No-wait flowshop scheduling problem to minimize the number of tardy jobs

This research addresses the m-machine no-wait flowshop scheduling problem with the objective of minimizing the number of tardy jobs. The problem is known to be NP-hard even for the two machines, and literature reveals that no heuristics have been developed for this problem. In this paper, we propose an efficient heuristic based on simulated annealing, where we first adapt the single-machine optimal algorithm to our problem to develop two new heuristics, NOTA and NOTM. An improved simulated annealing heuristic, called SA-GI, is then developed by feeding the best performing heuristic among NOTA, NOTM, and EDD into the simulated annealing algorithm. A second proposed heuristic, called SA-IP, further improves the SA-GI solution by using insertion and pair-wise exchange techniques. Based on the computational experiments, the overall relative percentage errors of the heuristic SA, SA-GI, and SA-IP are 8.848, 8.428, and 0.207, respectively. The computational times of the three heuristics are close to each other, and the largest average time is less than one second, and hence, the computational time is not an issue. Therefore, the heuristic SA-IP is the best one.     

Stochastic flow-shop scheduling with minimizing the expected number of tardy jobs

In this research, minimizing the expected number of tardy jobs in a dynamic m machine flow-shop scheduling problem, i.e., $ {F_m}\left| {{r_j}\left| {{\text{E}}\left[ {\sum {{U_j}} } \right]} \right.} \right. $ is investigated. It is assumed that the jobs with deterministic processing times and stochastic due dates arrive randomly to the flow-shop cell. The due date of each job is assumed to be normally distributed with known mean and variance. A dynamic method is proposed for this problem by which the m machine stochastic flow-shop problem is decomposed into m stochastic single-machine sub-problems. Then, each sub-problem is solved as an independent stochastic single-machine scheduling problem by a mathematical programming model. Comparison of the proposed method with the most effective rule of thumb for the proposed problem, i.e., shortest processing time first rule shows that the proposed method performs 23.9 % better than the SPT rule on average for industry-size scheduling 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.     

Solving job shop scheduling problems using artificial immune system

The n-job, m-machine job shop scheduling (JSS) problem is one of the general production scheduling problems. Many existing heuristics give solutions for small size problems with near optimal solutions. This paper deals with the criterion of makespan minimization for the job shop scheduling of different size problems. The proposed computational method of artificial immune system algorithm (AIS) is used for finding optimal makespan values of different size problems. The artificial immune system algorithm is tested with 130 benchmark problems [10 (ORB1-ORB5 & ARZ5-ARZ9), 40 (LA01-LA40) and 80 (TA01-TA80)]. The results show that the AIS algorithm is an efficient and effective algorithm which gives better results than the Tabu search shifting bottleneck procedure (TSSB) as well as the best solution of shifting bottleneck procedure ( SB-GLS1 ) of Balas and Vazacopoulos.     

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.     

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.     

Greedy randomised dispatching heuristics for the single machine scheduling problem with quadratic earliness and tardiness penalties

In this paper, we present greedy randomised dispatching heuristics for the single-machine scheduling problem with quadratic earliness and tardiness costs and no machine idle time. The several heuristic versions differ, on the one hand, on the strategies involved in the construction of the greedy randomised schedules. On the other hand, these versions also differ on whether they employ only a final improvement step or perform a local search after each greedy randomised construction. The proposed heuristics were compared with existing procedures as well as with optimum solutions for some instance sizes. The computational results show that the proposed procedures clearly outperform their underlying dispatching heuristic, and the best of these procedures provide results that are quite close to the optimum. The best of the proposed algorithms is the new recommended heuristic for large instances as well as a suitable alternative to the best existing procedure for the larger of the middle-sized instances.     

Minimizing the earliness/tardiness costs on parallel machine with learning effects and deteriorating jobs: a mixed nonlinear integer programming approach

In this study, we introduce a mixed nonlinear integer programming formulation for parallel machine earliness/tardiness (ET) scheduling with simultaneous effects of learning and linear deterioration, sequence-dependent setups, and a common due-date for all jobs. By the effects of learning and linear deterioration, we propose that the processing time of a job is defined by increasing function of its execution start time and position in the sequence. The developed model allows sequence-dependent setups and sequence-dependent early/tardy penalties. The model can easily provide the optimal solution to problems involving about eleven jobs and two machines.     

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 genetic algorithm for the single machine preemptive scheduling problem with linear earliness and quadratic tardiness penalties

In this paper, we consider the single machine preemptive scheduling problem with linear earliness and quadratic tardiness penalties, with no machine idle time. The problem is strongly NP-hard. We proposed a new mathematical model, with non-linear terms and integer variables. We develop a genetic algorithm for solving the problem in medium and large size. The proposed procedure is compared with optimal solutions for the smaller instance sizes. The genetic procedure is also quite close to the optimum and provided an optimal solution for most of the test problems. Numerical examples show that the proposed algorithm is efficient and effective. Scheduling with early and tardy penalties has received extensive attention from the scheduling community because of its practical significance. Single machine scheduling environments actually occur in several practical applications. Also, the performance of many production systems is often determined by the schedules for a single bottleneck machine. Furthermore, the study of single machine problems frequently provides outcomes that prove functional for more complex scheduling areas.     

Minimizing the makespan and the system unavailability in parallel machine scheduling problem: a similarity-based genetic algorithm

This paper is devoted to ponder a joint production and maintenance problem. For solving the problem, a genetic algorithm named similarity-based subpopulation genetic algorithm (SBSPGA) is introduced. SBSPGA is presented based on a well-known evolutionary algorithm, the subpopulation genetic algorithm II (SPGA-II). Compared with the SPGA-II, the innovation of the SBSPGA could be divided into two parts: (1) using a similarity model for the elitism strategy and (2) performing the algorithm in just one stage. To tackle the maintenance aspect, reliability models are employed in this paper. The aim of this paper was to optimize two objectives: minimization of the makespan for the production part and minimization of the system unavailability for the maintenance part. To execute our proposed problem, two decisions must be made at the same time: achieving the best assignment of n jobs on m machines to minimize the makespan and determining the time at which the preventive maintenance activities must be performed to minimize the system unavailability. The maintenance activity numbers and the maintenance intervals are not fixed in advanced. Promising the acquired results, a benchmark with tremendous number of test instances (more than 5,000) is employed.     

Minimizing the number of tool switches on a flexible machine

This article analyzes a tool switching problem arising in certain flexible manufacturing environments. A batch of jobs have to be successively processed on a single flexible machine. Each job requires a subset of tools, which have to be placed in the tool magazine of the machine before the job can be processed. The tool magazine has a limited capacity, and, in general, the number of tools needed to produce all the jobs exceeds this capacity. Hence, it is sometimes necessary to change tools between two jobs in a sequence. The problem is then to determine a job sequence and an associated sequence of loadings for the tool magazine, such that the total number of tool switches is minimized. This problem has been previously considered by several authors; it is here revisited, both from a theoretical and from a computational viewpoint. Basic results concerning the computational complexity of the problem are established. Several heuristics are proposed for its solution, and their performance is computationally assessed.     

Minimizing total tardiness for the machine scheduling and worker assignment problems in identical parallel machines using genetic algorithms

The concept of parallel machines has been widely used in manufacturing. This article proposes a genetic algorithm (GA) approach to minimize total tardiness of a set of tasks for identical parallel machines and worker assignment to machines. A spreadsheet-based GA approach is presented to solve the problem. A domain-independent general purpose GA is used, which is an add-in to the spreadsheet software. The paper demonstrates an adaptation of the proprietary GA software to the problem of minimizing total tardiness for the worker assignment scheduling problem for identical parallel machine models. Two 100 I/P/n/m/W problems taken from Hu (Int J Adv Manuf Technol 23:383–388, 2004, Int J Adv Manuf Technol 29:165–169, 2006) for a similar study are simulated. The performance of GA is superior to SES-A/LMC approach used by Hu and very close to the Exhaustive search procedure. It is shown that the spreadsheet GA implementation makes it very easy to adapt the problem for any set of objective measures without changing the actual model. Empirical analysis has been carried out to study the effect of GA parameters, namely, crossover rate, mutation rate, and the population size.     

Optimization of milling parameters using artificial neural network and artificial immune system

The present paper is an attempt to predict the effective milling parameters on the final surface roughness of the work-piece made of Ti-6Al-4V using a multi-perceptron artificial neural network. The required data were collected during the experiments conducted on the mentioned material. These parameters include cutting speed, feed per tooth and depth of cut. A relatively newly discovered optimization algorithm entitled, artificial immune system is used to find the best cutting conditions resulting in minimum surface roughness. Finally, the process of validation of the optimum condition is presented.     

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.     

Minimizing the number of experimental tribological tests on the friction machine of reciprocating motion

The theory of the equivalence of friction units tests for a large number of samples to lengthy tests of one sample for friction machines of reciprocating motion based on the Birkhoff-Khinchin theorem for processes that meet the criteria of ergodicity and stationarity has been developed. It has been established that a large part of the examined friction pairs under the indicated test conditions meets the specified criteria.     

模糊制造系统中的不同尺寸工件单机批调度优化

将工件尺寸不同的单机批调度问题扩展到模糊制造系统中,建立了基于模糊批加工时间和模糊批间隔时间的制造跨度模型,提出了一种集成粒子群优化和差异演化的混合算法,将制造跨度最小化.为提高算法的收敛速度,设计了基于工件优先值向量的统一编码方式,并采用线性的缩放因子以确保足够的差异化信息;为解决差异演化算法早熟收敛的问题,将粒子群优化的全局搜索技术嵌入了差异演化算法;最后,在解码时利用批调度的启发式算法,将混合算法的个体加以优化分批.仿真实验结果验证了该混合算法的求解性能优于目前文献中的其他算法.     

Cycle time variance minimization in dynamic scheduling of single machine systems

In this paper, we study the minimization of variance of cycle times in a dynamic single machine system where jobs arrive continuously over time. Numerous production systems give rise to single machine models, and a multiple-machine environment where the performance of a bottleneck machine determines the performance of the entire system reduces to a single machine problem [16]. Minimizing cycle time variance helps in safe predictions of the completion of job production and thus in providing the same quality of service to the customers. This allows an improved ability to meet the due dates reliably, and thus the greater coordination with further downstream operations on the jobs, as highly preferred in semiconductor manufacturing. Scheduling the bottleneck process to minimize the time of presence of the jobs in process minimizes the deterioration of cycle time-related performance measures. Low values of cycle time-related measures are also preferred for low risk of wafer contamination associated with it during processing. New scheduling rules are developed to minimize both the cycle time variance and the maximum cycle time for single machine system, wherein the machine/process is always utilized to the maximum extent and in the extreme case is heavily loaded with jobs for processing. The performance of the proposed rules is compared with the rules available in the literature and the results are presented for the objectives of minimizing cycle time variance and maximum cycle time at higher levels of machine utilization.     

On the scheduling with past-sequence-dependent setup times and learning effects on a single machine

This paper deals with a single-machine scheduling problem with setup time and learning effects. The setup times are proportional to the length of the already processed jobs, i.e., the setup times are job-independent and past-sequence-dependent, and the learning effects are job-independent and position-dependent. The objective is to minimize the sum of earliness penalties subject to no tardy jobs. Wang, Wang, Gao, and Huang [Int J Adv Manuf Technol 48: 739–746, 2010] showed that an optimal sequence for this problem could be obtained by arranging jobs in non-increasing order of processing times. In this paper, we first demonstrate that this result is incorrect, and then introduce new exact solution strategies that polynomially solve problems whose earliness penalties are strictly increasing functions of job earliness. Polynomial time solutions are also presented for some special cases.