Scheduling Of Batch Processes Research Articles

Short-term Scheduling of Non-sequential Multipurpose Batch Processes with Transfer and Set-up Times Under Various Intermediate Storage Policies

In this paper, a mixed integer linear programming (MILP) model for short-term scheduling of non-sequential multipurpose batch processes is presented. The processes consist of a single production line, i.e. one unit per stage. The intermediate storage policies considered are unlimited intermediate storage (UIS), no intermediate storage (NIS), zero-wait (ZW) and finite intermediate storage (FIS) policies. Transfer and sequence dependent setup times are also taken into account under four intermediate storage policies. The objective of this study is to determine the optimal production sequence for minimizing makespan under the different storage policies. The basic idea of the proposed MILP model comes from the fact that the production sequence can be determined by comparing the orders of all pairs of products. In contrast to previously published models, the proposed model has fewer binary and continuous variables and fewer constraints, and can be solved in significantly less computational time. The effectiveness of the proposed formulation is illustrated by several examples, and the numerical results and comparisons are provided.

Batch-Processing Scheduling with Setup Times

The problem is to minimize the total weighted completion time on a single batch-processing machine with setup times. The machine can process a batch of at most B jobs at one time, and the processing time of a batch is given by the longest processing time among the jobs in the batch. The setup time of a batch is given by the largest setup time among the jobs in the batch. This batch-processing problem reduces to the ordinary uni-processor scheduling problem when B = 1. In this paper we focus on the extreme case of B = +∞, i.e. a batch can contain any number of jobs. We present in this paper a polynomial-time approximation algorithm for the problem with a performance guarantee of 2. We further show that a special case of the problem can be solved in polynomial time.

Receiver set partitioning and sequencing for multicasting traffic in a WDM lightwave single-hop network

This paper considers a receiver set partitioning and sequencing problem in a wavelength division multiplexing single-hop lightwave network for multicasting traffic. The problem is analysed in the approach of uncapacitated single batch-processing machine scheduling. In the analysis, several solution properties are characterized with respect to a mean flow time measure, based upon which two heuristic algorithms are developed, along with a dynamic programming algorithm. Several numerical experiments show that the heuristic algorithms generate good schedules. The problem is extended to consider two measures simultaneously including the mean flow time and the number of transmissions, for which the proposed algorithms also perform well.

Simple Continuous-Time Formulation for Short-Term Scheduling of Batch and Continuous Processes

A new and simple general mathematical formulation for scheduling multipurpose plants involving batch and/or continuous processes, based on the resource−task network (RTN) representation, is presented. The formulation uses a uniform-time-grid continuous-time representation and results in a very efficient mixed integer linear programming model that can be solved to optimality for a given number of event points. The performance of the formulation is illustrated through the solution of two case studies that have been thoroughly examined in the literature: the first involves a continuous plant and is solved for three different storage policies, and the second concerns a batch plant. The formulation is shown to compare favorably to existing continuous-time formulations. More specifically, a new optimal solution is obtained for the finite intermediate storage scenario of the first case that is also a global optimal solution.

Incorporating heat integration in batch process scheduling

This work presents a methodology for incorporating heat integration in batch process scheduling. The formerly introduced S-graph approach [AIChE J. 48 (2002) 2557–2570] for solving multipurpose scheduling problems is proved to be appropriate for the representation of both scheduling problems and the corresponding heat exchanger network synthesis problem. The proposed procedure is based on the branch-and-bound framework, where two optimisation problems, the scheduling and the heat integration one, are considered simultaneously instead of consecutively. This method is primarily based on combinatorics and combinatorial algorithms. Solution of several examples illustrates the efficiency of the proposed approach and the benefits of considering heat exchanger network synthesis while scheduling batch processes.

A New Algorithm for Cyclic Scheduling and Design of Multipurpose Batch Plants

Many researchers have studied the scheduling, planning, and design of multipurpose batch processes. However, not so many studies have treated design and scheduling or design and planning simultaneously. The complexity of these systems stems from the fact that plant configuration must be determined for the purpose of process scheduling, yet scheduling must be done to devise the plant configuration. In the present study, a new algorithm for determining the best multipurpose scheduling and plant configuration is suggested. Since the objective function of the problem is nonlinear, it is linearized using a separable programming method. The proposed method consists of a number of procedures. First, a feasible configuration is obtained. Next, both the optimum equipment size and cyclic scheduling are determined for the plant configuration obtained in the first procedure. Last, the evolutionary design method proposed by Fuchino et al.(J. Chem. Eng. Jpn. 1994, 27, 57−64) is used to find the solution that minimizes the total cost. The efficacy of the proposed approach is demonstrated in three examples. Usually, equipment sizes are considered by a continuous variable in mixed integer linear programming and task processing time is assumed to be constant. However, most types of equipment are manufactured only in discrete volume classes. In addition, processing times are dependent on batch sizes. Hence, to apply the optimization methods developed here to real industries, the method was modified such that the volumes of equipment are considered as discrete variables and the processing time is a function of batch size.

An MILP Continuous-Time Framework for Short-Term Scheduling of Multipurpose Batch Processes Under Different Operation Strategies

This work introduces a novel MILP continuous-time framework to the optimal short-term scheduling of non-sequential multipurpose batch processes with intermediate storage vessels. It is based on a problem representation that describes the batch sequence at any processing/storage unit by providing the full set of predecessors for every batch. Different operation modes can be considered by making minor changes in the problem model. The proposed framework can also handle sequence-dependent changeovers as well as multiple storage tanks available to receive material from one or several processing units. Three example problems involving up to fifteen batches and six processing tasks were successfully solved. Compared with previous work, a drastic reduction in both problem size and CPU time has been achieved.

A New Framework for Batch Process Optimization Using the Flexible Recipe

Batch processes are characterized by a high degree of flexibility that can be appropriately exploited to obtain a maximum production profit. In principle, the nominal production recipe assumes an optimum balance between quality and costs for batches of products. However, in practice, this optimum performance is achieved only when this balance is extended to management of the entire batch plant. In this work, a framework is presented that fully exploits this inner flexibility of batch processes at the plant level. The framework considers a batch recipe model that interacts with a plant-wide model to constitute the so-called flexible recipe model. First, the potential use of this framework is shown by integrating a general multipurpose batch process scheduling algorithm into a general linear recipe model. Next, this framework is illustrated in practice using a real industrial scenario that exhibits complex recipe behavior. Finally, the benefits of considering the flexible recipe concept for the scheduling of batch processes are discussed.

Continuous-Time Optimization Approach for Medium-Range Production Scheduling of a Multiproduct Batch Plant

The medium-range production scheduling problem of a multiproduct batch plant is studied. The methodology consists of a decomposition of the whole scheduling period to successive short horizons. A mathematical model is proposed to determine each short horizon and the products to be included. Then a novel continuous-time formulation for short-term scheduling of batch processes with multiple intermediate due dates is applied to each time horizon selected, leading to a large-scale mixed-integer linear programming (MILP) problem. Special structures of the problem are further exploited to improve the computational performance. An integrated graphical user interface implementing the proposed optimization framework is presented. The effectiveness of the proposed approach is illustrated with a large-scale industrial case study that features the production of 35 different products according to a basic three-stage recipe and its variations by sharing 10 pieces of equipment.

Optimal Scheduling of the Single Line Multi-purpose Batch Process with Re-circulation Products.

The semi-conductor integrated circuit electronic devices process has many re-circulation production paths through the stages of product manufacturing. These kinds of processes can be defined as the multi-purpose batch process with re-circulation products if they produce more than two products. In this paper, we have developed the completion time algorithms for a single line multi-purpose batch process including re-circulation products with consideration of the non-zero set-up times and transfer times. We also developed the optimization method, genetic algorithm, for optimal scheduling of a multi-purpose batch process including re-circulation products. Several randomly generated examples were tested using the proposed algorithm, and the Gantt chart results are presented. We used Genetic Algorithm for solving the scheduling problems, and optimal solutions are also presented.

バッチプロセスにおける制御用処方情報とスケジューリング用情報の一元管理方法

バッチプロセスにおける制御用処方情報とスケジューリング用情報の一元管理方法

A Novel Nonuniform Discrete Time Formulation for Short-Term Scheduling of Batch and Continuous Processes

We propose a novel nonuniform time discretization method (NUDM) formulation for a short-term scheduling problem of batch and continuous operations. It aims to reduce the size of resultant MILP models by avoiding the use of a high dimensioned task-time matching binary variable defined in previous NUDM approaches. We devised several efficient constraints, with subdivided binary variables assigned to the start, process, and end event of each task. Several types of examples show that the proposed formulation is both general and efficient. For instance, we discuss fixed and variable processing time problems, and a sequence-dependent setup-time problem. A simple optimization algorithm tailored for a periodic scheduling problem is also proposed.

Optimal control of large-scale batch production by evolutionary computation

The common mathematical programming approach to the short-term scheduling and control of batch processes often leads to nonstandard NP-complete mixed integer nonlinear programming (MINLP) problems. It is shown that the scheduling problem can also be formulated as an optimal control problem. By the utilization of a simulation model of the process optimal operational schedules can then be found by the methods of evolutionary computation. The new approach is demonstrated by the optimization of the schedule of batches in a model of a chemical process.

A genetic algorithm of optimal scheduling for multi-purpose batch process with re-circulation products

In this paper we have developed the completion times algorithms of single line multi-purpose batch process including re-circulation products under consideration of the non-zero set-up times and transfer times. We also developed the optimization method, genetic algorithm, for optimal scheduling of mUlti-purpose batch process including re-circulation products. Finally the performance of the proposed algorithms was tested by several randomly generated examples and the Gantt chart results are presented. We used Genetic Algorithm for solving the scheduling problems and optimal solutions are also presented.

An Improved RTN Continuous-Time Formulation for the Short-term Scheduling of Multipurpose Batch Plants

This paper presents an improved general mathematical programming formulation for optimal scheduling of batch processes based on the resource−task network (RTN) representation. The formulation uses a continuous-time representation and results in a mixed integer linear programming problem. It is a relaxation of the problem presented by Schilling (Schilling, G. Optimal Scheduling of Multipurpose Plants. Ph.D. Thesis, University of London, London, U., K., 1997). By allowing, if possible, finite storage within the processing tasks resource equipments of the involved raw materials and/or products, the proposed approach leads to simpler and less degenerate mathematical models. These models can be solved in significantly less CPU time, when compared to other RTN continuous-time formulations. Three published example problems are presented to illustrate the effectiveness of the proposed formulation. Finally, we show that the STN-based continuous-time scheduling formulation of Ierapetritou and Floudas (Ierapetritou,...

Batch process schedule optimization under parameter volatility

A general strategy to treat the uncertainties in parameters of batch process scheduling has been developed. The strategy consists of three algorithms: flexible planning, flexible scheduling and reactive schedule adaptation. In this paper, we introduce the flexible scheduling and the reactive schedule adaptation algorithms. The flexible scheduling algorithm is based on both a Monte Carlo simulation and a simulated annealing. It can deal with multiple uncertain parameters and any type of probability density function for the uncertain parameter. We seek the flexible schedule that maximizes the expected profit, including net present values of products less raw material and processing costs, as well as due date penalties, inventory costs and setup costs. In reality, the values of uncertain parameters always change after the batch process schedule and plan are set up. Since the flexible schedule has periods of free time that can be used to accommodate uncertainties during the actual production, the reactive schedule adaptation algorithm can modify the flexible schedule in response to any change in an uncertain parameter with little or no penalty. This algorithm finds a new optimal or suboptimal solution under the new condition by using a combination of different local search methods, which are described.

Scheduling of non-sequential multipurpose batch processes under finite intermediate storage policy

In this study, we present a mathematical model for optimal scheduling of non-sequential multipurpose batch processes under finite intermediate storage (FIS) policy. In non-sequential multipurpose batch processes, the production routes of products may be different from one another and may be in opposite direction. Consequently, in order to reduce idle time of units and to raise the efficiency of process, we have to make operation sequences of products in each unit different by considering the production route of each product. For the formulation of this problem, we represented the starting and finishing time of a task in each unit with two coordinates. One is based on products, and the other is based on operation sequences. Then, we matched the variables used in the two coordinates into one with binary variables and logical constraints. We formulated this problem as an MILP model. Compared with Jung, J. H., Lee, H., Yang, D. R. and Lee, I. (1994) [Completion times and optimal scheduling for serial multi-product processes with transfer and setup times in zero wait (ZW) policy. Computers & Chemical Engineering, 18(6), 537] and Kim, M. S., Jung, J. H. and Lee I. (1996) [Optimal scheduling of multiproduct batch processes for various intermediate storage policies. Industrial Engineering & Chemical Research, 27, 1840] who used an MINLP model for multiproduct scheduling problems, we su9ggest an MILP model, even though we handle sequence dependent setup times in multipurpose processes. Therefore, the proposed model can guarantee the optimality of the solutions. We applied this model to two examples to show the effectiveness of the model. The MILP solver we used to solve these problems is GAMS/ OSL and H/W is IBM RS/6000 (model 350).

Intermediate storage tank operation strategies in the production scheduling of multi-product batch processes

Multi-product batch processes use intermediate storage tanks to increase plant productivity and operational efficiency. In this paper, relations are developed for production scheduling models of the multi-product batch processes with storage time constraints of the intermediate storage tank. Numerical formulas are obtained to determine the makespan and the completion times of products on each unit. These results are extended to accommodate the general serial process networks with storage time and the product constraints of the intermediate storage tank. Next, the effects of the location and the number of the intermediate storage tank on the production scheduling are considered. From the above analysis, a MIPL model to find the maximum makespan is proposed. Applications of the developed model are presented with an example.

Completion times algorithm and optimal scheduling of single line multi-purpose batch process

For study of engineering facts, generally the operation of batch plants was classified into two types. One is the operation of multi-product batch process which produce multiple products with the same processing paths, the other is that of multi-purpose batch process which produce multiple products through the different production routes ( Reklaitis, (1990)). Also, according to Voudouris (1996), the multi-purpose batch plants are divided into two categories, sequential plants and non-sequential batch plants. In this paper we develop the completion times algorithm of nonsequential multi-purpose batch plants which have one unit in each stage under UIS policy. We also propose an efficient scheduling method for those plants. The proposed scheduling method composed two step approaches. In the first step, modified-RAES heuristics for initial solution of multi-purpose batch process scheduling was developed. At the second step, we suggested the Modified Simulated Annealing (MSA) method with adjusting parameters of Simulated Annealing (SA) by Ku and Karimi (1991). To evaluate the performance and efficiency of this study, we have tested about 200 problems and could get the outperformed results.

Continuous Time Representation Approach to Batch and Continuous Process Scheduling. 1. MINLP Formulation

The problem of decision timing in the context of batch and continuous process scheduling is addressed in this paper. Representation of time in any scheduling model affects the number of integer variables and the convexity of the model. The usual procedure in batch and continuous process scheduling is to divide the scheduling interval into equal size intervals so as to achieve the required accuracy. This construction generates a formulation with a potentially very large number of binary variables. In this paper, the time events arising in the schedule are modeled directly, and thus the use of binary variables over periods during which no real changes in system state occur is avoided. Furthermore, such a representation of time offers the potential for direct integration of operations scheduling and control which is difficult to achieve in the usual equal size interval approach. The problem is formulated as a mixed integer nonlinear program (MINLP). Issues pertaining to the efficient solution of this problem...