Short-term Scheduling Of Batch Plants Research Articles

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...

Rigorous Unit-Specific Event-Based Model for Short-Term Scheduling of Batch Plants Using Conditional Sequencing and Unit-Wait Times

Continuous-time models have evolved as a promising tool for formulating problems related to short-term scheduling. This article presents an analysis, advantages, and limitations of recent models proposed in the literature for short-term scheduling of batch plants based on unit-specific event-based time representation. The purpose of this study is to generalize and enhance previous unit-specific event-based scheduling models for efficient handling of various issues such as nonsimultaneous material transfers, comprehensive sequencing constraints for handling of different storage policies, unit-wait policies, and utility resources. Accordingly, a rigorous unit-specific event-based model has been proposed that allows for conditional sequencing of each production and consumption task, only if the material produced by a given production task is used by a given consumption task. The proposed approach leads to reduction in number of events, and the model can effectively handle scheduling problems with different storage policies: UIS, FIS, NIS, and ZW. It can can also handle different unit-wait policies. The proposed conditional sequencing concept is also extended for efficient handling of utility resources, thus resulting in further reduction in number of events required compared to the published literature.

Unification of STN and RTN based models for short-term scheduling of batch plants with shared resources

State-task-network (STN) and resource-task-network (RTN) representations are popularly used for formulating mathematical models of scheduling problems. In contrast to STN representation, RTN representation offers unified treatment for different resources such as processing and storage units, material states and utilities. In global-event (or single-time grid) based models processing tasks occurring in different units are aligned globally, hence, they explicitly do not distinguish handling of resources such as utilities and material states. While, unit-specific event (or multi-time grid) based models offer better computational performance due to requirement of lesser number of events, but there is no unified treatment for handling of utility or discrete resources due to heterogeneous location of events. Usually, global alignment is enforced for different tasks that use the same utility, while for material states unit-specific alignment is used. Hence, for unit-specific event-based models it is desirable to have a unified framework for handling of material states and utility resources, which, not only offers a unification of STN and RTN formulations, but, potentially can result in further reduction in the number of events required to find optimal solutions. In this work, we propose a unified framework and develop two unit-specific event-based approaches for STN and RTN representations by incorporating a novel resource balance that offers these two unifications. The key features of the proposed approach are: (i) all resources are treated in unified way for the first time, (ii) simplified handling of multiple orders using the concept of active task, (iii) handling of shared storage problems in non-aggregated storage tanks by considering explicit storage tasks. The proposed features are demonstrated on few benchmark examples from literature.

Improved three-index unit-specific event-based model for short-term scheduling of batch plants

Short-term scheduling of batch operations has been an important research area in the past two decades. Recently, Shaik and Floudas (Industrial and Engineering Chemistry Research, 2009, 48, 2947) proposed a novel unified model for short-term scheduling using unit-specific event-based continuous-time representation employing three-index binary and continuous variables. In their comparative study it was shown that the unified model has superior performance among all the models compared in their work. In this work, we present an improved model by taking advantage of the three-index variables and effectively incorporating the concept of active task leading to fewer constraints and big-M terms. We propose improvements in allocation, duration and sequencing constraints, and investigate the effect of big-M terms in several constraints to enable solution of large-scale problems. The computational performance of the proposed formulation is compared with the original three-index model through various examples drawn from literature including Westenberger–Kallrath challenging benchmark problem.

MILP Sensitivity Analysis for Short-Term Scheduling of Batch Plants under Uncertainty

In this paper, An integrated framework is developed to handle uncertainty in short-term scheduling based on the idea of inference-based sensitivity analysis for MILP problems and the utilization of a branch and bound solution methodology. The proposed method leads to the determination of the importance of different parameters and the constraints on the objective function and the generation and evaluation of a set of alternative schedules given the variability of the uncertain parameters. The main advantage of the proposed method is that no substantial complexity is added compared with the solution of the deterministic case because the only additional required information is the dual information at the leaf nodes of the branch-and-bound tree. Two case studies are presented to highlight the information extracted by the proposed approach and the complexity involved compared with parametric programming studies.

Short-Term Scheduling of Batch Plants with Parallel Reactors Forming Mobile Workgroups

We address the problem of short-term scheduling of parallel batch reactors followed by continuously operating finishing trains to form workgroups which is motivated by a real world problem at the Dow Chemical Co. The proposed MILP formulation is based on the recent planning model of Erdirik-Dogan and Grossmann (AIChE J. 2007, 53, 2284−2300) and features additional constraints for handling complex arrangements arising from the workgroups. Several examples are presented to illustrate the proposed model.

A Novel Particle Swarm Optimization Algorithm for Short-Term Scheduling of Batch Plants with Parallel Units

A Novel Particle Swarm Optimization Algorithm for Short-Term Scheduling of Batch Plants with Parallel Units

Unit-specific event-based continuous-time approach for short-term scheduling of batch plants using RTN framework

The problem of short-term scheduling of batch plants has received remarkable attention in the past two decades. The state-task-network (STN) and resource-task-network (RTN) process representations are extensively used in modeling scheduling problems. In this paper, we propose a new model to investigate the RTN representation for unit-specific event-based models. For handling dedicated finite storage, a novel formulation is proposed without the need for considering storage as a separate task. The performance of the proposed model is evaluated along with several other continuous-time models from the literature based on the STN and RTN process representations. The various models are assessed based on our implementations using several benchmark example problems from the literature. Two different objective functions, maximization of profit and minimization of makespan, are considered. Two storage policies, unlimited and dedicated finite storage cases are also considered.

Improving unit-specific event based continuous-time approaches for batch processes: Integrality gap and task splitting

In this work, we address a challenging issue in the area of batch processing scheduling, namely the ability to reduce or even close the integrality gap for large-scale scheduling problems. Because of the multipurpose and multiproduct characteristics of batch plants, their resulting scheduling problems can be highly combinatorial in nature with many variables and constraints. In order to help reduce this complexity, a number of preprocessing steps are performed and new sets of rigorous constraints are incorporated within a novel and effective continuous-time formulation for the short-term scheduling of batch plants. Several example problems are solved to demonstrate the effectiveness of the proposed algorithmic techniques. In addition, a new rigorous mathematical model is proposed to help reduce the complexity experienced in unit-specific event based, continuous-time formulations. A challenging benchmark problem involving several complicating features is solved for several demand instances in order to further demonstrate the effectiveness of the proposed approach.

Petri-net based formulation and algorithm for short-term scheduling of batch plants

Effective scheduling of operations in batch plants has a great potential for high economic returns, in which the formulation and optimal solution algorithm are the main issues of study. Petri-nets have proven to be a promising technique to solve many difficult problems associated with the modeling, formal analysis, design and coordination control of discrete event systems. One of the major advantages of using a Petri-net model is that the same model can be used for the analysis of behavioral properties and performance evaluation, as well as for the systematic construction of discrete event simulators and controllers. This paper aims to present a Petri-net based approach for the scheduling of operations in batch plants. Firstly, the short-term scheduling of batch plants is formulated using timed Petri-net. Secondly, the heuristic search algorithm for scheduling of batch plants is given, which is based on generating and checking the markings in the reachability tree of the Petri-net model. Finally, the novel formulation and algorithm are tested using two simulation case studies, and compared against traditional methods.

A hybrid MILP/CP decomposition approach for the continuous time scheduling of multipurpose batch plants

A hybrid Mixed-Integer Linear Programming (MILP)/Constraint Programming (CP) decomposition algorithm is proposed for the short-term scheduling of batch plants that rely on the State Task Network (STN) representation. The decisions about the type and number of tasks performed, as well as the assignment of units to tasks are made by the MILP master problem (MP). The CP subproblem checks the feasibility of a specific assignment and generates integer cuts for the master problem. A graph-theoretic preprocessing that determines time windows for the tasks and equipment units is also performed to enhance the performance of the algorithm. To exclude as many infeasible configurations as possible, three classes of integer cuts are generated. Various objective functions such as the minimization of assignment cost, the minimization of makespan for fixed demand and the maximization of profit for a fixed time horizon can be accommodated. Variable batch-sizes and durations, different storage policies, and resource constraints are taken into account. The proposed framework is very general and can be used for the solution of almost all batch scheduling problems. Numerical results show that for some classes of problems, the proposed algorithm can be two to three orders of magnitude faster than standalone MILP and CP models.

A New Simple Effective Continuous-time Model for Scheduling of General Batch Plants.

Batch processes are widely used in producing high-value chemical products for its good flexibility. The problem of short-term scheduling of batch plants is to determine the optimal utilization of available resources over a given time horizon. Models of most previous works in this domain rely on the definition of time slots or time events so that they involve many binary variables and constraints. In this paper, a new MILP model for scheduling of both multi-product and multi-purpose batch plants with unit-depended changeovers is introduced. Problems are described based on the concept of task in order to deal with complex instances. The proposed formulation uses a continuous time domain representation that does not rely on the definition of time slots or time events. Binary variables for sequencing are defined to indicate whether one task is prior to another in the processing sequence without concerning their accurate position. The model is also simplified by considering the specialty of symmetrical and complemental feature of the binary variables. In a result the number of both binary variables and constraints has been reduced significantly. Moreover, different heuristic rules for preordering can be flexibly embedded into the new model and directly assign the value of binary variables. Therefore much CPU time is saved even maybe without loss of rigorous optimality. Several case studies are presented that illustrate the efficiency of the new model. Comparisons with some previous works are also provided.

Petri-Net Based Modelling and Scheduling of Batch Processing Plants – A Heuristic Algorithm

Effective scheduling of operations in batch plants has a great potential for high economic returns, in which formulation and optimal solution algorithm are the main issues of study. This study aims to investigate petri-net based approaches to ultimately accommodate complex scheduling problems (such as mixed batch continuous plants) where traditional techniques have difficulties in dealing with. The timed petri-net based heuristic search algorithms for short-term scheduling of batch plants are explored. Theoretical results will be applied to the simulation case studies.

Short-term scheduling of batch plants with multiple intermediate due dates

The problem of short-term scheduling often involves the satisfaction of variable product demands at specific due dates within the time horizon under consideration. Ierapetritou and Floudas, [2, 3] presented a novel continuous time formulation to effectively address the problem of short-term scheduling in batch, continuous and mixed production facilities where product demands are specified at the end of time horizon. The primary objective of this paper is to extend the continuous time formulation so as to deal with intermediate due dates. The mathematical model is developed and the features of the problem are further exploited to result in the most efficient solution of the problem. Two examples are provided to illustrate the capabilities of the proposed approach.

Effective Continuous-Time Formulation for Short-Term Scheduling. 1. Multipurpose Batch Processes

During the last decade, the problem of production scheduling has been realized to be one of the most important problems in industrial plant operations especially when multipurpose/multiproduct batch processes are involved. This paper presents a novel mathematical formulation for the short-term scheduling of batch plants. The proposed formulation is based on a continuous time representation and results in a mixed integer linear programming (MILP) problem. The novel elements of the proposed formulation are (i) the decoupling of the task events from the unit events, (ii) the time sequencing constraints, and (iii) its linearity. In contrast to the previously presented continuous-time scheduling formulations, the proposed approach leads to smaller and simpler mathematical models which exhibit fewer binary and continuous variables, have smaller integrality gaps, require fewer constraints, need fewer linear programming relaxations, and can be solved in significantly less CPU time. Several examples are presented ...

STBS: A continuous-time MILP optimization for short-term scheduling of batch plants

This is a paper on mixed integer linear programming models for short-term scheduling of batch plants as described by Pinto and Grossmann (1995, 1996). The models rely on continuous-time representation and make use of pre-ordering constraints, which can be either imposed as a separate set of constraints or can be included in the underlying representation for the model. We also describe the computer interface STBS which automatically formulates the models and generates solution outputs such as Gantt charts and order paths. As shown in the results, problems up to 50 orders in 25 machines and five stages can be solved in approximately 20 min.

Short-term scheduling: New mathematical models vs algorithmic improvements

In this paper, a novel formulation is presented for the short-term scheduling of batch plants. The proposed formulation is based on a continuous time representation and results in a Mixed Integer Linear Programming (MILP) problem. In contrast to the previously published continuous-time scheduling formulations, the proposed approach leads to smaller and simpler mathematical models which exhibit fewer binary and continuous variables, have smaller integrality gaps, require fewer constraints, need fewer linear programming relaxations, and can be solved in significantly less CPU time. Several examples are presented that illustrate the effectiveness of the proposed formulation and comparisons with other approaches are provided.

An Alternate MILP Model for Short-Term Scheduling of Batch Plants with Preordering Constraints

An alternate model is presented when preordering constraints are imposed in the short term scheduling of batch plants. The idea is to include the assumption of preordering of orders to units in the underlying representation for the model, as opposed to including preordering as a separate set of constraints. The resulting model not only is conceptually simple but also results in shorter solution times.