区间数可重入混合流水车间调度与预维护协同优化

针对加工时间不确定的可重入混合流水车间调度与预维护协同优化问题,构建以区间最大完工时间、区间总碳排放和区间总预维护费用为优化目标的集成调度模型.针对问题特性,通过设计改进的可能度计算方法,定义区间意义下解的Pareto占优关系.提出一种改进的离散鲸鱼群算法,通过同步调度与维护策略,实现制造与维护的联合优化;设计个体间距离计算策略,寻找“最近较优个体”;设计个体位置移动策略以及多邻域搜索策略,有效地平衡全局搜索和局部搜索,提高收敛精度.通过大量的仿真实验和结果对比分析,表明了所提出的算法对于求解区间数可重入混合流水车间调度和预维护协同优化问题的有效性和可行性.     

Optimizing distributed no-wait flow shop scheduling problem with setup times and maintenance operations via iterated greedy algorithm

Nowadays, distributed scheduling problem is a reality in many companies. Over the last years, an increasingly attention has been given to the distributed flow shop scheduling problem and the addition of constraints to the problem. This article introduces the distributed no-wait flow shop scheduling problem with sequence-dependent setup times and maintenance operations to minimize makespan. A mixed-integer linear programming (MILP) is to mathematically describe the problem and heuristic procedures to incorporate maintenance operations to job scheduling are proposed. An Iterated Greedy with Variable Search Neighborhood (VNS), named IG_NM, is proposed to solve small and large instances with size of 4,800 and 13,200 problems, respectively. Computational experiments were conducted to evaluate the performance of IG_NM in comparison with MILP and the most recent methods of literature of distributed flow shop scheduling problems. Statistical results show that in the trade-off between effectiveness and efficiency the proposed IG_NM outperformed other metaheuristics of the literature.     

Distributed assembly permutation flow shop problem; Single seekers society algorithm

The distributed manufacturing and assembly systems have an important role at the point of overcoming the difficulties faced by today's mass-production industry. By using both of these systems together in the same production system, the advantages of this integration can make industries more flexible and stronger. Besides, optimizing these systems is more complicated since the multiple production systems can undoubtfully affect the production system’s performance. In this paper, two new mixed-integer linear programming (MILP) models are proposed for the distributed assembly permutation flow shop problem (DAPFSP), inspiring by the multiple-travelling salesman structure. Moreover, a single seekers society (SSS) algorithm is proposed for solving the DAPFSP to minimize the maximum completion time of all products. The performance of the proposed MILP models is evaluated using 900 small-sized benchmark instances. The proposed MILP models were effective and were able to find more optimal solutions or improve the best-found solutions for the small-sized DAPFSP benchmark instances. Similarly, the SSS algorithm is statistically compared with the best-known algorithms developed for solving the DAPFSP on 900 small and 810 large-sized benchmark instances. The proposed SSS algorithm shows superior performance compared to other algorithms in solving the small-sized DAPFSP instances in terms of finding better solutions. In addition, it is as effective as the best performing algorithms developed to solve the large-sized DAPFSP instances. Furthermore, the best-found solutions for 40 numbers of test problems reported to be improved in this paper.     

Integrated staffing and scheduling for an aircraft line maintenance problem

This paper studies the problem of constructing the workforce schedules of an aircraft maintenance company. The problem involves both a staffing and a scheduling decision. We propose an enumerative algorithm with bounding in which each node of the enumeration tree represents a mixed integer linear problem (MILP). We reformulate the MILP such that it becomes tractable for commercial MILP solvers. Extensive computational tests on 40 instances that are derived from a real-life setting indicate that the algorithm is capable of finding close-to-optimal solutions.     

A genetic algorithm for permutation flow shop scheduling under make to stock production system

The permutation flow shop scheduling is a well-known combinatorial optimization problem that arises in many manufacturing systems. Over the last few decades, permutation flow shop problems have widely been studied and solved as a static problem. However, in many practical systems, permutation flow shop problems are not really static, but rather dynamic, where the challenge is to schedule n different products that must be produced on a permutation shop floor in a cyclical pattern. In this paper, we have considered a make-to-stock production system, where three related issues must be considered: the length of a production cycle, the batch size of each product, and the order of the products in each cycle. To deal with these tasks, we have proposed a genetic algorithm based lot scheduling approach with an objective of minimizing the sum of the setup and holding costs. The proposed algorithm has been tested using scenarios from a real-world sanitaryware production system, and the experimental results illustrates that the proposed algorithm can obtain better results in comparison to traditional reactive approaches.     

解决具有混合约束柔性流水车间调度问题的粒子群优化算法

针对既存在阻塞限制工件又存在无等待约束工件的柔性流水车间调度问题, 提出了一种离散粒子群优化的求解方法。该方法采用基于排列的编码形式, 设计了推进—迭代算法进行解码并计算问题目标值, 利用离散粒子群优化算法进行全局优化, 利用迭代贪婪(iterated greedy, IG)算法提高种群个体的局部搜索能力。此外, 根据问题特点, 提出最早释放优先(first release first, FRF)和最早完工优先(first complete first, FCF)两种机器分配策略。仿真结果表明, 所提出的方法求解混合约束下柔性流水车间调度问题是可行的、有效的。     

An efficient local search for minimizing completion time variance in permutation flow shops

This paper illustrates that by exploiting the structure of hard combinatorial optimization problems, efficient local search schemes can be designed that guarantee performance in solution quality and computational time. A two-phase local search algorithm is developed and applied to the permutation flow shop scheduling problem, with the objective of minimizing the completion time variance. New and significant analytical insights necessary for effectively solving the permutation flow shop problem are also presented and used in this research. Computational results indicate that for test problems, the local search obtained optimal solutions for many instances, within few seconds of CPU time. For other benchmark problems with jobs between 50 and 100, the proposed algorithm, ADJ-Reduced improved the existing best known values within a practical time frame.     

A bi-objective possibilistic programming model for open shop scheduling problems with sequence-dependent setup times, fuzzy processing times, and fuzzy due dates

We are concerned with an open shop scheduling problem having sequence-dependent setup times. A novel bi-objective possibilistic mixed-integer linear programming model is presented. Sequence-dependent setup times, fuzzy processing times and fuzzy due dates with triangular possibility distributions are the main constraints of this model. An open shop scheduling problem with these considerations is close to the real production scheduling conditions. The objective functions are to minimize total weighted tardiness and total weighted completion times. To solve small-sized instances for Pareto-optimal solutions, an interactive fuzzy multi-objective decision making (FMODM) approach, called TH method proposed by Torabi and Hassini, is applied. Using this method, an equivalent auxiliary single-objective crisp model is obtained and solved optimally by the Lingo software. For medium to large size examples, a multi-objective particle swarm optimization (MOPSO) algorithm is proposed. This algorithm consists of a decoding procedure using a permutation list to reduce the search area in the solution space. Also, a local search algorithm is applied to generate good initial particle positions. Finally, to evaluate the effectiveness of the MOPSO algorithm, the results are compared with the ones obtained by the well-known SPEA-II, using design of experiments (DOE) based on some performance metrics.     

面向多目标流水车间调度的多种群多目标遗传算法

针对制造型企业普遍存在的流水车间调度问题,建立了以最小化最迟完成时间和总延迟时间为目标的多目标调度模型,并提出一种基于分解方法的多种群多目标遗传算法进行求解.该算法将多目标流水车间调度问题分解为多个单目标子问题,并分阶段地将这些子问题引入到算法迭代过程进行求解.算法在每次迭代时,依据种群的分布情况选择各子问题的最好解及与其相似的个体分别为当前求解的子问题构造子种群,通过多种群的进化完成对多个子问题最优解的并行搜索.通过对标准测试算例进行仿真实验,结果表明所提出的算法在求解该问题上能够获得较好的非支配解集.     

Minimizing makespan in permutation flow shop scheduling problems using a hybrid metaheuristic algorithm

This paper proposes a hybrid metaheuristic for the minimization of makespan in permutation flow shop scheduling problems. The solution approach is robust, fast, and simply structured, and comprises three components: an initial population generation method based on a greedy randomized constructive heuristic, a genetic algorithm (GA) for solution evolution, and a variable neighbourhood search (VNS) to improve the population. The hybridization of a GA with VNS, combining the advantages of these two individual components, is the key innovative aspect of the approach. Computational experiments on benchmark data sets demonstrate that the proposed hybrid metaheuristic reaches high-quality solutions in short computational times. Furthermore, it requires very few user-defined parameters, rendering it applicable to real-life flow shop scheduling problems.     

基于灾变机制的预防性维护和生产调度集成优化方法

为了解决生产车间中多品种任务的生产调度与预防性维护集成优化问题,综合考虑其加工顺序、生产批量及预防性维护策略等要素,在订单充足的前提下,以总制造成本和加工时间最小化为联合优化目标,建立了生产调度与预防性维护集成优化模型。针对模型特点,在非支配排序遗传算法框架的基础上,基于灾变机制和荣誉空间,引入截断和拼接操作算子,提出一种变长度染色体单亲遗传算法对模型进行求解,并在不同参数条件和问题规模下,通过仿真实验验证了该算法解决复杂生产任务调度和预防性维护集成优化问题的有效性。     

A water-flow algorithm for flexible flow shop scheduling with intermediate buffers

We investigate the flexible flow shop scheduling problem with limited or unlimited intermediate buffers. A common objective of the problem is to find a production schedule that minimizes the completion time of jobs. Other objectives that we also consider are minimizing the total weighted flow time of jobs and minimizing the total weighted tardiness time of jobs. We propose a water-flow algorithm to solve this scheduling problem. The algorithm is inspired by the hydrological cycle in meteorology and the erosion phenomenon in nature. In the algorithm, we combine the amount of precipitation and its falling force to form a flexible erosion capability. This helps the erosion process of the algorithm to focus on exploiting promising regions strongly. To initiate the algorithm, we use a constructive procedure to obtain a seed permutation. We also use an improvement procedure for constructing a complete schedule from a permutation that represents the sequence of jobs in the first stage of the scheduling problem. To evaluate the proposed algorithm, we use benchmark instances taken from the literature and randomly generated instances of the scheduling problem. The computational results demonstrate the efficacy of the algorithm. We have also obtained several improved solutions for the benchmark instances using the proposed algorithm. We further illustrate the algorithm’s capability for solving problems in practical applications by applying it to a maltose syrup production problem.     

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.     

Two-machine flow shop scheduling integrated with preventive maintenance planning

This paper investigates an integrated optimisation problem of production scheduling and preventive maintenance (PM) in a two-machine flow shop with time to failure of each machine subject to a Weibull probability distribution. The objective is to find the optimal job sequence and the optimal PM decisions before each job such that the expected makespan is minimised. To investigate the value of integrated scheduling solution, computational experiments on small-scale problems with different configurations are conducted with total enumeration method, and the results are compared with those of scheduling without maintenance but with machine degradation, and individual job scheduling combined with independent PM planning. Then, for large-scale problems, four genetic algorithm (GA) based heuristics are proposed. The numerical results with several large problem sizes and different configurations indicate the potential benefits of integrated scheduling solution and the results also show that proposed GA-based heuristics are efficient for the integrated problem.     

Effective constructive heuristics and meta-heuristics for the distributed assembly permutation flowshop scheduling problem

This paper addresses a novel distributed assembly permutation flowshop scheduling problem that has important applications in modern supply chains and manufacturing systems. The problem considers a number of identical factories, each one consisting of a flowshop for part-processing plus an assembly line for product-processing. The objective is to minimize the makespan. To suit the needs of different CPU time and solution quality, we present a mixed integer linear model, three constructive heuristics, two variable neighborhood search methods, and an iterated greedy algorithm. Important problem-specific knowledge is obtained to enhance the effectiveness of the algorithms. Accelerations for evaluating solutions are proposed to save computational efforts. The parameters and operators of the algorithms are calibrated and analyzed using a design of experiments. To prove the algorithms, we present a total of 16 adaptations of other well-known and recent heuristics, variable neighborhood search algorithms, and meta-heuristics for the problem and carry out a comprehensive set of computational and statistical experiments with a total of 810 instances. The results show that the proposed algorithms are very effective and efficient to solve the problem under consideration as they outperform the existing methods by a significant margin.     

一种用于车间作业调度问题的智能枚举算法

车间作业调度问题是优化组合中一个著名的难题,即使规模不大的算例,优化算法的时间也很长。文章提出了一种求解车间作业调度问题的快速智能枚举算法,选取了22个标准算例作为算法的测试试验集,该算法在较短的时间内找到了17个算例的最优解,试验结果表明智能枚举算法确实是一种快速的、有效的求解车间作业调度问题的近似算法。     

应用强化学习算法求解置换流水车间调度问题

面对日益增长的大规模调度问题,新型算法的开发越显重要.针对置换流水车间调度问题,提出了一种基于强化学习Q-Learning调度算法.通过引入状态变量和行为变量,将组合优化的排序问题转换成序贯决策问题,来解决置换流水车间调度问题.采用所提算法对OR-Library提供Flow-shop国际标准算例进行测试,并与已有的一些算法对比,结果表明算法的有效性.     

A novel MILP model for job shop scheduling problem with mobile robots

The mobile robot is the essential equipment for automated logistics in the intelligent workshop, but the literature on shop scheduling rarely considers transport resources. This paper studies the integrated scheduling of machines and mobile robots, which can facilitate the efficiency of production systems. For the job shop scheduling problem with mobile robots (JSPMR), the existing mathematical models are too complex to obtain the optimal solution in an efficient time. Therefore, a novel mixed integer linear programming (MILP) model is proposed to minimize the makespan. Firstly, in view of the property of the problem, a disjunctive graph model is modified to describe the relationship between transport and processing tasks. Secondly, a more accurate and simplified MILP is proposed based on the modified disjunctive graph model. Two related proofs are given to prove the proposed model satisfies all special situations. Thirdly, the proposed MILP is tested on the well-known benchmark, including 82 instances. The proposed model is the first MILP model to obtain optimal solutions for all instances. Finally, 40 larger-scale instances are presented based on a real-world engineering case and used to validate the performance of models further. The comparison results verify the effectiveness and superior computational performance of the proposed model.     

A methodology for joint optimization for maintenance planning, process quality and production scheduling

Performance of a manufacturing system depends significantly on the shop floor performance. Traditionally, shop floor operational policies concerning maintenance scheduling, quality control and production scheduling have been considered and optimized independently. However, these three aspects of operations planning do have an interaction effect on each other and hence need to be considered jointly for improving the system performance. In this paper, a model is developed for joint optimization of these three aspects in a manufacturing system. First, a model has been developed for integrating maintenance scheduling and process quality control policy decisions. It provided an optimal preventive maintenance interval and control chart parameters that minimize expected cost per unit time. Subsequently, the optimal preventive maintenance interval is integrated with the production schedule in order to determine the optimal batch sequence that will minimize penalty-cost incurred due to schedule delay. An example is presented to illustrate the proposed model. It also compares the system performance employing the proposed integrated approach with that obtained by considering maintenance, quality and production scheduling independently. Substantial economic benefits are seen in the joint optimization.     

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.