Minimization of maximum tardiness on unrelated parallel machines with process restrictions and setups

We consider the problem of schedulingN jobs onM unrelated parallel machines to minimize maximum tardiness. Each job has a due date and requires a single stage of processing. A setup for dies is incurred if the type of the job scheduled is different from the previous one on that machine. For each die type, the number of dies is restricted. Because of the mechanical structure of the machines and the fitness of dies to each machine, the processing time depends on both the job and the machine. In this paper, an efficient heuristic based on guided search, record-to-record travel, and tabu lists is presented to minimize maximum tardiness. Computational characteristics of the proposed heuristic are evaluated through extensive experiments, which show that the proposed heuristic outperforms a simulated annealing method tested and is able to prescribe the optimal solutions for problems in small scales.     

Minimization of maximum tardiness on unrelated parallel machines with process restrictions and setups

We consider the problem of scheduling N jobs on M unrelated parallel machines to minimize maximum tardiness. Each job has a due date and requires a single stage of processing. A setup for dies is incurred if the type of the job scheduled is different from the previous one on that machine. For each die type, the number of dies is restricted. Because of the mechanical structure of the machines and the fitness of dies to each machine, the processing time depends on both the job and the machine. In this paper, an efficient heuristic based on guided search, record-to-record travel, and tabu lists is presented to minimize maximum tardiness. Computational characteristics of the proposed heuristic are evaluated through extensive experiments, which show that the proposed heuristic outperforms a simulated annealing method tested and is able to prescribe the optimal solutions for problems in small scales.     

Algorithms for flexible flow shop problems with unrelated parallel machines, setup times, and dual criteria

In textile industries, production facilities are established as multi-stage production flow shop facilities, where a production stage may be made up of parallel machines. This known as a flexible or hybrid flow shop environment. This paper considers the problem of scheduling n independent jobs in such an environment. In addition, we also consider the general case in which parallel machines at each stage may be unrelated. Each job is processed in ordered operations on a machine at each stage. Its release date and due date are given. The preemption of jobs is not permitted. We consider both sequence- and machine-dependent setup times. The problem is to determine a schedule that minimizes a convex combination of makespan and the number of tardy jobs. A 0–1 mixed integer program of the problem is formulated. Since this problem is NP-hard in the strong sense, we develop heuristic algorithms to solve it approximately. Firstly, several basic dispatching rules and well-known constructive heuristics for flow shop makespan scheduling problems are generalized to the problem under consideration. We sketch how, from a job sequence, a complete schedule for the flexible flow shop problem with unrelated parallel machines can be constructed. To improve the solutions, polynomial heuristic improvement methods based on shift moves of jobs are applied. Then, genetic algorithms are suggested. We discuss the components of these algorithms and test their parameters. The performance of the heuristics is compared relative to each other on a set of test problems with up to 50 jobs and 20 stages.     

Scheduling on unrelated parallel machines with sequence- and machine-dependent setup times and due-date constraints

We consider the unrelated parallel-machine scheduling problem with sequence- and machine-dependent setup times and due-date constraints. There are N jobs, each having a due date and requiring a single operation on one of the M machines. A setup is required if there is a switch from processing one type of job to another. Due to the characteristics of machines, the processing time depends upon the job and machine on which the job is processed, and the setup time is sequence and machine dependent. In addition, certain jobs have strict due-date constraints. An effective heuristic based on a modified apparent-tardiness-cost-with-setup procedure, the simulated annealing method, and designed improvement procedures is proposed to minimize the total tardiness of this scheduling problem. Computational characteristics of the proposed heuristic are evaluated through an extensive experiment using a newly created data set. Computational results show that the proposed heuristic is able to effectively improve the initial solutions, obtained by a modified apparent-tardiness-cost-with-setup procedure, and obtains better results than a random descent heuristic.     

Parallel machine scheduling with earliness-tardiness penalties and space limits

In order to maximize an availability of machine and utilization of space, the parallel machines scheduling problem with space limit is frequently discussed in the industrial field. In this paper, we consider the parallel machine scheduling problem in which n jobs having different release times, due dates, and space limits are to be scheduled on m parallel machines. The objective function is to minimize the weighted sum of earliness and tardiness. To solve this problem, a heuristic is developed which is divided into three modules hierarchically: job selection, machine selection and job sequencing, and solution improvement. To illustrate its effectiveness, a proposed heuristic is compared with genetic algorithm (GA), hybrid genetic algorithm (HGA), and tabu search (TS), which are well-known meta-heuristics in a large number of randomly generated test problems based on the field situation. Also, we determine the job selection rule that is suitable to the problem situation considered in this paper and show the effectiveness of our heuristic method.     

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.     

调整时间与顺序相关的等同并行机调度

调整时间与顺序相关的等同并行机调度在生产服务业与制造业中有着十分广泛的应用背景,具有计算复杂性的主要特点。调整时间与顺序相关的等同并行机调度是将被加工工件集的各工件分配给等同并行机资源,并安排工件的加工次序。它是决策的一种形式,其目的是优化一个或多个目标。研究以最小化被加工工件最大完工时间为目标的调整时间与顺序相关的等同并行机调度,建立该问题的数学规划模型,根据问题的结构特点开发基于两段式染色体表达的遗传算法以获得该问题的近似最优解;在所建立数学规划模型的基础上,引入所求解问题的下界对近似最优解的质量进行评价。对具有不同规模的问题实例进行计算试验,计算结果表明所设计的遗传算法能够在可接受的计算时间内获得合理的解。     

Workflow balancing strategies in parallel machine scheduling

Workflow balancing on a shop floor helps to remove bottlenecks present in the manufacturing system. Workflow refers to the total time during which the work centres are busy. Idle time is not taken into account when calculating workflow. Earlier researchers have not specified the method for jobs to be executed in parallel in order to balance the workflow to each machine. In many manufacturing environments, multiple processing stations are used in parallel to obtain adequate capacity. In parallel machine scheduling there are m machines to which n jobs are to be assigned based on different priority strategies. The procedure is based on the idea of workload balancing and on balancing the workload among machines. In this paper, workflow and workload are assumed to have the same meaning. A machine with the lowest workflow is selected for assignment of a new job from the list of unfinished jobs. Different priority strategies are followed for the selection of jobs. Three different strategies are considered, namely random (RANDOM), shortest processing time (SPT) and longest processing time (LPT) for the selection of jobs for workflow balancing. The relative percentage of imbalance (RPI) is adopted among the parallel machines to evaluate the performance of these strategies in a standard manufacturing environment. The LPT rule shows better performance for the combination of larger job sizes and higher number of work centres or machines. A computer program was coded for validation in a standard manufacturing environment on an IBM/PC compatible system in the C++ language.     

Minimizing total weighted tardiness on heterogeneous batch processing machines with incompatible job families

This paper addresses a specific class of scheduling parallel batching problem, which is observed in steel casting industries. The focus of this research is to minimize the total weighted tardiness on heterogeneous batch processing machines under conditions of dynamic job arrivals, incompatible job families and non-identical job sizes. This type of parallel batching problem arises in a number of different settings, including diffusion in wafer fabrication, heat treatment operations in aircraft industries, and metal working. The problem is viewed as a three stage-decision-problem: the first stage involves selecting a machine from the heterogeneous batch processing machines for scheduling; the second stage involves the selection of a job family from the available incompatible job families; and the third stage involves the selection of a set of jobs to create a batch from the selected job family based on the capacity of the selected batch-processing machine. Since the problem is NP-hard, a few greedy heuristics are proposed. The computational experiments show that the proposed greedy heuristic algorithms are capable of consistently obtaining near-optimal solutions (statistically estimated) in very reasonable computational time on a Pentium III 650 Mz with 128 MB RAM.     

Minimizing total weighted tardiness on heterogeneous batch processing machines with incompatible job families

This paper addresses a specific class of scheduling parallel batching problem, which is observed in steel casting industries. The focus of this research is to minimize the total weighted tardiness on heterogeneous batch processing machines under conditions of dynamic job arrivals, incompatible job families and non-identical job sizes. This type of parallel batching problem arises in a number of different settings, including diffusion in wafer fabrication, heat treatment operations in aircraft industries, and metal working. The problem is viewed as a three stage-decision-problem: the first stage involves selecting a machine from the heterogeneous batch processing machines for scheduling; the second stage involves the selection of a job family from the available incompatible job families; and the third stage involves the selection of a set of jobs to create a batch from the selected job family based on the capacity of the selected batch-processing machine. Since the problem is NP-hard, a few greedy heuristics are proposed. The computational experiments show that the proposed greedy heuristic algorithms are capable of consistently obtaining near-optimal solutions (statistically estimated) in very reasonable computational time on a Pentium III 650 Mz with 128 MB RAM.     

Scheduling algorithms for two-stage reentrant hybrid flow shops: minimizing makespan under the maximum allowable due dates

We consider the scheduling problem in hybrid flow shops that consist of two stages in series, each of which has multiple identical parallel machines. Each job has reentrant flow, i.e., the job visits each production stage several times. The problem is to determine the allocation of jobs to machines as well as the sequence of the jobs assigned to each machine for the objective of minimizing makespan subject to the maximum allowable due dates in the form of a constraint set with a certain allowance. To solve the problem, two types of algorithms are suggested: (a) a branch and bound algorithm that gives optimal semi-permutation schedules; and (b) heuristic algorithms that give non-permutation schedules. To show their performances, computational experiments were done on a number of test problems and the results are reported. In particular, one of the heuristics is competitive to the branch and bound algorithm with respect to the solution quality while requiring much shorter computation times.     

互替机床提前/延期惩罚调度问题的启发式算法

对以作业提前或延期惩罚因素之和最小为目标函数的互替机床调度问题进行了描述，提出和阐述了一种四段式启发式算法，并通过大量不同规模的问题仿真对该算法进行了评价分析，结果表明该算法可行、有效。     

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.     

Scheduling on identical parallel machines to minimize total completion time with deadline and machine eligibility constraints

This study addresses the identical parallel machine scheduling problem with job deadlines and machine eligibility constraints to minimize total job completion time. Jobs must be completed before or at a deadline and preemptions are not allowed. Every job is allowed to be processed on a specified subset of machines. This problem is NP-hard. A heuristic and a branch and bound algorithm are developed to solve the problem. For the branch and bound algorithm, a lower bound based on the dual solution of the assignment problem is proposed and the heuristic serves as the initial upper bound. Many dominance rules are developed to curtail the branching nodes during the search procedure. Computational results indicate that the lower bound improves the performance of those in the literature in terms of execution time, and heuristic consistently generates a good quality schedule.     

Mathematical model and parallel genetic algorithm for hybrid flexible flowshop lot streaming problem

Lot streaming is the technique of splitting a given job into sublots to allow the overlapping of successive operations in multi-stage manufacturing systems thereby reducing production makespan. Several research articles appeared in literature to solve this problem and most of these studies are limited to pure flowshop environments where there is only a single machine in each stage. On the other hand, because of the applicability of hybrid flowshops in different manufacturing settings, the scheduling of these types of shops is also extensively studied by several authors. However, the issue of lot streaming in hybrid flowshop environment is not well studied. In this paper, we aim to contribute in bridging the gap between the research efforts in flowshop lot streaming and hybrid flowshop scheduling. We propose a mathematical model and a genetic algorithm for the lot streaming problem of several jobs in multi-stage flowshops where at each stage there are unrelated parallel machines. The jobs may skip some of the stages, and therefore, the considered system is a complex generalized flowshop. The proposed genetic algorithm is executed on both sequential and parallel computing platforms. Numerical examples showed that the parallel implementation greatly improved the computational performance of the developed heuristic.     

Performance Comparison of Some Classes of Flexible Flow Shops and Job Shops

Flexible manufacturing systems (FMSs) for two-stage production may possess a variety of operating flexibilities in the form of tooling capabilities for the machines and alternative routings for each operation. In this paper, we compare the throughput performance of several flexible flow shop and job shop designs. We consider two-stage assembly flow shops with m parallel machines in stage 1 and a single assembly facility in stage 2. Every upstream operation can be processed by any one of the machines in stage 1 prior to the assembly stage. We also study a similar design where every stage 1 operation is processed by a predetermined machine. For both designs, we present heuristic algorithms with good worst-case error bounds and show that the average performance of these algorithms is near optimal. The algorithms presented are used to compare the performance of the two designs with each other and other related flexible flow shop designs. It is shown, both analytically and experimentally, that the mode of flexibility possessed by a design has implications on the throughput performance of the production system.     

Heuristics for makespan minimization on parallel batch processing machines with unequal job ready times

This research aims at minimizing the makespan of a set of identical batch processing machines arranged in parallel. Each job is defined by its processing time, ready time, and size. Each machine can process several jobs simultaneously as long as the machine capacity is not exceeded. The batch processing and ready times depend upon the batch composition. The batch processing time is equal to the longest processing job in the batch, and the batch ready time is equal to the largest ready time among those jobs in the batch. The problem under study is NP-hard. Consequently, a constructive heuristic is proposed and its performance with respect to solution quality and computational cost is compared against other solution approaches found in the literature. The computational experiments on a set of randomly generated instances show that the performance of the proposed heuristic is competitive with respect to solution quality and requires little computational cost.     

面向实际生产的冲压车间调度问题研究

在大部分对汽车冲压车间调度的研究中,冲压车间被简化为一类job shop模型的作业车间。根据汽车双向冲压生产线的实际生产特点,笔者提出了基于工艺约束并行机的双向冲压生产线调度模型。在该模型中,工件按设备顺序在生产线两端同时加工,且加工的工件及其加工时间和完工时间受两端工件工序数目约束。然后设计了启发规则和遗传算法混合的求解算法,最后以最大完工时间为优化指标进行验证,得到了具有很强实际应用价值的调度结果。     

Scheduling jobs on parallel machines: a restricted tabu search approach

Many real scheduling problems are often much more complex than problems that are analytically tractable. The main difficulty in obtaining optimal job schedules arises from the existence of sequence dependent setup times among jobs and job release times. In this paper, we present a restricted tabu search algorithm that schedules jobs on parallel machines in order to minimise the maximum lateness of the jobs. The jobs have release times and due dates, and sequence-dependent setup times exist between the jobs. The parallel machines are either identical or non-identical in terms of the processing times of the jobs. The restricted tabu search algorithm employs a restricted search with the elimination of non-effective job moves, for finding the best neighbourhood schedule. The restricted search algorithm reduces search effort significantly while obtaining good quality final schedule. The experimental results show that the proposed algorithm obtains much better solutions more quickly than other heuristic algorithms such as the Rolling Horizon Procedure (RHP) heuristic, the basic tabu search and simulated annealing.     

A due date density-based categorising heuristic for parallel machines scheduling

The effective management of shop floor resources is an important factor in achieving the goals of a manufacturing company. The need for effective scheduling is particularly strong in complex manufacturing environments. This paper presents an efficient due date density-based categorising heuristic to minimise the total weighted tardiness (TWT) of a set of tasks with known processing times, due dates, weights and sequence-dependent setup times for parallel machines scheduling. The proposed heuristic is composed of four phases. In the first phase, jobs are listed by the earliest due date (EDD). The second phase computes the due date gaps between listed jobs and categorises the jobs based on the due date density. In the third phase, the sequence of jobs is improved by a tabu search (TS) method. The fourth phase allocates each job to machines. The comprehensive simulation results show that the proposed heuristic performs better than other existing heuristics at a significantly reduced total weighted tardiness.