Two-machine, no-wait job shop problem with separable setup times and single-server constraints

No-wait job shop scheduling problems refer to the set of problems in which a number of jobs are available for processing on a number of machines in a job shop context with the added constraint that there should be no waiting time between consecutive operations of the jobs. In this paper, a two-machine, no-wait job shop problem with separable setup times and a single-server constraint is considered. The considered performance measure is the makespan. This problem is strongly NP-hard. A mathematical model of the problem is developed and a number of propositions are proven for the special cases. Moreover, a genetic algorithm is proposed in this paper to find the optimal (or near-optimal) solutions. In order to evaluate the developed algorithm, a number of small instances are solved to optimality using the developed mathematical model. The proposed algorithm is able to find the optimal solution of all of these cases. For larger instances, the developed algorithm has been compared with the 2-opt algorithm as well as a proposed lower bound. Computational results show the efficiency of the proposed algorithm in generating good quality solutions compared to the developed lower bounds and 2-opt algorithm.     

Application of chance-constrained programming for stochastic group shop scheduling problem

In this paper, we study a group shop scheduling (GSS) problem subject to uncertain release dates and processing times. The GSS problem is a general formulation including the other shop scheduling problems such as the flow shop, the job shop, and the open shop scheduling problems. The objective is to find a job schedule which minimizes the total weighted completion time. We solve this problem based on the chance-constrained programming. First, the problem is formulated in a form of stochastic programming and then prepared in a form of deterministic mixed binary integer linear programming such that it can be solved by a linear programming solver. To solve the problem efficiently, we develop an efficient hybrid method. Exploiting a heuristic algorithm in order to satisfy the constraints, an ant colony optimization algorithm is applied to construct high-quality solutions to the problem. The proposed approach is tested on instances where the random variables are normally, uniformly, or exponentially distributed.     

Pareto archived simulated annealing for job shop scheduling with multiple objectives

In this paper, the job shop scheduling problem is studied with the objectives of minimizing the makespan and the mean flow time of jobs. The simultaneous consideration of these objectives is the multi-objective optimization problem under study. A metaheuristic procedure based on the simulated annealing algorithm called Pareto archived simulated annealing (PASA) is proposed to discover non-dominated solution sets for the job shop scheduling problems. The seed solution is generated randomly. A new perturbation mechanism called segment-random insertion (SRI) scheme is used to generate a set of neighbourhood solutions to the current solution. The PASA searches for the non-dominated set of solutions based on the Pareto dominance or through the implementation of a simple probability function. The performance of the proposed algorithm is evaluated by solving benchmark job shop scheduling problem instances provided by the OR-library. The results obtained are evaluated in terms of the number of non-dominated schedules generated by the algorithm and the proximity of the obtained non-dominated front to the Pareto front.     

Makespan minimization in a job shop with a BPM using simulated annealing

A scheduling problem commonly observed in the metal working industry has been studied in this research effort. A job shop equipped with one batch processing machine (BPM) and several unit-capacity machines has been considered. Given a set of jobs, their process routes, processing requirements, and size, the objective is to schedule the jobs such that the makespan is minimized. The BPM can process a batch of jobs as long as its capacity is not exceeded. The batch processing time is equal to the longest processing job in the batch. If no batches were to be formed, the scheduling problem under study reduces to the classical job shop problem with makespan objective, which is known to be nondeterministic polynomial time-hard. A network representation of the problem using disjunctive and conjunctive arcs, and a simulated annealing (SA) algorithm are proposed to solve the problem. The solution quality and run time of SA are compared with CPLEX, a commercial solver used to solve the mathematical formulation and with four dispatching rules. Experimental study clearly highlights the advantages, in terms of solution quality and run time, of using SA to solve large-scale problems.     

考虑工序相关性的动态Job shop调度问题启发式算法

提出一类考虑工序相关性的、工件批量到达的动态Job shop 调度问题,在对工序相关性进行了定义和数学描述的基础上,进一步建立了动态Job shop 调度问题的优化模型。设计了一种组合式调度规则RAN(FCFS,ODD),并提出了基于规则的启发式算法以及该类动态Job shop 调度问题的算例生成方法。为验证算法和比较评估调度规则的性能,对算例采用文献提出的7种调度规则和RAN(FCFS,ODD)进行了仿真调度,对调度结果的分析表明了算法的有效性和RAN(FCFS,ODD)调度规则求解所提出的动态Job Shop 调度问题的优越性能。     

Genetic algorithms for minimizing makespan in a flow shop with two capacitated batch processing machines

This paper considers a flow shop with two batch processing machines. The processing times of the job and their sizes are given. The batch processing machines can process multiple jobs simultaneously in a batch as long as the total size of all the jobs in a batch does not exceed its capacity. When the jobs are grouped into batches, the processing time of the batch is defined by the longest processing job in the batch. Batch processing machines are expensive and a bottleneck. Consequently, the objective is to minimize the makespan (or maximize the machine utilization). The scheduling problem under study is NP-hard, hence, a genetic algorithm (GA) is proposed. The effectiveness (in terms of solution quality and run time) of the GA approach is compared with a simulated annealing approach, a heuristic, and a commercial solver which was used to solve a mixed-integer formulation of the problem. Experimental study indicates that the GA approach outperforms the other approaches by reporting better solution.     

Bottleneck identification procedures for the job shop scheduling problem with applications to genetic algorithms

Two bottleneck identification algorithms (one for bottleneck machines and the other for bottleneck jobs) are presented for the job shop scheduling problem in which the total weighted tardiness must be minimized. The scheduling policies on bottleneck machines can have significant impact on the final scheduling performance, and therefore, they need to be optimized with more computational effort. Meanwhile, bottleneck jobs that can cause considerable deterioration to the solution quality also need to be considered with higher priority. In order to describe the characteristic information concerning such bottleneck machines and bottleneck jobs, a statistical approach is devised to obtain the bottleneck characteristic values for each machine, and, in addition, a fuzzy inference system is employed to transform human knowledge into the bottleneck characteristic values for each job. These bottleneck characteristic values reflect the features of both the objective function and the current optimization stage. Finally, the effectiveness of the two procedures is verified by specifically designed genetic algorithms.     

Production planning in virtual cell of reconfiguration manufacturing system using genetic algorithm

This paper focuses on the scheduling problem of the reconfiguration manufacturing system (RMS) for execution level, where the final objective is to output a production plan. The practical situation in Chinese factory is analyzed, and the characteristics are summarized into the contradiction between flow and job shop production. In order to handle this problem, a new production planning algorithm in virtual cells is proposed for RMS using an improved genetic algorithm. The advantages of this algorithm have three parts: (1) the virtual cell reconfiguration is formed to assist making production plans through providing relationship among task families and machines from cell formation; (2) The operation buffer algorithm is developed for flow style production in cells, which can realize the nonstop processing for flow style jobs; and (3) The multicell sharing method is proposed to schedule job shop jobs in order to fully utilize manufacturing capability among machines in multicells. Based on the above advantages, an improved genetic algorithm is developed to output scheduling plan. At last, the algorithm is tested in different instances with LINGO and the other genetic algorithm, and then the scheduling solution comparison shows the proposed algorithm can get a better optimum result with the same time using the comparison algorithm.     

面向IC生产模式的Job Shop调度问题的研究

针对即时定制生产模式的车间调度的特点,提出基于粒子群算法(PSO)的车间调度问题的解决方案.利用粒子群算法本身的优越性解决复杂的车间作业排序问题,克服了传统调度算法存在寻优效率低或全局寻优能力差的弱点.对粒子群的编码及寻优操作进行研究,确定了更适合车间调度问题的编码和操作方式,并将算法进行编程,应用到系统的车间调度部分.仿真结果表明,通过设置适当的参数,可以快速地得到理想的排序结果,能够适用于IC生产模式的车间调度问题.     

Dynamic flexible job shop scheduling with alternative process plans: an agent-based approach

This paper studies a flexible job shop problem considering dynamic events such as stochastic job arrivals, uncertain processing times, and unexpected machine breakdowns. Also, the considered job shop problem has routing flexibility and process flexibility. A multi-agent scheduling system has been developed for solution with good quality and robustness. A pheromone-based approach is proposed for coordination among agents. The proposed multi-agent approach is compared with five dispatching rules from literature via simulation experiments to statistical analysis. The simulation experiments are performed under various experimental settings such as shop utilization level, due date tightness, breakdown level, and mean time to repair. The results show that the proposed agent-based approach performs well under all problem settings.     

Combined column generation and constructive heuristic for a proportionate flexible flow shop scheduling

In a proportionate flow shop problem, jobs have to be processed through a fixed sequence of machines, and processing time for each job is equal on all machines. Such a problem has seldom been tackled. Proportionate flexible flow shop (PFFS) scheduling problems combine the properties of proportionate flow shop scheduling problems and parallel machine scheduling problems. This study presents a combined approach based on column generation (CG) for a PFFS problem with the criterion to minimize the objective of the total weighted completion time (TWCT). Minimizing TWCT in a PFFS problem significantly differs from the parallel-identical-machine scheduling problem, an optimal schedule in which jobs on each machine are in the weighted shortest processing time (WSPT) order. This combined approach adopts a CG approach to effectively handle job assignments to machines, and a constructive heuristic to obtain an optimal sequence for a single machine. Experimental results show the effectiveness of the combined approach in obtaining excellent quality solutions in a reasonable time, especially for large-scale problems.     

A clustering-based modified variable neighborhood search algorithm for a dynamic job shop scheduling problem

The dynamic job shop scheduling (DJSS) problem occurs when some real-time events are taken into account in the ordinary job shop scheduling problem. Most researches about the DJSS problem have focused on methods in which the problem’s input data structure and their probable relationship are not considered in the optimization process while some useful information can be extracted from such data. In this paper, the variable neighborhood search (VNS) combined with the k-means algorithm as a modified VNS (MVNS) algorithm is proposed to address the DJSS problem. The k-means algorithm as a cluster analysis algorithm is used to place similar jobs according to their processing time into the same clusters. Jobs from different clusters are considered to have greater probability to be selected when an adjacent for a solution is made in an optimization process using the MVNS algorithm. To deal with the dynamic nature of the problem, an event-driven policy is also selected. Computational results obtained using the proposed method in comparison with VNS and other common algorithms illustrate better performance in a variety of shop floor conditions.     

多目标柔性作业车间调度决策精选机制研究

针对多目标柔性作业车间调度优化无法找到唯一最优解的问题，提出多目标遗传算法和层次分析法模糊综合评判的分阶段优化策略。提出优化阶段和精选阶段的优化任务，优化阶段选出一组Pareto解集，精选阶段从Pareto解集中选出最优解；在精选阶段运用层次分析法和模糊评判集成的策略精选调度决策。决策算例证明提出的方法是可行的，可很好地帮助决策者选择出一个最满意的解。     

A modified shifting bottleneck heuristic for the reentrant job shop scheduling problem with makespan minimization

This paper proposes a modified shifting bottleneck heuristic (MSBH) for the reentrant job shop scheduling problem (RJSSP) with makespan minimization objective. Recently, the reentrant job shop has come into prominence as a new type of manufacturing shop. The principle characteristic of a reentrant job shop is that a job may visit certain machines more than once during the process flow, whereas in the classic job shop, each job visits a machine only once. The shifting bottleneck heuristic (SBH) is one of the most successful heuristic approaches for the classical job shop scheduling problem, which decomposes the problem into a number of single-machine subproblems. This paper adapts the SBH for the RJSSP and proposes a new sequencing heuristic for the single-machine maximum lateness subproblem considering the reentrant jobs in order to handle large-size RJSSPs. It also uses a subproblem criticality measure that further shortens the implementation time. The proposed MSBH is tested by using instances up to 20 machines and 100 jobs, and it is illustrated that good quality solutions can be obtained in reasonable computational times. A real-life application of the MSBH is also given as a case study to evaluate its performance.     

Lot streaming in a two-machine mixed shop

Most classical scheduling models overlook the fact that products are often produced in job lots and assume that job lots are indivisible single entities, although an entire job lot consists of many identical items. However, splitting an entire lot (process batch) into sublots (transfer batches) to be moved to downstream machines allows the overlapping of different operations on the same product while work needs to be completed on the upstream machine. This approach is known as lot streaming in scheduling theory. In this study, the lot streaming problem of multiple jobs in a two-machine mixed shop where there are two different job types as flow shop and open shop is addressed so as to minimize the makespan. The optimal solution method is developed for the mixed shop scheduling problem in which lot streaming can improve the makespan.     

考虑关键件加工质量的双资源约束车间调度算法

在工人异质性和机床类型多样的资源约束型车间中,针对资源抢占使加工质量向非关键件倾斜从而导致关键件加工质量无法保障的情况,建立了以完工时间为主要优化目标,以关键件加工质量、整体加工质量为辅助优化目标的双资源(工人/机床)约束柔性作业车间调度问题模型,并提出一种两级嵌套蚁群算法。首先采用工件候选集、资源候选集生成满足关键件加工要求的可行调度解;然后为工序寻找更合适的开工时间,针对机床类型、人机时窗差异设计了基于时窗的活动调度策略以提高算法的局部寻优能力;进而提出了一种保质策略,使关键件和总体工件加工质量水平持续提高;最后,通过算例测试验证了保质策略和两级嵌套蚁群算法的有效性。     

基于分层蚁群遗传算法的多目标柔性作业车间调度方法

针对离散制造柔性作业车间实际工况,提出了一种基于分层蚁群遗传算法的柔性作业车间资源驱动的多目标调度方法,其基本特征是：基于连续生产中不同调度周期剩余或空闲资源等调度相关实时信息;基于完工时间和机床负荷等多目标;采用分层蚁群-遗传混合算法进行决策,通过逐步筛选,获得优化解。该方法特别适用于车间资源变化、任务执行情况变化、急件任务必须插入等情况下的动态调度。应用标准案例并设计相关组合案例进行了测试,与MOGV混合算法相比,25%的案例计算结果优于MOGV算法,最大完工时间减少5%~7%,62.5%的案例计算结果等同MOGV算法。因此,该智能调度方法不仅可以有效地取得对指定优先目标的最佳优化效果,且可自动获得多目标综合的最优解,智能调度效果显著。     

Minimizing makespan in a group shop with fuzzy release dates and processing times

This paper deals with a fuzzy group shop scheduling problem. The group shop scheduling problem is a general formulation that includes the flow shop, the job shop, and the open shop scheduling problems. Job release dates and processing times are considered to be triangular fuzzy numbers. The objective is to find a job schedule that minimizes the maximum completion time or makespan. First, the problem is formulated in a form of fuzzy programming and then prepared in a form of deterministic mixed binary integer linear programming by applying the chance-constrained programming. To solve the problem, an efficient genetic algorithm hybridized with an improvement procedure is developed. Both Lamarckian and Baldwinian versions are then implemented and evaluated through computational experiments.     

多目标批量生产柔性作业车间优化调度

研究批量生产中以生产周期、最大提前/最大拖后时间、生产成本以及设备利用率指标(机床总负荷和机床最大负荷)为调度目标的柔性作业车间优化调度问题。提出批量生产优化调度策略,建立多目标优化调度模型,结合多种群粒子群搜索与遗传算法的优点提出具有倾向性粒子群搜索的多种群混合算法,以提高搜索效率和搜索质量。仿真结果表明,该模型及算法较目前国内外现有方法更为有效和合理。最后,从现实生产实际出发给出多目标批量生产柔性调度算例,结果可行,可对生产实践起到一定的指导作用。     

基于过滤定向搜索的Job-Shop调度算法及评价

对以Makespan最小为目标的Job Shop调度问题进行了研究。首先对Job Shop调度问题进行了描述,在此基础上建立了一种求解Job Shop调度问题的启发式优化算法———基于过滤定向搜索的算法,同时结合实例对算法的优化过程作了具体描述。最后通过不同规模的Benchmark实例对该算法进行了仿真评价,结果表明基于过滤定向搜索的算法搜索效率高,解的性能好,是一种有效的优化算法。