presented for cyclic scheduling of multipurpose batch plants. The unified framework reduces to a simple case in the absence of cyclic scheduling. The task extending to the next cycle is integrated with the short term scheduling constraints using the active task concept. Further, the framework is also extended for simultaneous cyclic scheduling and heat integration of multipurpose batch plants. The computational performance of the unified framework is evaluated with benchmark examples taken from the literature.

Continuous‐time scheduling formulation for multipurpose batch plants

AbstractShort‐term scheduling of batch processes is a complex combinatorial problem with remarkable impact on the total revenue of chemical plants. It consists of the optimal allocation of limited resources to tasks over time in order to manufacture final products following given batch recipes. This article addresses the short‐term scheduling of multipurpose batch plants, using a mixed integer linear programming formulation based on the state‐task network representation. It employs both single‐grid and multi‐grid continuous‐time representations, derived from generalized disjunctive programming. In comparison to other multigrid scheduling models in the literature, the proposed multi‐grid model uses no big‐M constraints and leads to more compact mathematical models with strong linear relaxations, which often results in shorter computational times. The single‐grid counterpart of the formulation is not as favorable, as it leads to weaker linear relaxations than the multi‐grid approach and is not capable of handling changeover time constraints.

On the application of a metaheuristic suite with parallel implementations for the scheduling of multipurpose batch plants

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.

A novel metaheuristic framework for the scheduling of multipurpose batch plants

A genetic algorithm (GA) is proposed along with a general framework for the scheduling of a typical multipurpose/product batch plant. The majority of literature regarding these problems make use of mathematical programming methods. Modelling problems in this manner leads to numerous binary variables relating to material balance and sequence of batches along long time horizons, thus resulting in large computational time. The proposed GA does not suffer the same scalability issues of mathematical programming approaches. The GA makes use of a coupled chromosome system with specific crossover and mutation functions utilised with the purpose of profit maximisation. Results show that optimal or close-to-optimal solutions can be achieved with a reduction of up to 98.53% computational time in certain cases.

Mixed-integer programming models for simultaneous batching and scheduling in multipurpose batch plants

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.

Discrete-time mixed-integer programming models for short-term scheduling in multipurpose environments

We present new discrete-time mixed-integer linear programming formulations for short-term scheduling in multi-purpose batch plants, the most general sequential production environment. We first discuss how multi-purpose batch plants can be expressed using State-Task Network and Resource-Task Network representations through batch-based definition of states (resources) and tasks. We then develop two models based on each representation that account for limited intermediate storage, and discuss extensions such as limited shared resources and time-varying resource availability/cost. Finally, we present several case studies to illustrate the applicability and performance of the proposed models.

A multitasking continuous time formulation for short-term scheduling of operations in multipurpose plants

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.

An improved model for Heat Integration of intermittent process streams in multipurpose batch plants

This paper presents a mathematical technique for simultaneous Heat Integration (HI) and process scheduling in multipurpose batch plants. Taking advantage of the intermittent continuous behaviour of process streams during transfer between processing units, as determined by the production recipe, the presented formulation aims to maximise the coincidence of availability of hot and cold stream pairs with feasible temperature driving forces for heat recovery, whilst taking into consideration process scheduling constraints. Distinct from similar contributions in the published literature, time is treated as one of the key optimisation variables instead of a predefined parameter, in which case the production schedule is allowed to change. HI during stream transfer has the added benefit of shortened processing time, which invariably improves the throughput, as more batches are likely to be processed within a given time horizon, compared to conventional heating and cooling in situ. Application of the proposed model to a case study shows improvements of up to 50% in utility cost savings and more than two-thirds in product revenue. In addition, further analysis reveals that the use of only three additional heat exchangers can achieve a more than 80% improvement in profit.

Heat integration of intermittently available continuous streams in multipurpose batch plants

Presented in this paper is a mathematical technique for simultaneous heat integration and process scheduling in multipurpose batch plants. Taking advantage of the intermittent continuous behavior of process streams during transfer from one processing unit to another, as determined by the recipe, the presented formulation aims to maximize the coincidence of availability of hot and cold stream pairs with feasible temperature driving forces, while taking into consideration process scheduling constraints. Contrary to similar contributions in published literature, time is treated as one of the key optimization variables instead of a parameter fixed a priori. Heat integration during stream transfer has the added benefit of shortened processing time, which invariably improves throughput, as more batches are likely to be processed within a given time horizon, compared to conventional heating and cooling in situ. Application of the proposed model to a case study shows improvements of more than 30% in energy savings and up to 15% in product output.

Modeling and Optimization for Short-term Scheduling of Multipurpose Batch Plants

In the past two decades, short-term scheduling of multipurpose batch plants has received significant attention. Most scheduling problems are modeled using either state-task-network or resource-task-network (RTN) process representation. In this paper, an improved mixed integer linear programming model for short-term scheduling of multipurpose batch plants under maximization of profit is proposed based on RTN representation and unit-specific events. To solve the model, a hybrid algorithm based on line-up competition algorithm and linear programming is presented. The proposed model and hybrid algorithm are applied to two benchmark examples in literature. The simulation results show that the proposed model and hybrid algorithm are effective for short-term scheduling of multipurpose batch plants.

Simultaneous regular and non-regular production scheduling of multipurpose batch plants: A real chemical–pharmaceutical case study

Regular and non-regular production can often be found in multipurpose batch plants, requiring two distinct operating strategies: campaign and short-term production. This paper proposes a solution approach for simultaneous scheduling of campaign and short-term products in multipurpose batch plants. Regular products follow a cyclic schedule and must cover several product deliveries during the scheduling horizon, while non-regular products have a non-cyclic schedule. The proposed approach explores the Resource-Task Network (RTN) discrete-time formulation. Moreover, a rolling horizon approach, and reformulation and branching strategies have been applied to deal with the computational complexity of the scheduling problem. Real case instances of a chemical–pharmaceutical industry are solved, showing the applicability of the solution approach.

Design and Synthesis of Multipurpose Batch Plants Using a Robust Scheduling Platform

The increasing interest in multipurpose batch plants is evident, because of their inherent flexibility to cope with an ever changing market environment. These plants are easily reconfigured for product modifications, to cover a wide range of operating conditions. They are also suitable for producing different products within the same facility. In spite of this advantage, the design, synthesis, and scheduling of multipurpose batch plants can be a challenging task. This paper addresses design, synthesis, and scheduling simultaneously. It is known that the scheduling platform employed has a significant impact on the computational performance of the overall model in the design and synthesis of batch plants. The recent scheduling model that results in better computational efficiencies is extended to incorporate design and synthesis. Computational studies are presented to illustrate the effectiveness of the proposed model. A comparison with earlier formulations showed that better computational times and objective functions were obtained by this work.

A novel technique for prediction of time points for scheduling of multipurpose batch plants

This paper presents a mathematical technique for prediction of the optimal number of time points in short-term scheduling of multipurpose batch plants. The mathematical formulation is based on state sequence network (SSN) representation. The developed method is based on the principle that the optimal number of time points depends on how frequent the critical unit is used throughout the time horizon. In the context of this work, a critical unit refers to a unit that is most frequently used and it is active for most of the time points when it is compared to other units. A linear model is used to predict how many times the critical unit is used. In conjunction with knowledge of recipe, this information is used to determine the optimal number of time points. The statistical R2 value obtained between the predicted and actual number of optimal time points in all the problems considered was 0.998, which suggests that the developed method is accurate in determining optimal number of time points. Consequently this avoids costly computational times due to iterations. In the model by Majozi and Zhu (2001) the sequence constraint that pertains to tasks that consume and produce the same state, the starting time of the consuming task at time point p must be later than the finishing time of the producing task at the previous time point p−1. This constraint is relaxed by the proposed models if the state is not used at the current time point p. This relaxation gives a better objective value as compared to previous models. An added feature of the proposed models is their ability to exactly handle fixed intermediate storage (FIS) operational philosophy, which has proven to be a subtle drawback in published scheduling techniques.

S-graph Based Parallel Algorithm to the Scheduling of Multipurpose Batch Plants.

S-graph Based Parallel Algorithm to the Scheduling of Multipurpose Batch Plants.

Optimal Event Point Determination for Short-Term Scheduling of Multipurpose Batch Plants via Unit-Specific Event-Based Continuous-Time Approaches

In the past two decades, three types of continuous-time models have been developed for the short-term scheduling of multipurpose batch plants: sequence-based, slot-based, and event-based models. Both slot- and event-based models require an iterative procedure proposed by Ierapetritou and Floudas (Ind. Eng. Chem. Res. 1998, 37, 4341) to determine the number of event points or slots, which results in increased computational time and no optimal number of event points or slots in some cases. In this work, we first enhance the recently proposed three-index unit-specific event-based model developed by Shaik and Floudas (Ind. Eng. Chem. Res. 2009, 48, 2947) and extend it to handle different wait policies. Then, we develop a general framework to obtain the optimal number of event points where an iterative procedure is employed to obtain the maximum number of event points and determine the critical intermediate states. The approach proposed by Janak and Floudas (Comput. Chem. Eng. 2008, 32, 913) is used to obtain ...

A novel precedence-based and heuristic approach for short-term scheduling of multipurpose batch plants

Many continuous-time formulations have been proposed during the last decades for short-term scheduling of multipurpose batch plants. Although these models establish advantages over discrete-time representations, they are still inefficient in solving moderate-size problems, such as maximization of profit in long horizon, and minimization of makespan. Unlike existing literature, this paper presents a new precedence-based mixed integer linear programming (MILP) formulation for short-term scheduling of multipurpose batch plants. In the new model, multipurpose batch plants are described with a modified state-task network (STN) approach, and binary variables express the assignments and sequences of batch processing and storing. To eliminate the drawback of precedence-based formulations which commonly include large numbers of batches, an iterative procedure is developed to determine the appropriate number of batch that leads to global optimal solution. Moreover, four heuristic rules are proposed to selectively prefix some binary variables to 0 or 1, thereby reducing the overall number of binary variables significantly. To evaluate model performance, our model and the best models reported in the literature (S&K model and I&F model) are utilized to solve several benchmark examples. The result comparison shows that our model is more effective to find better solution for complex problems when using heuristic rules. Note that our approach not only can handle unlimited intermediate storage efficiently as well as the I&F model, but also can solve scheduling problems in limited intermediate storage more quickly than the S&K model.

Optimal Modeling of Simultaneous Design and Scheduling of Multipurpose Batch Plants over Multi-Period Production with Optimal Production Split Ratio

Optimal Modeling of Simultaneous Design and Scheduling of Multipurpose Batch Plants over Multi-Period Production with Optimal Production Split Ratio

Effective scheduling of a large-scale paint production system

Due to the large variety of options offered to customers, batch production schemes are highly accepted in the paint industry implying that scheduling plays an important role in optimal allocation of plant resources among multiple products. Since in a batch process, the cleaning of equipment units is the major source of waste, waste minimization is also to be taken into account in determining the schedule. The formerly developed S-graph framework [Sanmartí E, Holczinger T, Puigjaner L, Friedler F. Combinatorial framework for effective scheduling of multipurpose batch plants. AIChE Journal 2002;48(11):2557–70.] proved to be highly effective in solving multipurpose batch scheduling; it has now been specialized for solving paint production scheduling problems including waste minimization. The efficacy of the new approach is illustrated with the solution of large-scale paint production scheduling problems.