Scheduling Of Batch Plants Research Articles

Multicut logic‐based Benders decomposition for discrete‐time scheduling and dynamic optimization of network batch plants

AbstractThis study presents the first application of a logic‐based Benders decomposition (LBBD) technique in the field of simultaneous scheduling and dynamic optimization (SSDO), applied to network batch processes with a discrete‐time scheduling formulation. The proposed algorithm employs neighborhood information of ordered discrete decisions (e.g., batching variables) to generate cuts, rather than relying on traditional cut generation techniques based on dual information that are implemented in generalized Benders decomposition (GBD) algorithms. The proposed algorithm relies on solving multiple subproblems per iteration, which is a feature that allows the generation of multiple cuts per iteration thus producing accurate approximations of the objective function in shorter computational times. This results in the herein proposed multicut logic‐based discrete Benders decomposition (MLD‐BD) algorithm, which enables features such as a pruning strategy, and a cut‐off technique. Two case studies are used to demonstrate the computational advantages of the MLD‐BD framework against GBD and heuristic methodologies.

A time-bucket MILP formulation for optimal lot-sizing and scheduling of real-world chemical batch plants

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.

Machine Learning and Inverse Optimization for Estimation of Weighting Factors in Multi-Objective Production Scheduling Problems

In recent years, scheduling optimization has been utilized in production systems. To construct a suitable mathematical model of a production scheduling problem, modeling techniques that can automatically select an appropriate objective function from historical data are necessary. This paper presents two methods to estimate weighting factors of the objective function in the scheduling problem from historical data, given the information of operation time and setup costs. We propose a machine learning-based method, and an inverse optimization-based method using the input/output data of the scheduling problems when the weighting factors of the objective function are unknown. These two methods are applied to a multi-objective parallel machine scheduling problem and a real-world chemical batch plant scheduling problem. The results of the estimation accuracy evaluation show that the proposed methods for estimating the weighting factors of the objective function are effective.

Cyclic scheduling and heat integration of batch process: Design of heat storage vessels

Scheduling over longer time horizons has limitations such as large problem size and computational complexity. Therefore, there is universal concern to establish novel modeling approaches to efficiently manage various complex characteristics. In this work, a rigorous Unit Specific Event Based model (USEB) is proposed for long-term scheduling of batch plants. The proposed approach addresses the complete scheduling of long-term operational horizon by considering start-up, cycle and finishing periods. The start-up period takes care of intermediate material states requirement at the beginning of first cycle and finishing period effectively utilizes the leftover intermediate states in final cycle. Using active task concept, the cyclic scheduling, direct and indirect heat integration possibilities are accurately modelled by considering design of heat storage vessels. This comprehensive computational approach highlights the importance of judicious use of direct and indirect heat integration in process industries and cyclic scheduling for complex and long term scheduling problems.

Novel hybrid discrete differential evolution algorithm for the multi-stage multi-purpose batch plant scheduling problem

The multi-stage multi-product batch plant scheduling problem is an important part of batch chemical industry scheduling problems. Different from the multi-purpose batch scheduling problem, this problem can be characterized by multiple stages with non-identical parallel units, and multiple batches of customer orders. Numerous methodologies for this problem have been investigated to addressing scheduling cases of different production systems in the past two decades. This paper focus on the large-scale batch plant scheduling problem by minimizing the make-span in the scheduling horizon. And a novel hybrid discrete differential evolutionary algorithm is proposed to handle this problem. First, a novel two-line encoding scheme is constructed based on discrete and continuous variables. The sequence of orders is represented by a time-based representation method. Second, two novel mutation methods are proposed within the framework of encoding method. Two methods provide multiple search directions which helps improve the exploration ability and diversity of the population. At last, two local permutation methods are applied to improve the local optimal for the algorithm. The proposed work is tested through several real industrial instances with different sizes and characteristics by comparing with mixed integer linear programming method and meta-heuristic algorithms. The improvement of proposed work is also analyzed by the instances. The results report the efficiency and effectiveness of the novel proposed evolutionary algorithm in solving large scale multi-stage multi-product batch plant scheduling problem.

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...

Integration of Scheduling and Control Under Stochastic Parametric Uncertainty with Varying Unit Operation Times for Chemical Batch Plants: A Back-Off Approach

Abstract A new back-off methodology is presented in this work as an approach for solving MIDO formulations arising for the optimal scheduling and control of flow-shop batch plants under stochastic parametric uncertainty. The proposed algorithm decomposes the MIDO problem into a scheduling problem, a dynamic optimization problem and a unit time operation minimization problem. These problems are solved iteratively using back-off terms. Parametric uncertainty is modeled using statistical distribution functions and are embedded in the algorithm to ensure dynamic feasibility of the optimal control actions under stochastic realizations in those parameters. The proposed algorithm identifies scheduling and control decisions offline. To exemplify this methodology, the integration of scheduling and control of a flow-shop batch plant is considered. The results show that unit operation times chosen from optimization are better suited to accommodate stochastic parametric uncertainty while the control actions enforce process operational and product quality constraints at reasonable costs.

A simple unit specific event based modeling framework for short term scheduling and heat integration of batch plants: Design and optimization of heat storage vessels

Energy conservation has been one of the prime research objectives of the global scientific community. Heat integration has been a promising intensification technique for energy conservation in chemical industries. In this work, a simple unit-specific event-based framework is proposed for short term scheduling and heat integration. Using the concept of active task, various modelling issues such as task alignments, energy balances, direct and indirect heat integrations have been handled precisely with minimum number of equations and variables. The effect of the amount of thermal fluid, initial temperature and number of storage vessels on profit is systematically analyzed. The accuracy of the proposed framework is demonstrated using three benchmark examples. The proposed model could effectively incorporate the direct and indirect heat integration and external utility usage. The computational results show that this integration leads to an optimum of two heat storage vessels as against three reported by Sebelebele and Majozi (2017).

Cooperative hybrid evolutionary algorithm for large scale multi-stage multi-product batch plants scheduling problem

As an important part of batch chemical industry scheduling problems, the multi-stage multi-product batch plant scheduling problem (MMSP) has been widely studied for decades. This problem is characterized by multiple stages with non-identical parallel units and operate based on customer orders. In this paper, we focus on the large scale MMSP and treat the minimization of make-span as the objective function. An efficient cooperative hybrid evolutionary algorithm is proposed based on the framework of cooperative co-evolution. First, a novel two-line encoding scheme is developed to represent the unit assignment and sequencing for orders respectively. Second, modified estimation of distribution algorithm (EDA) and differential evolutionary (DE) operations are proposed according to the feature of MMSP. EDA operation with a novel population-based incremental learning strategy is applied to handle the unit assignment variables. And novel DE operation based on a novel encoding method is adopted to deal with sequence variables. Then, two selection strategies are applied to preserve optimal and sub-optimal solutions for the proposed algorithm. The critical path based local search algorithm is adopted to further improve the efficiency of local optimization. The proposed algorithm has been tested by several instances with different sizes and characteristics. The numerical results and comparisons show that the proposed work is very competitive in solving large scale MMSP.

A comprehensive framework for synthesis and design of heat-integrated batch plants: Consideration of intermittently-available streams

Significant opportunities for energy savings in batch plants exist through Heat Integration of intermittently-available material transfer streams between processing and storage units. Such opportunities may, however, be limited by the structure of the process flowsheet and the scheduling in place. This work presents results obtained when the design, scheduling and Heat Integration of multipurpose batch plants are carried out simultaneously. A rigorous stream-task-oriented scheduling formulation is presented, which enables explicit description of the movements of the intermittently-available streams. This thorough treatment of streams opens up more degrees of freedom than realised in previous stream Heat Integration formulations. On such a basis, design and Heat Integration constraints are added, to result in a mixed integer nonlinear programming formulation. The optimisation objective is to maximise annual net profit, which is a trade-off between production throughput, capital costs, and operational costs arising from hot and cold utility consumption. When applied to a literature example, results show higher annual net profit and reduction in utility costs by as much as 15%, compared to when each of the design, scheduling and Heat Integration steps are carried out in sequence.

Biogeography-based optimization algorithm for large-scale multistage batch plant scheduling

The batch process is characterized by many varieties, small batches, redundant production equipment, flexible production process, and high-added-value products. This process is widely used in chemical, plastic, rubber, pharmaceutical, fine chemical, metallurgical, steel, food, and other industries. The optimized scheduling scheme of the batch process can effectively enhance enterprise competitiveness and improve economic benefits. Multistage Multiproduct Scheduling Problem (MMSP) is an important branch of batch scheduling problems. It is difficult to solve MMSP within a reasonable time by traditional mathematical programming, because once the scale of scheduling problems increases, the solution space expands exponentially. This study proposes a metaheuristic approach based on a time key biogeography-based optimization algorithm to solve MMSP. This new time key representation contains two vectors, which represent the processing sequence and equipment allocation of orders respectively. In accordance with the time information in the new representation, we add the preference of equipment processing time to migration and calculate the probability of every mutation value. In addition, the elite solution is combined with the active scheduling technique and modified Nawaz-Enscore-Ham (NEH) algorithm to improve the search accuracy of the proposed algorithm. To test the performance of Improved Time Key Biogeography-Based Optimization (Improved-TKBBO) algorithm, its results are compared with computational results of mathematical programming, Genetic Algorithm (GA), and Line-up Competition Algorithm (LCA). Simulation results show that the proposed Improved-TKBBO can solve the large-scale MMSP with non-identical parallel units effectively.

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.

Simultaneous Scheduling and Heat Integration of Batch Plants Using Unit-Specific Event Based Modelling

AbstractOver the past few decades of sustainable development, energy savings in batch processing facilities has played a vital role. The increasing trend in production of high value and low volume products in food, pharmaceutical industries and fine/specialty chemicals is driving the development of material, energy and water integrated scheduling techniques for multiproduct/multipurpose batch plants. In the present study, a three index Unit Specific Event Based (USEB) model is proposed for the simultaneous short-term scheduling and heat integration of batch plants. A mixed integer linear programming (MILP) model is proposed to handle direct heat integration. The performance of the proposed model is evaluated by considering two benchmark examples.

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.

Decomposition approaches for the design and scheduling of multiproduct multistage batch plants with parallel lines

Multiproduct chemical batch plants, often equipped with parallel production lines, are facilities where similar products are produced by sharing available equipment and time. Hence, when designing such plants, the operational use should be considered simultaneously. In this paper, the design and scheduling problem of a batch plant with parallel lines is addressed, using the Resource-Task Network formulation. The proposed mixed-integer linear programming model aims at minimising total costs through the optimisation of the number of lines to install, their design and the number, size and timings of the batches of every product on the installed lines. Besides an integral (exact) approach, we applied three decomposition approaches to tackle the computational complexity associated with this problem: line decomposition, bottleneck decomposition and a combination of both. Through several examples, it is shown that all three decomposition approaches reduce the computation times significantly compared to the integral approach, while obtaining (near) optimal solutions.

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.

Integration between Dynamic Optimization and Scheduling of Batch Processes under Uncertainty: A Back-off Approach

Abstract The aim of this study is to present a decomposition algorithm that employs a new back-off methodology to consider stochastic-based parameter uncertainty for the integration of dynamic optimization and scheduling of multi-unit batch plants. This is achieved by solving a series of optimization problems involving scheduling and control decisions. Simulations based on Monte Carlo sampling techniques are used to propagate uncertainty into the system and determine back-off terms for the process operational constraints. At each step in the algorithm, back-off terms are updated such that the system moves away from the nominal solution until a convergence criterion is met, obtaining a solution that satisfies constraints up to a user-defined probability limit. This algorithm, when applied to a multi-product multi-unit batch plant, produces an optimal schedule and control profiles that remain dynamically feasible in the presence of stochastic-based uncertain parameters.

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.

Short-Term Scheduling of Batch Plants: Reformulation for Handling Material Transfer at the Same Event

This work presents a new variant of a unit-specific event-based model for short-term scheduling of batch plants. The motivation behind the proposed model is to further reduce number of events necessary to efficiently solve a given scheduling model. The main novelty in the proposed formulation is that the production and consumption tasks of each intermediate state are modeled to take place at the same event, in contrast to existing batch scheduling models where the consumption tasks normally start at the next event compared to the production tasks. This is the first time such a feature has been attempted in batch process scheduling, although it has been done in scheduling of continuous plants. Also, this is the first attempt where we are able to model the unit-specific events in their true sense, where the first event in each unit actually takes up the first event. The model is primarily applicable and useful for problems involving no recycle streams, although a hybrid approach has been suggested for probl...

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.