两阶段流水车间批调度问题的蚁群优化算法

针对差异工件(工件尺寸不同)两阶段流水车间的批处理机调度问题,提出一种以最小化加工时间跨度为目标的蚁群优化算法.根据批中工件在每阶段加工时间的相似程度(标准差衡量),得到一个能够提高批中工件加工时间相似水平的启发式信息.同时,改进蚁群算法的编码方案,并引入局部优化算法来提高优化性能.仿真结果表明,与现有算法相比,该算法在工件规模较大的情况下具有较好的求解性能.     

瓶颈指向的启发式算法求解混合流水车间调度问题

针对以最小化时间表长为目标的复杂混合流水车间调度问题,提出了一种将机器布局和工件加工时间特征紧密结合的启发式算法.首先,充分利用各阶段平均机器负荷一般不相等的特点确定瓶颈阶段,构建初始工件排序.其次,针对在瓶颈阶段前加工时间较短而瓶颈阶段后加工时间相对较长的工件,在第1阶段优先开始加工.同时,在瓶颈阶段前的每一个阶段,每当有工件等待加工或同时完工时,优先选择瓶颈阶段前剩余加工时间最短的工件加工;在瓶颈阶段以及瓶颈阶段之后,则优先选择这台机器后剩余加工时间最长的工件加工.最后,采用工件交换和插入操作改进初始调度.用Carlier和Neron的Benchmark算例测试提出的启发式算法.将计算结果与NEH启发式算法进行了比较,平均偏差降低了0.0555%,表明这个启发式算法是有效的.     

混合遗传算法求解带不相关并行机的HFSSP

研究了带不相关并行机和批生产约束的混合流水车间调度问题,其中初始阶段为串行批处理机,相邻加工阶段间工件的运输时间独立于加工时间。针对该问题,以最小化最大完工时间(makespan)为目标,建立了整数规划模型,提出一种结合NEH启发式算法、局域搜索和自适应遗传算法的混合遗传算法获取近优解。采用NEH启发式算法产生初始工件加工序列群以提高群质量,提出自适应参数调节机制设计交叉变异概率,进而利用交叉和变异操作改进解的质量。最后,通过局域搜索产生邻域解以更新遗传算法(GA)的解。仿真实验测试了不同规模的实例,与其他基于GA的混合算法的性能进行对比,结果表明所提出的混合遗传算法优于其他算法,能在合理的计算时间内得到较好的近优解。     

带机器人制造单元的作业车间调度仿真

针对带有机器人制造单元的作业车间调度优化问题, 在若干加工机器上可以加工具有特定加工工序的若干工件, 并且搬运机器人可以将工件在装卸载站与各加工机器间进行搬运. 在实际生产过程中, 由于不确定性, 特别是带有存货的加工单元, 要求工件的完工时间在一个时间窗内, 而不是一个特定的时间点. 因此针对此情况的作业车间, 考虑到其在求解问题过程中的复杂性和约束性等特点, 研究了在时间窗约束下, 目标值为最小化工件完成时间提前量和延迟量的总权重. 提出了一种将文化基因算法与邻域搜索技术(变邻域下降搜索)相结合的改进元启发式算法, 在求得最优目标值的同时, 可得到最优值的工件加工序列及机器人搬运序列. 通过实验结果表明, 所提出的算法有效且优于传统文化基因算法与遗传算法.     

单台批处理机总加权完成时间最小化的启发式算法

批处理机总加权完成时间最小化问题的复杂性目前还没有确定,因此有必要研究该问题的启发式算法．基于对该问题最优解性质的分析,提出了工件分批的最优性质．分别基于WSPT规则和SPT规则对工件进行总排序,利用工件最优分批性质进行分批,提出了两种启发式算法（简称WSPTS和SPTS）．为了检验算法的性能．将提出的算法与此问题的基准算法和常规算法进行了比较,结果表明,启发式算法WSPTS要优于其他的算法,而SPTS算法的性能最优．     

带不相关并行机和有限缓冲MHFS调度的混合启发式算法

研究每阶段含不相关并行机的多阶段混合流水车间问题(MHFSP),工件的加工时间取决于所分配的机器,相邻阶段之间缓冲区能力有限.鉴于直接求解该NP-hard问题较为困难,将其转化为带阻塞和不相关并行机的MHFSP (BMHFSP-UPM),建立整数规划模型,基于遗传算法(GA)和禁忌搜索(TS)提出一种混合启发式算法(HHGA&TS)进行求解.在该算法中,设计基于多阶段并行加工的二维矩阵编码方案,继而基于二维矩阵元胞组的初始解群体表述设计参数自适应策略;引入基于工件位-基因位的单点倒置交叉以及基于机器号的单点变异过程,利用GA求解机制完成解更新过程;设计机器号次序交换(MNE)、工件位置交换(JNE)、工件工序变异(JNM)三种邻域解移动规则,从而完成基于MNE-JNE-JNM的TS二次优化.仿真实验测试了多达120个工件的720组不同规模实例,结果表明,相较于GA、TS及NEH-IGA,所提出的混合启发式算法在解的质量方面表现更佳.     

并行机成组调度问题的启发式算法

研究了优化目标为总拖后/提前时间最小化的并行机成组调度问题,提出了一种三阶段启发式近似求解算法。首先把并行机问题看成单机问题,以最小化总拖后时间为优化目标排列工件的加工次序;然后将工件按第一阶段所求得的次序指派到最先空闲的并行的机器上;最后采用改进的GTW算法对各机器上的工件调度插入适当的空闲时间。计算表明该算法能够在很短的时间内给出大规模调度问题的近似最优解。     

考虑学习效应的最小化延误总时间的单机批次排序问题

一些生产场景中,工件以批次作业的形式被安排生产,工件批量大、加工工序基本相同,所以标准工时相同,而且实际加工时间会受到学习效应的影响.为此,讨论学习效应的最小化延误总时间的单机批次排序问题,对该问题建立数学模型.该问题属于NP-hard问题,采用动态规划算法(DP)和模拟退火算法(SA)求解该问题,通过实验分析不同规模时DP的执行时间与SA的执行时间和求解误差的变化趋势,比较SA与其他实践中常用的经典规则的求解效果.最后得出DP适合批次数小于13的小规模问题,可以得到精确解;与经典规则相比,SA至少可以使目标函数降低20%,表明SA算法具有有效性.SA解决大规模问题时效果较优,并得出SA的执行时间和误差随着控制参数改变的变化趋势.     

一类具有特殊阻塞约束的两阶段流水车间成组调度模型与算法

从钢铁企业的管加工生产中抽象出一类具有特殊阻塞约束的两阶段流水车间成组调度问题.与传统阻塞约束不同,工件是否发生阻塞并非取决于缓冲区容量,而是取决于工件自身的规格、尺寸等属性.针对此调度问题,以最小化最大完工时间(makespan)为目标建立混合整数线性规划模型,并通过三划分问题的多项式归结证明问题的强NP难特性,进而将问题划分为工件组排序和工件组内工件排序两个子问题,提出一种基于协同进化的分布估计算法.算法针对两个子问题各自特点进行独立编码,分别设计启发式规则构造初始种群,并提出带有工件区块结构特征的概率模型来指导种群进化.基于实际生产数据设计多种问题规模的实验,从而表明所提出模型和算法的有效性.     

一种柔性车间快速启发式调度算法

柔性作业车间调度问题比传统的Job-shop问题更复杂也更符合实际生产实际.为了快速有效地求解这类问题,设计出一种基于综合分派规则的快速启发式调度算法.基于综合分派规则的调度算法,以一批工件总完工时间最短为目标,在调度过程中通过动态调整工件的加工优先级并为每道工序分配最适合的机器进行加工,可迅速求得满意的较优解.与其他方法进行对比实验结果证实了算法的有效性,在实际调度系统的应用中也证明了算法的实用性.     

Minimizing makespan on a three-machine flowshop batch scheduling problem with transportation using genetic algorithm

This paper studies the minimization of makespan in a three-machine flowshop scheduling problem in which a batch processing machine is located between two single processing machines on first and third stages. In this study also transportation capacity and transportation among machines times are explicitly considered.We establish a mixed integer programming model and propose a heuristic algorithm based on the basic idea of Johnson's algorithm. Since the problem under study is NP-hard, a genetic algorithm is also proposed to minimize makespan. The effectiveness of our solution procedures is evaluated through computational experiments. The results obtained from the computational study have shown that the genetic algorithm is a viable and effective approach that is capable to produce consistently good results.     

Machine scheduling with job class setup and delivery considerations

We study machine scheduling problems in which the jobs belong to different job classes and they need to be delivered to customers after processing. A setup time is required for a job if it is the first job to be processed on a machine or its processing on a machine follows a job that belongs to another class. Processed jobs are delivered in batches to their respective customers. The batch size is limited by the capacity of the delivery vehicles and each shipment incurs a transport cost and takes a fixed amount of time. The objective is to minimize the weighted sum of the last arrival time of jobs to customers and the delivery (transportation) cost. For the problem of processing jobs on a single machine and delivering them to multiple customers, we develop a dynamic programming algorithm to solve the problem optimally. For the problem of processing jobs on parallel machines and delivering them to a single customer, we propose a heuristic and analyze its performance bound.     

Tabu search heuristic for two-machine flowshop with batch processing machines

Batch processing machines are frequently encountered in many industrial environments. A batch processing machine is one which can process several jobs simultaneously as a batch. The processing time of a batch is equal to the largest processing time of any job in the batch. This study deals with the problem of scheduling jobs in a flowshop with two batch processing machines such that the makespan is minimized. A heuristic based on Tabu search (TS) technique is proposed. The proposed heuristic is compared with a heuristic based on mixed integer linear programming (MILP). Because the complexity of the MILP-based heuristic is depended on the number of job batches, the comparison is under up-to-eight batches problem. In order to measure the proposed TS-based heuristic in larger batch problem, the relative error percentage with the lower bound (REP_LB) is used. The results show that the proposed heuristic is efficient and effective for the problems with relative large job sizes.     

A hybrid genetic heuristic for scheduling parallel batch processing machines with arbitrary job sizes

This paper investigates the scheduling problem of parallel identical batch processing machines in which each machine can process a group of jobs simultaneously as a batch. Each job is characterized by its size and processing time. The processing time of a batch is given by the longest processing time among all jobs in the batch. Based on developing heuristic approaches, we proposed a hybrid genetic heuristic (HGH) to minimize makespan objective. To verify the performance of our algorithm, comparisons are made through using a simulated annealing (SA) approach addressed in the literature as a comparator algorithm. Computational experiments reveal that affording the knowledge of problem through using heuristic procedures, gives HGH the ability of finding optimal or near optimal solutions in a reasonable time.     

Minimizing makespan in a flow shop with two batch-processing machines using simulated annealing

This paper aims at minimizing the makespan of two batch-processing machines in a flow shop. The processing times and the sizes of the jobs are known and non-identical. The machines can process a batch as long as its capacity is not exceeded. The processing time of a batch is the longest processing time among all the jobs in that batch. The problem under study is NP-hard for makespan objective. Consequently, a heuristic based on Johnson's algorithm and a simulated annealing (SA) algorithm is proposed. Random instances were generated to verify the effectiveness of the proposed approaches. The results obtained from SA were compared with the proposed heuristic and a commercial solver. The SA outperformed both the heuristic and the commercial solver. On larger problem instances, the heuristic outperformed the commercial solver.     

Decomposition heuristics for minimizing earliness–tardiness on parallel burn-in ovens with a common due date

This paper considers a scheduling problem for parallel burn-in ovens in the semiconductor manufacturing industry. An oven is a batch processing machine with restricted capacity. The batch processing time is set by the longest processing time among those of all the jobs contained in the batch. All jobs are assumed to have the same due date. The objective is to minimize the sum of the absolute deviations of completion times from the due date (earliness–tardiness) of all jobs. We suggest three decomposition heuristics. The first heuristic applies the exact algorithm due to Emmons and Hall (for the nonbatching problem) in order to assign the jobs to separate early and tardy job sets for each of the parallel burn-in ovens. Then, we use job sequencing rules and dynamic programming in order to form batches for the early and tardy job sets and sequence them optimally. The second proposed heuristic is based on genetic algorithms. We use a genetic algorithm in order to assign jobs to each single burn-in oven. Then, after forming early and tardy job sets for each oven we apply again sequencing rules and dynamic programming techniques to the early and tardy jobs sets on each single machine in order to form batches. The third heuristic assigns jobs to the m early job sets and m tardy jobs sets in case of m burn-in ovens in parallel via a genetic algorithm and applies again dynamic programming and sequencing rules. We report on computational experiments based on generated test data and compare the results of the heuristics with known exact solution for small size test instances obtained from a branch and bound scheme.     

A scheduling algorithm based on the singular value decomposition heuristic method in a distributed manufacturing system

Because distributed manufacturing technology is the foundation of modernized production and traditional heuristic methods exhibit problems of high complexity and low efficiency, this paper designs a scheduling algorithm based on the singular value decomposition heuristic (SVDH) method. The algorithm uses the device distribution and the transportation relationship between devices in a distributed manufacturing system. The algorithm takes the sequence relationship between tasks and the distance between devices as the implicit relationship between the task and the device. The algorithm makes use of the implicit relationship to amend the processing time matrix of the task and corrects the processing time matrix that contains the transportation relationship. Singular value decomposition principal component analysis is performed on the corrected processing time to find the most suitable processing device for each process, and an initial solution matrix is established. The heuristic solution is used to optimize the initial solution to find the optimal scheduling result based on the initial solution matrix. The establishment of the initial solution can effectively reduce the computational complexity of the heuristic solution, realize a parallelizing solution, and improve the efficiency of the heuristic solutions. In addition, the SVDH scheduling result has a lower transfer time between devices due to the consideration of the topology of tasks and devices, that is, the transit time. In this paper, the experiments are conducted on the heuristic performance, scheduling results, and transportation time. The experimental results show the advantages of SVDH over general heuristic algorithms in terms of efficiency and transit time.     

Unbounded parallel-batch scheduling with family jobs and delivery coordination

We study a scheduling problem that integrates parallel-batch production with family jobs and job delivery at the same time. The jobs are first processed on an unbounded parallel-batch machine and then delivered in batches to their specified customers by a transportation vehicle. We assume that jobs from different families (customers) cannot be processed together by the batch machine and also transported together by the vehicle. The objective is to minimize the time when the vehicle finishes delivering the last delivery batch to its customer and returns to the machine. We first show that the problem is NP-hard, and then propose for it a heuristic algorithm with a worst-case performance ratio of 3/2.     

Scheduling unrelated parallel batch processing machines with non-identical job sizes and unequal ready times

This research analyzes the problem of scheduling a set of n jobs with arbitrary job sizes and non-zero ready times on a set of m unrelated parallel batch processing machines so as to minimize the makespan. Unrelated parallel machine is a generalization of the identical parallel processing machines and is closer to real-world production systems. Each machine can accommodate and process several jobs simultaneously as a batch as long as the machine capacity is not exceeded. The batch processing time and the batch ready time are respectively equal to the largest processing time and the largest ready time among all the jobs in the batch. Motivated by the computational complexity and the practical relevance of the problem, we present several heuristics based on first-fit and best-fit earliest job ready time rules. We also present a mixed integer programming model for the problem and a lower bound to evaluate the quality of the heuristics. The small computational effort of deterministic heuristics, which is valuable in some practical applications, is also one of the reasons that motivates this study. The results show that the heuristic proposed in this paper has a superior performance compared to the heuristics based on ideas proposed in the literature.     

Heuristics for minimizing total completion time and maximum lateness on identical parallel machines with setup times

This paper aims at minimizing the total completion time together with the maximum lateness. Jobs are processed by parallel machines in batches. A setup is required before processing a batch, which is common for all jobs in the batch. Jobs are continuously processed after the setup time. The processing length of a batch is the sum of the setup time and processing times of the jobs it contains. Due to the availability constraint, the completion time of a job is the time when a batch is totally processed. Considering due dates, the jobs need to be processed in a way that the total completion time and the maximum lateness are minimized. This problem is a kind of NP-hard so first we present a constructive heuristic to solve the problem. Then we propose a genetic algorithm whose initial population is formed by using the heuristic approach. Computational experiments are carried out to evaluate the performance of the proposed algorithms.