Integrated scheduling and flexible maintenance in deteriorating multi-state single machine system using a reinforcement learning approach

This paper studies an integrated optimization problem of production scheduling and flexible preventive maintenance (PM) in a multi-state single machine system with deteriorating effects. A flexible PM strategy is proposed to proactively cope with machine failures while ensuring relatively regular PM intervals, which is composed of time-based PM (TBPM) and condition-based PM (CBPM). TBPM is conducted within every flexible time window and CBPM is implemented immediately after the most deteriorated yet still functional state. An illustrative case is presented using the enumeration approach to demonstrate the integration of production scheduling and machine maintenance. Then, Q-learning-based solution framework (QLSF) is further designed with proper state and action sets and reward functions to facilitate the determination of appropriate production scheduling rule under the constraint of the flexible maintenance. Numerical experiments show that the proposed QLSF outperforms the other four state-of-the-art scheduling rules in different scenarios. Moreover, the performance of the proposed flexible PM strategy is also examined and validated in comparison with three candidate maintenance strategies, i.e., run-to-failure corrective maintenance (CM), combination of TBPM and CM, and CBPM. The proposed flexible maintenance and solution approach can enrich the relevant academic knowledge base, and provide managerial insights and guidance in practical production systems.     

Joint optimization of job scheduling and maintenance planning for a two-machine flow shop considering job-dependent operating condition

Two-machine flow shops are widely adopted in manufacturing systems. To minimize the makespan of a sequence of jobs, joint optimization of job scheduling and preventive maintenance (PM) planning has been extensively studied for such systems. In practice, the operating condition (OC) of the two machines usually varies from one job to another because of different processing covariates, which directly affects the machines’ failure rates, PM plans, and expected job completion times. This fact is common in many real systems, but it is often overlooked in the related literature. In this study, we propose a joint decision-making strategy for a two-machine flow shop with resumable jobs. The objective is to minimize the expected makespan by taking into account job-dependent OC. We consider two situations. In the first situation, where the failure rate of a machine under a fixed OC is constant, a hybrid processing time model is proposed to obtain the optimal job sequence based on the Johnson's law. For the second situation, where the failure rate of a machine is time-varying, the job sequence and PM plan are jointly optimized. An enumeration method is adopted to find the optimal job sequence and PM plan for a small-scale problem, and a genetic algorithm-based method is proposed to solve a large-scale problem. Numerical examples are provided to demonstrate the necessity of considering the effect of job-dependent OC and the effectiveness of the proposed method in handing such joint decision-making problems in manufacturing systems.     

求解柔性作业车间调度的GATOC混合方法

柔性作业车间调度问题是经典作业车间调度问题的扩展,它允许工序在可选加工机器集中任意一台上加工,加工时间随加工机器不同而不同。针对柔性作业车间调度问题的特点,提出一种基于约束理论的局部搜索方法,对关键路径上的机器的负荷率进行比较,寻找瓶颈机器,以保证各机器之间的负荷平衡。为了克服传统遗传算法早熟和收敛慢的缺点,设计多种变异操作,增加种群多样性。为了更好保留每代中的优良解,设计了基于海明距离的精英解保留策略。运用提出的算法求解基准测试问题,验证了算法的可行性和有效性。     

An effective heuristic for flexible job-shop scheduling problem with maintenance activities

Most production scheduling problems, including the standard flexible job-shop scheduling problem (FJSP), assume that machines are continuously available. However, in most realistic situations, machines may become unavailable during certain periods due to preventive maintenance (PM). In this paper, a flexible job-shop scheduling problem with machine availability constraints is considered. Each machine is subject to preventive maintenance during the planning period and the starting times of maintenance activities are either flexible in a time window or fixed beforehand. Moreover, two cases of maintenance resource constraint are considered: sufficient maintenance resource available or only one maintenance resource available. To deal with this variant FJSP problem with maintenance activities, a filtered beam search (FBS) based heuristic algorithm is proposed. With a modified branching scheme, the machine availability constraint and maintenance resource constraint can be easily incorporated into the proposed algorithm. Simulation experiments are conducted on some representative problems. The results demonstrate that the proposed filtered beam search based heuristic algorithm is a viable and effective approach for the FJSP with maintenance activities.     

基于改进遗传算法的单机成组作业调度

提出了单机成组作业调度的改进遗传算法。优化目标为总流程时间的单机成组作业调度问题明显是NP-hard问题,此问题的多项式求解方法不能求取最优解,而一些启发式算法也只能求出此问题的次优解。为获得单机成组作业最优调度,通过采用整数实值编码,随机采样选择,单点交叉以及变异检查,设计了单机成组作业调度的改进遗传算法。仿真结果表明,算法能够找到此问题的最优解,其性能优于加权最短加工时间(WSPT)启发式算法。改进遗传算法能够灵活解决各种单目标调度及多目标调度问题。     

Unrelated parallel-machine scheduling with aging effects and multi-maintenance activities

Machine maintenance is often performed in manufacturing to prevent premature machine failures with a view to sustaining production efficiency. In this paper we study the parallel-machine scheduling problem with aging effects and multi-maintenance activities simultaneously. We assume that each machine may be subject to several maintenance activities over the scheduling horizon. A machine reverts to its initial condition after maintenance and the aging effects start anew. The objective is to find jointly the optimal maintenance frequencies, the optimal positions of the maintenance activities, and the optimal job sequences such that the total machine load is minimized. We apply the group balance principle to obtain the optimal positions of the maintenance activities and the number of jobs in each group in the scheduling sequence on each machine. We provide an efficient algorithm to solve the problem when the maintenance frequencies on the machines are given.     

Hybrid genetic algorithms with dispatching rules for unrelated parallel machine scheduling with setup time and production availability

This article considers the unrelated parallel machine scheduling problem with sequence- and machine-dependent setup times and machine-dependent processing times. Furthermore, the machine has a production availability constraint to each job. The objective of this problem is to determine the allocation policy of jobs and the scheduling policy of machines to minimize the total completion time. To solve the problem, a mathematical model for the optimal solution is derived, and hybrid genetic algorithms with three dispatching rules are proposed for large-sized problems. To assess the performance of the algorithms, computational experiments are conducted and evaluated using several randomly generated examples.     

A heuristic algorithm to minimize total weighted tardiness on a single machine with release times

This paper attempts to solve a single machine‐scheduling problem, in which the objective function is to minimize the total weighted tardiness with different release dates of jobs. To address this scheduling problem, a heuristic scheduling algorithm is presented. A mathematical programming formulation is also formulated to validate the performance of the heuristic scheduling algorithm proposed herein. Experimental results show that the proposed heuristic algorithm can solve this problem rapidly and accurately. Overall, this algorithm can find the optimal solutions for 2200 out of 2400 randomly generated problems (91.67%). For the most complicated 20 job cases, it requires less than 0.0016 s to obtain an ultimate or even optimal solution. This heuristic scheduling algorithm can therefore efficiently solve this kind of problem.     

A hybrid artificial immune algorithm for a realistic variant of job shops to minimize the total completion time

This paper investigates an extended problem of job shop scheduling to minimize the total completion time. With aim of actualization of the scheduling problems, many researchers have recently considered realistic assumptions in their problems. Two of the most applied assumptions are to consider sequence-dependent setup times and machine availability constraints (MACs). In this paper, we deal with a specific case of MACs caused by preventive maintenance (PM) operations. Contrary to the previous papers considering fixed or/and conservative policies, we consider flexible PM operations, in which PM operations may be postponed or expedited as required. A simple technique is employed to schedule production jobs along with the flexible MACs caused by PM. To solve the given problem, we present a novel meta-heuristic method based on the artificial immune algorithm (AIA) incorporating some advanced features. For further enhancement, the proposed AIA is hybridized with a simple and fast simulated annealing (SA). To evaluate the proposed algorithms, we compare our proposed AIA with three well-known algorithms taken from the literature. Finally, we find that the proposed AIA outperforms other algorithms.     

求解工件车间调度问题的一种新的邻域搜索算法

该文提出了一种新的求解工件车间调度(job shop scheduling)问题的邻域搜索算法．问题的目标是：在满足约束条件的前提下使得调度的makespan尽可能地小．定义了一种新的优先分配规则以生成初始解;定义了一种新的邻域结构;将邻域搜索跟单机调度结合在一起;提出了跳坑策略以跳出局部最优解并且将搜索引向有希望的方向．计算了当前国际文献中的一组共58个benchmark问题实例,算法的优度高于当前国外学者提出的两种著名的先进算法．其中对18个10工件10机器的实例,包括最著名的难解实例ft10,在可接受的时间内都找到了最优解．这些实例是当前文献中报导的所有规模为10工件10机器的实例．     

A heuristic method for two-stage hybrid flow shop with dedicated machines

This paper considers a two-stage hybrid flow shop scheduling problem with dedicated machines, in which the first stage contains a single common critical machine, and the second stage contains several dedicated machines. Each job must be first processed on the critical machine in stage one and depending on the job type, the job will be further processed on the dedicated machine of its type in stage two. The objective is to minimize the makespan. To solve the problem, a heuristic method based on branch and bound (B&B) algorithm is proposed. Several lower bounds are derived and four constructive heuristics are used to obtain initial upper bounds. Then, three dominance properties are employed to enhance the performance of the proposed heuristic method. Extensive computational experiments on two different problem categories each with various problem configurations are conducted. The results show that the proposed heuristic method can produce very close-to-optimal schedules for problems up to 100 jobs and five dedicated machines within 60 s. The comparisons with solutions of two other meta-heuristic methods also prove the better performance of the proposed heuristic method.     

A robust hybrid approach based on particle swarm optimization and genetic algorithm to minimize the total machine load on unrelated parallel machines

This paper dealt with an unrelated parallel machines scheduling problem with past-sequence-dependent setup times, release dates, deteriorating jobs and learning effects, in which the actual processing time of a job on each machine is given as a function of its starting time, release time and position on the corresponding machine. In addition, the setup time of a job on each machine is proportional to the actual processing times of the already processed jobs on the corresponding machine, i.e., the setup times are past-sequence-dependent (p-s-d). The objective is to determine jointly the jobs assigned to each machine and the order of jobs such that the total machine load is minimized. Since the problem is NP-hard, optimal solution for the instances of realistic size cannot be obtained within a reasonable amount of computational time using exact solution approaches. Hence, an efficient method based on the hybrid particle swarm optimization (PSO) and genetic algorithm (GA), denoted by HPSOGA, is proposed to solve the given problem. In view of the fact that efficiency of the meta-heuristic algorithms is significantly depends on the appropriate design of parameters, the Taguchi method is employed to calibrate and select the optimal levels of parameters. The performance of the proposed method is appraised by comparing its results with GA and PSO with and without local search through computational experiments. The computational results for small sized problems show that the mentioned algorithms are fully effective and viable to generate optimal/near optimal solutions, but when the size of the problem is increased, the HPSOGA obtains better results in comparison with other algorithms.     

考虑多目标的柔性工艺与调度集成优化算法

针对工艺规划与车间调度集成优化问题,在考虑零件的加工工序柔性、工序次序柔性及加工机器柔性的基础上,以最大完工时间、总加工成本和总拖期时间为优化目标,对多目标柔性工艺与车间调度集成问题建模,提出一种基于改进人工蜂群算法的多目标柔性工艺与车间调度集成优化策略,并提出邻域变异操作以及全局交叉操作,对种群进行更新。引入Pareto方法,通过对适应度评价、贪婪准则、Pareto最优解集构造和保存以及解得多样性维护等方面进行改进,设计了一种基于Pareto方法的多目标人工蜂群算法。最后,通过采用基本人工蜂群算法及改进人工蜂群算法对六个工件、五台机床的柔性工艺与车间调度集成问题进行优化,验证了改进算法的有效性。     

An approximate nondominated sorting genetic algorithm to integrate optimization of production scheduling and accurate maintenance based on reliability intervals

With the development of intelligent manufacturing, production scheduling and preventive maintenance are widely applied in industry to enhance production efficiency and machine reliability. Therefore, according to the different processing states and the physical degradation phenomena of the machine, this paper proposes an accurate maintenance (AM) model based on reliability intervals, which have different maintenance activities in diverse intervals and overcome the shortcoming of the single reliability threshold maintenance model used in the past. Combining the flexible job-shop scheduling problem (FJSP), an integrated multiobjective optimization model is established with production scheduling and accurate maintenance. To strengthen the ability of the evolutionary algorithm to solve the presented model/problem, we propose a novel genetic algorithm, named the approximate nondominated sorting genetic algorithm III (ANSGA-III), which is inspired by NSGA-III. To improve the performance of the Pareto dominance principle, the local search, the elite storage for the original algorithm, the approximate dominance principle, the variable neighborhood search, and the elite preservation strategy are proposed. Then, we employ a scheduling example to verify and evaluate the availability of the above three improved operations and the proposed algorithm. Next, we compare ANSGA-III against five recently proposed algorithms, representing the state-of-the-art on similar problems. Finally, we apply ANSGA-III to solve the integrated optimization model, and the results reveal that the machine can maintain higher availability and reliability when compared to other models in our experiments. Consequently, the superiority of the proposed model based on accurate maintenance of reliability intervals is demonstrated, and the optimal reliability threshold between the yellow and red areas is found to be 0.82.     

复杂并行机调度问题基于分解的优化算法

针对纺织生产过程中广泛存在的带特殊工艺约束的大规模并行机调度问题，提出了一种基于分解的优化算法。首先将原调度问题分解为机台选择和工件排序两个子问题，然后针对机台选择子问题提出一种进化规划算法，并采用一种具有多项式时间复杂度的最优算法求解工件排序子问题，以得到问题特征信息（即每台机器对应拖期工件数的最小值），该问题特征信息用以指导进化规划算法的迭代过程。不同规模并行机调度问题的数值计算结果及实际制造企业应用效果表明，本文提出的算法是有效的。     

An integrated search heuristic for large-scale flexible job shop scheduling problems

The flexible job shop scheduling problem (FJSP) is a generalization of the classical job shop scheduling problem (JSP), where each operation is allowed to be processed by any machine from a given set, rather than one specified machine. In this paper, two algorithm modules, namely hybrid harmony search (HHS) and large neighborhood search (LNS), are developed for the FJSP with makespan criterion. The HHS is an evolutionary-based algorithm with the memetic paradigm, while the LNS is typical of constraint-based approaches. To form a stronger search mechanism, an integrated search heuristic, denoted as HHS/LNS, is proposed for the FJSP based on the two algorithms, which starts with the HHS, and then the solution is further improved by the LNS. Computational simulations and comparisons demonstrate that the proposed HHS/LNS shows competitive performance with state-of-the-art algorithms on large-scale FJSP problems, and some new upper bounds among the unsolved benchmark instances have even been found.     

Use of (max, +) algebra for scheduling and optimization of HVLV systems subject to preventive maintenance

High-Variety, Low-Volume (HVLV) manufacturing systems are built to produce parts of several types in small quantities and under multiple production objectives. They relate to job-shop systems well known by researchers. One of the most studied assumptions of HVLV systems scheduling is considering that machines may be periodically unavailable during the production scheduling. This article deals with an analytical integrating method using (max, +) algebra to model HVLV scheduling problems subject to preventive maintenance (PM) while considering machines availability constraints. Each machine is subject to PM while maintaining flexibility for the start time of the maintenance activities during the planning period. The proposed model controls the placement of maintenance activities along the production operations. Indeed, the sequencing of maintenance activities on the machines depends on the criteria to minimize and may be different for each criteria value. For preventive maintenance, the proposed model aims to generate the best sequencing between activities while respecting the planning program that satisfy the optimal criteria values. In order to illustrate the performance of the proposed methodology, a simulation example is given.     

New integration of preventive maintenance and production planning with cell formation and group scheduling for dynamic cellular manufacturing systems

This paper proposes a new integration method for cell formation, group scheduling, production, and preventive maintenance (PM) planning problems in a dynamic cellular manufacturing system (CMS). The cell formation sub-problem aims to form part families and machine groups, which minimizes the inter-cell material handling, under-utilization, and relocation costs. The production planning aspect is a multi-item capacitated lot-sizing problem accompanied by sub-contracting decisions, while the group scheduling problem deals with the decisions on the sequential order of the parts and their corresponding completion times. The purpose of the maintenance sub-problem is to determine the availability of the system and the time when the noncyclical perfect PM must be implemented to reduce the number of corrective actions. Numerical examples are generated and solved by Bender’s decomposition pack in GAMS to evaluate the interactions of the proposed model. Statistical analysis, based on a nonparametric method, is also used to study the behavior of the model’s cost components in two different situations. It is shown that by adding the PM planning decisions to the tactical decisions of the dynamic CMS, the optimal configuration and production plans of the system are heavily affected. The results indicate that omitting the PM actions increases the number of sudden failures, which leads to a higher total cost. Finally, it is concluded that the boost in the total availability of the dynamic CMS is one of the main advantages of the proposed integrated method.     

Hybrid Evolutionary Algorithm for job scheduling under machine maintenance

The job scheduling problem (JSP) belongs to the well-known combinatorial optimization domain. After scheduling, if a machine maintenance issue affects the scheduled processing of jobs, the delivery of jobs must be delayed. In this paper, we have first proposed a Hybrid Evolutionary Algorithm (HyEA) for solving JSPs. We have then analyzed the effect of machine maintenance, whether preventive or breakdown, on the job scheduling. For the breakdown maintenance case, it is required to revise the algorithm to incorporate a rescheduling option after the breakdown occurs. The algorithm has been tested by solving a number of benchmark problems and thence comparing them with the existing algorithms. The experimental results provide a better understanding of job scheduling and the necessary rescheduling operations under process interruption.     

Group shops scheduling with makespan criterion subject to random release dates and processing times

This paper deals with a stochastic group shop scheduling problem. The group shop scheduling problem is a general formulation that includes the other shop scheduling problems such as the flow shop, the job shop and the open shop scheduling problems. Both the release date of each job and the processing time of each job on each machine are random variables with known distributions. The objective is to find a job schedule which minimizes the expected makespan. First, the problem is formulated in a form of stochastic programming and then a lower bound on the expected makespan is proposed which may be used as a measure for evaluating the performance of a solution without simulating. To solve the stochastic problem efficiently, a simulation optimization approach is developed that is a hybrid of an ant colony optimization algorithm and a heuristic algorithm to generate good solutions and a discrete event simulation model to evaluate the expected makespan. The proposed approach is tested on instances where the random variables are normally, exponentially or uniformly distributed and gives promising results.