Non-permutation flowshop scheduling with dual resources

Typically, in order to process jobs in a flowshop both machines and labor are required. However, in traditional scheduling problems, labor is assumed to be plentiful and only machine is considered to be a constraint. This assumption could be due to the lower cost of labor compared to machines or the complexity of dual-resource constrained problems. In this paper a mathematical model is developed to minimize the work-in-process inventory while maximizing the service level in a flowshop with dual resources. The model focuses on optimizing a non-permutation flowshop. There are different skill levels considered for labor and the setup times on machines are sequence-dependent. Jobs are allowed to skip one or more stages in the flowshop. Job release and machine availability times are considered to be dynamic. The problem is solved in two layers. The outer layer is a search algorithm to find the schedule of jobs on the machine (traditional flowshop scheduling problem) and the inner layer is a three-step heuristic to find a schedule of jobs on labor in accordance to the machine schedule. Three different search algorithms are developed to solve the proposed NP-hard problem. First algorithm can solve a permutation flowshop while the other two are developed to solve a non-permutation flowshop. The comparison between the optimal solution and the search algorithms in small examples shows a good performance of the algorithms with an average deviation of only 2.00%. An experimental design analyzes the effectiveness and efficiency of the algorithms statistically. The results show that non-permutation algorithms perform better than the permutation algorithm, although the former are less efficient. The effectiveness and efficiency in all three algorithms have an inverse relation. To the best of our knowledge, this research is the first of its kind to provide a comprehensive mathematical model for dual resource flowshop scheduling problem.     

A hybrid artificial immune algorithm for a realistic variant of job shops to minimize the total completion time

This paper investigates an extended problem of job shop scheduling to minimize the total completion time. With aim of actualization of the scheduling problems, many researchers have recently considered realistic assumptions in their problems. Two of the most applied assumptions are to consider sequence-dependent setup times and machine availability constraints (MACs). In this paper, we deal with a specific case of MACs caused by preventive maintenance (PM) operations. Contrary to the previous papers considering fixed or/and conservative policies, we consider flexible PM operations, in which PM operations may be postponed or expedited as required. A simple technique is employed to schedule production jobs along with the flexible MACs caused by PM. To solve the given problem, we present a novel meta-heuristic method based on the artificial immune algorithm (AIA) incorporating some advanced features. For further enhancement, the proposed AIA is hybridized with a simple and fast simulated annealing (SA). To evaluate the proposed algorithms, we compare our proposed AIA with three well-known algorithms taken from the literature. Finally, we find that the proposed AIA outperforms other algorithms.     

Minimizing job completion time variance for service stability on identical parallel machines

This paper addresses a job scheduling problem on multiple identical parallel machines so as to minimize job completion time variance (CTV). CTV minimization is closely related to the Just-In-Time philosophy and the service stability concept since it penalizes both earliness and tardiness. Its applications can be found in many real-life areas such as Internet data packet dispatching and production planning. This paper focuses on the unrestricted case of the problem where idle times are allowed to exist before machines start to process jobs. We prove several dominant properties about the optimal solution to the problem. For instance, we prove that the mean completion time (MCT) on each machine should be the same under an optimal schedule. Based on these properties, an efficient heuristic algorithm is proposed. Computational experiments are conducted to test the performance of the proposed algorithm. The outputs demonstrate that the proposed algorithm is near optimal for small problem instances and greatly outperforms some existing algorithms for large problem instances.     

Solving single machine scheduling under disruption with discounted costs by quantum-inspired hybrid heuristics

In this paper we study machine disruption on scheduling problem. We focus on the case where the weighted discounted shortest processing time (WDSPT) rule is optimal for original single machine scheduling problem. After a subset of jobs have finished processing, we learn that the machine would be disrupted for some period of time in the future. Therefore a new schedule is needed considering both original objective and the deviation from the initial schedule. The original objective is measured by the weighted discounted total completion time and the deviation is measured by the variances in jobs’ completion times. According to the characteristics of optimal schedule, we design one hybrid heuristic algorithm, combining the advantages of qubit representation in quantum computing and Non-dominated Sorting Genetic Algorithm (NSGA-II). By analyzing the solutions diversity and proximity to optimal Pareto front on several metrics, we demonstrate that the proposed algorithm is effective for machine disruption management.     

Setting due dates to minimize the total weighted possibilistic mean value of the weighted earliness-tardiness costs on a single machine

In this paper, it is investigated how to sequence jobs with fuzzy processing times and predict their due dates on a single machine such that the total weighted possibilistic mean value of the weighted earliness-tardiness costs is minimized. First, an optimal polynomial time algorithm is put forward for the scheduling problem when there are no precedence constraints among jobs. Moreover, it is shown that if general precedence constraints are involved, the problem is NP-hard. Then, four reduction rules are proposed to simplify the constraints without changing the optimal schedule. Based on these rules, an optimal polynomial time algorithm is proposed when the precedence constraint is a tree or a collection of trees. Finally, a numerical experiment is given.     

Completion time variance minimisation on two identical parallel processors

The problem of scheduling jobs to minimise completion time variance (CTV) is a well-known problem in scheduling research. CTV is categorized as a non-regular performance measure and its value may decrease by increasing the job completion times. This objective is relevant in situations where providing uniform service to customers is important, and is in-line with just-in-time philosophy. The problem concerned in this paper is to schedule n jobs on two identical parallel machines to minimise CTV. We consider the unrestricted version of the problem. The problem is said to be restricted when a machine is not allowed to remain idle when jobs are available for processing. It may be necessary to delay the start of job processing on a machine in order to reduce the completion time deviations. This gives rise to the unrestricted version of the problem. We discuss several properties of an optimal schedule to the problem. In this paper, we develop a lower bound on CTV for a known partial schedule and propose a branch and bound algorithm to solve the problem. Optimal solutions are obtained and results are reported.     

Common due date assignment and scheduling with ready times

We consider the problem of scheduling a set of nonsimultaneously available jobs on one machine. Each job has a ready time only at or after which the job can be processed. All the jobs have a common due date, which needs to be determined. The problem is to determine a due date and a schedule so as to minimize a total penalty depending on the earliness, tardiness and due date. We show that this problem is strongly NP-hard and give an efficient algorithm that finds an optimal due date and schedule when either the job sequence is predetermined or all jobs have the same processing time. We also propose three approximation algorithms for the general and special cases together with their experimental analysis.

Scope and purpose

We consider the single machine due date assignment problem for scheduling jobs which are ready for processing at different times. The problem under consideration arises in production planning and scheduling concerning the setting of appropriate due dates for a number of customer orders arriving over time. Most of the earlier publications on this subject assumed that the jobs are ready for processing simultaneously. This assumption is too restrictive for real-life production systems where jobs arrive at different times. We show that the problem with unequal ready times is NP-hard and develop fast heuristic algorithms for it, and exact algorithms for two special cases.     

就绪时间受限的负荷单机环境下返工工件重调度方法

研究了返工工件的单机重调度问题.在初始调度中初始工件带有不同的就绪时间,优化目标为最小化初始工件等待时间和;重调度时在满足每个初始工件最大等待时间约束情况下安排返工工件的生产,优化目标为最小化所有工件等待时间和.文中首先建立了RRSM （Rescheduling for reworks on single machine）问题模型,并证明其为NP难问题.然后,提出并证明了三个RRSM问题性质,进而根据诸性质设计了求解RRSM问题的动态插入启发式（Dynamic insert heuristic,DIH）算法.证明了应用DIH算法能在多项式时间内求得两种特殊RRSM问题的最优解. 最后,分析了DIH算法解的特点,给出了最优解的判定方法,并通过算例说明了DIH算法的有效性.     

An aggregation procedure for the deterministic job-shop problem

A new approach is proposed in this paper to solve the job-shop scheduling problem. Instead of considering operations or machines, the construction of partial schedules by dealing with jobs, one after the other, is suggested. A partial schedule for given jobs is characterized by the sequence of their operations on each machine. The principle of the algorithm is to aggregate a new job on the current schedule, i.e. to insert its operations without altering the previous order. Two main theoretical results are presented: firstly, the selection procedure for jobs and secondly, the aggregation algorithm. Next the method is explained using a simple example. Finally, the authors present and comment on computational results for an implementation of the algorithm, for some well-known job-shop problems.     

Single machine total completion time minimization scheduling with a time-dependent learning effect and deteriorating jobs

In this article, we consider a single machine scheduling problem with a time-dependent learning effect and deteriorating jobs. By the effects of time-dependent learning and deterioration, we mean that the job processing time is defined by a function of its starting time and total normal processing time of jobs in front of it in the sequence. The objective is to determine an optimal schedule so as to minimize the total completion time. This problem remains open for the case of ?1?a?a denotes the learning index; we show that an optimal schedule of the problem is V-shaped with respect to job normal processing times. Three heuristic algorithms utilising the V-shaped property are proposed, and computational experiments show that the last heuristic algorithm performs effectively and efficiently in obtaining near-optimal solutions.     

Preemptive online scheduling with rejection of unit jobs on two uniformly related machines

We consider preemptive online and semi-online scheduling of unit jobs on two uniformly related machines. Jobs are presented one by one to an algorithm, and each job has a rejection penalty associated with it. A new job can either be rejected, in which case the algorithm pays its rejection penalty, or it can be scheduled preemptively on the machines, in which case it may increase the maximum completion time of any machine in the schedule, also known as the makespan of the constructed schedule. The objective is to minimize the sum of the makespan of the schedule of all accepted jobs and the total penalty of all rejected jobs. We study two versions of the problem. The first one is the online problem where the jobs arrive unsorted, and the second variant is the semi-online case, where the jobs arrive sorted by a non-increasing order of penalties. We also show that the variant where the jobs arrive sorted by a non-decreasing order of penalties is equivalent to the unsorted one. We design optimal online algorithms for both cases. These algorithms have smaller competitive ratios than the optimal competitive ratio for the more general problem with arbitrary processing times (except for the case of identical machines), but larger competitive ratios than the optimal competitive ratio for preemptive scheduling of unit jobs without rejection.     

存储资源受限时的数据密集工作流调度算法

针对数据密集型科学工作流需要大量的数据传送和数据存储的问题,在执行节点可用存储资源受限的情况下,构造计算作业与数据作业分离的工作流模型,设计数据与计算分离后的工作流生成算法,增加数据转送作业、数据清除作业、数据作业及其依赖关系。给出资源受限情况下数据密集工作流的预估存储调度算法,并对其进行系统评价,取得了较好的效果。     

基于改进的RA算法的混合Flowshop调度问题的求解

针对混合Flowshop系统的最小化Makespan调度问题,提出基于改进的RA斜度指标的启发式算法来对工件进行排序,采用FAM算法来分配设备并给出其最优值的下界检验该算法。仿真结果表明该方法优于目前最好的启发式算法能较好地解决混合Flowshop的调度问题。     

Minimizing makespan on a single burn-in oven with job families and dynamic job arrivals

This paper considers a scheduling problem for a single burn-in oven in the semiconductor manufacturing industry where the oven is a batch processing machine and each batch processing time is represented by the largest processing time among those of all the jobs contained in the batch. Each job belongs to one of the given number of families. Moreover, the release times of the jobs are different from one another. The objective measure of the problem is the maximum completion time (makespan) of all jobs. A dynamic programming algorithm is proposed in the order of polynomial time complexity for a situation where the number of job families is given (fixed). A computational experiment is performed to compare the time complexity of the proposed algorithm with that of another exact algorithm evaluating all possible job sequences based on batching-dynamic programming (BDP). The results of the experiment show that the proposed algorithm is superior to the other.Scope and purposeThis paper considers a scheduling problem on the burn-in operation in a semiconductor manufacturing process. The burn-in operation is a bottleneck process in the final testing process which is one of four major steps including wafer fabrication, wafer probe, assembly, and final testing steps. Thus, its scheduling is very important to improve the productivity of the whole manufacturing line. The objective of this paper is to find a solution technique that will find the optimal schedule that minimizes makespan for problems which are found in the semiconductor manufacturing industry.     

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.     

Single machine due-date scheduling of jobs with decreasing start-time dependent processing times

We study the problem of scheduling jobs whose processing times are decreasing functions of their starting times. We consider the case of a single machine and a common decreasing rate for the processing times. The problem is to determine an optimal combination of the due date and schedule so as to minimize the sum of due date, earliness and tardiness penalties. We give an O(n log n) time algorithm to solve this problem.     

Minimizing the makespan on a single machine with flexible maintenances and jobs’ release dates

This paper addresses the production scheduling problem on a single machine with flexible periodic preventive maintenances (PM), where jobs’ release dates are also considered. Both resumable and non-resumable cases are studied. For the resumable case, it is proved that the problem can be solved in polynomial time with Earliest Release Date (ERD) rule. For the non-resumable case, it is proved to be NP-Hard in strong sense. And, a mixed integer programming (MIP) mathematical model is provided. Then, an effective heuristic ERD-LPT based on the properties of optimal solution is proposed. Meanwhile, a branch-and-bound algorithm (B and B) that utilizes several dominance rules is developed to search the optimal schedule for small-to-medium sized problems. Computational results indicate that the proposed heuristic is highly accurate and the two algorithms are complementary in dealing with different sized problems. Furthermore, the improvement of the integration between production scheduling and PM is significant compared with the First-in-First-out (FIFO) rule which is adopted commonly in industry.     

Resource optimal control in some single-machine scheduling problems

We consider a problem to schedule a set of jobs on a single machine under the constraint that the maximum job completion time does not exceed a given limit. Before a job is released for processing, it must undergo some preprocessing treatment which consumes resources. It is assumed that the release time of a job is a positive strictly decreasing continuous function of the amount of resources consumed. The objective is to minimize the total resource consumption. We show that ordering jobs in nonincreasing processing times yields an optimal solution. We then consider a bicriterion approach to the problem in which the maximum job completion time and the resource consumption are simultaneously minimized and present a polynomial time solution algorithm. Finally, we consider a related problem in which the job release times are given but the processing times are functions of the amount of resource consumed. We show that ordering jobs in nondecreasing release times gives an optimal solution and that the problem to minimize both the maximum completion time and resource consumption is polynomially solvable     

一种带有链约束的连续型批处理机调度问题

针对链式约束下工件释放时间和工期同序的情况,证明了即使所有工件都是单位加工时间时,极小化最大拖期问题也是强NP-难的.对于工件的零时刻都到达且同一链中工件工期相同的特殊情况,给出了多项式时间的最优算法.     

A new Lagrangian relaxation algorithm for hybrid flowshop scheduling to minimize total weighted completion time

We investigate the problem of scheduling n jobs in s-stage hybrid flowshops with parallel identical machines at each stage. The objective is to find a schedule that minimizes the sum of weighted completion times of the jobs. This problem has been proven to be NP-hard. In this paper, an integer programming formulation is constructed for the problem. A new Lagrangian relaxation algorithm is presented in which precedence constraints are relaxed to the objective function by introducing Lagrangian multipliers, unlike the commonly used method of relaxing capacity constraints. In this way the relaxed problem can be decomposed into machine type subproblems, each of which corresponds to a specific stage. A dynamic programming algorithm is designed for solving parallel identical machine subproblems where jobs may have negative weights. The multipliers are then iteratively updated along a subgradient direction. The new algorithm is computationally compared with the commonly used Lagrangian relaxation algorithms which, after capacity constraints are relaxed, decompose the relaxed problem into job level subproblems and solve the subproblems by using the regular and speed-up dynamic programming algorithms, respectively. Numerical results show that the new Lagrangian relaxation method produces better schedules in much shorter computation time, especially for large-scale problems.