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.     

A deadlock-free scheduling with sequence-dependent setup times

This paper presents a novel approach to job shop scheduling with sequence-dependent setup times. The scheduling modeling is based on timed Petri nets. Control arcs are introduced to alleviate deadlocks, thus ensuring sequence-dependent setups. Based on siphon-related truncation, an efficient branch and bound algorithm for deadlock-free scheduling is devised. In addition, an effective priority rule is defined to handle large-scale problems. A series of experiments illustrate the validity of the priority rule and the scalability of our method for large-scale problems.     

Solving single-machine total weighted tardiness problems with sequence-dependent setup times by meta-heuristics

Simulated annealing (SA), genetic algorithms (GA), and tabu search (TS) are the three well known meta-heuristics for combinatorial optimization problems. In this paper, single-machine total weighted tardiness problems with sequence-dependent setup times are solved by SA, GA, and TS approaches. A random swap and insertion search is applied in SA, and a mutation operator performed by a greedy local search is used in a GA. Similarly, a swap and an insertion tabu list are adopted in TS. To verify these proposed approaches, computational experiments were conducted on benchmark problem sets. The experimental results show that these approaches find new upper bound values for most benchmark problems within reasonable computational expenses.     

Hybrid metaheuristics for unrelated parallel machine scheduling with sequence-dependent setup times

This paper proposes several hybrid metaheuristics for the unrelated parallel-machine scheduling problem with sequence-dependent setup times given the objective of minimizing the weighted number of tardy jobs. The metaheuristics begin with effective initial solution generators to generate initial feasible solutions; then, they improve the initial solutions by an approach, which integrates the principles of the variable neighborhood descent approach and tabu search. Four reduced-size neighborhood structures and two search strategies are proposed in the metaheuristics to enhance their effectiveness and efficiency. Five factors are used to design 32 experimental conditions, and ten test problems are generated for each condition. Computational results show that the proposed hybrid metaheuristics are significantly superior to several basic tabu search heuristics under all the experimental conditions.     

Bi-objective hybrid flow shop scheduling with sequence-dependent setup times and limited buffers

The bi-objective hybrid flow shop problem with sequence-dependent setup times and limited buffers is mentioned in this paper. In this environment, there are limited buffer spaces between any two successive stages; thus, maybe there is not enough room for queues of jobs that are waiting in the system for their next operations. This problem is shown to be NP-hard in the strong sense. Up to now, some heuristic and metaheuristic approaches are proposed to minimize makespan or total tardiness of jobs. This paper presents several methods for optimization which consider two objectives simultaneously. The resolution of several specific instances from the open literature with the adaptations of non-dominated sorting genetic algorithm and sub-population genetic algorithm suggest that the proposed algorithms are effective and useful methods for solving this problem.     

Dynamic job-shop scheduling with sequence-dependent setup times: simulation modeling and analysis

This paper presents the salient aspects of a simulation-based experimental study of scheduling rules for scheduling a dynamic job shop in which the setup times are sequence-dependent. A discrete event simulation model of the job shop system is developed for the purpose of experimentation. Seven scheduling rules from the literature are incorporated in the simulation model. Five new setup-oriented scheduling rules are proposed and implemented. Simulation experiments were conducted under various experimental conditions characterized by factors such as shop load, setup time ratios, and due date tightness. The results indicate that setup-oriented rules provide better performance than ordinary rules. The difference in performance between these two groups of rules increases with the increase in shop load and setup time ratio. One of the proposed rules performs better for mean flow time and mean tardiness measures.     

An ant colony algorithm for scheduling in flowshops with sequence-dependent setup times of jobs

The problem of scheduling in flowshops with sequence-dependent setup times of jobs is considered and solved by making use of ant colony optimization (ACO) algorithms. ACO is an algorithmic approach, inspired by the foraging behavior of real ants, that can be applied to the solution of combinatorial optimization problems. A new ant colony algorithm has been developed in this paper to solve the flowshop scheduling problem with the consideration of sequence-dependent setup times of jobs. The objective is to minimize the makespan. Artificial ants are used to construct solutions for flowshop scheduling problems, and the solutions are subsequently improved by a local search procedure. An existing ant colony algorithm and the proposed ant colony algorithm were compared with two existing heuristics. It was found after extensive computational investigation that the proposed ant colony algorithm gives promising and better results, as compared to those solutions given by the existing ant colony algorithm and the existing heuristics, for the flowshop scheduling problem under study.     

Robust metaheuristics for group scheduling with sequence-dependent setup times in hybrid flexible flow shops

This paper considers group scheduling problem in hybrid flexible flow shop with sequence-dependent setup times to minimize makespan. Group scheduling problem consists of two levels, namely scheduling of groups and jobs within each group. In order to solve problems with this context, two new metaheuristics based on simulated annealing (SA) and genetic algorithm (GA) are developed. A design procedure is developed to specify and adjust significant parameters for SA- and GA-based metaheuristics. The proposed procedure is based on the response surface methodology and two types of objective function are considered to develop multiple-objective decision making model. For comparing metaheuristics, makespan and elapsed time to obtain it are considered as two response variables representing effectiveness and efficiency of algorithms. Based on obtained results in the aspect of makespan, GA-based metaheuristic is recommended for solving group scheduling problems in hybrid flexible flow shop in all sizes and for elapsed time SA-based metaheuristic has better results.     

Study on job shop scheduling with sequence-dependent setup times using biological immune algorithm

Sequence-dependent setup times are one of the most important factors for the optimization of scheduling the production targets. Usually, they include the changing of tools, fixtures, cutting tools and the cleaning of production equipments. Some of them are relevant not only to the sequence requirement of the products to be processed on the equipment, but also to the processing requirement of the adjoining sequence. In this paper, a job shop scheduling problem with sequence-dependent setup times is described. A mixed integer program model is adopted to deal with this type of problem, and a scheduling algorithm based on biologic immunity mechanism is introduced. The result shows that the antibody encoding method and the mechanism of antibody proliferation and suppression can not only ensure the diversity of the antibody, but can also greatly improve the effectiveness of dealing with complex problems. Finally, a scheduling problem of finishing processing for a woollen mill is analyzed with its result described.     

Modeling and scheduling open shops with sequence-dependent setup times to minimize total completion time

It is known that in many real industrial settings, some setup is carried out before the process of a job. Usually, the magnitude of this setup depends on the order of two consecutive jobs. In this case, the setup is called sequence-dependent. This paper deals with open shop scheduling with sequence-dependent setup times to minimize the total completion time. The problem is formulated as an effective mixed integer linear programming model that best characterizes and solves to optimality small-sized instances of the problem under consideration. Since the electromagnetism-like metaheuristic (EM) is successfully applied to some NP-hard problems, we have been motivated to employ and assess the effectiveness of EM to solve the open shop with setup times. To further enhance EM, a local search engine in form of a fast and simple simulated annealing is incorporated. In order to evaluate the performance of the proposed algorithms, an experiment is designed where the proposed methods are compared against some algorithms in the literature. The related results are analyzed by statistical tools. The experimental results and statistical analyses demonstrate that the proposed model and EM are effective for the problem.     

Two meta-heuristics for solving a new two-machine flowshop scheduling problem with the learning effect and dynamic arrivals

This paper develops a new mathematical model and proposes two meta-heuristics for solving a two-machine flowshop scheduling problem that minimizes bi-objectives, namely the total idle time and the mean deviation from a common due data. In this paper, we assume the arrival time of jobs is dynamic, in which each job has a time window and can arrive in its time window randomly. We also assume the learning effect on the processing times considering as a position-dependent effect. Since the problem is an NP-hard one, we present a multiobjective genetic algorithm (MOGA) and a multiobjective simulated annealing (MOSA) algorithm to solve the given problems. The computational results confirm that the proposed MOGA has a better solution in comparison with the proposed MOSA, especially in large-sized problems.     

An immune algorithm for hybrid flow shop scheduling problem with time lags and sequence-dependent setup times

This paper deals with hybrid flow shop scheduling problems considering time lags and sequence-dependent setup times which have wide application in real-world problems. Most of the researches on operations scheduling problems have ignored time lags. A mathematical model is presented which is capable of solving the small size of the considered problem in a reasonable time. Since these problems are strongly NP-hard, a meta-heuristic algorithm based on the immune algorithm is developed. The optimization criterion considered in this paper is the minimization of the makespan. Numerical experiments are used to evaluate the performance and effectiveness of the proposed algorithm. The results of the proposed algorithm are compared with the presented mathematical programming model and a benchmark algorithm. Computational results indicate that the proposed algorithm can produce near-optimal solutions in a short computational time. Moreover, it can be applied easily in real factory conditions and for large-sized problems.     

Development and analysis of constructive heuristic algorithms for flow shop scheduling problems with sequence-dependent setup times

This paper focuses on the problem of determining a permutation schedule for n jobs in an m-machine flow shop that operates in a sequence-dependent setup time (SDST) environment. Two constructive heuristic algorithms are developed with the minimisation of makespan as the objective. The first heuristic algorithm termed as setup ranking algorithm obtains the sequence using the setup times of jobs only. The second heuristic algorithm, fictitious job setup ranking algorithm (FJSRA), is developed using the concept of fictitious jobs. Pairs of jobs with minimum setup time between them constitute the fictitious jobs. Both these algorithms are compared with an existing constructive algorithm. For the purpose of experimentation, Taillard benchmark problems are used to develop SDST benchmark problems at eight different levels of sequence-dependent setup times. Graphical analysis, relative performance index analysis and statistical analysis are carried out on the results obtained for all the eight sets of benchmark problems. The analysis reveals that FJSRA emerges as the better algorithm for larger problems and for smaller problems with higher level of setup time. The results of statistical analysis are used to develop setup time dominance matrix for deciding upon the algorithm to be used for a particular size of problem.     

Due-date scheduling on parallel machines with job splitting and sequence-dependent major/minor setup times

This paper addresses job scheduling problems with parallel machines. To satisfy customers better in a manufacturing company, meeting due dates has been an important performance metric. Besides the numerous other factors affecting due date satisfaction, the splitting of a job through parallel machines can contribute to the reduction of production lead time, resulting in less job tardiness against their due dates. Thus, this paper presents heuristic algorithms for minimizing total tardiness of jobs to meet their due dates in a manufacturing shop with identically functioning machines. The algorithms take into account job splitting and sequence-dependent major/minor setup times. The performance of the proposed heuristics is compared with that of past three algorithms in the literature.     

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.     

Metaheuristics for scheduling a no-wait flowshop manufacturing cell with sequence-dependent family setups

This paper examines the no-wait flowshop manufacturing cell scheduling problem (FMCSP) with sequence-dependent family setup times. To the best of our knowledge, the present study is among the first to investigate FMSCPs with no-wait consideration, though it is a necessary production constraint in many real-world applications. In view of the strongly NP-hard nature of this problem, three metaheuristic-based algorithms were proposed and empirically evaluated for effectively finding optimal schedules. The experimental results demonstrate that the proposed algorithms are effective and efficient at finding good quality solutions for the FMCSP with makespan criterion.     

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。     

Makespan minimization of a flowshop sequence-dependent group scheduling problem

The flowshop sequence dependent group scheduling problem with minimization of makespan as the objective (F _m |fmls, S _plk, prmu|C _max ) is considered in this paper. It is assumed that several groups with different number of jobs are assigned to a flow shop cell that has m machines. The goal is to find the best sequence of processing the jobs in each group and the groups themselves with minimization of makespan as the objective. A mathematical model for the research problem is developed in this paper. As the research problem is shown to be NP-hard, a hybrid ant colony optimization (HACO) algorithm is developed to solve the problem. A lower bounding technique based on relaxing a few constraints of the mathematical model developed for the original problem is proposed to evaluate the quality of the HACO algorithm. Three different problem structures, with two, three, and six machines, are used in the generation of the test problems to test the performance of the algorithm and the lower bounding technique developed. The results obtained from the HACO algorithm and those that have appeared in the published literature are also compared. The comparative results show that the HACO algorithm has a superior performance compared to the best available algorithm based on memetic algorithm with an average percentage deviation of around 1.0% from the lower bound.