Integrating simulation and optimization to schedule a hybrid flow shop with maintenance constraints

The scheduling problems have been discussed in the literature extensively under the assumption that machines are continuously available. However, in most real life industrial settings a machine can be unavailable for many reasons, such as unforeseen breakdowns (stochastic unavailability) or due to a scheduled preventive maintenance where the periods of unavailability are known in advance (deterministic unavailability). In this paper, we deal with the hybrid flow shop scheduling problem under maintenance constraints to optimize several objectives based on flow time and due date. In this model, we take also on consideration setup, cleaning and transportation times. This paper has three goals. The first is to show how we can integrate simulation and optimization to tackle this practical problem which is NP-hard on the strong sense. The second is to illustrate by an experimentation study that the performance of heuristics applied to this problem can be affected by the percentage of the breakdown times. The last is to show that this approach can perform better than NEH heuristics under certain conditions.     

Process plan and part routing optimization in a dynamic flexible job shop scheduling environment: an optimization via simulation approach

This paper presents an optimization via simulation approach to solve dynamic flexible job shop scheduling problems. In most real-life problems, certain operation of a part can be processed on more than one machine, which makes the considered system (i.e., job shops) flexible. On one hand, flexibility provides alternative part routings which most of the time relaxes shop floor operations. On the other hand, increased flexibility makes operation machine pairing decisions (i.e., the most suitable part routing) much more complex. This study deals with both determining the best process plan for each part and then finding the best machine for each operation in a dynamic flexible job shop scheduling environment. In this respect, a genetic algorithm approach is adapted to determine best part processing plan for each part and then select appropriate machines for each operation of each part according to the determined part processing plan. Genetic algorithm solves the optimization phase of solution methodology. Then, these machine-operation pairings are utilized by discrete-event system simulation model to estimate their performances. These two phases of the study follow each other iteratively. The goal of methodology is to find the solution that minimizes total of average flowtimes for all parts. The results reveal that optimization via simulation approach is a good way to cope with dynamic flexible job shop scheduling problems, which usually takes NP-Hard form.     

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     

Flexible job shop scheduling under condition-based maintenance: Improved version of imperialist competitive algorithm

Maintenance activities have been ignored in many studies on scheduling problems where all machines are assumed to be available without interruption in the planning horizon. However, in realistic situations, they might be unavailable due to preventive maintenance, basic maintenance or unforeseen breakdowns. In this paper, we simulate a condition-based maintenance (CBM) for flexible job shop scheduling problem (FJSP) and consider the combination of Sigmoid function and Gaussian distribution to improve the CBM simulation. This study proposes an improved imperialist competitive algorithm (ICA) for the FJSP scheduling problem with the objective of the makespan minimization. The performance of the proposed algorithm is enhanced with a hybridization of ICA with simulated annealing (SA), after diagnosing standard ICA disadvantages and shortcomings. This ICA also includes a simulation part to handle CBM requirements. Various parameters of the novel ICA are reviewed to calibrate the algorithm with the help of the Taguchi experimental design. Experimental results show the high performance of the novel ICA in comparison with the standard ICA. The obtained results demonstrate that the novel ICA is an effective algorithm for FJSP under CBM. Finally, the performance of ICA is evaluated compared to other popular algorithms.     

Scheduling two-stage hybrid flow shop with availability constraints

Most of the literature on scheduling assumes that machines are always available. However, in real life industry, machines may be subject to some unavailability periods due to maintenance activities such as breakdowns (stochastic case) and preventive maintenance (deterministic case). In this paper we investigate the two-stage hybrid flow shop scheduling problem with only one machine on the first stage and m machines on the second stage to minimize the makespan. We consider that each machine is subject to at most one unavailability period. The start time and the end time of each period are known in advance (deterministic case) and only the non-resumable case is studied. First we discuss the complexity of the problem. Afterwards, we give the Branch and Bound model for this problem. Last, we calculate the worst-case performances of three heuristics: LIST algorithm, LPT algorithm and H-heuristic.     

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.     

Two-generation Pareto ant colony algorithm for multi-objective job shop scheduling problem with alternative process plans and unrelated parallel machines

The flexibilities of alternative process plans and unrelated parallel machines are benefit for the optimization of the job shop scheduling problem, but meanwhile increase the complexity of the problem. This paper constructs the mathematical model for the multi-objective job shop scheduling problem with alternative process plans and unrelated parallel machines, splits the problem into two sub-problems, namely flexible processing route decision and task sorting, and proposes a two-generation (father and children) Pareto ant colony algorithm to generate a feasible scheduling solution. The father ant colony system solves the flexible processing route decision problem, which selects the most appropriate process node set from the alternative process node set. The children ant colony system solves the sorting problem of the process task set generated by the father ant colony system. The Pareto ant colony system constructs the applicable pheromone matrixes and heuristic information with respect to the sub-problems and objectives. And NSGAII is used as comparison whose genetic operators are re-defined. The experiment confirms the validation of the proposed algorithm. By comparing the result of the algorithm to NSGAII, we can see the proposed algorithm has a better performance.     

基于Petri网的JSP动态分类调度

以带有控制器的 Petri 网为建模工具对柔性生产调度中的离散事件建模,通过构建Petri 网控制器使系统的运行满足期望的目标,同时利用混合遗传算法获得调度结果,用于解决作业车间的加工受到机床、操作工人等资源制约条件下的动态优化调度。为了保证生产的平稳性,最大限度地维持车间的生产能力,提出了针对不同的扰动进行分类处理的新方法,首先基于机床故障修复时间、工人离岗时间及取消订单包含任务的多少进行分类调度,然后根据机床故障修复后以及工人回岗后剩余任务的多少决定是否进行再一次的调度,最后对算法进行了仿真研究。     

遗传算法求解柔性job shop 调度问题

在分析柔性job shop调度问题特点的基础上，提出一种新的求解该问题的遗传算法，即利用编码方法表示各工序的优先调度顺序及工序的加工机器，由此产生可行的调度方案，使得问题的约束条件在染色体中得以体现．所设计的遗传算子不仅能避免非法调度解的出现，保证后代的多样性，而且可使算法具有记忆功能．仿真结果证明了该算法的有效性．     

Generating robust and flexible job shop schedules using genetic algorithms

The problem of finding robust or flexible solutions for scheduling problems is of utmost importance for real-world applications as they operate in dynamic environments. In such environments, it is often necessary to reschedule an existing plan due to failures (e.g., machine breakdowns, sickness of employees, deliveries getting delayed, etc.). Thus, a robust or flexible solution may be more valuable than an optimal solution that does not allow easy modifications. This paper considers the issue of robust and flexible solutions for job shop scheduling problems. A robustness measure is defined and its properties are investigated. Through experiments, it is shown that using a genetic algorithm it is possible to find robust and flexible schedules with a low makespan. These schedules are demonstrated to perform significantly better in rescheduling after a breakdown than ordinary schedules. The rescheduling performance of the schedules generated by minimizing the robustness measure is compared with the performance of another robust scheduling method taken from literature, and found to outperform this method in many cases.     

Greedy randomized adaptive search for dynamic flexible job-shop scheduling

Dynamic flexible job shop scheduling problem is studied under the events such as new order arrivals, changes in due dates, machine breakdowns, order cancellations, and appearance of urgent orders. This paper presents a constructive algorithm which can solve FJSP and DFJSP with machine capacity constraints and sequence-dependent setup times, and employs greedy randomized adaptive search procedure (GRASP). Besides, Order Review Release (ORR) mechanism and order acceptance/rejection decisions are also incorporated into the proposed method in order to adjust capacity execution considering customer due date requirements. The lexicographic method is utilized to assess the objectives: schedule instability, makespan, mean tardiness and mean flow time. A group of experiments is also carried out in order to verify the suitability of the GRASP in solving the flexible job shop scheduling problem. Benchmark problems are formed for different problem scales with dynamic events. The event-driven rescheduling strategy is also compared with periodical rescheduling strategy. Results of the extensive computational experiment presents that proposed approach is very effective and can provide reasonable schedules under event-driven and periodic scheduling scenarios.     

Stochastic scheduling problems with general position-based learning effects and stochastic breakdowns

The focus of this study is to analyze position-based learning effects in single-machine stochastic scheduling problems. The optimal permutation policies for the stochastic scheduling problems with and without machine breakdowns are examined, where the performance measures are the expectation and variance of the makespan, the expected total completion time, the expected total weighted completion time, the expected weighted sum of the discounted completion times, the maximum lateness and the maximum tardiness.     

Scheduling unit length jobs on parallel machines with lookahead information

This paper studies two closely related online-list scheduling problems of a set of n jobs with unit processing times on a set of m multipurpose machines. It is assumed that there are k different job types, where each job type can be processed on a unique subset of machines. In the classical definition of online-list scheduling, the scheduler has all the information about the next job to be scheduled in the list while there is uncertainty about all the other jobs in the list not yet scheduled. We extend this classical definition to include lookahead abilities, i.e., at each decision point, in addition to the information about the next job in the list, the scheduler has all the information about the next h jobs beyond the current one in the list. We show that for the problem of minimizing the makespan there exists an optimal (1-competitive) algorithm for the online problem when there are two job types. That is, the online algorithm gives the same minimal makespan as the optimal offline algorithm for any instance of the problem. Furthermore, we show that for more than two job types no such online algorithm exists. We also develop several dynamic programming algorithms to solve a stochastic version of the problem, where the probability distribution of the job types is known and the objective is to minimize the expected makespan.     

A genetic algorithm and the Monte Carlo method for stochastic job-shop scheduling

This paper proposes a method for solving stochastic job‐shop scheduling problems using a hybrid of a genetic algorithm in uncertain environments and the Monte Carlo method. First, the genetic algorithm in uncertain environments is applied to stochastic job‐shop scheduling problems where the processing times are treated as stochastic variables. The Roulette strategy is adopted for selecting the optimum solution having the minimum expected value for makespan. Applying crossover based on Giffler and Thompson's algorithm results in two offspring inheriting the ancestor's characteristics as the operation completion times averaged up to the parent's generation. Individuals having very high frequency through all generations are selected as the good solutions. Second, the Monte Carlo method is effectively used for finding out the approximately optimum solution among these good solutions.     

Scheduling problem in a two-machine flow line with the N-step prior-job-dependent set-up times

The purpose of this study is to develop effective scheduling methodologies for the shop scheduling problem of a flow line. The flow line consists of two machines where only the second machine has separable, external, and sequence-dependent set-up times. The length of set-up times required for a job depends not on the immediately preceding job but on the job which is n steps prior to it. The problem is solved by a dynamic programming with the objective of minimizing the make span. An optimal schedule is found utilizing the sequence dominance condition. Since the computational requirements of the dynamic programming are impracticably demanding for large-sized problems, a genetic algorithm is developed and its performance is examined through a comparative study.     

A multi objective optimization approach for flexible job shop scheduling problem under random machine breakdown by evolutionary algorithms

This paper addresses the stable scheduling of multi-objective problem in flexible job shop scheduling with random machine breakdown. Recently, numerous studies are conducted about robust scheduling; however, implementing a scheme which prevents a tremendous change between scheduling and after machine breakdown (preschedule and realized schedule, respectively) can be critical for utilizing available resources. The stability of the schedule can be detected by a slight deviation of start and completion time of each job between preschedule and realized schedule under the uncertain conditions. In this paper, two evolutionary algorithms, NSGA-II and NRGA, are applied to combine the improvement of makespan and stability simultaneously. A simulation approach is used to evaluate the state and condition of the machine breakdowns. After the introduction of the evaluation criteria, the proposed algorithms are tested on a variety of benchmark problems. Finally, through performing statistical tests, the algorithm with higher performance in each criterion is identified.     

考虑工件移动时间的柔性作业车间调度问题研究

分析生产车间的实际生产状况,建立了考虑工件移动时间的柔性作业车间调度问题模型,该模型考虑了以往柔性作业车间调度问题模型所没有考虑的工件在加工机器间的移动时间,使柔性作业车间调度问题更贴近实际生产,让调度理论更具现实性。通过对已有的改进遗传算法的遗传操作进行重构,设计出有效求解考虑工件移动时间的柔性作业车间调度问题的改进遗传算法。最后对实际案例进行求解,得到调度甘特图和析取图,通过对甘特图和析取图的分析验证了所建考虑工件移动时间的柔性作业车间调度问题模型的可行性和有效性。     

A neural network model and algorithm for the hybrid flow shop scheduling problem in a dynamic environment

A hybrid flow shop (HFS) is a generalized flow shop with multiple machines in some stages. HFS is fairly common in flexible manufacturing and in process industry. Because manufacturing systems often operate in a stochastic and dynamic environment, dynamic hybrid flow shop scheduling is frequently encountered in practice. This paper proposes a neural network model and algorithm to solve the dynamic hybrid flow shop scheduling problem. In order to obtain training examples for the neural network, we first study, through simulation, the performance of some dispatching rules that have demonstrated effectiveness in the previous related research. The results are then transformed into training examples. The training process is optimized by the delta-bar-delta (DBD) method that can speed up training convergence. The most commonly used dispatching rules are used as benchmarks. Simulation results show that the performance of the neural network approach is much better than that of the traditional dispatching rules.This revised version was published in June 2005 with corrected page numbers.     

遗传算法解柔性作业车间调度问题应用综述

柔性作业车间调度问题是典型的NP难问题,对实际生产应用具有指导作用。近年来,随着遗传算法的发展,利用遗传算法来解决柔性作业车间调度问题的思想和方法层出不穷。为了促进遗传算法求解柔性作业车间调度问题的进一步发展,阐述了柔性作业车间调度问题的研究理论,对已有改进方法进行了分类,通过对现存问题的分析,探讨了未来的发展方向。     

Integration of deep reinforcement learning and multi-agent system for dynamic scheduling of re-entrant hybrid flow shop considering worker fatigue and skill levels

In real-life manufacturing systems, production management is often affected by urgent demands and unexpected interruptions, such as new job insertions, machine breakdowns and operator unavailability. In this context, agent-based techniques are useful and able to respond quickly to dynamic disturbances. The ability of agents to recognize their environment and make decisions can be further enhanced by deep reinforcement learning (DRL). This paper investigates a novel dynamic re-entrant hybrid flow shop scheduling problem (DRHFSP) considering worker fatigue and skill levels to minimize the total tardiness of all production tasks. An integrated architecture of DRL and MAS (DRL-MAS) is proposed for real-time scheduling in dynamic environments. Two DRL models are proposed for different sub-decisions, where a reward-shaping technique combining long-term and short-term returns is proposed for the job sequence and machine selection sub-decisions, and an attention-based network is proposed for the worker assignment sub-decision for efficient feature extraction and decision making. Numerical experiments and case studies demonstrate the superior performance of the proposed DRL models compared with existing scheduling strategies.