基于Petri网的批处理调度研究

批处理过程存在于复杂的动态环境中,来自主客观的干扰及问题固有的易变性,会导致各种过程参数的变化,因此,需要研究对意外事件作出快速反应的动态调度方法,以捕捉生产环境的实时变化。该文针对批处理过程中最常出现的操作处理时间波动,提出了基于Petri网仿真技术的批处理过程动态调度方法。仿真结果表明,该方法能有效地改善调度性能,为批处理过程动态调度的研究提供了新思路。     

A fuzzy-mixed-integer goal programming model for a parallel-machine scheduling problem with sequence-dependent setup times and release dates

This paper presents a new mixed-integer goal programming (MIGP) model for a parallel-machine scheduling problem with sequence-dependent setup times and release dates. Two objectives are considered in the model to minimize the total weighted flow time and the total weighted tardiness simultaneously. Due to the complexity of the above model and uncertainty involved in real-world scheduling problems, it is sometimes unrealistic or even impossible to acquire exact input data. Hence, we consider the parallel-machine scheduling problem with sequence-dependent set-up times under the hypothesis of fuzzy processing time's knowledge and two fuzzy objectives as the MIGP model. In addition, a quite effective and applicable methodology for solving the above fuzzy model are presented. At the end, the effectiveness of the proposed model and the denoted methodology is demonstrated through some test problems.     

Scheduling of multi-component products in a two-stage flexible flow shop

In this research, the problem of scheduling and sequencing of two-stage assembly-type flexible flow shop with dedicated assembly lines, which produce different products according to requested demand during the planning horizon with the aim of minimizing maximum completion time of products is investigated. The first stage consists of several parallel machines in site I with different speeds in processing components and one machine in site II, and the second stage consists of two dedicated assembly lines. Each product requires several kinds of components with different sizes. Each component has its own structure which leading to difference processing times to assemble. Products composed of only single-process components are assigned to the first assembly line and products composed of at least a two-process component are assigned to the second assembly line. Components are placed on the related dedicated assembly line in the second phase after being completed on the assigned machines in the first phase and final products will be produced by assembling the components. The main contribution of our work is development of a new mathematical model in flexible flow shop scheduling problem and presentation of a new methodology for solving the proposed model. Flexible flow shop problems being an NP-hard problem, therefore we proposed a hybrid meta-heuristic method as a combination of simulated annealing (SA) and imperialist competitive algorithms (ICA). We implement our obtained algorithm and the ones obtained by the LINGO9 software package. Various parameters and operators of the proposed Meta-heuristic algorithm are discussed and calibrated by means of Taguchi statistical technique.     

含有AGV的柔性车间调度优化研究

实际车间生产中,为了实现自动化生产越来越多企业投资AGV（Automated guided vehicle）来搬运工件。为了研究AGV最优调度方案和最佳AGV数量,本文建立使用AGV搬运的柔性车间调度模型。针对该模型的特点,本文提出基于搬运工序、机床和AGV分配的粒子编码方式,并结合遗传算法的思想采用新的粒子群算法更新位置方式。通过数值算例验证了改进粒子群算法的有效性和可行性,并发现AGV符合边际效用递减规律,即随着AGV数量的增加,总加工时间减少,但每增加一台AGV缩短的时间变少。     

Modeling and Solving Lot-Splitting Scheduling Problem Based on Process

In flexible job-shop batch scheduling problem, the optimal lot-size of different process is not always the same because of different processing time and set-up time. Even for the same process of the same workpiece, the choice of machine also affects the optimal lot-size. In addition, different choices of lot-size between the constrained processes will impact the manufacture efficiency. Considering that each process has its own appropriate lot-size, we put forward the concept of scheduling with lot-splitting based on process and set up the scheduling model of lot-splitting to critical path process as the core. The model could update the set of batch process and machine selection strategy dynamically to determine processing route and arrange proper lot-size for different processes, to achieve the purpose of optimizing the makespan and reducing the processing batches effectively. The experiment results show that, comparing with lot-splitting scheduling scheme based on workpiece, this model optimizes the makespan and improves the utilization efficiency of the machine. It also greatly decreases the machined batches(42%) and reduces the complexity of shop scheduling production management.     

An improved heuristic for parallel machine weighted flowtime scheduling with family set-up times

This paper studies the identical parallel machine scheduling problem with family set-up times and an objective of minimizing total weighted completion time (weighted flowtime). The family set-up time is incurred whenever there is a switch of processing from a job in one family to a job in another family. A heuristic is proposed in this paper for the problem. Computational results show that the proposed heuristic outperforms an existing heuristic, especially for large-sized problems, in terms of both solution quality and computation times. The improvement of solution quality is as high as 4.753% for six-machine problem and 7.822% for nine-machine problem, while the proposed heuristic runs three times faster than the existing one.     

Soft computing for scheduling with batch setup times and earliness-tardiness penalties on parallel machines

A model for scheduling grouped jobs on identical parallel machines is addressed in this paper. The model assumes that a set-up time is incurred when a machine changes from processing one type of component to a different type of component, and the objective is to minimize the total earliness-tardiness penalties. In this paper, the algorithm of soft computing, which is a fuzzy logic embedded Genetic Algorithm is developed to solve the problem. The efficiency of this approach is tested on several groups of random problems and shows that the soft computing algorithm has potential for practical applications in larger scale production systems.     

考虑非确定加工时间的柔性作业车间调度问题研究

加工时间不确定的柔性作业车间调度问题已逐渐成为生产调度研究的热点。采用区间表示加工时间范围,利用时间Petri网建立区间柔性作业车间调度问题形式化模型,并运用网模型的状态类图进行可达性分析,计算出所有可行变迁触发序列。通过对触发序列的时序分析,提出一种有效的逆向分步法来构造触发序列的时间约束不等式,进而求解线性规划问题来获得最小完工时间下界(上界)的优化调度策略。最后利用实例分析验证了模型及所提方法的正确性和可行性,为实际的区间柔性作业车间调度问题提供有效方案。     

加工时间不确定的炼钢-连铸鲁棒优化调度方法

炼钢-连铸生产存在着复杂的物理和化学变化,加工时间在实际生产中呈现出较强的波动性,基于标准加工时间建立的调度方案难以满足实际生产需求.针对加工时间不确定的炼钢-连铸调度问题,采用鲁棒优化方法,构造“盒子+多面体”型不确定集处理加工时间信息,建立以总等待时间最小为目标的炼钢-连铸鲁棒优化调度模型.针对模型中存在两种不同类型决策变量的情况,即离散型的指派变量和连续型的鲁棒对等转换变量,结合两类变量特征提出一种混合编码遗传算法,并针对染色体的混合编码特征提出并行进化策略.算法中引入精英策略和自适应的调节参数方法,以提高搜索能力.最后基于不同规模的实际生产数据进行仿真实验,验证了鲁棒优化调度模型和算法的有效性.     

A new evolutionary clustering search for a no-wait flow shop problem with set-up times

This paper addresses the m-machine no-wait flow shop problem where the set-up time of a job is separated from its processing time. The performance measure considered is the total flowtime. A new hybrid metaheuristic Genetic Algorithm–Cluster Search is proposed to solve the scheduling problem. The performance of the proposed method is evaluated and the results are compared with the best method reported in the literature. Experimental tests show superiority of the new method for the test problems set, regarding the solution quality.     

面向铝挤压的作业排产优化

在深入研究铝挤压生产特点的基础上,以最小化加工总流经时间（total flow time,TFT）为目标建立了两类铝挤压作业排产优化模型,采用改进的人工蜜蜂群算法对其求解．该算法根据铝挤压排产问题的特点重新设计了解的表达与新解的产生方式．仿真实验结果表明,提出的方法能够有效减少产品加工的总流经时间．     

Strong NP-hardness of the single machine multi-operation jobs total completion time scheduling problem

We consider the single machine multi-operation jobs total completion time scheduling problem. Each job consists of several operations that belong to different families. In a schedule, each family of job operations may be processed in batches with each batch incurring a set-up time. A job completes when all of its operations have been processed. The objective is to minimize the sum of the job completion times. In the literature, the computational complexity of this problem is posed as open. We show that the problem is strongly NP-hard even when the set-up times are common and the processing time of each operation is 0 or 1.     

A bi-objective possibilistic programming model for open shop scheduling problems with sequence-dependent setup times, fuzzy processing times, and fuzzy due dates

We are concerned with an open shop scheduling problem having sequence-dependent setup times. A novel bi-objective possibilistic mixed-integer linear programming model is presented. Sequence-dependent setup times, fuzzy processing times and fuzzy due dates with triangular possibility distributions are the main constraints of this model. An open shop scheduling problem with these considerations is close to the real production scheduling conditions. The objective functions are to minimize total weighted tardiness and total weighted completion times. To solve small-sized instances for Pareto-optimal solutions, an interactive fuzzy multi-objective decision making (FMODM) approach, called TH method proposed by Torabi and Hassini, is applied. Using this method, an equivalent auxiliary single-objective crisp model is obtained and solved optimally by the Lingo software. For medium to large size examples, a multi-objective particle swarm optimization (MOPSO) algorithm is proposed. This algorithm consists of a decoding procedure using a permutation list to reduce the search area in the solution space. Also, a local search algorithm is applied to generate good initial particle positions. Finally, to evaluate the effectiveness of the MOPSO algorithm, the results are compared with the ones obtained by the well-known SPEA-II, using design of experiments (DOE) based on some performance metrics.     

A PTAS for parallel batch scheduling with rejection and dynamic job arrivals

In the parallel batch scheduling model, a group of jobs can be scheduled together as a batch while the processing time of this batch is the greatest processing time among its members; in the model of scheduling with rejection, any job can be rejected with a corresponding penalty cost added to the objective value. In this paper, we present a PTAS for the combined model of the above two scheduling models where jobs arrive dynamically. The objective is to minimize the sum of the makespan of the accepted jobs and the total penalty of the rejected ones. Our basic approaches are dynamic programming and roundings.     

Single-machine scheduling with sum-of-logarithm-processing-times-based learning considerations

Scheduling with learning effects has attracted growing attention of the scheduling research community. A recent survey classifies the learning models in scheduling into two types, namely position-based learning and sum-of-processing-times-based learning. However, the actual processing time of a given job drops to zero precipitously as the number of jobs increases in the first model and when the normal job processing times are large in the second model. Motivated by this observation, we propose a new learning model where the actual job processing time is a function of the sum of the logarithm of the processing times of the jobs already processed. The use of the logarithm function is to model the phenomenon that learning as a human activity is subject to the law of diminishing return. Under the proposed learning model, we show that the scheduling problems to minimize the makespan and total completion time can be solved in polynomial time. We further show that the problems to minimize the maximum lateness, maximum tardiness, weighted sum of completion times and total tardiness have polynomial-time solutions under some agreeable conditions on the problem parameters.     

Scheduling of parallel identical machines to maximize the weighted number of just-in-time jobs

We study the problem of nonpreemptively scheduling n jobs on m identical machines in parallel to maximize the weighted number of jobs that are completed exactly at their due dates. We show that this problem is solvable in polynomial time even if positive set-up times are allowed. Moreover, we show that if due date tolerances are permitted, then already the single-machine case is NP-hard even if all set-up times are zero and all weights are the same.Scope and purposeMost of the literature in the field of deterministic scheduling deals with regular measures of performance, that is with minimizing objective functions that are nondecreasing in job completion times. With the growing interest in just-in-time production, the demand for research into problems with irregular performance measures has considerably increased (see Baker and Scudder, Oper Res 38(1) (1990) 22). This note provides an efficient algorithm for finding nonpreemptive schedules that are optimal with respect to a special type of irregular performance measures in the case of identical machines in parallel.     

Hybrid genetic algorithms with dispatching rules for unrelated parallel machine scheduling with setup time and production availability

This article considers the unrelated parallel machine scheduling problem with sequence- and machine-dependent setup times and machine-dependent processing times. Furthermore, the machine has a production availability constraint to each job. The objective of this problem is to determine the allocation policy of jobs and the scheduling policy of machines to minimize the total completion time. To solve the problem, a mathematical model for the optimal solution is derived, and hybrid genetic algorithms with three dispatching rules are proposed for large-sized problems. To assess the performance of the algorithms, computational experiments are conducted and evaluated using several randomly generated examples.     

A dynamically scheduled parallel DSP architecture for stream flow programming

This paper presents a dynamically scheduled parallel DSP architecture for general purpose DSP computations. The architecture consists of multiple DSP processors and of one or more scheduling units. DSP applications are first captured by stream flow graphs, and then stream flow graphs are statically mapped onto a parallel architecture. The ordering and starting time of DSP tasks are determined by the scheduling unit(s) using a dynamic scheduling algorithm.The main contributions of this paper are summarized as follows:• A scalable parallel DSP architecture: The parallel DSP architecture proposed in this paper is scalable to meet signal processing requirements. For parallel DSP architectures with large configurations, the scheduling unit may become a performance bottleneck. A distributed scheduling mechanism is proposed to address this problem.• A mapping algorithm: An algorithm is proposed to systematically map a stream flow graph onto a parallel DSP architecture.• A dynamic scheduling algorithm: We propose a dynamic scheduling algorithm that will only schedule a node for execution when both input data and output storage space are available. Such scheduling algorithm will allow buffer sizes to be determined at compile time.• A simulation study: Our simulation study reveals the relationships among the grain-size, the processor utilization, and the scheduling capability. We believe these relationships have significant impact on parallel computer architecture design involving dynamic scheduling.     

Petri net modeling and deadlock analysis of parallel manufacturing processes with shared-resources

Multiple resource-sharing is a common situation in parallel and complex manufacturing processes and may lead to deadlock states. To alleviate this issue, this paper presents the method of modeling parallel processing flows, sharing limited number of resources, in flexible manufacturing systems (FMSs). A new class of Petri net called parallel process net with resources (PPNRs) is introduced for modeling such FMSs. PPNRs have the capacity to model the more complex resource-sharing among parallel manufacturing processes. Furthermore, this paper presents the simple diagnostic and remedial procedures for deadlocks in PPNRs. The proposed technique for deadlock detection and recovery is based on transition vectors which have the power of determining the structural aspects as well as the process flow condition in PPNRs. Moreover, the proposed technique for dealing with deadlocks is not a siphon-based thus the large-scale PPNRs for real-life FMSs can be tackled. Finally, the proposed method of modeling and deadlock analysis in the FMS having parallel processing is demonstrated by a practical example.     

A cyclic approach to large-scale short-term planning in chemical batch production

We deal with the scheduling of processes on a multi-product chemical batch production plant. Such a plant contains a number of multi-purpose processing units and storage facilities of limited capacity. Given primary requirements for the final products, the problem consists in dividing the net requirements for the final and the intermediate products into batches and scheduling the processing of these batches. Due to the computational intractability of the problem, the monolithic MILP models proposed in the literature can generally not be used for solving large-scale problem instances. The cyclic solution approach presented in this paper starts from the decomposition of the problem into a batching and a batch-scheduling problem. The complete production schedule is obtained by computing a cyclic subschedule, which is then repeated several times. In this way, good feasible schedules for large-scale problem instances are found within a short CPU time.