求解Job Shop问题的一种免疫模拟退火算法

针对以最小化加权拖期和为优化目标的Job Shop调度问题,提出了一种基于瓶颈工件识别的免疫模拟退火算法。为描述各工件对最终调度性能影响的关键程度,定义了工件瓶颈特征量并提出基于人工调度经验的模糊推理系统以计算该特征量值。根据瓶颈工件需优先调度这一思路设计了一种有效利用工件瓶颈特征信息的免疫机制。在模拟退火过程中引入该免疫算法,并进行了大量数值计算实验。对不同规模问题的计算实例表明,该算法能够加快优化过程的收敛速度,取得较好的优化结果。     

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.     

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.     

A rolling horizon job shop rescheduling strategy in the dynamic environment

In this paper, the job shop scheduling problem in a dynamic environment is studied. Jobs arrive continuously, machines breakdown, machines are repaired and due dates of jobs may change during processing. Inspired by the rolling horizon optimisation method from predictive control technology, a periodic and event-driven rolling horizon scheduling strategy is presented and adapted to continuous processing in a changing environment. The scheduling algorithm is a hybrid of genetic algorithms and dispatching rules for solving the job shop scheduling problem with sequence-dependent set-up time and due date constraints. Simulation results show that the proposed strategy is more suitable for a dynamic job shop environment than the static scheduling strategy.     

Due-date scheduling on parallel machines with job splitting and sequence-dependent major/minor setup times

This paper addresses job scheduling problems with parallel machines. To satisfy customers better in a manufacturing company, meeting due dates has been an important performance metric. Besides the numerous other factors affecting due date satisfaction, the splitting of a job through parallel machines can contribute to the reduction of production lead time, resulting in less job tardiness against their due dates. Thus, this paper presents heuristic algorithms for minimizing total tardiness of jobs to meet their due dates in a manufacturing shop with identically functioning machines. The algorithms take into account job splitting and sequence-dependent major/minor setup times. The performance of the proposed heuristics is compared with that of past three algorithms in the literature.     

并行多机提前/拖期调度的启发式算法

准时制生产模式要求生产任务必须在交货期内完成.实际生产中这一问题受很多约束的影响变得非常复杂.文章针对任务动态到达、任务转换存在的调整时间和交货期、提前/拖期单位成本各不相同的并行多机上任务排序问题进行了分析,设计了一种解决并行多机提前/拖期调度的启发式近似求解算法.大量实验数据和应用实例充分表明文章所提的启发式算法是有效的.     

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.     

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.     

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.     

Unrelated parallel machine scheduling with secondary resource constraints

This paper considers unrelated parallel machine scheduling with secondary resource constraints. There are n jobs, each needing to be processed on one of the fitted machines. A setup that includes detaching one die and attaching another from the fitted die type is incurred if the type of job scheduled is different from the last job on that machine. For each kind of die type, the number of dies available is limited. Due to the mechanical structure of the machines, the processing time of a job depends on the machine on which the job is processed, and some jobs are restricted to be processed only on certain machines. In this paper, a heuristic with a capability relative to a runtime and solution quality is developed to minimise the makespan. The performance of the presented heuristic is evaluated through extensive computational experiments. Computational results show that the presented heuristic outperforms the search method tested. It is expected that this research can be applied in industry where unrelated parallel machines are used to process different components and setups for auxiliary equipments are required.     

求解车间调度问题的改进型自适应遗传算法

针对作业车间调度问题,以最小化完工时间为目标,借鉴内分泌激素调节机制,提出了一种新颖的改进型自适应遗传算法.通过引入自适应交叉概率和变异概率因子,克服了传统的遗传算法在解决生产调度问题时存在的搜索精度低和收敛性难以控制等问题,并在Microsoft Visual C++6.0中实现了该算法.通过一个10工件、10机器作...     

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。     

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.     

A heuristic approach to minimize expected makespan in open shops subject to stochastic processing times and failures

Many real world situations exist where job scheduling is required. This is the case of some entities, machines, or workers who have to execute certain jobs as soon as possible. Frequently what happens is that several workers or machines are not available to perform their activities during some time periods, due to different circumstances. This paper deals with these situations, and considers stochastic scheduling models to study these problems. When scheduling models are used in practice, they have to take into account that some machines may not be working. That temporal lack of machine availability is known as breakdowns, which happen randomly at any time. The times required to repair those machines are also random variables. The jobs have operations with stochastic processing times, their own release times, and there is no precedence between them. Each job is divided into operations and each operation is performed on the corresponding specialized machine. In addition, in the problems considered, the order in which the operations of each job are done is irrelevant. We develop a heuristic approach to solve these stochastic open-shop scheduling problems where random machine breakdowns can happen. The proposed approach is general and it does not depend on the distribution types of the considered random input data. It provides solutions to minimize the expected makespan. Computational experiences are also reported. The results show that the proposed approach gives a solid performance, finding suitable solutions with short CPU times.     

A mixed integer programming formulation for scheduling of virtual manufacturing cells (VMCs)

We present a multi-objective mixed integer programming formulation for job scheduling in virtual manufacturing cells (VMCs). In a VMC, machines are dedicated to a part family as in a regular cell, but machines are not physically relocated in a contiguous area. Cell configurations are therefore temporary, and assignments are made to optimize the scheduling objective under changing demand conditions. We consider the case where there are multiple jobs with different processing routes. There are multiple machine types with several identical machines in each type and are located in different locations in the shop floor. The two scheduling objectives are makespan minimization and minimizing total traveling distance. Since batch splitting is permitted in the system, scheduling decisions must tell us the (a) assignment of jobs to the machines, (b) the job starting time at each machine, and (c) the part quantity processed on different machines due to batch splitting. Under these decision variables, the objective function is to minimize the sum of the makespan and total traveling distance/cost. Illustrative examples are given to demonstrate the implementation of the model.     

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 game-theory approach for job scheduling in networked manufacturing

This paper presents a new kind of scheduling solution for jobs in networked manufacturing environments. The main contributions of this study can be focused on three points: The first is to distinguish the concepts and requirements of job scheduling in the networked manufacturing environment form those in the traditional manufacturing environment. The second is to construct a game-theory mathematical model to deal with this new job scheduling problem. In this presented mathematical model, this new job scheduling problem is formulated as an N-person non-cooperative game with complete information. The players correspond to the jobs submitted, respectively, by related customers and the payoff of each job is defined as its makespan. Each player has a set of strategies which correspond to the feasible geographical distributive machines. Therefore, obtaining the optimal scheduling results is determined by the Nash equilibrium (NE) point of this game. In order to find the NE point, the last point is to design and develop a genetic algorithm (GA)-based solution algorithm to effectively solve this mathematical model. Finally, a numerical example is presented to demonstrate the feasibility of the approach.     

A two-criteria objective function flexible flowshop scheduling problem with machine eligibility constraint

This research deals with a flexible flowshop scheduling problem with the arrival and delivery of jobs in groups and processing them individually. Each group of jobs has a specific release time. Due to the special characteristics of each job, only a specific group of machines in each stage are eligible to process that job. All jobs in a group should be delivered at the same time after processing. The objectives of the problem are the minimization of the sum of the completion time of groups on one hand and the minimization of sum of the differences between the completion time of jobs and the delivery time of the group containing that job (waiting period) on the other hand. The problem can be stated as FF_c /r _j , M _j /irreg based on existing scheduling notations. This problem has many applications in the production and service industries such as ceramic tile manufacturing companies and restaurants. A mathematical model has been proposed to solve the problem. Since the research problem is shown to be NP-complete, a particle swarm optimization (PSO) algorithm is applied to solve the problem approximately. Based on the frequency of using local search procedure, four scenarios of PSO have been developed. The algorithms are compared by applying experimental design techniques on random test problems with different sizes. The results show that the PSO algorithm enhanced with local search for all particles has a weaker performance than the other scenarios in solving large-sized problems.     

Job scheduling and management of wearing tools with stochastic tool lifetimes

The problem of scheduling jobs using wearing tools is studied. Tool wearing is assumed to be stochastic and the jobs are processed in one machining centre provided with a limited capacity tool magazine. The aim is to minimize the expected average completion time of the jobs by choosing their processing order and tool management decisions wisely. All jobs are available at the beginning of the planning period. This kind of situation is met in production planning of CNC-machines. Previous studies concerning this problem have either assumed deterministic wearing for the tools or omitted the wearing completely. In our formulation of the problem, tool wearing is stochastic and the problem becomes very hard to solve analytically. A heuristic based on genetic algorithms is therefore given for the joint problem of job scheduling and tool management. The algorithm searches the most beneficial job sequence when the tool management decisions are made by a removal rule taking into account the future planned usage of the tools. The cost of each job sequence is evaluated by simulating the job processing. Empirical tests with heuristics indicate that by taking the stochastic information into account, one can reduce the average job processing time considerably.     

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。