Mathematical model and discrete artificial Bee Colony algorithm for distributed integrated process planning and scheduling

With the development of the globalization of economy and manufacturing industry, distributed manufacturing mode has become a hot topic in current production research. In the context of distributed manufacturing, one job has different process routes in different workshops because of heterogeneous manufacturing resources and manufacturing environments in each factory. Considering the heterogeneous process planning problems and shop scheduling problems simultaneously can take advantage of the characteristics of distributed factories to finish the processing task well. Thus, a novel network-based mixed-integer linear programming (MILP) model is established for distributed integrated process planning and scheduling problem (DIPPS). The paper designs a new encoding method based on the process network and its OR-nodes, and then proposes a discrete artificial bee colony algorithm (DABC) to solve the DIPPS problem. The proposed DABC can guarantee the feasibility of individuals via specially-designed mapping and switching operations, so that the process precedence constraints contained by the network graph can be satisfied in the entire procedure of the DABC algorithm. Finally, the proposed MILP model is verified and the proposed DABC is tested through some open benchmarks. By comparing with other powerful reported algorithms and obtaining new better solutions, the experiment results prove the effectiveness of the proposed model and DABC algorithm successfully.     

Maintenance costs and makespan minimization for assembly permutation flow shop scheduling by considering preventive and corrective maintenance

The joint optimization of production scheduling and maintenance planning has a significant influence on production continuity and machine reliability. However, limited research considers preventive maintenance (PM) and corrective maintenance (CM) in assembly permutation flow shop scheduling. This paper addresses the bi-objective joint optimization of both PM and CM costs in assembly permutation flow shop scheduling. We also propose a new mixed integer linear programming model for the minimization of the makespan and maintenance costs. Two lemmas are inferred to relax the expected number of failures and CM cost to make the model linear. A restarted iterated Pareto greedy (RIPG) algorithm is applied to solve the problem by including a new evaluation of the solutions, based on a PM strategy. The RIPG algorithm makes use of novel bi-objective-oriented greedy and referenced local search phases to find non-dominated solutions. Three types of experiments are conducted to evaluate the proposed MILP model and the performance of the RIPG algorithm. In the first experiment, the MILP model is solved with an epsilon-constraint method, showing the effectiveness of the MILP model in small-scale instances. In the remaining two experiments, the RIPG algorithm shows its superiority for all the instances with respect to four well-known multi-objective metaheuristics.     

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 heuristic algorithm for the distributed and flexible job-shop scheduling problem

The distributed manufacturing takes place in a multi-factory environment including several factories, which may be geographically distributed in different locations, or in a multi-cell environment including several independent manufacturing cells located in the same plant. Each factory/cell is capable of manufacturing a variety of product types. An important issue in dealing with the production in this decentralized manner is the scheduling of manufacturing operations of products (jobs) in the distributed manufacturing system. In this paper, we study the distributed and flexible job-shop scheduling problem (DFJSP) which involves the scheduling of jobs (products) in a distributed manufacturing environment, under the assumption that the shop floor of each factory/cell is configured as a flexible job shop. A fast heuristic algorithm based on a constructive procedure is developed to obtain good quality schedules very quickly. The algorithm is tested on benchmark instances from the literature in order to evaluate its performance. Computational results show that, despite its simplicity, the proposed heuristic is computationally efficient and promising for practical problems.     

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.     

Hybrid monkey search algorithm for flow shop scheduling problem under makespan and total flow time

This paper addresses a sub-population based hybrid monkey search algorithm to solve the flow shop scheduling problem which has been proved to be non-deterministic polynomial time hard (NP-hard) type combinatorial optimization problems. Minimization of makespan and total flow time are the objective functions considered. In the proposed algorithm, two different sub-populations for the two objectives are generated and different dispatching rules are used to improve the solution quality. To the best of our knowledge, this is the first application of monkey search algorithm to solve the flow shop scheduling problems. The performance of the proposed algorithm has been tested with the benchmark problems addressed in the literature. Computational results reveal that the proposed algorithm outperforms many other heuristics and meta-heuristics addressed in the literature.     

相关工件车间调度问题的拓扑算法

针对加工装配型离散制造企业实际生产的特点,提出了一类用于表示工序之间偏序关系的相关工件车间调度问题。为了利用已有的求解表示工序之间的线序关系的传统车间调度算法求解相关工件车间调度问题,设计了一种拓扑算法,该算法能够将工序之间的偏序关系转化为线序关系,将相关工件车间调度问题转化为传统的车间调度问题,通过实证研究,结果表明了拓扑算法是可行和高效的。     

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.     

A simulated annealing algorithm approach to hybrid flow shop scheduling with sequence-dependent setup times

One of the scheduling problems with various applications in industries is hybrid flow shop. In hybrid flow shop, a series of n jobs are processed at a series of g workshops with several parallel machines in each workshop. To simplify the model construction in most research on hybrid flow shop scheduling problems, the setup times of operations have been ignored, combined with their corresponding processing times, or considered non sequence-dependent. However, in most real industries such as chemical, textile, metallurgical, printed circuit board, and automobile manufacturing, hybrid flow shop problems have sequence-dependent setup times (SDST). In this research, the problem of SDST hybrid flow shop scheduling with parallel identical machines to minimize the makespan is studied. A novel simulated annealing (NSA) algorithm is developed to produce a reasonable manufacturing schedule within an acceptable computational time. In this study, the proposed NSA uses a well combination of two moving operators for generating new solutions. The obtained results are compared with those computed by Random Key Genetic Algorithm (RKGA) and Immune Algorithm (IA) which are proposed previously. The results show that NSA outperforms both RKGA and IA.     

A scheduling problem in blocking hybrid flow shop robotic cells with multiple robots

This paper addresses the robotic scheduling problem in blocking hybrid flow shop cells that consider multiple part types, unrelated parallel machines, multiple robots and machine eligibility constraints. Initially, a mixed integer linear programming (MILP) model is proposed to minimize the makespan for this problem. Due to the complexity of the model, a simulated annealing (SA) based solution approach is developed for its solution. To increase the efficiency of the SA algorithm, a new neighborhood structure based on block properties is applied. The performance of the proposed SA is assessed over a set of randomly generated instances. The computational results demonstrate that the SA algorithm is effective with the employed neighborhood structure. Additionally, this study shows that the appropriate number of robots depends on the sequence of processing operations to be performed at each stage.     

Fast scheduling of human-robot teams collaboration on synchronised production-logistics tasks in aircraft assembly

The deployment of human-robot teams (HRTs) promises to realise the potential of each team member regarding their distinct abilities and combines efficiency and flexibility in manufacturing operations. However, enabling effective coordination amongst collaborative tasks performed by humans and robots while ensuring safety and satisfying specific constraints is challenging. Motivated by real-world applications that Boeing and Airbus adopt HRTs in manufacturing operations, this paper investigates the allocating and coordinating of HRTs to support safe and efficient human-robot collaboration on synchronised production-logistics tasks in aircraft assembly. We connect the operations research and robotics communities by formulating the problem with precedence constraints, spatial constraints, temporal constraints, and synchronisation constraints that fits within the classic multi-robot task allocation (MRTA) category into a flexible job shop scheduling problem. Two exact approaches, including mixed-integer linear programming (MILP) and constraint programming (CP), are proposed to formulate and solve this problem. A benchmark set with 80 instances (e.g., small/medium-scale and large-scale instances) that corresponds to real dimensions of industrial problems with production tasks, subtasks, locations, deadlines, human worker eligibility and capacity, robot eligibility and capacity, material handling system capacity, and travel times is developed. Experimental evaluation with a total of 1200 independent tests on the benchmark set shows the superiority of the CP approach comparing the MILP approach for efficiently solving real-life scheduling problems of HRTs collaboration on synchronised production-logistics tasks in aircraft assembly.     

具有线性恶化加工时间的调度问题

讨论了工件具有线性恶化加工时间的调度问题.在这类问题中,工件的恶化函数为线性 函数.对单机调度问题中目标函数为极小化最大完工时间加权完工时间和,最大延误以及最大费 用等问题分别给出了最优算法.对两台机器极小化最大完工时间的Flowshop问题,证明了利用 Johnson规则可以得到最优调度.对于一般情况,如果同一工件的工序的加工时间均相等,则 Flowshop问题可以转化为单机问题.     

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.     

Flow shop scheduling with multiple operations and time lags

A scheduling system is proposed and developed for a special type of flow shop. In this flow shop there is one machine at each stage. A job may require multiple operations at each stage. The first operation of a job on stage j cannot start until the last operation of the job on stage j - 1 has finished. Pre-emption of the operations of a job is not allowed. The flow shop that the authors consider has another feature, namely time lags between the multiple operations of a job. To move from one operation of a job to another requires a finite amount of time. This time lag is independent of the sequence and need not be the same for all operations or jobs. During a time lag of a job, operations of other jobs may be processed. This problem originates from a flexible manufacturing system scheduling problem where, between operations of a job on the same workstation, refixturing of the parts has to take place in a load/unload station, accompanied by (manual) transportation activities. In this paper a scheduling system is proposed in which the inherent structure of this flow shop is used in the formulation of lowerbounds on the makespan. A number of lowerbounds are developed and discussed. The use of these bounds makes it possible to generate a schedule that minimizes makespan or to construct approximate solutions. Finally, some heuristic procedures for this type of flow shop are proposed and compared with some well-known heuristic scheduling rules for job shop/flow shop scheduling.An earlier version of this paper was presented at the First International Conference on Industrial Engineering and Production Management 1993, 2–4 June 1993, Mons, Belgium.     

基于机床超低待机状态的流水车间能耗调度

为降低流水车间能源消耗,引入一种数控机床的超低待机状态,相比于将数控机床待机状态切换为停机状态的节能研究,可在不停机情况下降低数控机床加工间隔状态的功率,避免数控机床频繁启停.针对流水车间加工状态、待机状态及超低待机状态三元调度问题,提出基于工序平移的混合遗传算法,分别定义了不同的工序邻域移动操作,实现数控机床待机状态向超低待机状态和停机状态的转化,形成主动节能调度策略,提升遗传算法求解考虑超低待机状态的流水车间调度问题的优化能力.实验研究表明,启用超低待机状态能够降低流水车间10%以上的能耗,且基于工序平移的混合遗传算法求解考虑超低待机状态的流水车间调度问题性能优于遗传算法.     

Scheduling jobs and maintenances in flexible job shop with a hybrid genetic algorithm

Most flexible job shop scheduling models assume that the machines are available all of the time. However, in most realistic situations, machines may be unavailable due to maintenances, pre-schedules and so on. In this paper, we study the flexible job shop scheduling problem with availability constraints. The availability constraints are non-fixed in that the completion time of the maintenance tasks is not fixed and has to be determined during the scheduling procedure. We then propose a hybrid genetic algorithm to solve the flexible job shop scheduling problem with non-fixed availability constraints (fJSP-nfa). The genetic algorithm uses an innovative representation method and applies genetic operations in phenotype space in order to enhance the inheritability. We also define two kinds of neighbourhood for the problem based on the concept of critical path. A local search procedure is then integrated under the framework of the genetic algorithm. Representative flexible job shop scheduling benchmark problems and fJSP-nfa problems are solved in order to test the effectiveness and efficiency of the suggested methodology. Received: June 2005 /Accepted: December 2005     

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.     

带工序跳跃的绿色混合流水车间机器与AGV联合调度

针对带工序跳跃的绿色混合流水车间机器和自动引导车(AGV)联合调度问题,提出改进memetic algorithm(MA)以同时最小化最大完工时间和总能耗.首先,设计基于工序、机器和转速的三层编码策略,最大程度保证算法在整个解空间中搜索;然后,设计混合种群初始化方法以提高初始种群解的质量,同时设计交叉和变异算子以及两种基于问题的邻域搜索策略来平衡算法的全局搜索和局部搜索能力;最后,通过大量仿真实验验证MA算法求解该问题的有效性和优越性.     

Local search heuristics for two-stage flow shop problems with secondary criterion

This paper develops and compares different local search heuristics for the two-stage flow shop problem with makespan minimization as the primary criterion and the minimization of either the total flow time, total weighted flow time, or total weighted tardiness as the secondary criterion. We investigate several variants of simulated annealing, threshold accepting, tabu search, and multi-level search algorithms. The influence of the parameters of these heuristics and the starting solution are empirically analyzed. The proposed heuristic algorithms are empirically evaluated and found to be relatively more effective in finding better quality solutions than the existing algorithms.Scope and purposeTraditional research to solve multi-stage scheduling problems has focused on single criterion. However, in industrial scheduling practices, managers develop schedules based on multi-criteria. Scheduling problems involving multiple criteria require significantly more effort in finding acceptable solutions and hence have not received much attention in the literature. This paper considers one such multiple criteria scheduling problem, namely, the two-machine flow shop problem where the primary criterion is the minimization of makespan and the secondary criterion is one of the three most popular performance measures, namely, the total flow time, total weighted flow time, or total weighted tardiness. Based on the principles of local search, development of heuristic algorithms, that can be adapted for several multi-criteria scheduling problems, is discussed. Using the example of the two-machine flow shop problem with secondary criterion, computational experiments are used to evaluate the utility of the proposed algorithms for solving scheduling problems with a secondary criterion.     

双种群混合遗传算法求解具有预防性维护的分布式柔性作业车间调度问题

在实际生产过程中,生产调度和设备维护相互影响,因此两者应该统筹优化.为研究具有预防性维护的分布式柔性作业车间调度问题,以最小化最大完工时间为目标,提出一种双种群混合遗传算法.结合问题特性,设计三维编码以及对应的机器解码方案,采用不同的策略初始化种群以均衡一部分工厂负载,为双种群设计不同的交叉变异算子提高算法的多样性,并利用交换精英解的方法实现两个种群的协作优化,同时针对关键工厂和预防性维护操作设计相应的局部搜索.最后对比现有算法,在同构和异构工厂的算例上进行实验,使用正交试验法优化算法参数设置.实验结果验证了局部搜索以及种群协作的有效性和双种群混合遗传算法求解具有预防性维护的分布式柔性作业车间调度问题的优越性.