Centralized Scheduling and Priority Implementation Heuristics for a Dynamic Job Shop Model

The problem considered is the scheduling of a job shop with job due dates, intermittent job arrivals, and statistical processing times. Centralized scheduling uses a sequence of static problems for generating priorities at review times. A multi-pass heuristic program, which has proven effective in earlier research, is applied to the up-dated static scheduling problem at each review time. A procedure is proposed for implementing priorities on the shop floor between review times. The procedure is expressly designed to integrate the scheduling of newly arriving jobs to modify the schedule. In simulation experiments using tardiness statistics for evaluation, centralized scheduling and the proposed implementation procedure proved to be an extremely effective combination. Comparison with another procedure that gives the centralized schedule precedence over new arrivals indicates the importance of the implementation procedure when periodic centralized scheduling is used in a dynamic situation.     

Batching and scheduling to minimize the makespan in the two-machine flowshop

In this paper, we consider a class of batching and scheduling problems in the two-machine flowshop where one of the machines is a discrete processor and the other one is a batch processor. The jobs are processed separately on the discrete processor and processed in batches on the batch processor. The processing time of a batch is equal to the total processing time of the jobs contained in it, and the completion time of a job in a batch is defined as the completion time of the batch containing it. A constant setup time is incurred whenever a batch is formed on the batch processor. The problem is to find the optimal batch compositions and the optimal schedule of the batches so that the makespan is minimized. All problems in this class are shown to be NP-complete in the ordinary sense. We also identify some polynomially solvable cases by introducing their corresponding solution methods.     

Impact of sequence-dependent setup time on job shop scheduling performance

In a production system using multi-purpose and flexible machines, reducing setup time is an important task for better shop performance. Numerous cases were reported about successful reduction of setup times by standardization of setup procedures. However, setup times have not been eliminated and remain an important element of real production problems for production systems such as commercial printing, plastics manufacturing, metal processing, etc. It is especially critical when the setup time is sequence dependent. In this situation, shop performance cannot be effectively improved without the aid of an appropriate scheduling procedure. Review of the past studies shows that there has not been a significant amount of research done on the scheduling procedure for a dynamic job shop with sequence dependent setup times. This paper investigates the job shop scheduling problems that are complicated by sequence-dependent setup times. The study classifies and tests scheduling rules by considering whether setup time and/or due date information is employed. These scheduling rules are evaluated in dynamic scheduling environments defined by due date tightness, setup times and cost structure. A simulation model of a nine machine job shop is used for the experiment. A hypothetical, asymmetric, setup time matrix is applied to the nine machines.     

Single-machine scheduling problems with a batch-dependent aging effect and variable maintenance activities

We consider single-machine scheduling problems with a batch-dependent ageing effect and variable maintenance activities between batches. The machine can process several jobs as a batch. It requires maintenance activities where the maintenance time depends on the flow time of the pre-batch, i.e. the batch processed before a batch. A job’s actual processing time is an increasing exponential function of its operation time within a batch. The objectives are to minimise the makespan and the total completion time. We develop polynomial time algorithms for the makespan minimisation problem and the total completion time minimisation problem under the condition that the ageing factor is greater than one. We also provide a mathematical programming approach and two heuristic algorithms to analyse the total completion time minimisation problem when the ageing factor is less than one for even one batch. The computational analysis indicates that the proposed heuristic algorithms are more efficient for the smaller ageing factor, whereas the Modified Shortest Processing Time algorithm is more efficient than the proposed heuristic algorithms for the larger ageing factor.     

Batch scheduling problem for a machinery factory with fixed-position layout

We consider a batch scheduling problem for a two-stage flow shop with fixed-position layout. In the first stage, a fixed number of jobs are assembled on a batch machine with a family batch setup time and a common processing time. In the second stage, the assembled jobs are individually performed for system integration on a discrete machine. The finished job is immediately packed and shipped if the payment has been made; otherwise, it is moved to a temporary storage area, incurring additional removal time. This study develops a mixed integer programming (MIP) to solve the problem of minimising the total completion time and proposes two heuristics for large-size problems. Computational results show that the proposed methods can be applied to resolve real-world problems similar to those in this study.     

A batch splitting method for a job shop scheduling problem in an MRP environment

The job shop scheduling problem has been a major target for many researchers. Unfortunately though, most of the previous research was based on assumptions that are different from the real manufacturing environment. Among those distorted assumptions, two assumptions about set-up time and job composition can greatly influence the performance of a schedule. First, most of the past studies ignored the impact of the before-arrival set-up time. If we know the sequence of operations in advance, we can obtain an improved schedule by preparing the setup before a job arrives. Secondly, most of the past studies assumed that a job consists of only a single part, that is a batch of size one. However, if we assume that a job consists of a batch size greater than one, as in many real manufacturing environments, then we can obtain an improved schedule because we can fill up the idle times of machines with jobs which have smaller processing times by splitting the original batches. However, the number of job orders may then increase due to the split, and the size of the scheduling problem would become too large to be solved in a practical time limit. Consequently, there may be an optimum batch size considering trade-off between better solution and tractability. The current study is the result of an attempt to find an acceptable solution when the production requirement from a MRP system for a planning period exceeds the capacity of a production system. We try to get an improved schedule by splitting the original batch into smaller batches, and consider setting up a machine before the actual arrival of jobs to that machine. Thereby we can meet the due date requirement without resorting to rescheduling of the master production schedule. For the given batch, we disaggregate it according to the algorithm we are proposing. A so-called 'modified shifting bottleneck procedure' is then applied to solve the job shop scheduling problem with a before-arrival family set-up time considering release date, transportation time and due date. The study also shows that we can adapt to unexpected dynamic events more elegantly by allowing the splitting of batches.     

有模具约束的并行机批量流调度问题研究

大多数调度问题均假设产品以单个或整批的方式进行生产,而实际生产过程中,会把产品分批后再进行生产。但当考虑模具约束时,对如何解决产品分批以及制定合理调度方案的问题,本文以最小化最大完工时间为优化目标,建立了考虑模具约束的并行机批量流调度模型,并提出了一种基于遗传算法和差分算法结合的混合差分遗传算法（DEGA）,实现分批与调度两个问题并行优化。最后通过对算例测试,DEGA算法得到更优的解,证明了该算法的优越性和稳定性。结合实际案例,验证了模型和算法的可行性。     

考虑工序并行的差异工件批调度研究

针对铸造车间差异工件组批多约束的问题,在工序可并行加工的前提下构建以最小化最大完工时间和最小化沙箱空置率为优化目标的并行工序批调度模型,设计一种改进和声算法求解该调度模型,提出一种单工序编解码方式和2种机器分配规则用于解决工件分批、沙箱选择、工序分配及机器选择的问题。在算法中提出一种新的和声产生方式和更新机制,同时为改善算法的局部搜索能力,加入模拟退火算法执行局部搜索过程。最后根据企业实际生产数据进行仿真实验,验证本文模型的有效性。     

Control of a Batch Processing Machine Serving Compatible Job Families

We consider the control of a single batch processing machine with random arrivals, random processing times, and compatible job families (jobs from different families may be processed together in the same batch, with the processing time distribution of the entire batch determined by the job family in the batch having the greatest expected processing time). The objective is to minimize the long-run average time that jobs spend in the system. We present properties possessed by the optimal policies and discuss the structure of these policies. We next develop a simple heuristic scheduling policy to control the machine. Simulation results are provided to demonstrate the effectiveness of our heuristic over a wide range of problem instances.     

Learning effective dispatching rules for batch processor scheduling

Batch processor scheduling, where machines can process multiple jobs simultaneously, is frequently harder than its unit-capacity counterpart because an effective scheduling procedure must not only decide how to group the individual jobs into batches, but also determine the sequence in which the batches are to be processed. We extend a previously developed genetic learning approach to automatically discover effective dispatching policies for several batch scheduling environments, and show that these rules yield good system performance. Computational results show the competitiveness of the learned rules with existing rules for different performance measures. The autonomous learning approach addresses a growing practical need for rapidly developing effective dispatching rules for these environments by automating the discovery of effective job dispatching procedures.     

A genetic algorithm based procedure for more realistic job shop scheduling problems

This work presents a robust procedure to solve job shop scheduling problems with large number of more realistic constraints such as jobs with several subassembly levels, alternative processing plans for parts and alternative resources for operations, requirement of multiple resources to process an operation (e.g. machine, tools, fixtures, staff), resource calendars, batch overlap and sequence dependent setups. Also, the approach considers multi-objective evaluation functions. The system uses modified schedule generation algorithms to obtain a set of initial solutions. Each initial solution is enhanced by a local improvement procedure. Then a hybrid genetic algorithm, which incorporates a local hill climbing procedure, is applied to the set of local optimum schedules.     

含不一致任务重量的同型熔炼炉批调度优化

为求解含不一致任务重量的同型熔炼炉批调度问题,建立了最小化最大任务完工时间优化模型,设计了一种混合粒子群算法（HPSO）。算法使用随机生成的任务序列作为粒子,采用批首次匹配（BFF）规则对任务序列分批,最长加工时间（LPT）规则将批分配到批处理机,并提出了一种最小完工时间差（MCD）规则对LPT调度结果进行优化;为避免早熟,算法引入交叉和变异操作搜索最优解。通过仿真实验与SA、GA算法对比,实验结果表明算法具有良好的性能。     

Exact and approximate methods for parallel multiple-area spatial scheduling with release times

Spatial scheduling problems involve scheduling jobs that each require certain amounts of two-dimensional space within a processing area of limited width and length. Thus, this requires not only assigning time slots to each job but also locations and orientations within the limited physical processing space as well. Such problems, often encountered in shipbuilding and aircraft manufacturing, are generally difficult to solve, and there is a relatively small amount of literature addressing these problems compared to other types of scheduling. In this paper, we consider a particularly complex class of spatial scheduling problems that involve scheduling each job into one of several possible processing areas in parallel to minimize the total amount of tardy time. In addition, each job has a release time before which it may not be processed. We introduce two methods for solving this type of problem: an integer programming (IP) model and a heuristic algorithm. We perform computational tests and comparisons of each method over a large number of generated benchmark problems with varying characteristics, and also compare these to a more naïve heuristic. Solving the IP model was effective for small problems but required excessive amounts of time for larger ones. The heuristic was effective and produced solutions of comparable quality to the IP model for many problems while requiring very little computational time.     

Minimising makespan on parallel batch processing machines with non-identical ready time and arbitrary job sizes

This paper considers the parallel batch processing machine scheduling problem which involves the constraints of unequal ready times, non-identical job sizes, and batch dependent processing times in order to sequence batches on identical parallel batch processing machines with capacity restrictions. This scheduling problem is a practical generalisation of the classical parallel batch processing machine scheduling problem, which has many real-world applications, particularly, in the aging test operation of the module assembly stage in the manufacture of thin film transistor liquid crystal displays (TFT-LCD). The objective of this paper is to seek a schedule with a minimum total completion time for the parallel batch processing machine scheduling problem. A mixed integer linear programming (MILP) model is proposed to optimise the scheduling problem. In addition, to solve the MILP model more efficiently, an effective compound algorithm is proposed to determine the number of batches and to apply this number as one parameter in the MILP model in order to reduce the complexity of the problem. Finally, three efficient heuristic algorithms for solving the large-scale parallel batch processing machine scheduling problem are also provided.     

Iterative algorithms for batching and scheduling to minimise the total job tardiness in two-stage hybrid flow shops

This study considers the batching and scheduling problem in two-stage hybrid flow shops in which each job with a distinct due-date is processed through two serial production stages, each of which has identical machines in parallel. Under the fundamental trade-off that large batch sizes with less frequent changeovers may reduce setup costs and hence increase machine utilisation, while small batch sizes may reduce job flow times and hence improve scheduling performance, the problem is to determine the number of batches, the batch compositions, the allocation of batches to the parallel machines at each stage, and the sequence of the batches allocated to each machine for the objective of minimising the total job tardiness. A mixed integer programming model is developed for the reduced problem in which the number of batches is given, and then, three iterative algorithms are proposed in which batching and scheduling are done repeatedly until a good solution is obtained. To show the performance of the algorithms, computational experiments were done on a number of test instances, and the results are reported. In particular, we show that the number of batches decreases as the ratio of the batch setup time to the job processing time increases.     

Scheduling parallel batch processing machines with arbitrary job sizes and incompatible job families

Motivated by a bottleneck operation in an MLCC (multi-layer ceramic capacitor) production line, we study the scheduling problem of parallel batch processing machines in which a number of jobs can be processed simultaneously in a machine as a batch. Volumes of the jobs are different from each other and each job belongs to the family in which all jobs have the same processing time. In this situation, we analyse three kinds of problems whose performance measures are makespan, total completion time, and total weighted completion time, respectively. Since these problems are known to be NP-hard, we propose a number of heuristics and design genetic algorithms for the problems. Through some computational experiments, we evaluate the performances of the heuristic algorithms proposed, including the genetic algorithms for each of three problems.     

Optimisation of flow-shop scheduling with batch processor and limited buffer

This paper deals with a flow-shop scheduling problem with limited intermediate buffer. Jobs are grouped in incompatible job families. Each job has to be processed by a batch processor followed by a discrete processor in the same order. The batch processor can process several jobs simultaneously so that all jobs of the same batch start and complete together. We assume that the capacity of batch processor is bounded. The batch processing time is identical for batches of the same family. A batch which has completed processing on the batch processor may block the processor until there is a free unit in the buffer. The objective is to determine a batching and scheduling for all jobs so as to minimise mean completion time. A lower bound and two heuristics algorithm are developed. Moreover, a two-stage method embedded with a Differential Evolution (DE) algorithm is also developed. DE is one of the latest evolutionary computation algorithms, which implements mutation, crossover, and selection operators to improve the candidate solutions iteratively. Three variants of DE are first compared with a continuous Genetic Algorithm employing the random key representation. Then, one variant of the DE with the best convergence speed is selected. Numerical experiments are conducted to evaluate the performances of the selected two-stage meta-heuristic and two heuristics.     

Family-based scheduling of shops with functional layouts

Simulation studies of job shop scheduling have typically assumed that either setup times are zero (subsumed within the processing time), or that every part has such a unique setup that no setup advantages can be gained by better scheduling policies. These studies also assume that the shop has exactly one copy of every machine. Some researchers have proposed heuristics that explicitly consider setup times and parallel machines in the context of a one stage shop with static arrivals. In contrast, family-based scheduling centred around setup time reduction has been credited with achieving economic savings in batch production industries where GT is employed. We motivate this study by the case of an existing realworld semi-conductor testing facility that has family setups, parallel machines and dynamic job arrival. Using this setting, we investigate whether benefits can still be obtained by using a family-based scheduling philosophy in those environments which do not permit the physical creation of cellular layouts due to the presence of process related or other constraints. We propose and evaluate two new dispatching procedures in a functional job shop that is modelled after the semiconductor testing facility. Results show that a family-based scheduling philosophy centred around coordinating machine setups is advantageous at relatively high setup to processing time ratios, while classic job shop rules suffice otherwise. Based on these results, we present recommendations for managing such environments. We also suggest future research directions in this area.     

Heuristic algorithms for scheduling heat-treatment furnaces of steel casting industries

This paper addresses a research problem of scheduling parallel, non-identical batch processors in the presence of dynamic job arrivals, incompatible job-families and non-identical job sizes. We were led to this problem through a real-world application involving the scheduling of heat-treatment operations of steel casting. The scheduling of furnaces for heat-treatment of castings is of considerable interest as a large proportion of the total production time is the processing times of these operations. In view of the computational intractability of this type of problem, a few heuristic algorithms have been designed for maximizing the utilization of heat-treatment furnaces of steel casting manufacturing. Extensive computational experiments were carried out to compare the performance of the heuristics with the estimated optimal value (using the Weibull technique) and for relative effectiveness among the heuristics. Further, the computational experiments show that the heuristic algorithms proposed in this paper are capable of obtaining near (statistically estimated) optimal utilization of heat-treatment furnaces and are also capable of solving any large size real-life problems with a relatively low computational effort.     

A note on scheduling jobs with missing operations in permutation flow shops

Flowshop scheduling problems are usually handled as permutation flowshops because of computational complexity although the technical framework in realworld problems often allows that jobs pass each other. Having a missing operation of a job on a machine, this job passing becomes a natural way to process jobs unless the underlying system is not an inflexible flow-line. However, when scheduling, missing operations are usually handled as zero processing time operations not allowing for any job passing. It is shown that even permitting job passing for missing operations while keeping the permutation constraint improves total completion time only under rather specific circumstances. We propose 'partial permutation flowshop sequencing' to overcome these specific formal requirements with respect to the real-world problem setting.