Deteriorating job scheduling to minimize the number of late jobs with setup times

Deteriorating jobs scheduling problems have been widely studied recently. However, research on scheduling problems with deteriorating jobs has rarely considered explicit setup times. With the current emphasis on customer service and meeting the promised delivery dates, we consider a single-machine scheduling problem to minimize the number of late jobs with deteriorating jobs and setup times in this paper. We derive some dominance properties, a lower bound, and an initial upper bound by using a heuristic algorithm to speed up the search process of the branch-and-bound algorithm. Computational experiments show that the algorithm can solve instances up to 1000 jobs in a reasonable amount of time.     

基于灰色综合关联分析的多目标优化方法

针对现有多目标优化方法存在的搜索性能弱、效率低等问题,提出一种基于灰色综合关联分析的多目标优化方法.该多目标优化方法采用单目标优化算法构建高质量的参考序列,计算参考序列与优化解的目标函数值序列之间的灰色综合关联度,定义基于灰色综合关联度的解支配关系准则,将灰色综合关联度作为多目标优化算法的适应度值.以带顺序相关调整时间的多目标流水车间调度问题作为应用对象,建立总生产成本、最大完工时间、平均流程时间及机器平均闲置时间的多目标函数优化模型.提出基于灰色关联分析的多目标烟花算法,对所建立的多目标优化模型进行优化求解.仿真实验表明,所提出多目标烟花算法的性能优于3种基于不同多目标优化方法的烟花算法及两种经典多目标算法,验证了所提出的多目标优化方法及多目标算法的可行性和有效性.     

Dominance rules for single machine schedule with sequence dependent setup and due date

Some dominance rules are proposed for the problems of scheduling N jobs on a single machine with due dates, sequence dependent setup times and no preemption. Two algorithms based on Ragatz＇ s branch and bound scheme are developed including the dominance rules where the objective is to minimize the maximum tardiness or the total tardiness. Computational experiments demonstrate the effectiveness of the dominance rules.     

Dominance rules for single machine schedule with sequence dependent setup and due date

Some dominance rules are proposed for the problems of scheduling N jobs on a single machine with due dates, sequence dependent setup times and no preemption. Two algorithms based on Ragatz's branch and bound scheme are developed including the dominance rules where the objective is to minimize the maximum tardiness or the total tardiness. Computational experiments demonstrate the effectiveness of the dominance rules.     

Minimizing total tardiness in a two-machine re-entrant flowshop with sequence-dependent setup times

We consider a two-machine re-entrant flowshop scheduling problem in which all jobs must be processed twice on each machine and there are sequence-dependent setup times on the second machine. For the problem with the objective of minimizing total tardiness, we develop dominance properties and a lower bound by extending those for a two-machine re-entrant flowshop problem (without sequence-dependent setup times) as well as heuristic algorithms, and present a branch and bound algorithm in which these dominance properties, lower bound, and heuristics are used. For evaluation of the performance of the branch and bound algorithm and heuristics, computational experiments are performed on randomly generated instances, and results are reported.     

An effective method for solving flow shop scheduling problems with fuzzy processing times

This paper show that fuzzy set theory can be useful in modelling and solving flow shop scheduling problems with uncertain processing times and illustrates a methodology for solving job sequencing problem which the opinions of experts greatly disagree in each processing time. Triangular fuzzy numbers (TFNs) are used to represent the processing times of experts. And the comparison methods based on the dominance property is sued to determine the ranking of the fuzzy numbers. By the dominance criteria, for each job, a major TFN and a minor TFN are selected and a pessimistic sequence with major TFNs and an optimistic sequence with minor TFNs are computer. Branch and bound algorithm for makespan in three-machine flow shop is utilized to illustrate the proposed methodology.     

The two-stage assembly scheduling problem to minimize total completion time with setup times

We address the two-stage assembly scheduling problem where there are m machines at the first stage and an assembly machine at the second stage. The objective is to schedule the available n jobs so that total completion time of all n jobs is minimized. Setup times are treated as separate from processing times. This problem is NP-hard, and therefore we present a dominance relation and propose three heuristics. The heuristics are evaluated based on randomly generated data. One of the proposed heuristics is known to be the best heuristic for the case of zero setup times while another heuristic is known to perform well for such problems. A new version of the latter heuristic, which utilizes the dominance relation, is proposed and shown to perform much better than the other two heuristics.     

An improved simulated annealing for hybrid flowshops with sequence-dependent setup and transportation times to minimize total completion time and total tardiness

In this communication, we strive to apply a novel simulated annealing to consider scheduling hybrid flowshop problems to minimize both total completion time and total tardiness. To narrow the gap between the theory and the practice of the hybrid flowshop scheduling, we integrate two realistic and practical assumptions which are sequence-dependent setup and transportation times into our problem. We apply a metaheuristic based on simulated annealing (SA) which strikes a compromise between intensification and diversification mechanisms to augment the competitive performance of our proposed SA. A comprehensive calibration of different parameters and operators are done. We employ Taguchi method to select the optimum parameters with the least possible number of experiments. For the purpose of performance evaluation of our proposed algorithm, we generate a benchmark against which the adaptations of high performing algorithms in the literature are brought into comparison. Moreover, we investigate the impacts of increase of number of jobs on the performance of our algorithm. The efficiency and effectiveness of our hybrid simulated annealing are inferred from all the computational results obtained in various situations.     

Using two-machine flowshop with maximum lateness objective to model multimedia data objects scheduling problem for WWW applications

The multimedia data objects scheduling problem for WWW applications is modeled using the two-machine flowshop problem of minimizing maximum lateness with separate setup times. We establish three dominance relations, and propose four heuristics. Also, we conduct computational experiments to compare the performance of the proposed heuristics and that of existing ones in the literature. The results of the computational experiments show that the proposed heuristics are quite efficient.Scope and purposeA two-machine flowshop scheduling problem involves scheduling a number of jobs on the machines in order to optimize a given criterion. The majority of research assumes that setup times are negligible or can be combined with the processing times. However, the latter assumption is invalid since it may lead to more idle time on the second machine. In the literature, the separate setup times problem has been mainly addressed with the completion-time-related objective functions such as makespan. However, there are many real-life situations in which a due-date-related objective function such as maximum lateness is more appropriate. The problem with maximum lateness objective has received limited attention from researchers as indicated by a recent survey paper. In this paper, we show a real-life situation in the Internet where the two-machine flowshop problem of minimizing maximum lateness with separate setup times can be used to model the multimedia object scheduling problem. We propose new improved heuristics for this problem and compare with existing ones in the literature.     

Scheduling problems with deteriorating jobs and learning effects including proportional setup times

Recently, interest in scheduling with deteriorating jobs and learning effects has kept growing. However, research in this area has seldom considered setup times. We introduce a new scheduling model in which job deterioration and learning, and setup times are considered simultaneously. In the proposed model, the actual processing time of a job is defined as a function of the setup and processing times of the jobs already processed and the job’s own scheduled position in a sequence. In addition, the setup times are assumed to be proportional to the actual processing times of the already scheduled jobs. We derive polynomial-time optimal solutions for some single-machine problems with or without the presence of certain conditions.     

An agent-based genetic algorithm for hybrid flowshops with sequence dependent setup times to minimise makespan

This paper deals with a variant of flowshop scheduling, namely, the hybrid or flexible flowshop with sequence dependent setup times. This type of flowshop is frequently used in the batch production industry and helps reduce the gap between research and operational use. This scheduling problem is NP-hard and solutions for large problems are based on non-exact methods. An improved genetic algorithm (GA) based on software agent design to minimise the makespan is presented. The paper proposes using an inherent characteristic of software agents to create a new perspective in GA design. To verify the developed metaheuristic, computational experiments are conducted on a well-known benchmark problem dataset. The experimental results show that the proposed metaheuristic outperforms some of the well-known methods and the state-of-art algorithms on the same benchmark problem dataset.     

A particle swarm optimization for a fuzzy multi-objective unrelated parallel machines scheduling problem

This paper proposes a novel multi-objective model for an unrelated parallel machine scheduling problem considering inherent uncertainty in processing times and due dates. The problem is characterized by non-zero ready times, sequence and machine-dependent setup times, and secondary resource constraints for jobs. Each job can be processed only if its required machine and secondary resource (if any) are available at the same time. Finding optimal solution for this complex problem in a reasonable time using exact optimization tools is prohibitive. This paper presents an effective multi-objective particle swarm optimization (MOPSO) algorithm to find a good approximation of Pareto frontier where total weighted flow time, total weighted tardiness, and total machine load variation are to be minimized simultaneously. The proposed MOPSO exploits new selection regimes for preserving global as well as personal best solutions. Moreover, a generalized dominance concept in a fuzzy environment is employed to find locally Pareto-optimal frontier. Performance of the proposed MOPSO is compared against a conventional multi-objective particle swarm optimization (CMOPSO) algorithm over a number of randomly generated test problems. Statistical analyses based on the effect of each algorithm on each objective space show that the proposed MOPSO outperforms the CMOPSO in terms of quality, diversity and spacing metrics.     

An Efficient Hybrid Algorithm for a Bi-objectives Hybrid Flow Shop Scheduling

This paper considers the problem of scheduling n independent jobs in g-stage hybrid flow shop environment. To address the realistic assumptions of the proposed problem, two additional traits were added to the scheduling problem. These include setup times, and the consideration of maximum completion time together with total tardiness as objective function. The problem is to determine a schedule that minimizes a convex combination of objectives. A procedure based on hybrid the simulated annealing; genetic algorithm and local search so-called HSA-GA-LS are proposed to handle this problem approximately. The performance of the proposed algorithm is compared with a genetic algorithm proposed in the literature on a set of test problems. Several performance measures are applied to evaluate the effectiveness and efficiency of the proposed algorithm in finding a good quality schedule. From the results obtained, it can be seen that the proposed method is efficient and effective.     

Integrating non-preemptive open shops scheduling with sequence-dependent setup times using advanced metaheuristics

In this article, we consider non-preemptive open shops scheduling problem (OSSP) where setup times are sequence-dependent (SDST) on each machine to minimize makespan. The contributions of this article are threefold. Firstly, we incorporate a very practical assumption in our problem, SDST, which, according to Allahverdi et al. (2008) [Allahverdi, A., Ng, C. T., Cheung, T. C. E., & Kovalyov, Y. M. (2008). A survey of scheduling problems with setup times or costs. European Journal of Operational Research, 187(3), 985–1032], no paper has ever attempted to integrate into OSSP. Secondly, we propose two new advanced metaheuristics: multi-neighborhood search simulated annealing and hybrid simulated annealing to tackle the problem at hand. Thirdly, for the first time, we adapt two well-known constructive heuristics: longest total processing time and longest total remaining processing from the literature so as to consider the case of SDSTs. We also apply genetic algorithm from the literature of OSSP to embrace the concepts of SDST. Since there is no standard SDST-OSSP benchmark, we make certain adaptations on the Taillard’s benchmark [Taillard, E. (1993). Benchmarks for basic scheduling problems. European Journal of Operational Research, 64, 278–285] to include setup times. An experimental design based on foregoing benchmark is conducted to evaluate the competitiveness and robustness of our proposed algorithm against some effective algorithms in the literature. The obtained results strongly support the high performance of our proposed algorithms with respect to other well-known heuristic and metaheuristic algorithms.     

Scheduling with multiple servers

In this paper, we consider the problem of scheduling a set of jobs on a set of identical parallel machines. Before the processing of a job can start, a setup is required which has to be performed by a given set of servers. We consider the complexity of such problems for the minimization of the makespan. For the problem with equal processing times and equal setup times we give a polynomial algorithm. For the problem with unit setup times, m machines and m − 1 servers, we give a pseudopolynomial algorithm. However, the problem with fixed number of machines and servers in the case of minimizing maximum lateness is proven to be unary NP-hard. In addition, recent algorithms for some parallel machine scheduling problems with constant precessing times are generalized to the corresponding server problems for the case of constant setup times. Moreover, we perform a worst case analysis of two list scheduling algorithms for makespan minimization.     

Hybrid flowshop scheduling with sequence‐dependent setup times by hybridizing max–min ant system,simulated annealing and variable neighbourhood search

This paper deals with the hybrid flowshop scheduling problems with sequence‐dependent setup times. To minimize the makespan, we propose hybrid metaheuristic approach, which integrates several features from ant colony optimization, simulated annealing and variable neighbourhood search in a new configurable scheduling algorithm. Our proposed algorithms are tuned by means of design of experiments approach. We present computational experiments on standard test problems and compare the results with the several algorithms presented previously. The results illustrate that the hybrid metaheuristic outperforms the other algorithms.     

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.     

A faster branch-and-bound algorithm for the earliness-tardiness scheduling problem

This paper addresses the one-machine scheduling problem with earliness-tardiness penalties. We propose a new branch-and-bound algorithm that can solve instances with up to 50 jobs and that can solve problems with even more general non-convex cost functions. The algorithm is based on the combination of a Lagrangean relaxation of resource constraints and new dominance rules.     

考虑机器检修的热轧钢管批量计划方法

本文从无缝钢管生产实际中提取并定义了周期性机器检修环境下的钢管热轧批量计划问题,基于无缝钢管生产的特殊性,将该问题抽象为一类考虑机器检修和机器调整时间的单机调度问题,并建立了以最小化机器闲置和机器调整时间为目标的数学模型.针对批量间的机器调整时间取决于钢管规格的变化这一特性,提出了最小调整时间排序规则,证明了该规则在不考虑检修计划时具有最优性.进而,以此为基础建立了循环求解框架,并设计了两阶段启发式算法.基于实际生产数据设计了多种问题规模的实验,验证了算法的有效性,并从实际应用角度对结果进行了分析.     

Scheduling algorithms for a semiconductor probing facility

This paper focuses on a scheduling problem in a semiconductor wafer probing facility. In the probing facility, wafer lots with distinct ready times are processed on a series of workstations, each with identical parallel machines. We develop a heuristic algorithm for the problem with the objective of minimizing total tardiness of orders. The algorithm employs a bottleneck-focused scheduling method, in which a schedule at the bottleneck workstation is constructed first and then schedules for other workstations are constructed based on the schedule at the bottleneck. For scheduling wafer lots at the bottleneck workstation, we consider prospective tardiness of the lots as well as sequence-dependent setup times required between different types of wafer lots. We also present a rolling horizon method for implementation of the scheduling method on a dynamic situation. The suggested methods are evaluated through a series of computational experiments and results show that the methods work better than existing heuristic methods.