A two-machine flowshop maximum tardiness scheduling problem with a learning effect

The primary objective of this paper is to study a two-machine flowshop scheduling problem with a learning effect where the goal is to find a sequence that minimizes the maximum tardiness. We employ a branch-and-bound method and a simulated annealing (SA) method to search for the optimal solution and a near-optimal solution, respectively. Computational results, using Fisher’s (Math Program 11:229–251 1971) framework, show that the mean and maximum number of nodes for the branch-and-bound algorithm decrease when the learning effect is stronger, the value of the tardiness factor is smaller, or the value of the due date range is larger. In addition, comparisons between the SA method and the earliest due date first (EDD) rule are provided for large-job sizes. Results indicate that the percentage of time that the SA solution outperforms the EDD solution decreases as the job size increases and the learning effect becomes greater. Additionally, the SA solution is never worse than the EDD solution.     

两机零等待流水车间调度问题的启发式算法

为实现两机零等待流水车间调度问题的总流程时间最小化,结合问题的结构信息提出了一种快速求解近优解的启发式算法。在该类问题中,工件在每台机器上的操作包括调整、加工和移除3部分,且调整和移除时间都与工件的加工时间相互分离。首先分析了该类问题的优化性质,结合优化性质进而构造出求解算法。在中小规模和大规模问题上,将启发式算法的结果分别与最优解和最优解的下界值进行了比较。大量数值计算实验表明了该算法的有效性和解决大规模实际问题的潜力。     

Two meta-heuristics for three-stage assembly flowshop scheduling with sequence-dependent setup times

In this paper, we consider a three-stage assembly flowshop scheduling problem with bi-objectives, namely the mean flow time and maximum tardiness. This problem can be considered as a production system model consisting of three stages: (1) different production operations are done in parallel, concurrently and independently, (2) the manufactured parts are collected and transferred to the next stage, and (3) these parts are assembled into final products. In this paper, sequence-dependent setup times and transfer times are also considered as two important presumptions in order to make the problem more realistic. We present a novel mathematical model for a production system with a new lower bound for the given problem. Obtaining an optimal solution for this type of complex, large-sized problem in reasonable computational time by using traditional approaches and optimization tools is extremely difficult. Thus, we propose two meta-heuristics, namely simulated annealing and tabu search, to solve a number of test problems generated at random. Finally, the computational results are illustrated and compared in order to show the efficiency of the foregoing meta-heuristics.     

Bicriteria scheduling of a two-machine flowshop with sequence-dependent setup times

A two-machine flowshop scheduling problem is addressed to minimize setups and makespan where each job is characterized by a pair of attributes that entail setups on each machine. The setup times are sequence-dependent on both machines. It is shown that these objectives conflict, so the Pareto optimization approach is considered. The scheduling problems considering either of these objectives are $ \mathcal{N}{\wp } - {\text{hard}} $ , so exact optimization techniques are impractical for large-sized problems. We propose two multi-objective metaheurisctics based on genetic algorithms (MOGA) and simulated annealing (MOSA) to find approximations of Pareto-optimal sets. The performances of these approaches are compared with lower bounds for small problems. In larger problems, performance of the proposed algorithms are compared with each other. Experimentations revealed that both algorithms perform very similar on small problems. Moreover, it was observed that MOGA outperforms MOSA in terms of the quality of solutions on larger problems.     

Makespan minimization for m-machine permutation flowshop scheduling problem with learning considerations

Increased complexity of current manufacturing systems together with dynamic conditions and permanent demands for flexible and robust functionality makes their management and control very difficult and challenging. Workflow simulation is an effective approach to investigate dynamic workflow scheduling policies and evaluate the overall manufacturing system performance. The results attained in simulation model can give directions on how to maximize system output when selecting an appropriate scheduling practice for a real system. In this paper, we investigate the abilities of multi-agent systems in combination with dynamic dispatching rules and failure handling mechanisms to manage dynamic environment conditions (such as machine failures) for systems in the production automation domain. We measure system robustness by systematically assessing the total system performance (e.g., number of finished products) in a number of representative test cases. We use an agent-based simulation environment, MAST, which has been validated with real-world hardware to strengthen the external validity of the simulation results. We investigated the performance of a re-scheduling component which uses four different policies that define how to adjust the system schedule in case of machine disturbances/failures. In the context of the empirical study the Complete Rerouting re-scheduling policy outperformed all other policies.     

自适应混合EDA求解一类三阶段装配流水线调度问题

针对生产过程中广泛存在的一类三阶段装配流水线调度问题,即带序相关设置时间的三阶段装配流水线调度问题,提出一种自适应混合分布估计算法,用于最小化平均完成时间和最大延迟时间的加权和。提出初始种群和初始概率分布模型生成机制,使概率分布模型能适当地积累较多优质解的信息,以提高AHEDA在进化初期的搜索能力。设计了基于信息熵的概率分布模型自适应更新机制和保留优良模式的新种群采样生成方法,增强了算法的全局搜索能力。引入基于Insert的邻域搜索来增强算法的局部搜索能力。最后通过仿真实验和算法比较验证了AHEDA的有效性。     

Two meta-heuristics for a multi-period minisum location–relocation problem with line restriction

This paper investigates a multiperiod rectilinear distance minisum location problem, as a mixed-integer nonlinear programming (MINLP) model with a line-shaped barrier restriction, in which the starting point of the barrier uniformly distributed in the plane. The objective function of this model is to minimize the sum of the costs associated with the expected weighted barrier distance of the new facility from the existing facilities and the costs incurred by location-dependent relocation during the planning horizon. Then, a lower bound based on the forbidden region is presented. To show the validation of the presented model, a number of numerical examples are illustrated. The associated results show that the optimization software is effective for small-sized problems. However, the optimization software is unable to find an optimum solution for large-sized problems in a reasonable time. Thus, two meta-heuristics, namely genetic algorithm (GA) and imperialist competitive algorithm (ICA), are proposed. Finally, the associated results are compared and discussed.     

Ant colony optimization technique for the sequence-dependent flowshop scheduling problem

In the real world, production scheduling systems, usually optimal job scheduling, requires an explicit consideration of sequence-dependent setup times. One of the most important scheduling criteria in practical systems is makespan. In this paper, the author presents an ant colony optimization (ACO) algorithm for the sequence-dependent permutation flowshop scheduling problem. The proposed ACO algorithm benefits from a new approach for computing the initial pheromone values and a local search. The proposed algorithm is tested on randomly generated problem instances and results indicate that it is very competitive with the existing best metaheuristics.     

A GRASP heuristic for the multi-objective permutation flowshop scheduling problem

This paper presents a multi-objective greedy randomized adaptive search procedure (GRASP)-based heuristic for solving the permutation flowshop scheduling problem in order to minimize two and three objectives simultaneously: (1) makespan and maximum tardiness; (2) makespan, maximum tardiness, and total flowtime. GRASP is a competitive metaheuristic for solving combinatorial optimization problems. We have customized the basic concepts of GRASP algorithm to solve a multi-objective problem and a new algorithm named multi-objective GRASP algorithm is proposed. In order to find a variety of non-dominated solutions, the heuristic blends two typical approaches used in multi-objective optimization: scalarizing functions and Pareto dominance. For instances involving two machines, the heuristic is compared with a bi-objective branch-and-bound algorithm proposed in the literature. For instances involving up to 80 jobs and 20 machines, the non-dominated solutions obtained by the heuristic are compared with solutions obtained by multi-objective genetic algorithms from the literature. Computational results indicate that GRASP is a promising approach for multi-objective optimization.     

A multi-objective electromagnetism algorithm for a bi-objective hybrid no-wait flowshop scheduling problem

This article studies multi-objective hybrid no-wait flowshop scheduling problems to minimize both makespan and total tardiness. This article mathematically formulates the problem using an effective multi-objective mixed integer linear programming models. Since the problem is NP-hard and it is difficult to find an optimal solution in a reasonable computational time, an efficient multi-objective electromagnetism algorithm (MOEA) is presented as the solution procedure. Electromagnetism algorithm is known as a flexible and effective population-based algorithm utilizing an attraction/repulsion mechanism to move the particles towards optimality. MOEA is carefully evaluated for its performance against multi-objective immune algorithms and the adaptation of a well-known multi-objective simulated annealing in the relevant literature by means of multi-objective performance measures and statistical tools. The results show that the proposed solution method outperforms the others.     

On flowshop scheduling problems with the aging effect and resource allocation

In this paper, we focus on real-life settings that require the development of new models of flowshop scheduling problems, where job processing times can increase with the number of processed jobs due to the aging effect and decrease by the allocation of additional resource. We analyse the makespan minimization flowshop problem with such model and also with the aging effect only. We prove that the considered problems and their special cases are still polynomially solvable under given conditions, and on their basis, we provide optimal polynomial time solution algorithms.     

An improved artificial bee colony algorithm for the blocking flowshop scheduling problem

This paper presents an improved artificial bee colony (IABC) algorithm for solving the blocking flowshop problem with the objective of minimizing makespan. The proposed IABC algorithm utilizes discrete job permutations to represent solutions and applies insert and swap operators to generate new solutions for the employed and onlooker bees. The differential evolution algorithm is employed to obtain solutions for the scout bees. An initialization scheme based on the problem-specific heuristics is presented to generate an initial population with a certain level of quality and diversity. A local search based on the insert neighborhood is embedded to improve the algorithm's local exploitation ability. The IABC is compared with the existing hybrid discrete differential evolution and discrete artificial bee colony algorithms based on the well-known flowshop benchmark of Taillard. The computational results and comparison demonstrate the superiority of the proposed IABC algorithm for the blocking flowshop scheduling problems with makespan criterion.     

Minimizing makespan in a single-machine scheduling problem with a learning effect and fuzzy processing times

In scheduling problems with learning effects, most research assumes that processing times are deterministic. This paper studies a single-machine scheduling problem with a position-based learning effect and fuzzy processing times where the objective is to minimize the makespan. The position-based learning effect of a job is assumed to be a function of its position. The processing times are considered to be triangular fuzzy numbers. Two different polynomial-time algorithms are developed for the problem. The first solution methodology is based on the fuzzy chance-constrained programming, whereas the second is based on a method to rank fuzzy numbers. Computational experiments are then conducted in order to evaluate the performance of the algorithms.     

民用航空发动机维修计划启发式算法

为制定合理的航空发动机维修计划,在分析送修时间和备发选择的影响因素的基础上,建立了航空发动机维修计划多目标组合优化模型.为描述备发对发位的适合程度,提出了备发软约束适合度的概念和计算方法.考虑到模型的复杂性,提出了一种基于逐步构解策略的启发式算法进行模型的求解,并对算法的时间复杂度进行了分析.在此基础上,提出了航空发动机维修计划方案集的构造方法和选择方法.采用某航空公司的实际数据对所提算法进行了验证,并开发了一个原型系统,结果表明了该算法的有效性.     

Scheduling in a two-machine flow-shop for earliness/tardiness under learning effect

In the literature, earliness/tardiness (E/T) problem was known as weighted absolute deviation problem, and both tardiness and earliness is very important performance criteria for scheduling problem. While total tardiness criteria provides adaptation for due date (ignoring results of earliness done jobs), it deals with only cost of tardiness. However this phenomenon has been started to change with just-in-time (JIT) production concept. On JIT production, earliness is as important as tardiness. The phenomenon of the learning effect has been extensively studied in many different areas of operational research. However, there have been a few studies in the general context of production scheduling such as flow-shop scheduling. This paper addresses the minimization of the total earliness/tardiness penalties under learning effects in a two-machine flow-shop scheduling problem. Jobs have a common due date. We present mathematical model to obtain an optimal schedule for a given job sequence. We also present heuristics that use genetic algorithm and tabu search, based on proposed properties. Furthermore, random search was used for showing the significance of the study by comparison purpose. A new set of benchmark problems is presented with the purpose of evaluating the heuristics. The experimental results show that the performance of proposed approach is quite well, especially for the instances of large size.     

求解混合流水车间调度问题的变量相关EDA算法

针对混合流水车间调度问题和分布估计算法的特点,提出将变量按工序分组,通过组内概率约束、组间概率耦合的方式建立混合流水车间调度问题变量间概率关系的新方法。对分布估计算法中的紧致遗传算法的种群产生和概率更新机制进行了改进,以解决流水车间调度问题等复杂问题。通过仿真实验、与其他算法比较以及在大规模生产实际问题中的应用,验证了该算法的有效性和鲁棒性。     

The two-stage assembly flowshop scheduling problem with bicriteria of makespan and mean completion time

In this paper, we address the two-stage assembly flowshop scheduling problem with a weighted sum of makespan and mean completion time criteria, known as bicriteria. Since the problem is NP-hard, we propose heuristics to solve the problem. Specifically, we propose three heuristics; simulated annealing (SA), ant colony optimization (ACO), and self-adaptive differential evolution (SDE). We have conducted computational experiments to compare the performance of the proposed heuristics. It is statistically shown that both SA and SDE perform better than ACO. Moreover, the experiments reveal that SA, in general, performs better than SDE, while SA consumes less CPU time than both SDE and ACO. Therefore, SA is shown to be the best heuristic for the problem.     

工序加工时间不确定条件下作业车间调度问题的区间数求解方法

针对一类难以获取工序加工时间变量的准确分布规律或隶属度函数的作业车间调度问题,采用区间数方法描述工序加工时间不确定变量,在分析工件完工时间区间与交货期时间窗的6种关系的基础上,分析归纳出提前/拖期惩罚取值区间的求解方法;论证了提前/拖期惩罚区间可以预估提前/拖期惩罚值的波动范围,为不确定调度问题转化为区间调度问题求解提供了理论支撑。以提前/拖期惩罚的取值区间为优化目标构建了区间调度模型。通过区间可能度方法对不同的提前/拖期指标区间值进行定量比较,解决了遗传算法求解区间调度模型时适应度值的比较问题。通过算例仿真验证了区间数定理和调度算法的有效性。