The liquid crystal injection scheduling problem (LCISP)

In this paper, the liquid crystal injection scheduling problem (LCISP) involving the constraints on limited maximum waiting times, unequal ready times, and machine setup times is considered to form the batches with incompatible product families and to sequence those batches on identical parallel batch processing machines. The batch scheduling problem, LCISP, has many applications, especially in thin film transistor liquid crystal display (TFT-LCD) factories at the cell assembly stage. In the LCISP, the objective is to minimise the total machine workload without violating the limited maximum waiting time restriction. Furthermore, machine setup times that are sequence dependent for two consecutive batches classified into different product families on the same machine are also considered. Since the LCISP involves constraints on limited maximum waiting times and sequence dependent setup times, it is more difficult to solve than the classical parallel batch processing machine scheduling problem with incompatible product families. These restrictions mean that the existing methods cannot be applied into real-world factories directly. Therefore, this paper proposes a mixed integer programming model to solve the LCISP exactly. In addition, two efficient solution procedures which solve the LCISP are also presented.     

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.     

Minimizing the total machine workload for the wafer probing scheduling problem

The Wafer Probing Scheduling Problem (WPSP) is a practical generalization of the parallel-machine scheduling problem, which has many real-world applications, particularly, in the Integrated Circuit (IC) manufacturing industry. In the wafer probing factories, the jobs are clustered by their product types, which must be processed on groups of identical parallel machines and be completed before the due dates. The job processing time depends on the product type, and the machine setup time is sequentially dependent on the orders of jobs processed. Since the wafer probing scheduling problem involves constraints on job clusters, job-cluster dependent processing time, due dates, machine capacity, and sequentially dependent setup time, it is more difficult to solve than the classical parallel-machine scheduling problem. In this paper, we consider the WPSP and formulate the WPSP as an integer programming problem to minimize the total machine workload. We demonstrate the applicability of the integer programming model by solving a real-world example taken from a wafer probing shop floor in an IC manufacturing factory.     

A method combining rules with genetic algorithm for minimizing makespan on a batch processing machine with preventive maintenance

This paper considers the problem of minimising makespan on a single batch processing machine with flexible periodic preventive maintenance. This problem combines two sub-problems, scheduling on a batch processing machine with jobs’ release dates considered and arranging the preventive maintenance activities on a batch processing machine. The preventive maintenance activities are flexible but the maximum continuous working time of the machine, which is allowed, is determined. A mathematical model for integrating flexible periodic preventive maintenance into batch processing machine problem is proposed, in which the grouping of jobs with incompatible job families, the starting time of batches and the preventive maintenance activities are optimised simultaneously. A method combining rules with the genetic algorithm is proposed to solve this model, in which a batching rule is proposed to group jobs with incompatible job families into batches and a modified genetic algorithm is proposed to schedule batches and arrange preventive maintenance activities. The computational results indicate the method is effective under practical problem sizes. In addition, the influences of jobs’ parameters on the performance of the method are analyzed, such as the number of jobs, the number of job families, jobs’ processing time and jobs’ release time.     

Minimizing makespan on parallel machines with release time and machine eligibility restrictions

Scheduling in the presence of machine eligibility restrictions when not all machines can process all the jobs is a practical problem into which there has been little research. Pinedo demonstrated that the least flexible job (LFJ) rule was optimal for minimizing makespan in a parallel machine environment (with equal processing times) when there are machine eligibility restrictions, the machine eligibility sets are nested, and no release time constraint exists. The results presented in this paper demonstrate that for the more realistic case when the machine eligibility sets are not nested (with unequal processing times known when a job is released), the longest processing time (LPT) rule performs better than the LFJ rule in the presence or absence of release time stipulations. The experimental results show that the order (job selection first or machine selection first) does not matter, which is consistent with Pinedo’s observation. The new heuristics that are evaluated in this paper provide important results for the parallel machine scheduling problem and their applications in the semiconductor industry, which motivated this research.     

Modelling and symmetry breaking in scheduling problems on batch processing machines

Problems of scheduling batch-processing machines to minimise the makespan are widely exploited in the literature, mainly motivated by real-world applications, such as burn-in tests in the semiconductor industry. These problems consist of grouping jobs in batches and scheduling them on machines. We consider problems where jobs have non-identical sizes and processing times, and the total size of each batch cannot exceed the machine capacity. The processing time of a batch is defined as the longest processing time among all jobs assigned to it. Jobs can also have non-identical release times, and in this case, a batch can only be processed when all jobs assigned to it are available. This paper discusses four different versions of batch scheduling problems, considering a single processing machine or parallel processing machines and considering jobs with or without release times. New mixed integer linear programming formulations are proposed as enhancements of formulations proposed in the literature, and symmetry breaking constraints are investigated to reduce the size of the feasible sets. Computational results show that the proposed formulations have a better performance than other models in the literature, being able to solve to optimality instances only considered before to be solved by heuristic procedures.     

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.     

Minimizing makespan in a no-wait flowshop with two batch processing machines using estimation of distribution algorithm

This paper studies the problem of minimising makespan in a no-wait flowshop with two batch processing machines (comprised of a parallel batch processing machine and a serial batch processing machine), non-identical job sizes and unequal ready times. We propose a population-based evolutionary method named estimation of distribution algorithm (EDA). Firstly, the individuals in the population are coded into job sequences. Then, a probabilistic model is built to generate new population and an incremental learning method is developed to update the probabilistic model. Thirdly, the best-fit heuristic is used to group jobs into batches and a least idle/waiting time approach is proposed to sequence the batches on batch processing machines. In addition, some problem-dependent local search heuristics are incorporated into the EDA to further improve the searching quality. Computational simulation and comparisons with some existing algorithms demonstrate the effectiveness and robustness of the proposed algorithm. Furthermore, the effectiveness of embedding the local search method in the EDA is also evaluated.     

JOB ASSIGNMENT ALGORITHMS ON UNIFORM PARALLEL MACHINES

Uniform parallel machine scheduling problems with a makespan measure cannot generally be solved within polynomial time complexity. This paper considers special problems with a single type of job on the uniform parallel machines, where each machine is available at a given ready time. Also the machine can be restricted on the number of jobs to be processed. The objective is to develop job assignment or batching algorithms which minimize makespan. When all the machines are available at time zero and have no restriction on the number of assignable jobs, a lower bound and optimal solution properties are derived. Based upon these properties, a polynomial algorithm is suggested to find the optimal job assignment on each machine. Three generalized problems are considered under the following situations: (1) some machines have capacity restrictions on the production batch, (2) each machine has its ready time, and (3) the jobs require series-parallel operations. The generalized problems arc also characterized and polynomial algorithms are developed for the same aim of optimal job assignment, except for the case of series-parallel operations. A heuristic algorithm is suggested with numerical tests for the series-parallel operations problem     

Operational fixed job scheduling problem under spread time constraints: a branch-and-price algorithm

This study addresses the operational fixed job scheduling problem under spread time constraints. The problem is to select a subset of jobs having fixed ready times and deadlines for processing on identical parallel machines such that total weight of the selected jobs is maximised. We first give a mathematical formulation of the problem and then reformulate it using Dantzig-Wolfe decomposition. We propose a branch-and-price algorithm that works on the reformulation of the problem. Computational results show that our algorithm is far superior to its competitor in the literature. It solves instances that could not be solved in one hour CPU time in less than a second and is able to solve large-scale instances in reasonable times which make it a computationally viable tool for decision-making.     

Spread time considerations in operational fixed job scheduling

In this study, we consider the operational fixed job scheduling problem on identical parallel machines. We assume that the jobs have fixed ready times and deadlines, and spread time constraints are imposed on machines. Our objective is to select a set of jobs for processing so as to maximise the total weight. We show that the problem is strongly NP-hard, and we investigate several special polynomially solvable cases. We propose a branch and bound algorithm that employs size reduction mechanisms, dominance conditions, and powerful lower and upper bounds. The computational results reveal that the branch and bound algorithm returns optimal solutions for problem instances with up to 100 jobs in reasonable solution times.     

Scheduling with shutdowns and sequence dependent set-up times

This paper considers a single machine scheduling problem with ready and due times constraints on jobs, shutdown constraints on the machine and sequence dependent set-up times among jobs. The shutdown is a disruptive event such as holiday, breaks or machine maintenance, and has a prespecified period when the machine will be interrupted. If no pre-emption is allowed for jobs, shutdown constraints divide the planning horizon into disconnected time windows. An optimization algorithm based on the branch-and-bound method is developed to minimize the maximum tardiness for solving the problem. This paper further develops the post-processing algorithm that manipulates the starting time of the shutdown period so as to reduce the obtained maximum tardiness. The post-processing algorithm can determine plural schedules to reduce the maximum tardiness, and the production manager will select the objective schedule among them for the interest of overall efficiency. Computational results for the proposed algorithms will indicate that the post-processing algorithm can improve upon the original solution and the problems with multiple shutdowns and with set-up times varying widely can be satisfactorily solved.     

A branch and bound algorithm for scheduling unit size jobs on parallel batching machines to minimize makespan

In this paper, we present a branch and bound algorithm for the parallel batch scheduling of jobs having different processing times, release dates and unit sizes. There are identical machines with a fixed capacity and the number of jobs in a batch cannot exceed the machine capacity. All batched jobs are processed together and the processing time of a batch is given by the greatest processing time of jobs in that batch. We compare our method to a mixed integer program as well as a method from the literature that is capable of optimally solving instances with a single machine. Computational experiments show that our method is much more efficient than the other two methods in terms of solution time for finding the optimal solution.     

A scheduling problem in glass manufacturing

In this paper, a production scheduling problem in glass manufacturing is studied. The production facility consists of multiple identical production lines and each production line includes a number of serially arranged machines. The production is characterized by semi-ordered processing times in each product family, and the last machine in each production line is a bottleneck machine. Significant changeover times are required when products of different families are produced on a production line. The scheduling problem was modeled as a parallel no-delay flowshop scheduling problem (PNDFSP). The PNDFSP combines the parallel machine scheduling problem (PMSP) with the no-delay flowshop scheduling problem (NDFSP). While PMSP and NDFSP have received considerable attention in the literature, PNDFSP has not been well studied. A mixed-integer programming formulation is developed and an efficient heuristic algorithm is proposed. The sequential heuristic algorithm considers simultaneously the line changeover time, no-delay effect, and line utilization in assigning product families to the production lines. The computational results are reported.     

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。     

Batch-scheduling problems through the flowshop with both receiving and delivery just in time

In scheduling literature, the flowshop problem is usually concerned only with finding a processing order of jobs on each machine. However, this paper addresses flowshop batch-scheduling problems, that is, to determine batch sizes of parts with a common due date, and to schedule the resulting batches. We propose an objective for the problems that not only minimizes inventory but also provides for receiving material just in time and delivery just in time. A heuristic method to solve the problem is proposed. An example is also provided to show how the proposed method works.     

Hybrid flowshop scheduling with family setup time and inconsistent family formation

This research considers a hybrid flowshop scheduling problem where jobs are organised in families according to their machine settings and tools. The family setup time arises when a machine shifts from processing one job family to another. The problem is compounded by the challenges that the formation of job families is different in different stages and only a limited number of jobs can be processed within one setup. This type of problem is common in the production process of standard metal components. This paper aims to propose two approaches to solve this problem. One is a metaheuristic in the form of a genetic algorithm and the other is a heuristic. The proposed approaches are compared and contrasted against the two relevant metaheuristic and heuristic adapted from solving a generalised sequence-dependent setup flowshop problem. Comparative results indicate that the proposed genetic algorithm has better performance on minimising makespan and the heuristic is more effective on reducing family setup time.     

Minimizing total tardiness on a batch processing machine with incompatible job families

Motivated by an application in semiconductor manufacturing, we study the problem of minimizing total tardiness on a batch processing machine with incompatibl8e job families, where all jobs of the same family have identical processing times and jobs of different families cannot be processed together. We present a dynamic programming algorithm which has polynomial time complexity when the number of job families and the batch machine capacity are fixed. We also examine various heuristic solution procedures which can provide near optimal solutions in a reasonable amount of computation time.     

A canned food scheduling problem with batch due date

This article considers a canned food scheduling problem where jobs are grouped into several batches. Jobs can be sent to the next operation only when all the jobs in the same batch have finished their processing, i.e. jobs in a batch, have a common due date. This batch due date problem is quite common in canned food factories, but there is no efficient heuristic to solve the problem. The problem can be formulated as an identical parallel machine problem with batch due date to minimize the total tardiness. Since the problem is NP hard, two heuristics are proposed to find the near-optimal solution. Computational results comparing the effectiveness and efficiency of the two proposed heuristics with an existing heuristic are reported and discussed.     

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.