Simultaneous minimization of total tardiness and waiting time variance on a single machine by genetic algorithms

This paper considers a single machine scheduling problem, with the objective of minimizing a linear combination of total tardiness and waiting time variance in which the idle time is not allowed. Minimizing total tardiness is always regarded as one of the most significant performance criteria in practical systems to avoid penalty costs of tardiness, and waiting time variance is an important criterion in establishing quality of service (QoS) in many systems. Each of these criteria is known to be non-deterministic polynomial-time hard (NP-hard); therefore, the linear combination of them is NP-hard too. For this problem, we developed a genetic algorithm (GA) by applying its general structure that further improves the initial population, utilizing some of heuristic algorithms. The GA is shown experimentally to perform well by testing on various instances.     

Minimizing cycle time in single machine scheduling with start time-dependent processing times

This paper considers the single machine scheduling problem with a new version of time-dependent processing times. The processing time of a job is defined as a piecewise linear function of its start time. It is preferred that the processing of each job be started at a specific time which means that processing the job before or after that time implies additional effort to accomplish the job. The job-processing time is a nonmonotonic function of its start time. The increasing rate of processing times is job independent and the objective is to minimize the cycle time. We show that the optimal schedule is V shaped and propose an optimal polynomial time algorithm for the problem.     

A hybrid genetic algorithm to minimize makespan for the single batch machine dynamic scheduling problem

This paper considers a single batch machine dynamic scheduling problem, which is readily found in the burn-in operation of semiconductor manufacturing. The batch machine can process several jobs as a batch simultaneously, within the capacity limit of the machine, and the processing time is represented by the longest processing time among all jobs in a batch. For a single batch machine problem with arbitrary job release time, we proposed an improved algorithm (merge-split procedure) to refine the solution obtained by the LPT-BFF heuristic, and two versions of a hybrid genetic algorithm (GA) are introduced in this paper. Each version of the hybrid GA diversifies job sequences using the GA operators in stage 1, forms batches in stage 2, and finally sequence the batches in stage 3. The difference is that merge-split procedures are involved in the second version of the hybrid GA. Computational experiments showed that the hybrid GA would obtain satisfactory average solution quality and the merge-split procedures would be good at reinforcing the solution consistency of the hybrid GA.     

基于组合拍卖的多主体单机调度问题

为解决分布式单机调度问题,设计了一种基于重复叫价组合拍卖的多主体调度机制.该机制采用基于约束的投标语言,将组合拍卖的一般形式与机器调度的建模技术相结合,建立了改进的竞胜标模型,该模型的全局目标同时兼顾了系统收益与机器利用率;在投标策略上,当前回合中未中标的投标者可以采用提高出价或放宽对时间需求的约束来参与下一回合的竞标.对该机制进行仿真实验的结果表明,与传统的单独采用组合拍卖解决机器调度问题的方法相比,该机制得到的调度方案在保证系统收益的前提下,提高了机器利用率.     

A meta-heuristic approach to single machine scheduling problems

A new meta-heuristic evolutionary algorithm, named a memetic algorithm, for solving single machine total weighted tardiness scheduling problems is presented in this paper. Scheduling problems are proved to be NP-hard (Non-deterministic polynomial-time hard) types of problems and they are not easily or exactly solved for larger sizes. Therefore, application of the meta-heuristic technique to solve such NP hard problems is pursued by many researchers. The memetic algorithm is a marriage between population-based global searches with local improvement for each individual. The algorithm is tested with benchmark problems available in the OR (operations research) library. The results of the proposed algorithm are compared with the best available results and were found to be nearer to optimal. The memetic algorithm performs better than the heuristics like earliest due date and modified due date.     

Robust and stable scheduling of a single machine with random machine breakdowns

For single-machine scheduling with random machine breakdowns, a new method considering both robustness and stability is proposed in this paper. The stability of the predictive schedule is measured by the sum of the absolute deviations between the planned job completion times and the realized ones. A surrogate measure is developed to evaluate the stability, assuming that there is only one breakdown. Generating a robust and stable schedule becomes a bi-objective optimization problem. A two-stage multi-population genetic algorithm is proposed to solve the bi-objective optimization problem. The method is applied to minimizing the total weighted tardiness of all jobs. The computational results show that the schedule generated by the proposed method is insensitive to disturbances, along with providing better robustness and stability.     

工件加工随机调度中优先约束问题的研究

讨论工件加工时间为任意随机分布的随机变量的单机随机调度问题,设工件间的约束为树优先约束,目标函数为极小化加权完工时间和的数学期望.这一模型在机械设计与制造行业中的多个元器组件加工,以及钢铁板坯轧制等众多实际生产制造领域中都具有广泛的应用背景.证明了工件加工时间为任意随机分布的随机变量的情况下,最大家庭树中的工件优先于家庭树中其它的工件加工,并且其工件连续加工所得到的调度为最优调度,给出了最优多项式算法,该算法可以被推广应用于实际的生产中,具有较强的实际应用性.     

Algorithms for the single machine total weighted completion time scheduling problem with release times and sequence-dependent setups

This paper considers the problem of scheduling n jobs on a single machine to minimize the total weighted completion time in the presence of sequence-dependent setup times and release times. To the best of our knowledge, little research has been devoted to this scheduling problem. Therefore, we developed two exact algorithms, including a constraint programming model and a branch-and-bound method for small problems. The obtained optimal solutions can be used as a benchmark for evaluating the performance of heuristics. With the complexity in mind, two heuristics, including a best index dispatch (BID) and a modified weighted shortest processing time (MWSPT) based on non-delay concepts are also proposed for large problems. The time complexities of the two proposed heuristics are O(n ⁴) and O(n ³), respectively. The computational results showed that the branch-and-bound method could solve most instances with 40 jobs under the time limit of 7,200 s. The BID heuristic is superior to the MWSPT in solution quality, although both can efficiently and effectively obtain near-optimal solutions for large instances.     

优化加权平均流程时间的平行机调度

平行机调度问题在工业界有着广泛应用,实际生产中瓶颈工序的调度很多属于这类问题.运用增强学习算法来研究以最小化作业的加权平均滞留时间为目标的动态平行机调度问题Qm I rj,sjk,Mj I ∑wjfj,考虑与作业顺序相关的转换时间和机器-作业资格约束.为了把调度问题转化为增强学习问题,定义了系统状态的表示方式,利用加权最短加工时间优先(WSPT)规则、Weng算法、排名(RA)算法和LFJ-RA(Least Flexible Job-Ranking Algorithm)算法构造行为,定义了与调度目标函数等价的报酬函数,并采用结合函数泛化器的Q学习算法来解决.实验表明Q学习算法对每个测试问题的调度结果都优于WSPT规则、排名算法、LFJ-RA算法和Weng算法.     

Two-agent group scheduling with deteriorating jobs on a single machine

This paper considers the two-agent scheduling problems with deteriorating jobs and group technology on a single machine, where the objective is to minimize the total completion time of the first agent with the restriction that the maximum cost of the second agent cannot exceed a given upper bound. Two agents compete to perform their respective jobs on a common single machine, and each agent has his own criterion to optimize. We introduce deteriorating jobs and group technology into the two-agent single-machine scheduling where the job processing times and group setup times are both functions of their starting times. There are two different linear deterioration functions. We propose the optimal properties and present the optimal polynomial time algorithms for two different scheduling problems, respectively.     

An investigation on single machine total weighted tardiness scheduling problems

The urge to produce products in the production line at a faster rate with no compromise in quality has led to scheduling gaining greater importance in the modern day industries. Scheduling is concerned with the allocation of limited resources to tasks over time. The investigations on various scheduling problems have been of constant interest to researchers worldwide. This paper deals with an investigation on the total weighted tardiness of the single machine scheduling problems. The problems are solved by a heuristic procedure, namely backward forward heuristics. The different methods of formulating the problem instances are discussed. The benchmark problems and their best known values available in the OR library are used for the comparison to find out the influence of Relative Due Date (RDD) and Tardiness Factor (TF) used to generate the problem instances.     

基于前序基因表达式编程的单机成组调度算法

建立了满足成组技术要求的带有提前/拖期惩罚的单机调度模型,考虑了订单达到时间不同、交货期窗口不同、机器调整时间与工件组加工顺序相关等多种情形;设计了基于基因表达式编程的多层染色体编码方案,将染色体对应于工件的优先规则公式;最后,实现了利用先进的前序基因表达式编程搜索技术求解该问题的算法,并通过实验验证了该算法的可行性和有效性.     

Simple heuristic to minimize total tardiness in a single machine scheduling problem

This paper discusses a simple heuristic to minimize the total tardiness in a single machine scheduling problem. The problem of minimizing total tardiness in single machine scheduling is a combinatorial problem. Hence, heuristic development for such problems is inevitable. In this paper, an attempt has been made to develop a simple heuristic, alternatively called greedy heuristic, to minimize the total tardiness in a single machine scheduling problem with n independent jobs, each having its processing time and due date. Further, its solution accuracy is compared with the optimal solution of a set of randomly generated problems using an ANOVA experiment. From the ANOVA experiment, it is observed that the solution of the simple heuristic proposed in this paper does not differ significantly from the optimal solution at a significance level of 0.05.     

Effective heuristics for the no-wait flow shop scheduling problem with total flow time minimization

The no-wait flow shop scheduling problem with total flow time criterion has important applications in industrial systems. Heuristics that explore specific characteristics of the problem are essential to find good solutions in limited computational time for many practical applications. This paper first presents two constructive heuristics, namely improved standard deviation heuristic (ISDH) and improved Bertolissi heuristic (IBH), by combining the standard deviation heuristic (Gao et al., Int J Adv Manf Technol 56:683–692, 2011) and Bertolliso heuristic (Bertolissi, J Mater Process Technol 107:459–465, 2000) with the procedure of the constructive heuristic of Laha (Int J Adv Manf Technol 41:97–109, 2009). Then, four composite heuristics, i.e., ISDH with local search, IBH with local search, ISDH with iteration, and IBH with iteration, are separately proposed using the insertion-based local search method and iteration operator to improve the solutions of the ISDH and IBH. Extensive computational experiments are carried out based on a set of well-known flow shop benchmark instances that are considered as no-wait flow shop instances. Computational results and comparisons show that the proposed composite heuristics perform significantly better than the existing ones, and the proposed composite heuristics further improve the presented constructive heuristics for the no-wait flow shop scheduling problem with total flow time criterion.     

虚拟生产系统的自适应动态调度机理及算法

为解决动态制造环境下虚拟生产系统的动态调度问题,提出了一种基于事件驱动的自适应动态调度方法。在该方法中,自适应动态调度机理首先通过检测获得虚拟生产系统所面临的动态事件,进而分析动态事件对调度产生的局部影响,并制定相应的自适应措施和规则,然后在自适应规则的指导下,采用改进的启发式受影响操作重调度算法作为自适应动态调度的算法,来确定调度中的受影响操作并对其做出相应的局部调整,从而以一种自适应的方式快速而平稳地完成虚拟生产系统的动态调度。最后,通过与一种典型的整体重调度方法（基于多智能体的调度方法）的比较,验证了该方法的可行性和有效性。     

Minimizing total flow time on a single flexible machine

In this study, we address a job sequencing and tool switching problem arising in flexible manufacturing systems. We consider the single machine problem of minimizing total flow time. We prove that the problem is NP-hard in the strong sense and show that the tool switching problem is polynomially solvable for a given sequence.We propose a branch-and-bound algorithm whose efficiency is improved by precedence relations and several lower and upper bounding techniques. Our computational results reveal that the branch and bound approach produces optimal solutions in reasonable times for moderate sized problems. Our upper bounds produce very satisfactory solutions; therefore they can be an attractive alternative to solve larger sized problems.     

Genetic algorithms for single machine scheduling with quadratic earliness and tardiness costs

In this paper, we consider the single machine scheduling problem with quadratic earliness and tardiness costs, and no machine idle time. We propose a genetic approach based on a random key alphabet and present several algorithms based on this approach. These versions differ on the generation of both the initial population and the individuals added in the migration step, as well as on the use of local search. The proposed procedures are compared with the best existing heuristics, as well as with optimal solutions for the smaller instance sizes. The computational results show that the proposed algorithms clearly outperform the existing procedures and are quite close to the optimum. The improvement over the existing heuristics increases with both the difficulty and the size of the instances. The performance of the proposed genetic approach is improved by the initialization of the initial population, the generation of greedy randomized solutions, and the addition of the local search procedure. Indeed, the more sophisticated versions can obtain similar or better solutions and are much faster. The genetic version that incorporates all the considered features is the new heuristic of choice for small and medium size instances.     

A fuzzy multi-objective programming for scheduling of weighted jobs on a single machine

This paper considers a classic model of weighted single machine scheduling problem and aims to improve it to a real-world application through fuzzy set theory. For this purpose, processing times and due dates of jobs are defined as fuzzy numbers. In the proposed model, two objectives are considered to be minimized: average tardiness and number of tardy jobs. The objectives are converted into fuzzy statement through fuzzy arithmetic. Because the problem is NP-hard, it is proposed to solve the model through three well-known meta-heuristic algorithms as Simulated Annealing, Tabu Search, and Genetic Algorithm albeit with some modifications. Comparative analysis of algorithms is attainable through different experimented results on generated benchmark problems with different sizes and difficulties. Efficiency of the developed algorithms is analyzed on the different versions of the model which come from the assumption of different parameters and/or components. Algorithms' behaviors to managerial insights are also considered in some sensitivity analysis experiments. The obtained results show the applicability of the proposed model in real-world scheduling problems.     

A nondominated ranked genetic algorithm for bi-objective single machine preemptive scheduling in just-in-time environment

Motivated by just-in-time (JIT) manufacturing, we study the bi-objective scheduling problem of minimizing the total weighted earliness and the number of tardy jobs on a single machine, in which machine idle time and preemption are allowed. The problem is known to be NP-hard. In this paper, we propose a new mathematical model, with nonlinear terms and integer variables which cannot be solved efficiently for medium- and large-sized problems. A method combining the new ranked-based roulette wheel selection algorithm with Pareto-based population ranking algorithm, named nondominated ranking genetic algorithm (NRGA), has been presented to find nondominated solutions in a reasonable time. Various operators and parameters of the proposed algorithm are reviewed to calibrate the algorithm by means of the Taguchi method. A number of numerical examples are solved to demonstrate the effectiveness of the proposed approach. The solutions obtained via NRGA are compared against solutions obtained via ε-constraint method in small-sized problems. Experimental results show that the proposed NRGA is competitive in terms of the quality and diversity of solutions in medium- and large-sized problems.